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B: Biomaterials and Membranes

Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion
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The Journal of Physical Chemistry B

Cite this: J. Phys. Chem. B 2024, 128, 18, 4404–4413
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https://doi.org/10.1021/acs.jpcb.3c07388
Published April 4, 2024

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Abstract

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The lateral mobility of molecules within the cell membrane is ultimately governed by the local environment of the membrane. Confined regions induced by membrane structures, such as protein aggregates or the actin meshwork, occur over a wide range of length scales and can impede or steer the diffusion of membrane components. However, a detailed picture of the origins and nature of these confinement effects remains elusive. Here, we prepare model lipid systems on substrates patterned with confined domains of varying geometries constructed with different materials to explore the influences of physical boundary conditions and specific molecular interactions on diffusion. We demonstrate a platform that is capable of significantly altering and steering the long-range diffusion of lipids by using simple oxide deposition approaches, enabling us to systematically explore how confinement size and shape impact diffusion over multiple length scales. While we find that a “boundary condition” description of the system captures underlying trends in some cases, we are also able to directly compare our systems to analytical models, revealing the unexpected breakdown of several approximate solutions. Our results highlight the importance of considering the length scale dependence when discussing properties such as diffusion.

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Introduction

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The cell membrane is a crowded, continuously fluctuating environment composed of a diverse population of lipids, proteins, and small molecules (Figure 1). Characterizing and understanding the dynamics of these components and how they interact are crucial to developing an effective description of both structural and functional aspects of the membrane. This has motivated extensive experimental and theoretical efforts to probe the motion of lipids over a wide range of length scales. (1−5) However, the complex, heterogeneous nature of biological membranes makes systematic exploration of the energy landscape of systems in vivo extremely challenging. Of particular importance is understanding how the effect of confinement manifests in these systems and shapes the behavior of membrane components. Confinement can influence the diffusion of small molecules in a wide range of contexts (6−12) spanning many length scales; one important example is the localization of membrane components by actin filaments, where domain sizes range from nanometer to micrometer scales. (13−17) Hierarchical, scale-dependent behavior has been observed in these networks, (18) having a range of geometries, spanning mesh-like irregular networks (19) to ordered rings. (17) This range of length scales and geometries motivates efforts to understand the driving forces between specific molecular interactions and physical boundary conditions, how this impacts processes such as diffusion and binding, and how this depends on the length scale.

Figure 1

Figure 1. Membranes are crowded, congested environments with obstructions spanning length scales from nanometers to microns. Schematic showing a membrane domain with a transmembrane protein (green), integral and peripheral proteins (purple), cholesterol (orange/red), glycosphingolipids (red), actin meshwork (navy), an ion channel (blue), and a lipid aggregate (dark gray). In this work, we probe the effect of the confinement geometry on both local and global scales.

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Diffusion plays a key role in many biological processes, ultimately determining the rate of encounter of membrane proteins and mass transport within the membrane. Developing a picture of how diffusion changes in response to different membrane perturbations is therefore of great importance, which has motivated many efforts at characterizing diffusion of systems such as particles in the presence of obstacles, (6,11,20−26) membrane flow under different conditions, (27,28) and components in curved membranes. (29−31) The ubiquity of confined environments in biological systems, such as ions in ion channels, (32) molecules in dendritic spines, (33) and ligands binding to cells, (34) has also motivated extensive theoretical descriptions of diffusion in these systems, (35−45) which have robustly demonstrated the nontrivial relationship between diffusion and geometry. (46−50) In many cases, however, the validity of these descriptions has not been experimentally tested, leaving unanswered questions about when specific molecular interactions can be neglected, when a confined membrane should be described as a continuous fluid or discrete particles, or how to treat irregularly shaped confined regions. Even in the simplest systems – a membrane composed of lipids, with no proteins or other small molecules – challenges remain. Simulating diffusion in these systems is substantially more complicated than it first appears (51,52) even in the absence of confinement because of subtle artifacts in finite-size simulations.
Here, we systematically explore how the effects of geometric confinement shape and control the motion of lipids in membranes at different length scales by using thin oxide structures to form easily fabricated obstacles. Using a combination of fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS) approaches, we characterize how these systems can be described globally in terms of “boundary conditions,” which depend on the geometry of confinement, while still locally retaining their native diffusion coefficient, revealing the complex scale-dependent behavior of these dynamics.

Materials and Methods

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Vesicle Preparation

Vesicles used in this study were prepared from 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and the label 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) (Rhod-PE), both purchased from Avanti Polar Lipids (Alabaster, AL). Prior to vesicle formation, Rhod-PE was stored in chloroform, DLPC in its powder form, and all lipids were stored at −20 °C. For FRAP measurements, a 1.2 mg/mL DLPC 0.5 mol % Rhod-PE solution was prepared by mixing appropriate amounts of DLPC, Rhod-PE, and chloroform (≥99%; Sigma-Aldrich; Darmstadt, Germany) and then dried under N2 gas and placed under vacuum for 24 h. The lipid film was rehydrated with phosphate-buffered saline (Boston BioProducts Inc.; Ashland, MA), and large unilamellar vesicles (LUVs) were formed by extruding through a 0.1 μm pore size polycarbonate membrane a total of 21 times. The mini-extruder set used to form LUVs was purchased from Avanti Polar Lipids. For FCS measurements, a 0.3 mg/mL DLPC 0.0025 mol % Rhod-PE solution was prepared following the same procedure.

Substrate Preparation

SiO2 substrates were formed by dicing wet thermal oxide wafers (University Wafers; South Boston, MA) into 1 cm × 1 cm chips. Substrates were subsequently cleaned by sonicating in 1:1 IPA:acetone for 2 min and then dried under N2 gas. Residual organic contaminants were removed by exposing the substrate to oxygen plasma treatment for 2 min (Anatech SP-100 Plasma System). Supported lipid bilayers were formed on the substrates immediately after the oxygen plasma cleaning using the vesicle fusion method, described in the following section.
TiO2-patterned substrates were formed by using photolithography. First, wet thermal oxide wafers were exposed to oxygen plasma treatment for 2 min. Immediately after the oxygen plasma cleaning, they were coated in a thin layer of S1813 photoresist by spinning at 4000 rpm for 1 min and then baking at 115 °C for 1 min. A quartz mask coated in chrome was used to pattern the photoresist. A Quintel 4000 Mask Aligner was used to expose the wafer for 7 s. The pattern was developed in AZ 726 MIF for 45 s, then rinsed with DI water for 1 min, and dried under N2 gas. The developed wafer was plasma-cleaned for 1 min. Using the Savannah 100 system, ∼4 nm of TiO2 (atomic force microscopy characterization shown in Figure S1) was grown on top of the wafer through atomic layer deposition (ALD) at 105 °C. Low-temperature deposition provides a cleaner liftoff, avoiding the potential destruction or outgassing of the resist layer. (53) After ALD, the S1813 photoresist was stripped by sonicating the wafer in acetone for 2 min and then drying under N2 gas, leaving a SiO2 substrate with TiO2 obstacles ∼4 nm in height. To investigate the material dependence, Al2O3-patterned substrates were made in the same way. Immediately before bilayer formation, the substrates were cleaned in 1:1 IPA:acetone (sonicating for 2 min) and then exposed to oxygen plasma treatment for 30 s.
The patterned substrates host three families of geometries: four circular pillars in a square array (termed “four pillars”), four arcs arranged in a circular array (“four channels”), and a continuous arc forming an almost-complete circle (“one channel”). These are shown schematically in Figure 2b. SiO2, TiO2-patterned, and Al2O3-patterned substrates were adhered to a CoverWell imaging gasket (Thermo Fisher Scientific; Waltham, MA) with double-sided Scotch tape.

Figure 2

Figure 2. (a) Schematic of the fabrication process, starting with a plain SiO2 substrate. The SiO2 substrate is lithographically patterned, developed, and then 2.5–5 nm of TiO2 or Al2O3 is deposited on the surface through atomic layer deposition (ALD). The substrate is cleaned, and supported lipid bilayers (SLBs) are formed on the SiO2 surfaces with the vesicle fusion method. The bottom left panel is a fluorescence image showing a SLB (dark gray) formed on a SiO2 substrate around TiO2 structures (black circles). Scale bar is 100 μm. (b) Three classes of structures used to explore geometric aspects of confinement.

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Supported Lipid Bilayers

Supported lipid bilayers (SLBs) were formed using the vesicle fusion method, described elsewhere. (54) Briefly, the TiO2-patterned substrates were placed on a hot plate held at 30 °C, well above the gel–fluid phase transition temperature of DLPC (−1 °C). (55) 30 μL of the LUVs was deposited on the substrates, followed by 90 μL of phosphate-buffered saline. The LUVs were left to incubate on the substrates for 10 min. After incubation, 700 μL of phosphate-buffered saline was added to the gasket. The substrate was washed with phosphate-buffered saline a total of 15 times. At the end of the washing step, a 30 × 22 mm coverslip (Thermo Fisher Scientific; Waltham, MA) was rolled on top of the substrate. For FCS measurements, the sides of the gasket were coated with clear nail polish (Sally Hanson Xtreme-Wear; CVS) on top to avoid sample drying. A step-by-step protocol for forming SLBs with the vesicle fusion method can be found in archived protocols online. (56) The full fabrication process is illustrated in Figure 2a.

Fluorescence Recovery After Photobleaching (FRAP)

FRAP measurements are discussed elsewhere in detail. (57) Here, SLBs were immediately imaged after formation with a Zeiss LSM 880 fluorescence microscope equipped with a 10× objective and a 561 nm diode laser (Oberkochen, Germany). Selected regions inside of the TiO2 geometries were bleached and monitored with the 561 nm laser (Figure 3; bleached radius 12.25 μm). The intensity of the bleached region was integrated and fit to obtain a characteristic diffusion time using eq 1: (58)
I(t)=I0+∑n(In−I0)⁡e−2Τn/t(J0(2Τnt)+J1(2Τnt))
(1)

Figure 3

Figure 3. FRAP enables imaging of the bilayer morphology and fluidity. Bilayers readily form and recover on SiO2 substrates, as shown in (a)–(c). (d) Recovery of fluorescence inside (red) and outside (blue) the pattern. Outside the pattern, the diffusion coefficient is consistent with literature values for other one-phase fluid bilayers at room temperature (4,59,60) (2.92 ± 0.07 μm2/s). Inside the pattern, the diffusion coefficient decreases; in the geometry shown, it decreases to 1.61 ± 0.04 μm2/s. The scale bar is 15 μm.

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where I0 is the fluorescence intensity just after the bleach, J0 and J1 are the modified Bessel functions of orders 0 and 1, respectively, In is the intensity contribution of species n at t = ∞, and Tn is the characteristic diffusion time of species n. In our experiments, satisfactory fits are given for n = 1. Eq 1 is derived for a system without obstructions; our use of this analysis here is motivated by the successful application of this equation in previous studies exploring obstructed diffusion, (21,61−63) and we note the agreement between this functional form and our experimental data (Figure 3d and Supporting Information). Diffusion coefficients were calculated using the following equation:
D=0.224×R2Tn
(2)
where R is the radius of the bleached region.
Data were collected for all geometries on one patterned substrate at a time. Each substrate had at least three repetitions of the patterns shown in Figure S2. One FRAP data collection consisted of measuring the diffusion within all geometries for each pattern; this was repeated twice for two different patterns on each substrate. Data were recorded in one batch for each substrate. Data were collected on three different substrates on three different days. All diffusion data were normalized with respect to diffusion measured outside of the patterns to account for the systematic differences in the environment.

Fluorescence Correlation Spectroscopy (FCS)

FCS measurements were carried out using a 532 nm diode-pumped solid-state laser (GEM, Novanta Photonics; Bedford, MA) at a power less than 100 μW in a confocal microscope setup described in the Supporting Information. Briefly, the 532 nm laser beam was used to illuminate a 100× (1.25 NA) oil immersion objective (Zeiss; Oberkochen, Germany). Fluorescence was collected through the objective, and the emission was filtered by a 550 nm long-pass dichroic mirror (Thorlabs; Newton, NJ). A single-mode fiber acted as a pinhole. The fluorescence signal was detected by an avalanche photodiode (Excelitas Technologies; Waltham, MA) coupled to the fiber and was correlated with the Time Tagger Series software from Swabian Instruments (Time Tagger Ultra, Swabian Instruments; Stuttgart, Germany). The FCS setup was calibrated using 10 nM solutions of Rhodamine 6G (TCI America; Portland, OR) (Rhod-6G) in Millipore water following previously established calibration procedures. (64,65)
Measurements were taken by positioning the laser focal spot in the center of the TiO2 geometries. Each acquisition consisted of 10 FCS measurements of 5 s duration recorded at that position. The correlation functions were fit with a 2D diffusion model:
G(Τ)=1N(1+ΤΤD)−1
(3)
where N is the average molecule number in the detection volume, Τ is the lag time, and TD is the average time of molecules diffusing through the detection volume. (64,66) FCS measurements were taken in the middle of each TiO2 geometry twice at different spatial locations on the TiO2-patterned substrates. The resultant TD and N were averaged for each pattern, and the diffusion coefficient was calculated from the subsequent average TD using the following equation:
D=w24ΤD
(4)
where w = 191 ± 7.42 nm is the beam waist obtained from the Rhod-6G calibration measurements. The error in w was calculated from the standard deviation of the results of 10 calibration acquisitions.

Numerical Simulation of Obstructed Diffusion

We simulate the expected FRAP response for different geometries by numerically solving the diffusion equation using VCell. (67,68) To model the TiO2 obstacles, we applied zero-flux boundary conditions around regions matching the geometries in our experiment. We initially generate a circular profile of nonzero concentration (representing the bleached lipids) and allow this to propagate. We simulate our experiment by integrating the concentration in this region at each time step and fitting the resulting curve to extract the effective diffusion coefficient in the same way as the experimental data.

Results and Discussion

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Effect of Confinement Geometry

Figure 4b shows the effective diffusion of DLPC lipids as a function of unobstructed fraction for the three different geometries obtained by FRAP, which probes >μm length scales. The unobstructed fraction for each geometry is defined as
σ=nl2πR
(6)

Figure 4

Figure 4. (a) The unobstructed fraction is defined as σ=nl2πR where n is the number of escape channels, l is their arclength, and R is the radius of the bleached region (dashed gray circle). (b) The unobstructed fraction vs the effective diffusion for the three different TiO2 geometries are compared. (c) Comparison of the unobstructed fraction vs the effective diffusion for the four channel TiO2 structures on SiO2 (black circles) and for the four channel Al2O3 structures on SiO2 (green stars).

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where n is the number of escape channels, l is the arc length of each escape channel, and R is the radius of the region shown schematically in Figure 4a. The FRAP data (Figure 4b) show a decrease in the effective diffusion coefficient as the unobstructed fraction decreases but also reveal a striking dependence on the geometry of the confining structure. Simply by changing the shape of the obstruction, we find that the micron-scale diffusion coefficient varies by a factor of up to four. Specifically, our FRAP data allow us to make two distinct observations: first, the pattern with a convex surface (“four pillars,” Figure 4b) shows a faster effective diffusion rate than either of the concave structures (“four channels” and “one channel,” Figure 4b); second, the arrangement of the escape channels (together in one channel or arranged regularly around the perimeter) impacts the effective diffusion, with a single larger channel giving rise to a slower effective diffusion than four smaller channels. The effect of confinement on the dynamics of membrane components has been well-studied in both experimental (15,16,19,20,22,25,57,61,69−79) and theoretical contexts. (10,80,81) Intuitively, it has been found that as the environment becomes increasingly crowded, the effective diffusion rate decreases, (7,11,25,26,82) leading to a common model for obstructed diffusion in FRAP experiments framed in terms of the average obstructed fraction. (83−85) Our observations are consistent with this general trend but also highlight the importance of not only the obstructed fraction but also the geometry of the obstacles when trying to extract the detailed dynamics of these systems.
In our experiments, we irradiated a constant area to bleach the fluorescent lipid and monitored the recovery. In the case of the four pillar geometry, however, this means that the lipid area in our probed region decreases as the radii of the pillars increase. We can consider the case where we scale the geometry and bleach radius to maintain a constant irradiated lipid area; here we expect the recovery time to scale as R2 (eq 1) for the unobstructed case, and our numerical simulations demonstrate that this also holds for our confined geometries (Supporting Information). Thus, we expect an appropriately normalized data set with varying pattern sizes to reproduce our data. However, this does lead to a potential explanation for the faster recovery of the four pillar geometry compared to the channel geometries for a given sigma; for a randomly diffusing lipid, the smaller free area of the four pillar geometry reduces the search area to find the exit.
The effect of concavity on confined dynamics has also previously been studied in silico in the context of membrane proteins and nanopores, (10,80) though the effect of specific lipid-surface interactions in these cases makes it challenging to isolate the purely geometric effects. More recently, both experimental and theoretical descriptions of colloidal particles around curved interfaces have found concavity-dependent diffusion behaviors with slower diffusion around concave structures, consistent with our FRAP observations. We emphasize that experiments performed by Modica et al. (86) probe fluorescent spheres several microns in diameter, many orders of magnitude different from our diffusing species, DLPC molecules, highlighting the broad importance of understanding the impact of geometry on confinement effects. However, even for a fixed degree of concavity, we also find that the effective diffusion coefficient depends on the arrangement of obstacles, as seen by comparing the clear variation in trends between the “four channel” and “one channel” data in Figure 4b.

Global and Local Probes of Diffusion

To probe the effect of length scale on the observed diffusion behavior in our confined systems, we also performed FCS measurements at the center of each geometry. Figure 5 shows the effective diffusion of DLPC lipids as a function of the unobstructed fraction obtained from both FRAP and FCS measurements. FRAP probes the global diffusion of lipids on the many micron-scale whereas FCS probes more localized dynamics on the hundred-nanometer scale (here, <300 nm). The FCS data were collected at the center point of the confined domains; the FRAP data were collected for the entire confined domain.

Figure 5

Figure 5. Effective diffusion for the three different TiO2 geometries (insets) obtained from FCS (diamonds) and FRAP (circles) measurements for (a) the four pillar geometry, (b) the four channel geometry, and (c) the one channel geometry.

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We observed distinctly different behaviors with each of these probes. The local behavior in the center of the confined domains, as determined by FCS, does not depend on the pattern shape or the size of the channels in the pattern and is constant within our experimental precision; in all cases, the diffusion coefficient is statistically indistinguishable from a reference measurement taken far from any confining pattern (Figure 5). The FRAP data, however, show a clear decrease in the effective diffusion coefficient as the unobstructed fraction decreases. The equivalence of FCS and FRAP measurements for extracting diffusion coefficients has been demonstrated extensively, (4,87−92) leading us to interpret our data in terms of length-scale dependent dynamics rather than any systematic difference between these two measurements. We assume that the diffusion measured by both FRAP and FCS is Brownian; we fit our FRAP data with the anomalous diffusion equation determined by Pastor et al. (93) and found fit parameters converged toward α = 1 (free diffusion case; Figure S4). Additionally, the radius of the confined regions (R ∼ 12.25 μm; Figures 3a–c and 4a) is significantly larger than the FCS beam waist (w ∼ 191 nm), allowing our FCS measurements to be described by the free diffusion case. (94) Differences between FRAP and submicron probes such as FCS or single-particle tracking can be observed in systems with heterogeneous environments, such as caveolae formation (95) or picket-fence protein structures, (96−98) where microscopic obstacles introduce length-scale dependent effective diffusion coefficients. We interpret the difference in our FCS and FRAP data in terms of free, unobstructed local diffusion (probed by FCS) and longer-range mass transport between the interior of the pattern and the outer lipid reservoir limited by the transit through the escape channels (probed by FRAP). Although FCS has higher spatial resolution than FRAP, in this case, we observe that FCS measurements are insensitive to the presence of obstacles. The FRAP data is collected over a larger area that includes the space near the domain boundaries, whereas the FCS data is collected in a small area in the center of the confined regions, rendering it agnostic to the existence of the domain walls. We interpret the observed differences in the FCS and FRAP data in terms of the inclusion of the portion of the bilayer near the domain boundaries in the FRAP measurements and the exclusion of this region in the FCS measurements. The opposite effect is observed by Calizo and Scarlata, (95) where FCS measurements were sensitive to the presence of caveolae domains, but FRAP measurements were not. Here, the size of the obstacles is on the same length scale as our bleached region in the FRAP experiments (many microns) whereas caveolae domains are on the same length scale as the FCS beam diameter (hundred(s) of nanometers). (95) However, similar effects to our data have been observed by Wawrezinieck et al. in simulating fully confined lipids, where diffusion slows as the probed length scale approaches that of the confining structure. (94) This comparison highlights the importance of considering the length scale of the confinement or obstruction and choosing an approach that is sensitive to effects on that scale. Probing smaller length scales does not inherently provide greater sensitivity to all types of confinement, which will be important when considering micron-scale confinement possible with actin filaments. (17−19,23)

Observed Trends Are Not Specific to TiO2

To explore whether the observed behaviors of the lipids are dependent on specific interactions with the TiO2 obstacles, we also generated systems using Al2O3 instead of TiO2. Both surfaces inhibit bilayer formation under our experimental conditions (99,100) but differ in their surface chemistries and have different detailed interactions with supported lipid bilayers. (101−106) Patterns from both materials show the same trends (Figures 4c and S6), indicating that the behaviors we see arise from nonspecific confinement geometry effects. The lack of material dependence motivates our description of confinement in terms of a general repulsive “boundary condition” imposed by the patterned material, as discussed below.

Confinement as a Narrow-Escape Problem

The so-called “narrow escape” problem – where species confined in a region can exit only through a few discrete channels – has been studied theoretically in a vast range of different geometries, (35,36,40−43,45,107−111) yet few of these have been directly tested against experiment. The confinement geometries used in our experiments were chosen, in part, to enable comparison with a range of theoretical and numerical approaches for calculating the effective diffusion of the lipids out of this region. Here, we directly compare our experimental data to analytical and numerical models commonly employed to describe the narrow escape problem to assess the correspondence with experiment.
In general, the narrow escape problem is formulated in terms of a local diffusion coefficient that is uniform across the sample region but where boundary conditions imposed by the confining structure impose an effective “global” diffusion coefficient limited by the exchange of species with the outside reservoir, consistent with our FRAP and FCS observations. Figure 6 shows the comparison between our experimental data and commonly used models from the literature, which describe our geometries. These models all describe the system in terms of a reflecting boundary (here, our TiO2 region) and an absorbing boundary (our escape channel) but differ in their approach to determining analytical expressions for these systems. Since we compare the diffusion normalized to the unconfined case, these models have no adjustable or system-specific parameters.

Figure 6

Figure 6. Comparison of experimental data with analytical models and numerical simulations for the various geometries in this work: (a) the four pillar geometry, (b) the four channel geometry, and (c) the one channel geometry. Descriptions of the models for each geometry are given in the main text.

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Interestingly, there is significant variation in the agreement between our experimental data and the results of the various models. For the four pillar geometry, we find that our numerical simulations, the perturbation theory-based approach of Mangeat et al. (107) (perturbation model), and the multipole expansion-based approach of Rayleigh (109) (Rayleigh model) agree with our FRAP data over the entire range of our experimental parameters (Figure 6a), with relatively minor variations between the expected effective diffusion coefficient. Numerical simulations of the diffusion also show the same general trend as our experimental data.
In contrast, the boundary-homogenization descriptions of Berezhkovskii and Barzykin (36) (BH model) and the narrow escape problem for a circular disk (110−112) (NET model) show marked deviations from our data both in quantitative value and in overall shape (Figure 6b,c). For the NET model, this is consistent with previous experimental observations, which show deviation from the model at σ > 0.05. (112) The boundary homogenization approach, however, is expected to hold for all values of σ, (36) but here we find that our experiments show different behavior for the entire experimental range. In contrast, our numerical simulations show qualitative agreement with the overall trend but consistently overestimate the effective diffusion of the confined lipid for the four channel and one channel structures.
One observation our comparison allows us to make is that the best agreement is observed in systems where zero-flux (Neumann) boundary conditions are employed (perturbation, Rayleigh models, and the numerical simulations), while the approach utilizing mixed boundary conditions (boundary homogenization) shows poorer agreement with our experimental results. However, the sensitivity of the boundary homogenization approach to the parametrization and functional form of the effective “trapping rate” provides an alternative explanation for the disagreement. Nevertheless, our results highlight not only the significant effect of confinement geometry on the diffusion of species in lipid membranes but also the need to experimentally test the limitations of analytical models developed, even for geometrically simple systems.

Conclusion

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We developed a novel lithography-based platform to study the diffusion of DLPC lipids inside confined regions. Global diffusion of lipids, probed by FRAP, was impeded inside the confined domains; the degree of this effect depends on the geometry of the domain but not on the material with which the domains were formed. This observation implies that the obstructed fraction is not the only parameter that determines how molecules diffuse in a crowded environment─the shape and form of the obstacles play a significant role in the diffusive behavior as well. We also demonstrate that the local effective diffusion of lipids in the center of the confined domain is the same as the effective diffusion of lipids in an obstacle-free membrane, emphasizing the importance of explicitly considering the length scale when describing dynamics. Lastly, the effective diffusion obtained from FRAP was compared with a range of theoretical models describing the system in terms of a repulsive “boundary condition.” Disagreement between the model for the concave geometries and the FRAP data indicates that there is underlying behavior not fully explained by the theoretical models.

Data Availability

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The data associated with this work are available at 10.5281/zenodo.10830128.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.3c07388

  • Additional information regarding the substrate preparation (Figures S1 and S2), FCS setup (Figure S3), appropriateness of FRAP fit (Figures S4 and S5), comparison between FRAP measurements for all TiO2 and Al2O3 geometries (Figure S6), and numerical simulations (Figures S7 and S8) (PDF)

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Author Information

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  • Corresponding Author
  • Author
    • Nicole Voce - Department of Physics, Northeastern University, Boston, Massachusetts 02115, United States
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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P.S. acknowledges support from Northeastern University Provost’s Office and TIER 1 Internal Seed Grant Program. P.S. thanks the Institute for Chemical Imaging of Living Systems at Northeastern University for consultation and imaging support

References

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    A review. There is great diversity in the compn. and structure of biol. lipid membranes. Investigators are beginning to appreciate the crucial role of lipids in many cellular processes, and characterize some of the lateral structures within membranes that could play a role in the activity of lipids. Simulations probe mol. level interactions between single mols., which provide complementary information to expts. Lipid membrane simulations have reached an exciting point, where the time and length scales of the simulations are approaching exptl. resolns. and can be used to interpret expts. on increasingly complex model membranes. The focus of this review is on recent mol. dynamics (MD) simulations of domain formation in lipid bilayers. The authors highlight a no. of recent examples where MD simulations are used in collaboration with expts. The authors review recent simulation studies on lipid-lipid interactions related to domain formation and on lipid-protein interactions relevant for lipid raft function.
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    Camley, B. A.; Brown, F. L. H. Dynamic Simulations of Multicomponent Lipid Membranes over Long Length and Time Scales. Phys. Rev. Lett. 2010, 105 (14), 148102,  DOI: 10.1103/PhysRevLett.105.148102
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    Guo, L.; Har, J. Y.; Sankaran, J.; Hong, Y.; Kannan, B.; Wohland, T. Molecular Diffusion Measurement in Lipid Bilayers over Wide Concentration Ranges: A Comparative Study. ChemPhyschem 2008, 9 (5), 721– 728,  DOI: 10.1002/cphc.200700611
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    Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study
    Guo, Lin; Har, Jia Yi; Sankaran, Jagadish; Hong, Yimian; Kannan, Balakrishnan; Wohland, Thorsten
    ChemPhysChem (2008), 9 (5), 721-728CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Mol. diffusion in biol. membranes is a detg. factor in cell signaling and cell function. In the past few decades, three main fluorescence spectroscopy techniques have emerged that are capable of measuring mol. diffusion in artificial and biol. membranes at very different concn. ranges and spatial resolns. The widely used methods of fluorescence recovery after photobleaching (FRAP) and single-particle tracking (SPT) can det. abs. diffusion coeffs. at high (> 100 μm-2) and very low surface concns. (single-mol. level), resp. Fluorescence correlation spectroscopy (FCS), on the other hand, is well-suited for the intermediate concn. range of about 0.1-100 μm-2. However, FCS in general requires calibration with a std. dye of known diffusion coeff., and yields only relative measurements with respect to the calibration. A variant of FCS, z-scan FCS, is calibration-free for membrane measurements, but requires several expts. at different well-controlled focusing positions. A recently established FCS method, electron-multiplying charge-coupled-device-based total internal reflection FCS (TIR-FCS), referred to here as imaging TIR-FCS (ITIR-FCS), is also independent of calibration stds., but to our knowledge no direct comparison between these different methods has been made. Herein, we seek to establish a comparison between FRAP, SPT, FCS, and ITIR-FCS by measuring the lateral diffusion coeffs. in two model systems, namely, supported lipid bilayers and giant unilamellar vesicles.
  5. 5
    Dolainsky, C.; Karakatsanis, P.; Bayerl, T. M. Lipid Domains as Obstacles for Lateral Diffusion in Supported Bilayers Probed at Different Time and Length Scales by Two-Dimensional Exchange and Field Gradient Solid State NMR. Phys. Rev. E 1997, 55 (4), 4512– 4521,  DOI: 10.1103/PhysRevE.55.4512
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    Minton, A. P. Confinement as a Determinant of Macromolecular Structure and Reactivity. Biophys. J. 1992, 63 (4), 1090– 1100,  DOI: 10.1016/S0006-3495(92)81663-6
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    Confinement as a determinant of macromolecular structure and reactivity
    Minton, Allen P.
    Biophysical Journal (1992), 63 (4), 1090-100CODEN: BIOJAU; ISSN:0006-3495.
    The confinement of macromols. within enclosures or pores of comparable dimensions results in significant size- and shape-dependent alterations of macromol. chem. potential and reactivity. Calcns. of the magnitude of this effect for model particles of different shapes in model enclosures of different shapes were carried out using the hard particle partition theory developed by J. C. Giddings, et al. (1968). The results indicate that the equil. consts. of reactions, such as isomerization, self-assocn., and site binding, that result in significant changes in macromol. size, shape, and/or mobility may be altered within pores by as much as several orders of magnitude relative to the value in the unbounded or bulk phase. Confinement also produces a substantial size-dependent outward force on the walls of an enclosure. These results are likely to be important within the fluid phase of biol. media, such as the cytoplasm of eukaryotic cells, contg. significant vol. fractions of large fibrous structures (e.g., the cytomatrix).
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    Löwe, M.; Kalacheva, M.; Boersma, A. J.; Kedrov, A. The More the Merrier: Effects of Macromolecular Crowding on the Structure and Dynamics of Biological Membranes. FEBS J. 2020, 287 (23), 5039– 5067,  DOI: 10.1111/febs.15429
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    The more the merrier: effects of macromolecular crowding on the structure and dynamics of biological membranes
    Lowe Maryna; Kedrov Alexej; Kalacheva Milara; Boersma Arnold J
    The FEBS journal (2020), 287 (23), 5039-5067 ISSN:.
    Proteins are essential and abundant components of cellular membranes. Being densely packed within the limited surface area, proteins fulfil essential tasks for life, which include transport, signalling and maintenance of cellular homeostasis. The high protein density promotes nonspecific interactions, which affect the dynamics of the membrane-associated processes, but also contribute to higher levels of membrane organization. Here, we provide a comprehensive summary of the most recent findings of diverse effects resulting from high protein densities in both living membranes and reconstituted systems and display why the crowding phenomenon should be considered and assessed when studying cellular pathways. Biochemical, biophysical and computational studies reveal effects of crowding on the translational mobility of proteins and lipids, oligomerization and clustering of integral membrane proteins, and also folding and aggregation of proteins at the lipid membrane interface. The effects of crowding pervade to larger length scales, where interfacial and transmembrane crowding shapes the lipid membrane. Finally, we discuss the design and development of fluorescence-based sensors for macromolecular crowding and the perspectives to use those in application to cellular membranes and suggest some emerging topics in studying crowding at biological interfaces.
  8. 8
    Kuznetsova, I. M.; Zaslavsky, B. Y.; Breydo, L.; Turoverov, K. K.; Uversky, V. N. Beyond the Excluded Volume Effects: Mechanistic Complexity of the Crowded Milieu. Molecules 2015, 20 (1), 1377– 1409,  DOI: 10.3390/molecules20011377
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    Beyond the excluded volume effects: mechanistic complexity of the crowded milieu
    Kuznetsova, Irina M.; Zaslavsky, Boris Y.; Breydo, Leonid; Turoverov, Konstantin K.; Uversky, Vladimir N.
    Molecules (2015), 20 (1), 1377-1409/1-1377-1409/33, 33 pp.CODEN: MOLEFW; ISSN:1420-3049. (MDPI AG)
    A review. Macromol. crowding is known to affect protein folding, binding of small mols., interaction with nucleic acids, enzymic activity, protein-protein interactions, and protein aggregation. Although for a long time it was believed that the major mechanism of the action of crowded environments on structure, folding, thermodn., and function of a protein can be described in terms of the excluded vol. effects, it is getting clear now that other factors originating from the presence of high concns. of "inert" macromols. in crowded soln. should definitely be taken into account to draw a more complete picture of a protein in a crowded milieu. This review shows that in addn. to the excluded vol. effects important players of the crowded environments are viscosity, perturbed diffusion, direct phys. interactions between the crowding agents and proteins, soft interactions, and, most importantly, the effects of crowders on solvent properties.
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    Jacobson, K.; Liu, P.; Lagerholm, B. C. The Lateral Organization and Mobility of Plasma Membrane Components. Cell 2019, 177 (4), 806– 819,  DOI: 10.1016/j.cell.2019.04.018
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    The Lateral Organization and Mobility of Plasma Membrane Components
    Jacobson, Ken; Liu, Ping; Lagerholm, B. Christoffer
    Cell (Cambridge, MA, United States) (2019), 177 (4), 806-819CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
    A review. Over the last several decades, an impressive array of advanced microscopic and anal. tools, such as single-particle tracking and nanoscopic fluorescence correlation spectroscopy, has been applied to characterize the lateral organization and mobility of components in the plasma membrane. Such anal. can tell researchers about the local dynamic compn. and structure of membranes and is important for predicting the outcome of membrane-based reactions. However, owing to the unresolved complexity of the membrane and the structures peripheral to it, identification of the detailed mol. origin of the interactions that regulate the organization and mobility of the membrane has not proceeded quickly. This Perspective presents an overview of how cell-surface structure may give rise to the types of lateral mobility that are obsd. and some potentially fruitful future directions to elucidate the architecture of these structures in more mol. detail.
  10. 10
    Goose, J. E.; Sansom, M. S. P. Reduced Lateral Mobility of Lipids and Proteins in Crowded Membranes. PLoS Comput. Biol. 2013, 9, e1003033  DOI: 10.1371/journal.pcbi.1003033
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    10
    Reduced lateral mobility of lipids and proteins in crowded membranes
    Goose, Joseph E.; Sansom, Mark S. P.
    PLoS Computational Biology (2013), 9 (4), e1003033CODEN: PCBLBG; ISSN:1553-7358. (Public Library of Science)
    Coarse-grained mol. dynamics simulations of the E. coli outer membrane proteins FhuA, LamB, NanC, OmpA and OmpF in a POPE/POPG (3:1) bilayer were performed to characterize the diffusive nature of each component of the membrane. At small observation times (<10 ns) particle vibrations dominate phospholipid diffusion elevating the calcd. values from the longer time-scale bulk value (>50 ns) of 8.5 × 10-7 cm2 s-1. The phospholipid diffusion around each protein was found to vary based on distance from protein. An asymmetry in the diffusion of annular lipids in the inner and outer leaflets was obsd. and correlated with an asymmetry in charged residues in the vicinity of the inner and outer leaflet head-groups. Protein rotational and translational diffusion were also found to vary with observation time and were inversely correlated with the radius of gyration of the protein in the plane of the bilayer. As the concn. of protein within the bilayer was increased, the overall mobility of the membrane decreased reflected in reduced lipid diffusion coeffs. for both lipid and protein components. The increase in protein concn. also resulted in a decrease in the anomalous diffusion exponent α of the lipid. Formation of extended clusters and networks of proteins led to compartmentalization of lipids in extreme cases.
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    Ellis, R. J. Macromolecular Crowding: Obvious but Underappreciated. Trends Biochem. Sci. 2001, 26 (10), 597– 604,  DOI: 10.1016/S0968-0004(01)01938-7
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    Macromolecular crowding: obvious but underappreciated
    Ellis, R. J.
    Trends in Biochemical Sciences (2001), 26 (10), 597-604CODEN: TBSCDB; ISSN:0968-0004. (Elsevier Science Ltd.)
    A review. Biol. macromols. evolve and function within intracellular environments that are crowded with other macromols. Crowding results in surprisingly large quant. effects on both the rates and the equil. of interactions involving macromols., but such interactions are commonly studied outside the cell in uncrowded buffers. The addn. of high concns. of natural and synthetic macromols. to such buffers enables crowding to be mimicked in vitro, and should be encouraged as a routine variable to study. The stimulation of protein aggregation by crowding might account for the existence of mol. chaperones that combat this effect. Pos. results of crowding include enhancing the collapse of polypeptide chains into functional proteins, the assembly of oligomeric structures and the efficiency of action of some mol. chaperones and metabolic pathways.
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    Sadjadi, Z.; Vesperini, D.; Laurent, A. M.; Barnefske, L.; Terriac, E.; Lautenschläger, F.; Rieger, H. Ameboid Cell Migration through Regular Arrays of Micropillars under Confinement. Biophys. J. 2022, 121 (23), 4615– 4623,  DOI: 10.1016/j.bpj.2022.10.030
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    Narhi, L. O.; Schmit, J.; Bechtold-Peters, K.; Sharma, D. Classification of Protein Aggregates. J. Pharm. Sci. 2012, 101 (2), 493– 498,  DOI: 10.1002/jps.22790
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    Classification of protein aggregates
    Narhi, Linda O.; Schmit, Jeremy; Bechtold-Peters, Karoline; Sharma, Deepak
    Journal of Pharmaceutical Sciences (2012), 101 (2), 493-498CODEN: JPMSAE; ISSN:0022-3549. (Wiley-Liss, Inc.)
    Comparison of protein aggregates/self-assocd. species between labs. and across disciplines is complicated by the imprecise language presently used to describe them. In this commentary, we propose a standardized nomenclature and classification scheme that can be applied to describe all protein aggregates. Five categories are described under which a given aggregate may be independently classified: size, reversibility/dissocn., conformation, covalent modification, and morphol. Possible subclassifications within each category, several examples of applications of the nomenclature, and difficulties in making appropriate assignments will be discussed. © 2011 Wiley-Liss, Inc. and the American Pharmacists Assocn. J Pharm Sci.
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    Mahler, H.-C.; Friess, W.; Grauschopf, U.; Kiese, S. Protein Aggregation: Pathways, Induction Factors and Analysis. J. Pharm. Sci. 2009, 98 (9), 2909– 2934,  DOI: 10.1002/jps.21566
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    Protein aggregation: Pathways, induction factors and analysis
    Mahler, Hanns-Christian; Friess, Wolfgang; Grauschopf, Ulla; Kiese, Sylvia
    Journal of Pharmaceutical Sciences (2009), 98 (9), 2909-2934CODEN: JPMSAE; ISSN:0022-3549. (Wiley-Liss, Inc.)
    A review. Control and anal. of protein aggregation is an increasing challenge to pharmaceutical research and development. Due to the nature of protein interactions, protein aggregation may occur at various points throughout the lifetime of a protein and may be of different quantity and quality such as size, shape, morphol. It is therefore important to understand the interactions, causes and analyses of such aggregates to control protein aggregation to enable successful products. This review gives a short outline of currently discussed pathways and induction methods for protein aggregation and describes currently employed set of anal. techniques and emerging technologies for aggregate detection, characterization and quantification. A major challenge for the anal. of protein aggregates is that no single anal. method exists to cover the entire size range or type of aggregates which may appear. Each anal. method not only shows its specific advantages but also has its limitations. The limits of detection and the possibility of creating artifacts through sample prepn. by inducing or destroying aggregates need to be considered with each method used. Therefore, it may also be advisable to carefully compare anal. results of orthogonal methods for similar size ranges to evaluate method performance. © 2008 Wiley-Liss, Inc. and the American Pharmacists Assocn. J Pharm Sci 98:2909-2934, 2009.
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    Albrecht, D.; Winterflood, C. M.; Sadeghi, M.; Tschager, T.; Noé, F.; Ewers, H. Nanoscopic Compartmentalization of Membrane Protein Motion at the Axon Initial Segment. J. Cell Biol. 2016, 215 (1), 37– 46,  DOI: 10.1083/jcb.201603108
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    Kusumi, A.; Nakada, C.; Ritchie, K.; Murase, K.; Suzuki, K.; Murakoshi, H.; Kasai, R. S.; Kondo, J.; Fujiwara, T. Paradigm Shift of the Plasma Membrane Concept from the Two-Dimensional Continuum Fluid to the Partitioned Fluid: High-Speed Single-Molecule Tracking of Membrane Molecules. Annu. Rev. Biophys. Biomol. Struct. 2005, 34, 351– 378,  DOI: 10.1146/annurev.biophys.34.040204.144637
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    16
    Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: High-speed single-molecule tracking of membrane molecules
    Kusumi, Akihiro; Nakada, Chieko; Ritchie, Ken; Murase, Kotono; Suzuki, Kenichi; Murakoshi, Hideji; Kasai, Rinshi S.; Kondo, Junko; Fujiwara, Takahiro
    Annual Review of Biophysics and Biomolecular Structure (2005), 34 (), 351-378, 6 platesCODEN: ABBSE4; ISSN:1056-8700. (Annual Reviews Inc.)
    A review. Recent advancements in single-mol. tracking methods with nanometer-level precision now allow researchers to observe the movement, recruitment, and activation of single mols. in the plasma membrane in living cells. In particular, on the basis of the observations by high-speed single-particle tracking at a frame rate of 40,000 frames per s, the partitioning of the fluid plasma membrane into submicron compartments throughout the cell membrane and the hop diffusion of virtually all of the mols. have been proposed. This could explain why the diffusion coeffs. in the plasma membrane are considerably smaller than those in artificial membranes, and why the diffusion coeff. is reduced upon mol. complex formation (oligomerization-induced trapping). Here, the authors 1st describe the high-speed single-mol. tracking methods, and then they critically review a new model of a partitioned fluid plasma membrane and the involvement of the actin-based membrane-skeleton "fences" and anchored-transmembrane protein "pickets" in the formation of compartment boundaries.
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    Rentsch, J.; Bandstra, S.; Sezen, B.; Sigrist, P. S.; Bottanelli, F.; Schmerl, B.; Shoichet, S.; Noé, F.; Sadeghi, M.; Ewers, H. Sub-Membrane Actin Rings Compartmentalize the Plasma Membrane. J. Cell Biol. 2024, 223 (4), e202310138  DOI: 10.1083/jcb.202310138
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    Sadegh, S.; Higgins, J. L.; Mannion, P. C.; Tamkun, M. M.; Krapf, D. Plasma Membrane Is Compartmentalized by a Self-Similar Cortical Actin Meshwork. Phys. Rev. X 2017, 7 (1), 011031,  DOI: 10.1103/PhysRevX.7.011031
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    Andrade, D. M.; Clausen, M. P.; Keller, J.; Mueller, V.; Wu, C.; Bear, J. E.; Hell, S. W.; Lagerholm, B. C.; Eggeling, C. Cortical Actin Networks Induce Spatio-Temporal Confinement of Phospholipids in the Plasma Membrane -A Minimally Invasive Investigation by STED-FCS. Sci. Rep. 2015, 5, 11454,  DOI: 10.1038/srep11454
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    Deverall, M. A.; Gindl, E.; Sinner, E.-K.; Besir, H.; Ruehe, J.; Saxton, M. J.; Naumann, C. A. Membrane Lateral Mobility Obstructed by Polymer-Tethered Lipids Studied at the Single Molecule Level. Biophys. J. 2005, 88 (3), 1875– 1886,  DOI: 10.1529/biophysj.104.050559
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    20
    Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level
    Deverall, M. A.; Gindl, E.; Sinner, E.-K.; Besir, H.; Ruehe, J.; Saxton, M. J.; Naumann, C. A.
    Biophysical Journal (2005), 88 (3), 1875-1886CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single mol. fluorescence microscopy. The obstacles are well-controlled concns. of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer mols. is well described by a percolating system with different percolation thresholds for lipids and proteins. Data anal. using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calcns. reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concns. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the anal. of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concns. of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few mols.
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    Ratto, T. V.; Longo, M. L. Obstructed Diffusion in Phase-Separated Supported Lipid Bilayers: A Combined Atomic Force Microscopy and Fluorescence Recovery after Photobleaching Approach. Biophys. J. 2002, 83 (6), 3380– 3392,  DOI: 10.1016/S0006-3495(02)75338-1
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    Brown, F. L. H.; Leitner, D. M.; McCammon, J. A.; Wilson, K. R. Lateral Diffusion of Membrane Proteins in the Presence of Static and Dynamic Corrals: Suggestions for Appropriate Observables. Biophys. J. 2000, 78 (5), 2257– 2269,  DOI: 10.1016/S0006-3495(00)76772-5
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    Heinemann, F.; Vogel, S. K.; Schwille, P. Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex. Biophys. J. 2013, 104 (7), 1465– 1475,  DOI: 10.1016/j.bpj.2013.02.042
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    Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex
    Heinemann, Fabian; Vogel, Sven K.; Schwille, Petra
    Biophysical Journal (2013), 104 (7), 1465-1475CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and mol. interactions. It is assumed that the membrane-assocd. cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin d. and redn. in mobility was obsd. for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addn. of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the anal. of the exptl. FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner.
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    Polanowski, P.; Sikorski, A. Motion in a Crowded Environment: The Influence of Obstacles’ Size and Shape and Model of Transport. J. Mol. Model. 2019, 25 (3), 84,  DOI: 10.1007/s00894-019-3968-9
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    Javanainen, M.; Hammaren, H.; Monticelli, L.; Jeon, J.-H.; S. Miettinen, M.; Martinez-Seara, H.; Metzler, R.; Vattulainen, I. Anomalous and Normal Diffusion of Proteins and Lipids in Crowded Lipid Membranes. Faraday Discuss. 2013, 161, 397– 417,  DOI: 10.1039/C2FD20085F
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    Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes
    Javanainen, Matti; Hammaren, Henrik; Monticelli, Luca; Jeon, Jae-Hyung; Miettinen, Markus S.; Martinez-Seara, Hector; Metzler, Ralf; Vattulainen, Ilpo
    Faraday Discussions (2013), 161 (Lipids & Membrane Biophysics), 397-417CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
    Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concn. of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is obsd. to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent assocd. with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations assocd. with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically obsd. in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the phys. limits of protein motion. Our results suggest that protein concn. is anything but const. in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.
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    Zhou, H.-X.; Rivas, G.; Minton, A. P. Macromolecular Crowding and Confinement: Biochemical, Biophysical, and Potential Physiological Consequences. Annu. Rev. Biophys. 2008, 37, 375– 397,  DOI: 10.1146/annurev.biophys.37.032807.125817
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    26
    Macromolecular crowding and confinement: Biochemical, biophysical, and potential physiological consequences
    Zhou, Huan-Xiang; Rivas, German; Minton, Allen P.
    Annual Review of Biophysics (2008), 37 (), 375-397CODEN: ARBNCV ISSN:. (Annual Reviews Inc.)
    A review. Expected and obsd. effects of vol. exclusion on the free energy of rigid and flexible macromols. in crowded and confined systems, and consequent effects of crowding and confinement on macromol. reaction rates and equil. are summarized. Findings from relevant theor./simulation and exptl. literature published from 2004 onward are reviewed. Addnl. complexity arising from the heterogeneity of local environments in biol. media, and the presence of nonspecific interactions between macromols. over and above steric repulsion, are discussed. Theor. and exptl. approaches to the characterization of crowding- and confinement-induced effects in systems approaching the complexity of living organisms are suggested.
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    Cremer, P. S.; Boxer, S. G. Formation and Spreading of Lipid Bilayers on Planar Glass Supports. J. Phys. Chem. B 1999, 103 (13), 2554– 2559,  DOI: 10.1021/jp983996x
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    Formation and Spreading of Lipid Bilayers on Planar Glass Supports
    Cremer, Paul S.; Boxer, Steven G.
    Journal of Physical Chemistry B (1999), 103 (13), 2554-2559CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    The fusion and spreading of phospholipid bilayers on glass surfaces was investigated as a function of pH and ionic strength. Membrane fusion to the support was favorable at high ionic strength and low pH for vesicles contg. a net neg. charge; however, neutral and pos. charged vesicles fused under all conditions attempted. This result suggests that van der Waals and electrostatic interactions govern the fusion process. Membrane spreading over a planar surface was favorable at low pH regardless of the net charge on the bilayer, and the process is driven by van der Waals forces. On the other hand membrane propagation is impeded at high pH or on highly curved surfaces. In this case a combination of hydration and bending interactions is primarily responsible for arresting the spreading process. These results provide a framework for understanding many of the factors that influence the effectiveness of scratches on planar supported bilayers as barriers to lateral diffusion and lead to a simple method to heal these scratches.
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    Kam, L.; Boxer, S. G. Spatially Selective Manipulation of Supported Lipid Bilayers by Laminar Flow: Steps Toward Biomembrane Microfluidics. Langmuir 2003, 19 (5), 1624– 1631,  DOI: 10.1021/la0263413
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    Spatially selective manipulation of supported lipid bilayers by laminar flow: Steps toward biomembrane microfluidics
    Kam, Lance; Boxer, Steven G.
    Langmuir (2003), 19 (5), 1624-1631CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    The ability to manipulate supported lipid bilayers after formation on a substrate has made possible new classes of both mol. and cellular level expts. In this report, we combine the unique properties of these lipid systems with laminar flow concepts to selectively remove, collect, and reconstitute lipid bilayers from specified regions of a surface. A stream of detergent soln. was directed over a preformed bilayer, resulting in the removal of bilayer material; mixing between adjacent flows at low Reynolds no. is diffusion limited, providing confinement of this stripping soln. and, consequently, bilayer removal with precision on the order of several micrometers. The freshly exposed surface allows formation of new connected bilayer when exposed to lipid vesicles. In conjunction with surface micropatterning and electrophoretic manipulation, we further demonstrate a first-generation, membrane-based sepn./purifn. strategy. Flow-based manipulation of lipid bilayers forms the basis of biomembrane microfluidics. In particular, the directed introduction of lipids or other materials provides a route toward dynamic formation and erasure of barriers to lipid diffusion. As examples of future applications of these methods, we discuss the sepn. of mobile from immobile membrane components and a route toward spatially resolved label-free anal. of compn. gradients in patterned supported membranes.
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    Iversen, L.; Mathiasen, S.; Larsen, J. B.; Stamou, D. Membrane Curvature Bends the Laws of Physics and Chemistry. Nat. Chem. Biol. 2015, 11 (11), 822– 825,  DOI: 10.1038/nchembio.1941
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    Membrane curvature bends the laws of physics and chemistry
    Iversen, Lars; Mathiasen, Signe; Larsen, Jannik Bruun; Stamou, Dimitrios
    Nature Chemical Biology (2015), 11 (11), 822-825CODEN: NCBABT; ISSN:1552-4450. (Nature Publishing Group)
    A review. A 'chem. biol. of cellular membranes' must capture the way that mesoscale perturbations tune the biochem. properties of constituent lipid and protein mols., and vice versa. Whereas the classical paradigm focuses on chem. compn., dynamic modulation of the phys. shape or curvature of a membrane is emerging as a complementary and synergistic modus operandi for regulating cellular membrane biol.
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    Woodward, X.; Stimpson, E. E.; Kelly, C. V. Single-Lipid Tracking on Nanoscale Membrane Buds: The Effects of Curvature on Lipid Diffusion and Sorting. Biochim. Biophys. Acta, Biomembr. 2018, 1860 (10), 2064– 2075,  DOI: 10.1016/j.bbamem.2018.05.009
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    Single-lipid tracking on nanoscale membrane buds: The effects of curvature on lipid diffusion and sorting
    Woodward, Xinxin; Stimpson, Eric E.; Kelly, Christopher V.
    Biochimica et Biophysica Acta, Biomembranes (2018), 1860 (10), 2064-2075CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    Nanoscale membrane curvature in cells is crit. for endocytosis/exocytosis and membrane trafficking. However, the biophys. ramifications of nanoscale membrane curvature on the behavior of lipids remain poorly understood. Here, we created an exptl. model system of membrane curvature at a physiol.-relevant scale and obtained nanoscopic information on single-lipid distributions and dynamics. Supported lipid bilayers were created over 50 and 70 nm radius nanoparticles to create membrane buds. Single-mol. localization microscopy was performed with diverse mixts. of fluorescent and non-fluorescent lipids. Variations in lipid acyl tales length, satn., head-group, and fluorescent labeling strategy were tested while maintaining a single fluid lipid phase throughout the membrane. Monte Carlo simulations were used to fit our exptl. results and quantify the effects of curvature on the lipid diffusion and sorting. Whereas varying the compn. of the non-fluorescent lipids yielded minimal changes to the curvature effects, the labeling strategy of the fluorescent lipids yielded highly varying effects of curvature. Most conditions yield single-population Brownian diffusion throughout the membrane; however, curvature-induced lipid sorting, slowing, and aggregation were obsd. in some conditions. Head-group labeled lipids such as DPPE-Texas Red and POPE-Rhodamine diffused >2.4× slower on the curved vs. the planar membranes; tail-labeled lipids such as NBD-PPC, TopFluor-PPC, and TopFluor-PIP2, as well as DiIC12 and DiIC18 displayed no significant changes in diffusion due to the membrane curvature. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.
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    Kusters, R.; Kapitein, L. C.; Hoogenraad, C. C.; Storm, C. Shape-Induced Asymmetric Diffusion in Dendritic Spines Allows Efficient Synaptic AMPA Receptor Trapping. Biophys. J. 2013, 105 (12), 2743– 2750,  DOI: 10.1016/j.bpj.2013.11.016
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    Stochastic models of intracellular transport
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    Reviews of Modern Physics (2013), 85 (1), 135-196CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
    A review. The interior of a living cell is a crowded, heterogeneous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chem. energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomols. to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of anal. methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state redn. methods, and mean-field approxns. are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.
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    Holcman, D.; Marchewka, A.; Schuss, Z. Survival Probability of Diffusion with Trapping in Cellular Neurobiology. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2005, 72 (3), 031910,  DOI: 10.1103/PhysRevE.72.031910
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    Skvortsov, A. Mean First Passage Time for a Particle Diffusing on a Disk with Two Absorbing Traps at the Boundary. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2020, 102 (1), 012123,  DOI: 10.1103/PhysRevE.102.012123
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    Berezhkovskii, A. M.; Makhnovskii, Y. A.; Monine, M. I.; Zitserman, V. Y.; Shvartsman, S. Y. Boundary Homogenization for Trapping by Patchy Surfaces. J. Chem. Phys. 2004, 121 (22), 11390– 11394,  DOI: 10.1063/1.1814351
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    Berezhkovskii, A. M.; Barzykin, A. V.; Zitserman, V. Y. One-Dimensional Description of Diffusion in a Tube of Abruptly Changing Diameter: Boundary Homogenization Based Approach. J. Chem. Phys. 2009, 131, 224110,  DOI: 10.1063/1.3271998
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    One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach
    Berezhkovskii, Alexander M.; Barzykin, Alexander V.; Zitserman, Vladimir Yu.
    Journal of Chemical Physics (2009), 131 (22), 224110/1-224110/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Redn. of three-dimensional (3D) description of diffusion in a tube of variable cross section to an approx. one-dimensional (1D) description was studied in detail previously only in tubes of slowly varying diam. Here an effective 1D description is discussed in the opposite limiting case when the tube diam. changes abruptly, i.e., in a tube composed of any no. of cylindrical sections of different diams. The key step of the approach is an approx. description of the particle transitions between the wide and narrow parts of the tube as trapping by partially absorbing boundaries with appropriately chosen trapping rates. Boundary homogenization is used to det. the trapping rate for transitions from the wide part of the tube to the narrow one. This trapping rate is then used in combination with the condition of detailed balance to find the trapping rate for transitions in the opposite direction, from the narrow part of the tube to the wide one. Comparison with numerical soln. of the 3D diffusion equation allows to test the approx. 1D description and to establish the conditions of its applicability. It was found that suggested 1D description works quite well when the wide part of the tube is not too short, whereas the length of the narrow part can be arbitrary. Taking advantage of this description in the problem of escape of diffusing particle from a cylindrical cavity through a cylindrical tunnel restricting assumptions accepted in earlier theories are lifted: the particle motion is considered in the tunnel and in the cavity on an equal footing, i.e., the assumption is relaxed of fast intracavity relaxation used in all earlier theories. As a consequence, the dependence of the escape kinetics on the particle initial position in the system can be analyzed. Moreover, using the 1D description the escape kinetics is analyzed at an arbitrary tunnel radius, whereas all earlier theories are based on the assumption that the tunnel is narrow. (c) 2009 American Institute of Physics.
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    Holcman, D.; Schuss, Z. Diffusion through a Cluster of Small Windows and Flux Regulation in Microdomains. Phys. Lett. A 2008, 372 (21), 3768– 3772,  DOI: 10.1016/j.physleta.2008.02.076
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    Yang, X.; Liu, C.; Li, Y.; Marchesoni, F.; Hänggi, P.; Zhang, H. P. Hydrodynamic and Entropic Effects on Colloidal Diffusion in Corrugated Channels. Proc. Natl. Acad. Sci. U. S. A. 2017, 114 (36), 9564– 9569,  DOI: 10.1073/pnas.1707815114
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    Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
    Yang, Xiang; Liu, Chang; Li, Yunyun; Marchesoni, Fabio; Hanggi, Peter; Zhang, H. P.
    Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (36), 9564-9569CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, e.g., ionic channels, zeolites, and nanopores. While extensive theor. and numerical studies on this subject have produced many important predictions, exptl. verification of the predictions are rare. This work exptl. measured colloidal diffusion time in microchannels with periodically varying width, and contrasted results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predicted the entropic effect of the varying channel width, they failed to account for hydrodynamic effects, including an overall decrease and a spatial variation of in-channel diffusivity. Neglecting such hydrodynamic effects, the theory and simulation underestimated the mean and std. deviation of first passage time by 40% in channels with a neck width twice the particle diam. The authors further showed the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of exptl. measured diffusivity. This work showed that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theor. and numerical models.
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    Malgaretti, P.; Pagonabarraga, I.; Miguel Rubi, J. Entropically Induced Asymmetric Passage Times of Charged Tracers across Corrugated Channels. J. Chem. Phys. 2016, 144, 3034901,  DOI: 10.1063/1.4939799
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    Bullerjahn, J. T.; Von Bülow, S.; Hummer, G. Optimal Estimates of Self-Diffusion Coefficients from Molecular Dynamics Simulations. J. Chem. Phys. 2020, 153, 2024116,  DOI: 10.1063/5.0008312
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    Vögele, M.; Hummer, G. Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes. J. Phys. Chem. B 2016, 120 (33), 8722– 8732,  DOI: 10.1021/acs.jpcb.6b05102
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    Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes
    Vogele Martin; Hummer Gerhard
    The journal of physical chemistry. B (2016), 120 (33), 8722-32 ISSN:.
    We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with t ln t and t(3/2) components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments.
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    Biercuk, M. J.; Monsma, D. J.; Marcus, C. M.; Becker, J. S.; Gordon, R. G. Low-Temperature Atomic-Layer-Deposition Lift-off Method for Microelectronic and Nanoelectronic Applications. Appl. Phys. Lett. 2003, 83 (12), 2405– 2407,  DOI: 10.1063/1.1612904
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    Low-temperature atomic-layer-deposition lift-off method for microelectronic and nanoelectronic applications
    Biercuk, M. J.; Monsma, D. J.; Marcus, C. M.; Becker, J. S.; Gordon, R. G.
    Applied Physics Letters (2003), 83 (12), 2405-2407CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    The authors report a method for depositing patterned dielec. layers with submicron features using at. layer deposition. The patterned films are superior to sputtered or evapd. films in continuity, smoothness, conformality, and min. feature size. Films were deposited at 100-150° using several different precursors and patterned using either electron-beam or photoresist. The low deposition temp. permits uniform film growth without significant outgassing or hardbaking of resist layers. A lift-off technique presented here gives sharp step edges with edge roughness as low as ∼10 nm. The authors also measure dielec. consts. (κ) and breakdown fields for the high-κ materials aluminum oxide (κ ∼ 8-9), hafnium oxide (κ ∼ 16-19), and zirconium oxide (κ ∼ 20-29), grown under similar low temp. conditions.
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    Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P. R. Production of Large Unilamellar Vesicles by a Rapid Extrusion Procedure. Characterization of Size Distribution, Trapped Volume and Ability to Maintain a Membrane Potential. Biochim. Biophys. Acta, Biomembr. 1985, 812 (1), 55– 65,  DOI: 10.1016/0005-2736(85)90521-8
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    Production of large unilamellar vesicles by a rapid extrusion procedure. Characterization of size distribution, trapped volume and ability to maintain a membrane potential
    Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P. R.
    Biochimica et Biophysica Acta, Biomembranes (1985), 812 (1), 55-65CODEN: BBBMBS; ISSN:0005-2736.
    A technique for the rapid prodn. of large unilamellar vesicles by repeated extrusion under moderate pressures (≤500 lb/in2) of multilamellar vesicles through polycarbonate filters (100 nm pore size) is demonstrated. In combination with freeze-thaw protocols where required, this procedure results in unilamellar vesicles with diams. in the range 60-100 nm and with trapped vols. in the region of 1-3 μL/μmol phospholipid. Advantages of this technique include the absence of org. solvents or detergents, the high lipid concns. (up to 300 μmol/mL) that can be employed and the high trapping efficiencies (up to 30%) that can be achieved. Further, the procedure for generating these LUVET's (large unilamellar vesicles by extrusion techniques) is rapid (≤10 min prepn. time) and can be employed to generate large unilamellar vesicles from a wide variety of lipid species and mixts. As a particular illustration of the utility of this vesicle prepn., LUVET systems exhibiting a membrane potential (Δψ) in response to a transmembrane Na+/K+ gradient (K+ inside) have been characterized. By employing the lipophilic cation methyltriphenylphosphonium (MTPP+), a K+ diffusion potential (Δψ < -100 mV) forms rapidly in the presence of the K+ ionophore valinomycin for soya phosphatidylcholine LUVET's. The values of Δψ obtained correlate well with the K+ concn. gradient across the membrane, and it is demonstrated that the decay of Δψ with time depends on the flux of Na+ into the vesicles.
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    Kučerka, N.; Nieh, M.-P.; Katsaras, J. Fluid Phase Lipid Areas and Bilayer Thicknesses of Commonly Used Phosphatidylcholines as a Function of Temperature. Biochim. Biophys. Acta, Biomembr. 2011, 1808 (11), 2761– 2771,  DOI: 10.1016/j.bbamem.2011.07.022
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    Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature
    Kucerka, Norbert; Nieh, Mu-Ping; Katsaras, John
    Biochimica et Biophysica Acta, Biomembranes (2011), 1808 (11), 2761-2771CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    The structural parameters of fluid phase bilayers composed of phosphatidylcholines with fully satd., mixed, and branched fatty acid chains, at several temps., were detd. by simultaneously analyzing small-angle neutron and x-ray scattering data. Bilayer parameters, such as area per lipid and overall bilayer thickness were obtained in conjunction with intrabilayer structural parameters (e.g. hydrocarbon region thickness). The results have allowed one to assess the effect of temp. and hydrocarbon chain compn. on bilayer structure. For example, for all lipids there is, not surprisingly, an increase in fatty acid chain trans-gauche isomerization with increasing temp. Also, this increase in trans-gauche isomerization scales with fatty acid chain length in mixed chain lipids. However, in the case of lipids with satd. fatty acid chains, trans-gauche isomerization is increasingly tempered by attractive chain-chain van der Waals interactions with increasing chain length. Finally, the results confirm a strong dependence of lipid chain dynamics as a function of double bond position along fatty acid chains.
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    Pincet, F.; Adrien, V.; Yang, R.; Delacotte, J.; Rothman, J. E.; Urbach, W.; Tareste, D. FRAP to Characterize Molecular Diffusion and Interaction in Various Membrane Environments. PLoS One 2016, 11 (7), e0158457  DOI: 10.1371/journal.pone.0158457
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    FRAP to characterize molecular diffusion and interaction in various membrane environments
    Pincet, Frederic; Adrien, Vladimir; Yang, Rong; Delacotte, Jerome; Rothman, James E.; Urbach, Wladimir; Tareste, David
    PLoS One (2016), 11 (7), e0158457/1-e0158457/19CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
    Fluorescence recovery after photobleaching (FRAP) is a std. method used to study the dynamics of lipids and proteins in artificial and cellular membrane systems. The advent of confocal microscopy two decades ago has made quant. FRAP easily available to most labs. Usually, a single bleaching pattern/area is used and the corresponding recovery time is assumed to directly provide a diffusion coeff., although this is only true in the case of unrestricted Brownian motion. Here, we propose some general guidelines to perform FRAP expts. under a confocal microscope with different bleaching patterns and area, allowing the experimentalist to establish whether the mols. undergo Brownian motion (free diffusion) or whether they have restricted or directed movements. Using in silico simulations of FRAP measurements, we further indicate the data acquisition criteria that have to be verified in order to obtain accurate values for the diffusion coeff. and to be able to distinguish between different diffusive species. Using this approach, we compare the behavior of lipids in three different membrane platforms (supported lipid bilayers, giant liposomes and sponge phases), and we demonstrate that FRAP measurements are consistent with results obtained using other techniques such as Fluorescence Correlation Spectroscopy (FCS) or Single Particle Tracking (SPT). Finally, we apply this method to show that the presence of the synaptic protein Munc18-1 inhibits the interaction between the synaptic vesicle SNARE protein, VAMP2, and its partner from the plasma membrane, Syn1A.
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    Soumpasis D M
    Biophysical journal (1983), 41 (1), 95-7 ISSN:0006-3495.
    We derive an exact closed formula for the fluorescence recovery curve measured in fluorescence photobleaching recovery experiments employing uniform circular laser beams. In contrast to the expression used currently, this result is very simple and free of mathematical drawbacks, thus facilitating the quantitative analysis of experimental data.
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    Korlach, J.; Schwille, P.; Webb, W. W.; Feigenson, G. W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. PNAS 1999, 96 (15), 8461– 8466,  DOI: 10.1073/pnas.96.15.8461
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    Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis
    Almeida, Paulo F. F.; Vaz, Winchil L. C.; Thompson, T. E.
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    Fluorescence recovery after photobleaching is used to perform an extensive study of the lateral diffusion of a phospholipid probe in the binary mixt. dimyristoylphosphatidylcholine/cholesterol, above the melting temp. of the phospholipid. In the regions of the phase diagram where a single liq. phase exists, diffusion can be quant. described by free vol. theory, using a modified Macedo-Litovitz hybrid equation. In the liq.-liq. immiscibility region, the temp. dependence of the diffusion coeff. is in excellent agreement with current theories of generalized diffusivities in composite two-phase media. A consistent interpretation of the diffusion data can be provided based essentially on the idea that the primary effect of cholesterol addn. to the bilayer is to occupy free vol. On this basis, a general interpretation of the phase behavior of this mixt. is also proposed.
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    Jung, M.; Vogel, N.; Köper, I. Nanoscale Patterning of Solid-Supported Membranes by Integrated Diffusion Barriers. Langmuir 2011, 27 (11), 7008– 7015,  DOI: 10.1021/la200027e
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    Nanoscale Patterning of Solid-Supported Membranes by Integrated Diffusion Barriers
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    Langmuir (2011), 27 (11), 7008-7015CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Ultraflat nanostructured substrates have been used as a template to create patterned solid-supported bilayer membranes with polymerizable tethered lipids acting as diffusion barriers. Patterns in the size range of 100 nm were successfully produced and characterized. The diffusion barriers were embedded directly into the phospholipid bilayer and could be used to control the fluidity of the membrane as well as to construct isolated membrane corrals. By using nanosphere lithog. to structure the templates it was possible to systematically adjust the lipid diffusion coeffs. in a range comparable to those obsd. in cellular membranes. Single colloids applied as mask in the patterning process yielded substrates for creation of isolated fluid membrane patches corralled by diffusion barriers. Numerous potential applications for this new model system can be envisioned, ranging from the study of cellular interactions or of mol. diffusion in confined geometries to biosensor arrays.
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    Motegi, T.; Takiguchi, K.; Tanaka-Takiguchi, Y.; Itoh, T.; Tero, R. Physical Properties and Reactivity of Microdomains in Phosphatidylinositol-Containing Supported Lipid Bilayer. Membranes 2021, 11 (5), 339,  DOI: 10.3390/membranes11050339
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    Morigaki, K.; Kiyosue, K.; Taguchi, T. Micropatterned Composite Membranes of Polymerized and Fluid Lipid Bilayers. Langmuir 2004, 20 (18), 7729– 7735,  DOI: 10.1021/la049340e
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    Micropatterned composite membranes of polymerized and fluid lipid bilayers
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    Langmuir (2004), 20 (18), 7729-7735CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Micropatterned composite membranes of polymd. and fluid lipid bilayers were constructed on solid substrates. Lithog. photopolymn. of a diacetylene-contg. phospholipid, 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DiynePC), and subsequent removal of nonreacted monomers by a detergent soln. (0.1 M sodium dodecyl sulfate (SDS)) yielded a patterned polymeric bilayer matrix on the substrate. Fluid lipid bilayers of phosphatidylcholine from egg yolk (egg-PC) were incorporated into the lipid-free wells surrounded by the polymeric bilayers through the process of fusion and reorganization of suspended small unilamellar vesicles. Spatial distribution of the fluid bilayers in the patterned bilayer depended on the degree of photopolymn. that in turn could be modulated by varying the applied UV irradn. dose. The polymeric bilayer domains blocked lateral diffusion of the fluid lipid bilayers and confined them in the defined areas (corrals), if the polymn. was conducted with a sufficiently large UV dose. On the other hand, lipid mols. of the fluid bilayers penetrated into the polymeric bilayer domains, if the UV dose was relatively small. A direct correlation was obsd. between the applied UV dose and the lateral diffusion coeff. of fluorescent marker mols. in the fluid bilayers embedded within the polymeric bilayer domains. Artificial control of lateral diffusion by polymeric bilayers may lead to the creation of complex and versatile biomimetic model membrane arrays.
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    Gao, Y.; Zhong, Z.; Geng, M. L. Calibration of Probe Volume in Fluorescence Correlation Spectroscopy. Appl. Spectrosc. 2007, 61 (9), 956– 962,  DOI: 10.1366/000370207781745883
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    Majer, G.; Melchior, J. P. Characterization of the Fluorescence Correlation Spectroscopy (FCS) Standard Rhodamine 6G and Calibration of Its Diffusion Coefficient in Aqueous Solutions. J. Chem. Phys. 2014, 140, 094201,  DOI: 10.1063/1.4867096
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    Yu, L.; Lei, Y.; Ma, Y.; Liu, M.; Zheng, J.; Dan, D.; Gao, P. A Comprehensive Review of Fluorescence Correlation Spectroscopy. Front. Phys. 2021, 9, 644450,  DOI: 10.3389/fphy.2021.644450
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    Schaff, J.; Fink, C. C.; Slepchenko, B.; Carson, J. H.; Loew, L. M. A General Computational Framework for Modeling Cellular Structure and Function. Biophys. J. 1997, 73 (3), 1135– 1146,  DOI: 10.1016/S0006-3495(97)78146-3
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    Cowan, A. E.; Moraru, I. I.; Schaff, J. C.; Slepchenko, B. M.; Loew, L. M. Spatial Modeling of Cell Signaling Networks. Methods Cell Biol. 2012, 110, 195– 221,  DOI: 10.1016/B978-0-12-388403-9.00008-4
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    Spatial modeling of cell signaling networks
    Cowan Ann E; Moraru Ion I; Schaff James C; Slepchenko Boris M; Loew Leslie M
    Methods in cell biology (2012), 110 (), 195-221 ISSN:0091-679X.
    The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.
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    Okazaki, T.; Inaba, T.; Tatsu, Y.; Tero, R.; Urisu, T.; Morigaki, K. Polymerized Lipid Bilayers on a Solid Substrate: Morphologies and Obstruction of Lateral Diffusion. Langmuir 2009, 25 (1), 345– 351,  DOI: 10.1021/la802670t
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    Polymerized Lipid Bilayers on a Solid Substrate: Morphologies and Obstruction of Lateral Diffusion
    Okazaki, Takashi; Inaba, Takehiko; Tatsu, Yoshiro; Tero, Ryugo; Urisu, Tsuneo; Morigaki, Kenichi
    Langmuir (2009), 25 (1), 345-351CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Substrate supported planar lipid bilayers (SPBs) are versatile models of the biol. membrane in biophys. studies and biomedical applications. The authors previously developed a methodol. for generating SPBs composed of polymeric and fluid phospholipid bilayers by using a photopolymerizable diacetylene phospholipid (DiynePC). Polymeric bilayers could be generated with micropatterns by conventional photolithog., and the d.p. could be controlled by modulating UV irradn. doses. After removing nonreacted monomers, fluid lipid membranes could be integrated with polymeric bilayers. Herein, the authors report on a quant. study of the morphol. of polymeric bilayer domains and their obstruction toward lateral diffusion of membrane-assocd. mols. At. force microscopy (AFM) observations revealed that polymd. DiynePC bilayers were formed as nanometer-sized domains. The ratio of polymeric and fluid bilayers could be modulated quant. by changing the UV irradn. dose for photopolymn. Lateral diffusion coeffs. of lipid mols. in fluid bilayers were measured by fluorescence recovery after photobleaching (FRAP) and correlated with the amt. of polymeric bilayer domains on the substrate. Controlled domain structures, lipid compns., and lateral mobility in the model membranes should allow the authors to fabricate model membranes that mimic complex features of biol. membranes with well-defined structures and physicochem. properties.
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    Groves, J. T.; Ulman, N.; Boxer, S. G. Micropatterning Fluid Lipid Bilayers on Solid Supports. Science 1997, 275 (5300), 651– 653,  DOI: 10.1126/science.275.5300.651
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    Micropatterning fluid lipid bilayers on solid supports
    Groves, Jay T.; Ulman, Nick; Boxer, Steven G.
    Science (Washington, D. C.) (1997), 275 (5300), 651-653CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Lithog. patterned grids of photoresist, aluminum oxide, or gold on oxidized silicon substrates were used to partition supported lipid bilayers into micrometer-scale arrays of isolated fluid membrane corrals. Fluorescently labeled lipids were obsd. to diffuse freely within each membrane corral but were confined by the micropatterned barriers. The concns. of fluorescent probe mols. in individual corrals were altered by selective photobleaching to create arrays of fluid membrane patches with differing compns. Application of an elec. field parallel to the surface induced steady-state concn. gradients of charged membrane components in the corrals. In addn. to producing patches of membrane with continuously varying compn., these gradients provide an intrinsically parallel means of acquiring information about mol. properties such as the diffusion coeff. in individual corrals.
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    Kung, L. A.; Kam, L.; Hovis, J. S.; Boxer, S. G. Patterning Hybrid Surfaces of Proteins and Supported Lipid Bilayers. Langmuir 2000, 16 (17), 6773– 6776,  DOI: 10.1021/la000653t
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    Patterning Hybrid Surfaces of Proteins and Supported Lipid Bilayers
    Kung, Li A.; Kam, Lance; Hovis, Jennifer S.; Boxer, Steven G.
    Langmuir (2000), 16 (17), 6773-6776CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Two methods for patterning surfaces with supported lipid bilayers and immobilized protein are described. First, proteins are used to fabricate corrals for supported lipid bilayers. Poly(dimethylsiloxane) stamps are used to deposit arbitrarily shaped patterns of thin layers of immobilized protein onto glass surfaces. This is followed by vesicle fusion into the regions that are not coated with proteins. Second, supported bilayer membranes are blotted to remove patterned regions of the membrane,1 and the blotted regions are filled in or caulked with protein from soln. In both cases, the lipid bilayer regions exhibit lateral fluidity, but each region is confined or corralled by the protein. These two methods can be combined and used iteratively to create arrays with increasing lateral complexity in both the fixed protein and mobile-supported membrane regions for biophys. studies or cell-based assays.
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    Morigaki, K.; Baumgart, T.; Offenhäusser, A.; Knoll, W. Patterning Solid-Supported Lipid Bilayer Membranes by Lithographic Polymerization of a Diacetylene Lipid. Angew. Chem., Int. Ed. 2001, 40 (1), 172– 174,  DOI: 10.1002/1521-3773(20010105)40:1<172::AID-ANIE172>3.0.CO;2-G
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    Patterning solid-supported lipid bilayer membranes by lithographic polymerization of diacetylene lipid
    Morigaki, Kenichi; Baumgart, Tobias; Offenhausser, Andreas; Knoll, Wolfgang
    Angewandte Chemie, International Edition (2001), 40 (1), 172-174CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH)
    The authors report a novel approach for creating patterned bilayers on solid supports. The basic idea is to imprint a pattern within the lipid bilayer by photochem. polymn. of the lipids.
  73. 73
    Hovis, J. S.; Boxer, S. G. Patterning Barriers to Lateral Diffusion in Supported Lipid Bilayer Membranes by Blotting and Stamping. Langmuir 2000, 16 (3), 894– 897,  DOI: 10.1021/la991175t
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    Patterning Barriers to Lateral Diffusion in Supported Lipid Bilayer Membranes by Blotting and Stamping
    Hovis, Jennifer S.; Boxer, Steven G.
    Langmuir (2000), 16 (3), 894-897CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Two new methods are introduced for patterning fluid lipid bilayer membranes on solid supports. These methods are based on the observation that supported membranes undergo self-limiting lateral expansion when bilayer material is removed from the surface or when it is deposited in a pattern on a surface. Spatially selective (patterned) removal of bilayer material can be achieved by using a poly(dimethylsiloxane) (PDMS) stamp. Following slight lateral expansion into the bilayer-free region created by this blotting process, stable barriers to lateral diffusion are formed. Inspection of the barrier regions indicates that nearly all of the bilayer material is removed, implying that it has been transferred to the stamp. As a consequence, it also proves possible to transfer the lifted material from the stamp onto a fresh surface. The transferred material retains the original pattern from the stamp and is also laterally mobile, and the mobility is confined to the printed region. Alternatively, bilayers assembled on a PDMS stamp can be printed onto fresh surfaces. Together these methods constitute a simple and powerful approach for prepg. patterned fluid bilayers in nearly any geometry.
  74. 74
    Hovis, J. S.; Boxer, S. G. Patterning and Composition Arrays of Supported Lipid Bilayers by Microcontact Printing. Langmuir 2001, 17 (11), 3400– 3405,  DOI: 10.1021/la0017577
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    Patterning and composition arrays of supported lipid bilayers by microcontact printing
    Hovis, Jennifer S.; Boxer, Steven G.
    Langmuir (2001), 17 (11), 3400-3405CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Fluid-supported lipid bilayers self-assemble on glass and SiO2 surfaces. We have found that it is also possible to assemble fluid bilayers on plasma-oxidized polydimethyl siloxane (PDMS) surfaces. Furthermore, it is possible to transfer or print the supported bilayer from raised PDMS surfaces, such as are typically used for microcontact printing, to fresh glass surfaces creating a supported bilayer membrane replica of the patterned PDMS surface on glass. These patterned islands of bilayer are fully fluid and indefinitely stable under water. The pattern is erased upon addn. of more vesicles leaving a continuous bilayer surface. By printing membrane islands of various sizes onto a glass surface that is prepatterned with a material that forms permanent barriers to lateral diffusion and then backfilling the open region with vesicles, it is possible to create arbitrary concn. or compn. arrays of membrane-assocd. components. These arrays may be useful for studies of membrane biophysics, for high throughput screening of compds. that target membrane components, and for probing and possibly controlling living cell-synthetic membrane interactions.
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    Etoc, F.; Balloul, E.; Vicario, C.; Normanno, D.; Liße, D.; Sittner, A.; Piehler, J.; Dahan, M.; Coppey, M. Non-Specific Interactions Govern Cytosolic Diffusion of Nanosized Objects in Mammalian Cells. Nat. Mater. 2018, 17 (8), 740– 746,  DOI: 10.1038/s41563-018-0120-7
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    Non-specific interactions govern cytosolic diffusion of nanosized objects in mammalian cells
    Etoc, Fred; Balloul, Elie; Vicario, Chiara; Normanno, Davide; Lisse, Domenik; Sittner, Assa; Piehler, Jacob; Dahan, Maxime; Coppey, Mathieu
    Nature Materials (2018), 17 (8), 740-746CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
    The diffusivity of macromols. in the cytoplasm of eukaryotic cells varies over orders of magnitude and dictates the kinetics of cellular processes. However, a general description that assocs. the Brownian or anomalous nature of intracellular diffusion to the architectural and biochem. properties of the cytoplasm has not been achieved. Here we measure the mobility of individual fluorescent nanoparticles in living mammalian cells to obtain a comprehensive anal. of cytoplasmic diffusion. We identify a correlation between tracer size, its biochem. nature and its mobility. Inert particles with size equal or below 50 nm behave as Brownian particles diffusing in a medium of low viscosity with negligible effects of mol. crowding. Increasing the strength of non-specific interactions of the nanoparticles within the cytoplasm gradually reduces their mobility and leads to subdiffusive behavior. These exptl. observations and the transition from Brownian to subdiffusive motion can be captured in a minimal phenomenol. model.
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    Stylianopoulos, T.; Poh, M.-Z.; Insin, N.; Bawendi, M. G.; Fukumura, D.; Munn, L. L.; Jain, R. K. Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions. Biophys. J. 2010, 99 (5), 1342– 1349,  DOI: 10.1016/j.bpj.2010.06.016
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    Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions
    Stylianopoulos, Triantafyllos; Poh, Ming-Zher; Insin, Numpon; Bawendi, Moungi G.; Fukumura, Dai; Munn, Lance L.; Jain, Rakesh K.
    Biophysical Journal (2010), 99 (5), 1342-1349CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Diffusive transport of macromols. and nanoparticles in charged fibrous media is of interest in many biol. applications, including drug delivery and sepn. processes. Exptl. findings have shown that diffusion can be significantly hindered by electrostatic interactions between the diffusing particle and charged components of the extracellular matrix. The implications, however, were not analyzed rigorously. Here, the authors present a math. framework to study the effect of charge on the diffusive transport of macromols. and nanoparticles in the extracellular matrix of biol. tissues. The model takes into account steric, hydrodynamic, and electrostatic interactions. The authors show that when the fiber size is comparable to the Debye length, electrostatic forces between the fibers and the particles result in slowed diffusion. However, as the fiber diam. increases the repulsive forces become less important. The authors' results explain the exptl. observations that neutral particles diffuse faster than charged particles. Taken together, the authors conclude that optimal particles for delivery to tumors should be initially cationic to target the tumor vessels and then change to neutral charge after exiting the blood vessels.
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    Ando, T.; Skolnick, J. Crowding and Hydrodynamic Interactions Likely Dominate in Vivo Macromolecular Motion. Proc. Natl. Acad. Sci. U. S. A. 2010, 107 (43), 18457– 18462,  DOI: 10.1073/pnas.1011354107
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    Lizana, L.; Bauer, B.; Orwar, O. Controlling the Rates of Biochemical Reactions and Signaling Networks by Shape and Volume Changes. Proc. Natl. Acad. Sci. U. S. A. 2008, 105 (11), 4099– 4104,  DOI: 10.1073/pnas.0709932105
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    Controlling the rates of biochemical reactions and signaling networks by shape and volume changes
    Lizana, L.; Bauer, B.; Orwar, O.
    Proceedings of the National Academy of Sciences of the United States of America (2008), 105 (11), 4099-4104CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    In biol. systems, chem. activity takes place in micrometer and nanometer-sized compartments that constantly change in shape and vol. These ever-changing cellular compartments embed chem. reactions, and we demonstrate that the rates of such incorporated reactions are directly affected by the ongoing shape reconfigurations. First, we show that the rate of product formation in an enzymic reaction can be regulated by simple vol. contraction-dilation transitions. The results suggest that mitochondria may regulate the dynamics of interior reaction path-ways (e.g., the Krebs cycle) by vol. changes. We then show the effect of shape changes on reactions occurring in more complex and structured systems by using biomimetic networks composed of micrometer-sized compartments joined together by nanotubes. Chem. activity was measured by implementing an enzymic reaction-diffusion system. During ongoing reactions, the network connectivity is changed suddenly (similar to the dynamic tube formations found inside Golgi stacks, for example), and the effect on the reaction is registered. We show that spatiotemporal properties of the reaction-diffusion system are extremely sensitive to sudden changes in network topol. and that chem. reactions can be initiated, or boosted, in certain nodes as a function of connectivity.
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    Eggeling, C.; Ringemann, C.; Medda, R.; Schwarzmann, G.; Sandhoff, K.; Polyakova, S.; Belov, V. N.; Hein, B.; Von Middendorff, C.; Schönle, A.; Hell, S. W. Direct Observation of the Nanoscale Dynamics of Membrane Lipids in a Living Cell. Nature 2009, 457 (7233), 1159– 1162,  DOI: 10.1038/nature07596
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    Direct observation of the nanoscale dynamics of membrane lipids in a living cell
    Eggeling, Christian; Ringemann, Christian; Medda, Rebecca; Schwarzmann, Guenter; Sandhoff, Konrad; Polyakova, Svetlana; Belov, Vladimir N.; Hein, Birka; von Middendorff, Claas; Schoenle, Andreas; Hell, Stefan W.
    Nature (London, United Kingdom) (2009), 457 (7233), 1159-1162CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Cholesterol-mediated lipid interactions are thought to have a functional role in many membrane-assocd. processes such as signaling events. Although several expts. indicate their existence, lipid nanodomains (rafts') remain controversial owing to the lack of suitable detection techniques in living cells. The controversy is reflected in their putative size of 5-200 nm, spanning the range between the extent of a protein complex and the resoln. limit of optical microscopy. Here we demonstrate the ability of stimulated emission depletion (STED) far-field fluorescence nanoscopy to detect single diffusing (lipid) mols. in nanosized areas in the plasma membrane of living cells. Tuning of the probed area to spot sizes ∼70-fold below the diffraction barrier reveals that unlike phosphoglycerolipids, sphingolipids and glycosylphosphatidylinositol-anchored proteins are transiently (∼10-20 ms) trapped in cholesterol-mediated mol. complexes dwelling within <20-nm diam. areas. The non-invasive optical recording of mol. time traces and fluctuation data in tunable nanoscale domains is a powerful new approach to study the dynamics of biomols. in living cells.
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    Garcia-Fandino, R.; Pineiro, A.; Trick, J. L.; Sansom, M. S. P. Lipid Bilayer Membrane Perturbation by Embedded Nanopores: A Simulation Study. ACS Nano 2016, 2016 (10), 3693– 3701,  DOI: 10.1021/acsnano.6b00202
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    Niemelä, P. S.; Miettinen, M. S.; Monticelli, L.; Hammaren, H.; Bjelkmar, P.; Murtola, T.; Lindahl, E.; Vattulainen, I. Membrane Proteins Diffuse as Dynamic Complexes with Lipids. J. Am. Chem. Soc. 2010, 132 (22), 7574– 7575,  DOI: 10.1021/ja101481b
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    Membrane Proteins Diffuse as Dynamic Complexes with Lipids
    Niemela, Perttu S.; Miettinen, Markus S.; Monticelli, Luca; Hammaren, Henrik; Bjelkmar, Par; Murtola, Teemu; Lindahl, Erik; Vattulainen, Ilpo
    Journal of the American Chemical Society (2010), 132 (22), 7574-7575CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    We describe how membrane proteins diffuse laterally in the membrane plane together with the lipids surrounding them. We find a no. of intriguing phenomena. The lateral displacements of the protein and the lipids are strongly correlated, as the protein and the neighboring lipids form a dynamical protein-lipid complex, consisting of ∼50-100 lipids. The diffusion of the lipids in the complex is much slower compared to the rest of the lipids. We also find a strong directional correlation between the movements of the protein and the lipids in its vicinity. The results imply that in crowded membrane environments there are no "free" lipids, as they are all influenced by the protein structure and dynamics. Our results indicate that, in studies of cell membranes, protein and lipid dynamics have to be considered together.
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    Długosz, M.; Trylska, J. Diffusion in Crowded Biological Environments: Applications of Brownian Dynamics. BMC Biophys. 2011, 4 (1), 3,  DOI: 10.1186/2046-1682-4-3
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    Saxton, M. J. Lateral Diffusion in an Archipelago. The Effect of Mobile Obstacles. Biophys. J. 1987, 52 (6), 989– 997,  DOI: 10.1016/S0006-3495(87)83291-5
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    Modica, K. J.; Xi, Y.; Takatori, S. C. Porous Media Microstructure Determines the Diffusion of Active Matter: Experiments and Simulations. Front. Phys. 2022, 10, 869175,  DOI: 10.3389/fphy.2022.869175
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    He, K.; Babaye Khorasani, F.; Retterer, S. T.; Thomas, D. K.; Conrad, J. C.; Krishnamoorti, R. Diffusive Dynamics of Nanoparticles in Arrays of Nanoposts. ACS Nano 2013, 7 (6), 5122– 5130,  DOI: 10.1021/nn4007303
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    Diffusive Dynamics of Nanoparticles in Arrays of Nanoposts
    He, Kai; Babaye Khorasani, Firoozeh; Retterer, Scott T.; Thomas, Darrell K.; Conrad, Jacinta C.; Krishnamoorti, Ramanan
    ACS Nano (2013), 7 (6), 5122-5130CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    The diffusive dynamics of dil. dispersions of nanoparticles of diam. 200-400 nm were studied in microfabricated arrays of nanoposts using differential dynamic microscopy and single particle tracking. Posts of diam. 500 nm and height 10 μm were spaced by 1.2-10 μm on a square lattice. As the spacing between posts was decreased, the dynamics of the nanoparticles slowed. The dynamics at all length scales were best represented by a stretched exponential rather than a simple exponential. Both the relative diffusivity and the stretching exponent decreased linearly with increased confinement and, equivalently, with decreased void vol. The slowing of the overall diffusive dynamics and the broadening distribution of nanoparticle displacements with increased confinement are consistent with the onset of dynamic heterogeneity and the approach to vitrification.
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    Macháň, R.; Foo, Y. H.; Wohland, T. On the Equivalence of FCS and FRAP: Simultaneous Lipid Membrane Measurements. Biophys. J. 2016, 111 (1), 152– 161,  DOI: 10.1016/j.bpj.2016.06.001
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    On the Equivalence of FCS and FRAP: Simultaneous Lipid Membrane Measurements
    Machan, Radek; Foo, Yong Hwee; Wohland, Thorsten
    Biophysical Journal (2016), 111 (1), 152-161CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) are widely used methods to det. diffusion coeffs. However, they often do not yield the same results. With the advent of camera-based imaging FCS, which measures the diffusion coeff. in each pixel of an image, and proper bleaching corrections, it is now possible to measure the diffusion coeff. by FRAP and FCS in the exact same images. The authors thus performed simultaneous FCS and FRAP measurements on supported lipid bilayers and live cell membranes to test how far the two methods differ in their results and whether the methodol. differences, in particular the high bleach intensity in FRAP, the bleach corrections, and the fitting procedures in the two methods explain obsd. differences. Overall, the FRAP bleach intensity does not measurably influence the diffusion in the samples, but bleach correction and fitting introduce large uncertainties in FRAP. The authors confirm the authors' results by simulations.
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    Stasevich, T. J.; Mueller, F.; Michelman-Ribeiro, A.; Rosales, T.; Knutson, J. R.; McNally, J. G. Cross-Validating FRAP and FCS to Quantify the Impact of Photobleaching on In Vivo Binding Estimates. Biophys. J. 2010, 99 (9), 3093– 3101,  DOI: 10.1016/j.bpj.2010.08.059
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    Cross-Validating FRAP and FCS to Quantify the Impact of Photobleaching on In Vivo Binding Estimates
    Stasevich, Timothy J.; Mueller, Florian; Michelman-Ribeiro, Ariel; Rosales, Tilman; Knutson, Jay R.; McNally, James G.
    Biophysical Journal (2010), 99 (9), 3093-3101CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Binding can now be quantified in live cells, but the accuracy of such measurements remains uncertain. To address this uncertainty, the authors compare fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS) measurements of the binding kinetics of a transcription factor, the glucocorticoid receptor, in the nuclei of live cells. The authors find that the binding residence time measured by FRAP is 15 times longer than that obtained by FCS. The authors show that this discrepancy is not likely due to the significant differences in concns. typically used for FRAP and FCS, nor is it likely due to spatial heterogeneity of the nucleus, improper calibration of the FCS focal vol., or the intentional FRAP photobleach. Instead, the authors' data indicate that photobleaching of bound mols. in FCS is mainly responsible. When this effect is minimized, FRAP and FCS measurements nearly agree, although cross-validation by other approaches is now required to rule out mutual errors. The authors' results demonstrate the necessity of a photobleach correction for FCS measurements of GFP-tagged mols. that are bound for >0.25 s, and represent an important step forward in establishing a gold std. for in vivo binding measurements.
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    Reitan, N. K.; Juthajan, A.; Lindmo, T.; de Lange Davies, C. Macromolecular Diffusion in the Extracellular Matrix Measured by Fluorescence Correlation Spectroscopy. J. Biomed. Opt. 2008, 13 (5), 054040,  DOI: 10.1117/1.2982530
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    Mazza, D.; Abernathy, A.; Golob, N.; Morisaki, T.; McNally, J. G. A Benchmark for Chromatin Binding Measurements in Live Cells. Nucleic Acids Res. 2012, 40, e119  DOI: 10.1093/nar/gks701
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    A benchmark for chromatin binding measurements in live cells
    Mazza, Davide; Abernathy, Alice; Golob, Nicole; Morisaki, Tatsuya; McNally, James G.
    Nucleic Acids Research (2012), 40 (15), e119CODEN: NARHAD; ISSN:0305-1048. (Oxford University Press)
    Live-cell measurement of protein binding to chromatin allows probing cellular biochem. in physiol. conditions, which are difficult to mimic in vitro. However, different studies have yielded widely discrepant predictions, and so it remains uncertain how to make the measurements accurately. To establish a benchmark the authors measured binding of the transcription factor p53 to chromatin by three approaches: fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS) and single-mol. tracking (SMT). Using new procedures to analyze the SMT data and to guide the FRAP and FCS anal., all three approaches yield similar ests. for both the fraction of p53 mols. bound to chromatin (only ∼20%) and the residence time of these bound mols. (∼1.8 s). The authors also apply these procedures to mutants in p53 chromatin binding. The authors' results support the model that p53 locates specific sites by first binding at sequence-independent sites.
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    Goksu, E. I.; Nellis, B. A.; Lin, W.-C.; Jr, J. H. S.; Groves, J. T.; Risbud, S. H.; Longo, M. L. Effect of Support Corrugation on Silica Xerogel–Supported Phase-Separated Lipid Bilayers. Langmuir 2009, 25, 3713– 3717,  DOI: 10.1021/la803851b
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    Effect of Support Corrugation on Silica Xerogel-Supported Phase-Separated Lipid Bilayers
    Goksu, Emel I.; Nellis, Barbara A.; Lin, Wan-Chen; Satcher, Joe H.; Groves, Jay T.; Risbud, Subhash H.; Longo, Marjorie L.
    Langmuir (2009), 25 (6), 3713-3717CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Lipid bilayers supported by substrates with nanometer-scale surface corrugations hold interest in understanding both nanoparticle-membrane interactions and the challenges of constructing models of cell membranes on surfaces with desirable properties, e.g., porosity. Here, the authors successfully form a two-phase (gel-fluid) lipid bilayer supported by nanoporous silica xerogel. Surface topol., lateral diffusion coeff., and lipid d. in comparison to mica-supported lipid bilayers were characterized by at. force microscopy, fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), and quant. fluorescence microscopy, resp. The authors found that the two-phase lipid bilayer follows the silica xerogel surface contours. The corrugation imparted on the lipid bilayer results in a lipid d. that is twice that on a flat mica surface in the fluid regions. In direct agreement with the doubling of actual bilayer area in a projected area, the authors find that the lateral diffusion coeff. (D) of fluid lipids on silica xerogel (∼1.7 μm2/s) is lower than on mica (∼3.9 μm2/s) by both FRAP and FCS techniques. Furthermore, the gel-phase domains on silica xerogel compared to mica were larger and less numerous. Overall, the authors' results suggest the presence of a relatively defect-free continuous two-phase lipid bilayer that penetrates approx. midway into the first layer of ∼50 nm silica xerogel beads.
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    Pastor, I.; Vilaseca, E.; Madurga, S.; Garcés, J. L.; Cascante, M.; Mas, F. Diffusion of α-Chymotrypsin in Solution-Crowded Media. A Fluorescence Recovery after Photobleaching Study. J. Phys. Chem. B 2010, 114 (11), 4028– 4034,  DOI: 10.1021/jp910811j
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  1. Luis S. Mayorga, Maria L. Mascotti, Bart M. H. Bruininks, Diego Masone. Confinement Induces Morphological and Topological Transitions in Multivesicles. ACS Nano 2025, 19 (4) , 4515-4527. https://doi.org/10.1021/acsnano.4c14171
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  • Abstract

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    Figure 1

    Figure 1. Membranes are crowded, congested environments with obstructions spanning length scales from nanometers to microns. Schematic showing a membrane domain with a transmembrane protein (green), integral and peripheral proteins (purple), cholesterol (orange/red), glycosphingolipids (red), actin meshwork (navy), an ion channel (blue), and a lipid aggregate (dark gray). In this work, we probe the effect of the confinement geometry on both local and global scales.

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    Figure 2

    Figure 2. (a) Schematic of the fabrication process, starting with a plain SiO2 substrate. The SiO2 substrate is lithographically patterned, developed, and then 2.5–5 nm of TiO2 or Al2O3 is deposited on the surface through atomic layer deposition (ALD). The substrate is cleaned, and supported lipid bilayers (SLBs) are formed on the SiO2 surfaces with the vesicle fusion method. The bottom left panel is a fluorescence image showing a SLB (dark gray) formed on a SiO2 substrate around TiO2 structures (black circles). Scale bar is 100 μm. (b) Three classes of structures used to explore geometric aspects of confinement.

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    Figure 3

    Figure 3. FRAP enables imaging of the bilayer morphology and fluidity. Bilayers readily form and recover on SiO2 substrates, as shown in (a)–(c). (d) Recovery of fluorescence inside (red) and outside (blue) the pattern. Outside the pattern, the diffusion coefficient is consistent with literature values for other one-phase fluid bilayers at room temperature (4,59,60) (2.92 ± 0.07 μm2/s). Inside the pattern, the diffusion coefficient decreases; in the geometry shown, it decreases to 1.61 ± 0.04 μm2/s. The scale bar is 15 μm.

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    Figure 4

    Figure 4. (a) The unobstructed fraction is defined as σ=nl2πR where n is the number of escape channels, l is their arclength, and R is the radius of the bleached region (dashed gray circle). (b) The unobstructed fraction vs the effective diffusion for the three different TiO2 geometries are compared. (c) Comparison of the unobstructed fraction vs the effective diffusion for the four channel TiO2 structures on SiO2 (black circles) and for the four channel Al2O3 structures on SiO2 (green stars).

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    Figure 5

    Figure 5. Effective diffusion for the three different TiO2 geometries (insets) obtained from FCS (diamonds) and FRAP (circles) measurements for (a) the four pillar geometry, (b) the four channel geometry, and (c) the one channel geometry.

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    Figure 6

    Figure 6. Comparison of experimental data with analytical models and numerical simulations for the various geometries in this work: (a) the four pillar geometry, (b) the four channel geometry, and (c) the one channel geometry. Descriptions of the models for each geometry are given in the main text.

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      There is no corresponding record for this reference.
    4. 4
      Guo, L.; Har, J. Y.; Sankaran, J.; Hong, Y.; Kannan, B.; Wohland, T. Molecular Diffusion Measurement in Lipid Bilayers over Wide Concentration Ranges: A Comparative Study. ChemPhyschem 2008, 9 (5), 721– 728,  DOI: 10.1002/cphc.200700611
      4
      Molecular diffusion measurement in lipid bilayers over wide concentration ranges: a comparative study
      Guo, Lin; Har, Jia Yi; Sankaran, Jagadish; Hong, Yimian; Kannan, Balakrishnan; Wohland, Thorsten
      ChemPhysChem (2008), 9 (5), 721-728CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Mol. diffusion in biol. membranes is a detg. factor in cell signaling and cell function. In the past few decades, three main fluorescence spectroscopy techniques have emerged that are capable of measuring mol. diffusion in artificial and biol. membranes at very different concn. ranges and spatial resolns. The widely used methods of fluorescence recovery after photobleaching (FRAP) and single-particle tracking (SPT) can det. abs. diffusion coeffs. at high (> 100 μm-2) and very low surface concns. (single-mol. level), resp. Fluorescence correlation spectroscopy (FCS), on the other hand, is well-suited for the intermediate concn. range of about 0.1-100 μm-2. However, FCS in general requires calibration with a std. dye of known diffusion coeff., and yields only relative measurements with respect to the calibration. A variant of FCS, z-scan FCS, is calibration-free for membrane measurements, but requires several expts. at different well-controlled focusing positions. A recently established FCS method, electron-multiplying charge-coupled-device-based total internal reflection FCS (TIR-FCS), referred to here as imaging TIR-FCS (ITIR-FCS), is also independent of calibration stds., but to our knowledge no direct comparison between these different methods has been made. Herein, we seek to establish a comparison between FRAP, SPT, FCS, and ITIR-FCS by measuring the lateral diffusion coeffs. in two model systems, namely, supported lipid bilayers and giant unilamellar vesicles.
    5. 5
      Dolainsky, C.; Karakatsanis, P.; Bayerl, T. M. Lipid Domains as Obstacles for Lateral Diffusion in Supported Bilayers Probed at Different Time and Length Scales by Two-Dimensional Exchange and Field Gradient Solid State NMR. Phys. Rev. E 1997, 55 (4), 4512– 4521,  DOI: 10.1103/PhysRevE.55.4512
      There is no corresponding record for this reference.
    6. 6
      Minton, A. P. Confinement as a Determinant of Macromolecular Structure and Reactivity. Biophys. J. 1992, 63 (4), 1090– 1100,  DOI: 10.1016/S0006-3495(92)81663-6
      6
      Confinement as a determinant of macromolecular structure and reactivity
      Minton, Allen P.
      Biophysical Journal (1992), 63 (4), 1090-100CODEN: BIOJAU; ISSN:0006-3495.
      The confinement of macromols. within enclosures or pores of comparable dimensions results in significant size- and shape-dependent alterations of macromol. chem. potential and reactivity. Calcns. of the magnitude of this effect for model particles of different shapes in model enclosures of different shapes were carried out using the hard particle partition theory developed by J. C. Giddings, et al. (1968). The results indicate that the equil. consts. of reactions, such as isomerization, self-assocn., and site binding, that result in significant changes in macromol. size, shape, and/or mobility may be altered within pores by as much as several orders of magnitude relative to the value in the unbounded or bulk phase. Confinement also produces a substantial size-dependent outward force on the walls of an enclosure. These results are likely to be important within the fluid phase of biol. media, such as the cytoplasm of eukaryotic cells, contg. significant vol. fractions of large fibrous structures (e.g., the cytomatrix).
    7. 7
      Löwe, M.; Kalacheva, M.; Boersma, A. J.; Kedrov, A. The More the Merrier: Effects of Macromolecular Crowding on the Structure and Dynamics of Biological Membranes. FEBS J. 2020, 287 (23), 5039– 5067,  DOI: 10.1111/febs.15429
      7
      The more the merrier: effects of macromolecular crowding on the structure and dynamics of biological membranes
      Lowe Maryna; Kedrov Alexej; Kalacheva Milara; Boersma Arnold J
      The FEBS journal (2020), 287 (23), 5039-5067 ISSN:.
      Proteins are essential and abundant components of cellular membranes. Being densely packed within the limited surface area, proteins fulfil essential tasks for life, which include transport, signalling and maintenance of cellular homeostasis. The high protein density promotes nonspecific interactions, which affect the dynamics of the membrane-associated processes, but also contribute to higher levels of membrane organization. Here, we provide a comprehensive summary of the most recent findings of diverse effects resulting from high protein densities in both living membranes and reconstituted systems and display why the crowding phenomenon should be considered and assessed when studying cellular pathways. Biochemical, biophysical and computational studies reveal effects of crowding on the translational mobility of proteins and lipids, oligomerization and clustering of integral membrane proteins, and also folding and aggregation of proteins at the lipid membrane interface. The effects of crowding pervade to larger length scales, where interfacial and transmembrane crowding shapes the lipid membrane. Finally, we discuss the design and development of fluorescence-based sensors for macromolecular crowding and the perspectives to use those in application to cellular membranes and suggest some emerging topics in studying crowding at biological interfaces.
    8. 8
      Kuznetsova, I. M.; Zaslavsky, B. Y.; Breydo, L.; Turoverov, K. K.; Uversky, V. N. Beyond the Excluded Volume Effects: Mechanistic Complexity of the Crowded Milieu. Molecules 2015, 20 (1), 1377– 1409,  DOI: 10.3390/molecules20011377
      8
      Beyond the excluded volume effects: mechanistic complexity of the crowded milieu
      Kuznetsova, Irina M.; Zaslavsky, Boris Y.; Breydo, Leonid; Turoverov, Konstantin K.; Uversky, Vladimir N.
      Molecules (2015), 20 (1), 1377-1409/1-1377-1409/33, 33 pp.CODEN: MOLEFW; ISSN:1420-3049. (MDPI AG)
      A review. Macromol. crowding is known to affect protein folding, binding of small mols., interaction with nucleic acids, enzymic activity, protein-protein interactions, and protein aggregation. Although for a long time it was believed that the major mechanism of the action of crowded environments on structure, folding, thermodn., and function of a protein can be described in terms of the excluded vol. effects, it is getting clear now that other factors originating from the presence of high concns. of "inert" macromols. in crowded soln. should definitely be taken into account to draw a more complete picture of a protein in a crowded milieu. This review shows that in addn. to the excluded vol. effects important players of the crowded environments are viscosity, perturbed diffusion, direct phys. interactions between the crowding agents and proteins, soft interactions, and, most importantly, the effects of crowders on solvent properties.
    9. 9
      Jacobson, K.; Liu, P.; Lagerholm, B. C. The Lateral Organization and Mobility of Plasma Membrane Components. Cell 2019, 177 (4), 806– 819,  DOI: 10.1016/j.cell.2019.04.018
      9
      The Lateral Organization and Mobility of Plasma Membrane Components
      Jacobson, Ken; Liu, Ping; Lagerholm, B. Christoffer
      Cell (Cambridge, MA, United States) (2019), 177 (4), 806-819CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
      A review. Over the last several decades, an impressive array of advanced microscopic and anal. tools, such as single-particle tracking and nanoscopic fluorescence correlation spectroscopy, has been applied to characterize the lateral organization and mobility of components in the plasma membrane. Such anal. can tell researchers about the local dynamic compn. and structure of membranes and is important for predicting the outcome of membrane-based reactions. However, owing to the unresolved complexity of the membrane and the structures peripheral to it, identification of the detailed mol. origin of the interactions that regulate the organization and mobility of the membrane has not proceeded quickly. This Perspective presents an overview of how cell-surface structure may give rise to the types of lateral mobility that are obsd. and some potentially fruitful future directions to elucidate the architecture of these structures in more mol. detail.
    10. 10
      Goose, J. E.; Sansom, M. S. P. Reduced Lateral Mobility of Lipids and Proteins in Crowded Membranes. PLoS Comput. Biol. 2013, 9, e1003033  DOI: 10.1371/journal.pcbi.1003033
      10
      Reduced lateral mobility of lipids and proteins in crowded membranes
      Goose, Joseph E.; Sansom, Mark S. P.
      PLoS Computational Biology (2013), 9 (4), e1003033CODEN: PCBLBG; ISSN:1553-7358. (Public Library of Science)
      Coarse-grained mol. dynamics simulations of the E. coli outer membrane proteins FhuA, LamB, NanC, OmpA and OmpF in a POPE/POPG (3:1) bilayer were performed to characterize the diffusive nature of each component of the membrane. At small observation times (<10 ns) particle vibrations dominate phospholipid diffusion elevating the calcd. values from the longer time-scale bulk value (>50 ns) of 8.5 × 10-7 cm2 s-1. The phospholipid diffusion around each protein was found to vary based on distance from protein. An asymmetry in the diffusion of annular lipids in the inner and outer leaflets was obsd. and correlated with an asymmetry in charged residues in the vicinity of the inner and outer leaflet head-groups. Protein rotational and translational diffusion were also found to vary with observation time and were inversely correlated with the radius of gyration of the protein in the plane of the bilayer. As the concn. of protein within the bilayer was increased, the overall mobility of the membrane decreased reflected in reduced lipid diffusion coeffs. for both lipid and protein components. The increase in protein concn. also resulted in a decrease in the anomalous diffusion exponent α of the lipid. Formation of extended clusters and networks of proteins led to compartmentalization of lipids in extreme cases.
    11. 11
      Ellis, R. J. Macromolecular Crowding: Obvious but Underappreciated. Trends Biochem. Sci. 2001, 26 (10), 597– 604,  DOI: 10.1016/S0968-0004(01)01938-7
      11
      Macromolecular crowding: obvious but underappreciated
      Ellis, R. J.
      Trends in Biochemical Sciences (2001), 26 (10), 597-604CODEN: TBSCDB; ISSN:0968-0004. (Elsevier Science Ltd.)
      A review. Biol. macromols. evolve and function within intracellular environments that are crowded with other macromols. Crowding results in surprisingly large quant. effects on both the rates and the equil. of interactions involving macromols., but such interactions are commonly studied outside the cell in uncrowded buffers. The addn. of high concns. of natural and synthetic macromols. to such buffers enables crowding to be mimicked in vitro, and should be encouraged as a routine variable to study. The stimulation of protein aggregation by crowding might account for the existence of mol. chaperones that combat this effect. Pos. results of crowding include enhancing the collapse of polypeptide chains into functional proteins, the assembly of oligomeric structures and the efficiency of action of some mol. chaperones and metabolic pathways.
    12. 12
      Sadjadi, Z.; Vesperini, D.; Laurent, A. M.; Barnefske, L.; Terriac, E.; Lautenschläger, F.; Rieger, H. Ameboid Cell Migration through Regular Arrays of Micropillars under Confinement. Biophys. J. 2022, 121 (23), 4615– 4623,  DOI: 10.1016/j.bpj.2022.10.030
      There is no corresponding record for this reference.
    13. 13
      Narhi, L. O.; Schmit, J.; Bechtold-Peters, K.; Sharma, D. Classification of Protein Aggregates. J. Pharm. Sci. 2012, 101 (2), 493– 498,  DOI: 10.1002/jps.22790
      13
      Classification of protein aggregates
      Narhi, Linda O.; Schmit, Jeremy; Bechtold-Peters, Karoline; Sharma, Deepak
      Journal of Pharmaceutical Sciences (2012), 101 (2), 493-498CODEN: JPMSAE; ISSN:0022-3549. (Wiley-Liss, Inc.)
      Comparison of protein aggregates/self-assocd. species between labs. and across disciplines is complicated by the imprecise language presently used to describe them. In this commentary, we propose a standardized nomenclature and classification scheme that can be applied to describe all protein aggregates. Five categories are described under which a given aggregate may be independently classified: size, reversibility/dissocn., conformation, covalent modification, and morphol. Possible subclassifications within each category, several examples of applications of the nomenclature, and difficulties in making appropriate assignments will be discussed. © 2011 Wiley-Liss, Inc. and the American Pharmacists Assocn. J Pharm Sci.
    14. 14
      Mahler, H.-C.; Friess, W.; Grauschopf, U.; Kiese, S. Protein Aggregation: Pathways, Induction Factors and Analysis. J. Pharm. Sci. 2009, 98 (9), 2909– 2934,  DOI: 10.1002/jps.21566
      14
      Protein aggregation: Pathways, induction factors and analysis
      Mahler, Hanns-Christian; Friess, Wolfgang; Grauschopf, Ulla; Kiese, Sylvia
      Journal of Pharmaceutical Sciences (2009), 98 (9), 2909-2934CODEN: JPMSAE; ISSN:0022-3549. (Wiley-Liss, Inc.)
      A review. Control and anal. of protein aggregation is an increasing challenge to pharmaceutical research and development. Due to the nature of protein interactions, protein aggregation may occur at various points throughout the lifetime of a protein and may be of different quantity and quality such as size, shape, morphol. It is therefore important to understand the interactions, causes and analyses of such aggregates to control protein aggregation to enable successful products. This review gives a short outline of currently discussed pathways and induction methods for protein aggregation and describes currently employed set of anal. techniques and emerging technologies for aggregate detection, characterization and quantification. A major challenge for the anal. of protein aggregates is that no single anal. method exists to cover the entire size range or type of aggregates which may appear. Each anal. method not only shows its specific advantages but also has its limitations. The limits of detection and the possibility of creating artifacts through sample prepn. by inducing or destroying aggregates need to be considered with each method used. Therefore, it may also be advisable to carefully compare anal. results of orthogonal methods for similar size ranges to evaluate method performance. © 2008 Wiley-Liss, Inc. and the American Pharmacists Assocn. J Pharm Sci 98:2909-2934, 2009.
    15. 15
      Albrecht, D.; Winterflood, C. M.; Sadeghi, M.; Tschager, T.; Noé, F.; Ewers, H. Nanoscopic Compartmentalization of Membrane Protein Motion at the Axon Initial Segment. J. Cell Biol. 2016, 215 (1), 37– 46,  DOI: 10.1083/jcb.201603108
      There is no corresponding record for this reference.
    16. 16
      Kusumi, A.; Nakada, C.; Ritchie, K.; Murase, K.; Suzuki, K.; Murakoshi, H.; Kasai, R. S.; Kondo, J.; Fujiwara, T. Paradigm Shift of the Plasma Membrane Concept from the Two-Dimensional Continuum Fluid to the Partitioned Fluid: High-Speed Single-Molecule Tracking of Membrane Molecules. Annu. Rev. Biophys. Biomol. Struct. 2005, 34, 351– 378,  DOI: 10.1146/annurev.biophys.34.040204.144637
      16
      Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: High-speed single-molecule tracking of membrane molecules
      Kusumi, Akihiro; Nakada, Chieko; Ritchie, Ken; Murase, Kotono; Suzuki, Kenichi; Murakoshi, Hideji; Kasai, Rinshi S.; Kondo, Junko; Fujiwara, Takahiro
      Annual Review of Biophysics and Biomolecular Structure (2005), 34 (), 351-378, 6 platesCODEN: ABBSE4; ISSN:1056-8700. (Annual Reviews Inc.)
      A review. Recent advancements in single-mol. tracking methods with nanometer-level precision now allow researchers to observe the movement, recruitment, and activation of single mols. in the plasma membrane in living cells. In particular, on the basis of the observations by high-speed single-particle tracking at a frame rate of 40,000 frames per s, the partitioning of the fluid plasma membrane into submicron compartments throughout the cell membrane and the hop diffusion of virtually all of the mols. have been proposed. This could explain why the diffusion coeffs. in the plasma membrane are considerably smaller than those in artificial membranes, and why the diffusion coeff. is reduced upon mol. complex formation (oligomerization-induced trapping). Here, the authors 1st describe the high-speed single-mol. tracking methods, and then they critically review a new model of a partitioned fluid plasma membrane and the involvement of the actin-based membrane-skeleton "fences" and anchored-transmembrane protein "pickets" in the formation of compartment boundaries.
    17. 17
      Rentsch, J.; Bandstra, S.; Sezen, B.; Sigrist, P. S.; Bottanelli, F.; Schmerl, B.; Shoichet, S.; Noé, F.; Sadeghi, M.; Ewers, H. Sub-Membrane Actin Rings Compartmentalize the Plasma Membrane. J. Cell Biol. 2024, 223 (4), e202310138  DOI: 10.1083/jcb.202310138
      There is no corresponding record for this reference.
    18. 18
      Sadegh, S.; Higgins, J. L.; Mannion, P. C.; Tamkun, M. M.; Krapf, D. Plasma Membrane Is Compartmentalized by a Self-Similar Cortical Actin Meshwork. Phys. Rev. X 2017, 7 (1), 011031,  DOI: 10.1103/PhysRevX.7.011031
      There is no corresponding record for this reference.
    19. 19
      Andrade, D. M.; Clausen, M. P.; Keller, J.; Mueller, V.; Wu, C.; Bear, J. E.; Hell, S. W.; Lagerholm, B. C.; Eggeling, C. Cortical Actin Networks Induce Spatio-Temporal Confinement of Phospholipids in the Plasma Membrane -A Minimally Invasive Investigation by STED-FCS. Sci. Rep. 2015, 5, 11454,  DOI: 10.1038/srep11454
      There is no corresponding record for this reference.
    20. 20
      Deverall, M. A.; Gindl, E.; Sinner, E.-K.; Besir, H.; Ruehe, J.; Saxton, M. J.; Naumann, C. A. Membrane Lateral Mobility Obstructed by Polymer-Tethered Lipids Studied at the Single Molecule Level. Biophys. J. 2005, 88 (3), 1875– 1886,  DOI: 10.1529/biophysj.104.050559
      20
      Membrane lateral mobility obstructed by polymer-tethered lipids studied at the single molecule level
      Deverall, M. A.; Gindl, E.; Sinner, E.-K.; Besir, H.; Ruehe, J.; Saxton, M. J.; Naumann, C. A.
      Biophysical Journal (2005), 88 (3), 1875-1886CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
      Obstructed long-range lateral diffusion of phospholipids (TRITC-DHPE) and membrane proteins (bacteriorhodopsin) in a planar polymer-tethered 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer is studied using wide-field single mol. fluorescence microscopy. The obstacles are well-controlled concns. of hydrophobic lipid-mimicking dioctadecylamine moieties in the polymer-exposed monolayer of the model membrane. Diffusion of both types of tracer mols. is well described by a percolating system with different percolation thresholds for lipids and proteins. Data anal. using a free area model of obstructed lipid diffusion indicates that phospholipids and tethered lipids interact via hard-core repulsion. A comparison to Monte Carlo lattice calcns. reveals that tethered lipids act as immobile obstacles, are randomly distributed, and do not self-assemble into large-scale aggregates for low to moderate tethering concns. A procedure is presented to identify anomalous subdiffusion from tracking data at a single time lag. From the anal. of the cumulative distribution function of the square displacements, it was found that TRITC-DHPE and W80i show normal diffusion at lower concns. of tethered lipids and anomalous diffusion at higher ones. This study may help improve our understanding of how lipids and proteins in biomembranes may be obstructed by very small obstacles comprising only one or very few mols.
    21. 21
      Ratto, T. V.; Longo, M. L. Obstructed Diffusion in Phase-Separated Supported Lipid Bilayers: A Combined Atomic Force Microscopy and Fluorescence Recovery after Photobleaching Approach. Biophys. J. 2002, 83 (6), 3380– 3392,  DOI: 10.1016/S0006-3495(02)75338-1
      There is no corresponding record for this reference.
    22. 22
      Brown, F. L. H.; Leitner, D. M.; McCammon, J. A.; Wilson, K. R. Lateral Diffusion of Membrane Proteins in the Presence of Static and Dynamic Corrals: Suggestions for Appropriate Observables. Biophys. J. 2000, 78 (5), 2257– 2269,  DOI: 10.1016/S0006-3495(00)76772-5
      There is no corresponding record for this reference.
    23. 23
      Heinemann, F.; Vogel, S. K.; Schwille, P. Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex. Biophys. J. 2013, 104 (7), 1465– 1475,  DOI: 10.1016/j.bpj.2013.02.042
      23
      Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex
      Heinemann, Fabian; Vogel, Sven K.; Schwille, Petra
      Biophysical Journal (2013), 104 (7), 1465-1475CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and mol. interactions. It is assumed that the membrane-assocd. cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin d. and redn. in mobility was obsd. for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addn. of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the anal. of the exptl. FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner.
    24. 24
      Polanowski, P.; Sikorski, A. Motion in a Crowded Environment: The Influence of Obstacles’ Size and Shape and Model of Transport. J. Mol. Model. 2019, 25 (3), 84,  DOI: 10.1007/s00894-019-3968-9
      There is no corresponding record for this reference.
    25. 25
      Javanainen, M.; Hammaren, H.; Monticelli, L.; Jeon, J.-H.; S. Miettinen, M.; Martinez-Seara, H.; Metzler, R.; Vattulainen, I. Anomalous and Normal Diffusion of Proteins and Lipids in Crowded Lipid Membranes. Faraday Discuss. 2013, 161, 397– 417,  DOI: 10.1039/C2FD20085F
      25
      Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes
      Javanainen, Matti; Hammaren, Henrik; Monticelli, Luca; Jeon, Jae-Hyung; Miettinen, Markus S.; Martinez-Seara, Hector; Metzler, Ralf; Vattulainen, Ilpo
      Faraday Discussions (2013), 161 (Lipids & Membrane Biophysics), 397-417CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
      Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concn. of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is obsd. to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent assocd. with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations assocd. with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically obsd. in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the phys. limits of protein motion. Our results suggest that protein concn. is anything but const. in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.
    26. 26
      Zhou, H.-X.; Rivas, G.; Minton, A. P. Macromolecular Crowding and Confinement: Biochemical, Biophysical, and Potential Physiological Consequences. Annu. Rev. Biophys. 2008, 37, 375– 397,  DOI: 10.1146/annurev.biophys.37.032807.125817
      26
      Macromolecular crowding and confinement: Biochemical, biophysical, and potential physiological consequences
      Zhou, Huan-Xiang; Rivas, German; Minton, Allen P.
      Annual Review of Biophysics (2008), 37 (), 375-397CODEN: ARBNCV ISSN:. (Annual Reviews Inc.)
      A review. Expected and obsd. effects of vol. exclusion on the free energy of rigid and flexible macromols. in crowded and confined systems, and consequent effects of crowding and confinement on macromol. reaction rates and equil. are summarized. Findings from relevant theor./simulation and exptl. literature published from 2004 onward are reviewed. Addnl. complexity arising from the heterogeneity of local environments in biol. media, and the presence of nonspecific interactions between macromols. over and above steric repulsion, are discussed. Theor. and exptl. approaches to the characterization of crowding- and confinement-induced effects in systems approaching the complexity of living organisms are suggested.
    27. 27
      Cremer, P. S.; Boxer, S. G. Formation and Spreading of Lipid Bilayers on Planar Glass Supports. J. Phys. Chem. B 1999, 103 (13), 2554– 2559,  DOI: 10.1021/jp983996x
      27
      Formation and Spreading of Lipid Bilayers on Planar Glass Supports
      Cremer, Paul S.; Boxer, Steven G.
      Journal of Physical Chemistry B (1999), 103 (13), 2554-2559CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      The fusion and spreading of phospholipid bilayers on glass surfaces was investigated as a function of pH and ionic strength. Membrane fusion to the support was favorable at high ionic strength and low pH for vesicles contg. a net neg. charge; however, neutral and pos. charged vesicles fused under all conditions attempted. This result suggests that van der Waals and electrostatic interactions govern the fusion process. Membrane spreading over a planar surface was favorable at low pH regardless of the net charge on the bilayer, and the process is driven by van der Waals forces. On the other hand membrane propagation is impeded at high pH or on highly curved surfaces. In this case a combination of hydration and bending interactions is primarily responsible for arresting the spreading process. These results provide a framework for understanding many of the factors that influence the effectiveness of scratches on planar supported bilayers as barriers to lateral diffusion and lead to a simple method to heal these scratches.
    28. 28
      Kam, L.; Boxer, S. G. Spatially Selective Manipulation of Supported Lipid Bilayers by Laminar Flow: Steps Toward Biomembrane Microfluidics. Langmuir 2003, 19 (5), 1624– 1631,  DOI: 10.1021/la0263413
      28
      Spatially selective manipulation of supported lipid bilayers by laminar flow: Steps toward biomembrane microfluidics
      Kam, Lance; Boxer, Steven G.
      Langmuir (2003), 19 (5), 1624-1631CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The ability to manipulate supported lipid bilayers after formation on a substrate has made possible new classes of both mol. and cellular level expts. In this report, we combine the unique properties of these lipid systems with laminar flow concepts to selectively remove, collect, and reconstitute lipid bilayers from specified regions of a surface. A stream of detergent soln. was directed over a preformed bilayer, resulting in the removal of bilayer material; mixing between adjacent flows at low Reynolds no. is diffusion limited, providing confinement of this stripping soln. and, consequently, bilayer removal with precision on the order of several micrometers. The freshly exposed surface allows formation of new connected bilayer when exposed to lipid vesicles. In conjunction with surface micropatterning and electrophoretic manipulation, we further demonstrate a first-generation, membrane-based sepn./purifn. strategy. Flow-based manipulation of lipid bilayers forms the basis of biomembrane microfluidics. In particular, the directed introduction of lipids or other materials provides a route toward dynamic formation and erasure of barriers to lipid diffusion. As examples of future applications of these methods, we discuss the sepn. of mobile from immobile membrane components and a route toward spatially resolved label-free anal. of compn. gradients in patterned supported membranes.
    29. 29
      Iversen, L.; Mathiasen, S.; Larsen, J. B.; Stamou, D. Membrane Curvature Bends the Laws of Physics and Chemistry. Nat. Chem. Biol. 2015, 11 (11), 822– 825,  DOI: 10.1038/nchembio.1941
      29
      Membrane curvature bends the laws of physics and chemistry
      Iversen, Lars; Mathiasen, Signe; Larsen, Jannik Bruun; Stamou, Dimitrios
      Nature Chemical Biology (2015), 11 (11), 822-825CODEN: NCBABT; ISSN:1552-4450. (Nature Publishing Group)
      A review. A 'chem. biol. of cellular membranes' must capture the way that mesoscale perturbations tune the biochem. properties of constituent lipid and protein mols., and vice versa. Whereas the classical paradigm focuses on chem. compn., dynamic modulation of the phys. shape or curvature of a membrane is emerging as a complementary and synergistic modus operandi for regulating cellular membrane biol.
    30. 30
      Woodward, X.; Stimpson, E. E.; Kelly, C. V. Single-Lipid Tracking on Nanoscale Membrane Buds: The Effects of Curvature on Lipid Diffusion and Sorting. Biochim. Biophys. Acta, Biomembr. 2018, 1860 (10), 2064– 2075,  DOI: 10.1016/j.bbamem.2018.05.009
      30
      Single-lipid tracking on nanoscale membrane buds: The effects of curvature on lipid diffusion and sorting
      Woodward, Xinxin; Stimpson, Eric E.; Kelly, Christopher V.
      Biochimica et Biophysica Acta, Biomembranes (2018), 1860 (10), 2064-2075CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
      Nanoscale membrane curvature in cells is crit. for endocytosis/exocytosis and membrane trafficking. However, the biophys. ramifications of nanoscale membrane curvature on the behavior of lipids remain poorly understood. Here, we created an exptl. model system of membrane curvature at a physiol.-relevant scale and obtained nanoscopic information on single-lipid distributions and dynamics. Supported lipid bilayers were created over 50 and 70 nm radius nanoparticles to create membrane buds. Single-mol. localization microscopy was performed with diverse mixts. of fluorescent and non-fluorescent lipids. Variations in lipid acyl tales length, satn., head-group, and fluorescent labeling strategy were tested while maintaining a single fluid lipid phase throughout the membrane. Monte Carlo simulations were used to fit our exptl. results and quantify the effects of curvature on the lipid diffusion and sorting. Whereas varying the compn. of the non-fluorescent lipids yielded minimal changes to the curvature effects, the labeling strategy of the fluorescent lipids yielded highly varying effects of curvature. Most conditions yield single-population Brownian diffusion throughout the membrane; however, curvature-induced lipid sorting, slowing, and aggregation were obsd. in some conditions. Head-group labeled lipids such as DPPE-Texas Red and POPE-Rhodamine diffused >2.4× slower on the curved vs. the planar membranes; tail-labeled lipids such as NBD-PPC, TopFluor-PPC, and TopFluor-PIP2, as well as DiIC12 and DiIC18 displayed no significant changes in diffusion due to the membrane curvature. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.
    31. 31
      Kusters, R.; Kapitein, L. C.; Hoogenraad, C. C.; Storm, C. Shape-Induced Asymmetric Diffusion in Dendritic Spines Allows Efficient Synaptic AMPA Receptor Trapping. Biophys. J. 2013, 105 (12), 2743– 2750,  DOI: 10.1016/j.bpj.2013.11.016
      There is no corresponding record for this reference.
    32. 32
      Bressloff, P. C.; Newby, J. M. Stochastic Models of Intracellular Transport. Rev. Mod. Phys. 2013, 85 (1), 135– 196,  DOI: 10.1103/RevModPhys.85.135
      32
      Stochastic models of intracellular transport
      Bressloff, Paul C.; Newby, Jay M.
      Reviews of Modern Physics (2013), 85 (1), 135-196CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
      A review. The interior of a living cell is a crowded, heterogeneous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chem. energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomols. to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review a wide range of anal. methods and models of intracellular transport is presented. In the case of diffusive transport, narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion are considered. In the case of active transport, Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state redn. methods, and mean-field approxns. are considered. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.
    33. 33
      Holcman, D.; Marchewka, A.; Schuss, Z. Survival Probability of Diffusion with Trapping in Cellular Neurobiology. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2005, 72 (3), 031910,  DOI: 10.1103/PhysRevE.72.031910
      There is no corresponding record for this reference.
    34. 34
      Northrup, S. H. Diffusion-Controlled Ligand Binding to Multiple Competing Cell-Bound Receptors. J. Phys. Chem. 1988, 92 (20), 5847– 5850,  DOI: 10.1021/j100331a060
      There is no corresponding record for this reference.
    35. 35
      Holcman, D.; Hoze, N.; Schuss, Z. Narrow Escape through a Funnel and Effective Diffusion on a Crowded Membrane. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2011, 84 (2), 039903,  DOI: 10.1103/PhysRevE.84.021906
      There is no corresponding record for this reference.
    36. 36
      Berezhkovskii, A. M.; Barzykin, A. V. Extended Narrow Escape Problem: Boundary Homogenization-Based Analysis. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2010, 82 (1), 011114,  DOI: 10.1103/PhysRevE.82.011114
      There is no corresponding record for this reference.
    37. 37
      Ammari, H.; Kalimeris, K.; Kang, H.; Lee, H. Layer Potential Techniques for the Narrow Escape Problem. J. Math. Pures Appl. 2012, 97 (1), 66– 84,  DOI: 10.1016/j.matpur.2011.09.011
      There is no corresponding record for this reference.
    38. 38
      Mangeat, M.; Rieger, H. The Narrow Escape Problem in a Circular Domain with Radial Piecewise Constant Diffusivity. J. Phys. Math. Theor. 2019, 52, 424002,  DOI: 10.1088/1751-8121/ab4348
      There is no corresponding record for this reference.
    39. 39
      Caginalp, C.; Chen, X. Analytical and Numerical Results for an Escape Problem. Arch. Ration. Mech. Anal. 2012, 203 (1), 329– 342,  DOI: 10.1007/s00205-011-0455-6
      There is no corresponding record for this reference.
    40. 40
      Skvortsov, A. Mean First Passage Time for a Particle Diffusing on a Disk with Two Absorbing Traps at the Boundary. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2020, 102 (1), 012123,  DOI: 10.1103/PhysRevE.102.012123
      There is no corresponding record for this reference.
    41. 41
      Berezhkovskii, A. M.; Monine, M. I.; Muratov, C. B.; Shvartsman, S. Y. Homogenization of Boundary Conditions for Surfaces with Regular Arrays of Traps. J. Chem. Phys. 2006, 124 (3), 122– 125,  DOI: 10.1063/1.2161196
      There is no corresponding record for this reference.
    42. 42
      Berezhkovskii, A. M.; Makhnovskii, Y. A.; Monine, M. I.; Zitserman, V. Y.; Shvartsman, S. Y. Boundary Homogenization for Trapping by Patchy Surfaces. J. Chem. Phys. 2004, 121 (22), 11390– 11394,  DOI: 10.1063/1.1814351
      There is no corresponding record for this reference.
    43. 43
      Berezhkovskii, A. M.; Barzykin, A. V.; Zitserman, V. Y. One-Dimensional Description of Diffusion in a Tube of Abruptly Changing Diameter: Boundary Homogenization Based Approach. J. Chem. Phys. 2009, 131, 224110,  DOI: 10.1063/1.3271998
      43
      One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach
      Berezhkovskii, Alexander M.; Barzykin, Alexander V.; Zitserman, Vladimir Yu.
      Journal of Chemical Physics (2009), 131 (22), 224110/1-224110/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Redn. of three-dimensional (3D) description of diffusion in a tube of variable cross section to an approx. one-dimensional (1D) description was studied in detail previously only in tubes of slowly varying diam. Here an effective 1D description is discussed in the opposite limiting case when the tube diam. changes abruptly, i.e., in a tube composed of any no. of cylindrical sections of different diams. The key step of the approach is an approx. description of the particle transitions between the wide and narrow parts of the tube as trapping by partially absorbing boundaries with appropriately chosen trapping rates. Boundary homogenization is used to det. the trapping rate for transitions from the wide part of the tube to the narrow one. This trapping rate is then used in combination with the condition of detailed balance to find the trapping rate for transitions in the opposite direction, from the narrow part of the tube to the wide one. Comparison with numerical soln. of the 3D diffusion equation allows to test the approx. 1D description and to establish the conditions of its applicability. It was found that suggested 1D description works quite well when the wide part of the tube is not too short, whereas the length of the narrow part can be arbitrary. Taking advantage of this description in the problem of escape of diffusing particle from a cylindrical cavity through a cylindrical tunnel restricting assumptions accepted in earlier theories are lifted: the particle motion is considered in the tunnel and in the cavity on an equal footing, i.e., the assumption is relaxed of fast intracavity relaxation used in all earlier theories. As a consequence, the dependence of the escape kinetics on the particle initial position in the system can be analyzed. Moreover, using the 1D description the escape kinetics is analyzed at an arbitrary tunnel radius, whereas all earlier theories are based on the assumption that the tunnel is narrow. (c) 2009 American Institute of Physics.
    44. 44
      Rupprecht, J. F.; Bénichou, O.; Grebenkov, D. S.; Voituriez, R. Exit Time Distribution in Spherically Symmetric Two-Dimensional Domains. J. Stat. Phys. 2015, 158 (1), 192– 230,  DOI: 10.1007/s10955-014-1116-6
      There is no corresponding record for this reference.
    45. 45
      Holcman, D.; Schuss, Z. Diffusion through a Cluster of Small Windows and Flux Regulation in Microdomains. Phys. Lett. A 2008, 372 (21), 3768– 3772,  DOI: 10.1016/j.physleta.2008.02.076
      There is no corresponding record for this reference.
    46. 46
      Yang, X.; Liu, C.; Li, Y.; Marchesoni, F.; Hänggi, P.; Zhang, H. P. Hydrodynamic and Entropic Effects on Colloidal Diffusion in Corrugated Channels. Proc. Natl. Acad. Sci. U. S. A. 2017, 114 (36), 9564– 9569,  DOI: 10.1073/pnas.1707815114
      46
      Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels
      Yang, Xiang; Liu, Chang; Li, Yunyun; Marchesoni, Fabio; Hanggi, Peter; Zhang, H. P.
      Proceedings of the National Academy of Sciences of the United States of America (2017), 114 (36), 9564-9569CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, e.g., ionic channels, zeolites, and nanopores. While extensive theor. and numerical studies on this subject have produced many important predictions, exptl. verification of the predictions are rare. This work exptl. measured colloidal diffusion time in microchannels with periodically varying width, and contrasted results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predicted the entropic effect of the varying channel width, they failed to account for hydrodynamic effects, including an overall decrease and a spatial variation of in-channel diffusivity. Neglecting such hydrodynamic effects, the theory and simulation underestimated the mean and std. deviation of first passage time by 40% in channels with a neck width twice the particle diam. The authors further showed the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of exptl. measured diffusivity. This work showed that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theor. and numerical models.
    47. 47
      Malgaretti, P.; Pagonabarraga, I.; Miguel Rubi, J. Entropically Induced Asymmetric Passage Times of Charged Tracers across Corrugated Channels. J. Chem. Phys. 2016, 144, 3034901,  DOI: 10.1063/1.4939799
      There is no corresponding record for this reference.
    48. 48
      Malgaretti, P.; Pagonabarraga, I.; Rubi, J. M. Entropic Transport in Confined Media: A Challenge for Computational Studies in Biological and Soft-Matter Systems. Front. Phys. 2013, 1, 21.  DOI: 10.3389/fphy.2013.00021 .
      There is no corresponding record for this reference.
    49. 49
      Burada, P. S.; Schmid, G.; Talkner, P.; Hänggi, P.; Reguera, D.; Rubí, J. M. Entropic Particle Transport in Periodic Channels. Biosystems 2008, 93 (1–2), 16– 22,  DOI: 10.1016/j.biosystems.2008.03.006
      There is no corresponding record for this reference.
    50. 50
      Kalinay, P.; Percus, J. K. Corrections to the Fick-Jacobs Equation. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2006, 74 (4), 041203,  DOI: 10.1103/PhysRevE.74.041203
      There is no corresponding record for this reference.
    51. 51
      Bullerjahn, J. T.; Von Bülow, S.; Hummer, G. Optimal Estimates of Self-Diffusion Coefficients from Molecular Dynamics Simulations. J. Chem. Phys. 2020, 153, 2024116,  DOI: 10.1063/5.0008312
      There is no corresponding record for this reference.
    52. 52
      Vögele, M.; Hummer, G. Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes. J. Phys. Chem. B 2016, 120 (33), 8722– 8732,  DOI: 10.1021/acs.jpcb.6b05102
      52
      Divergent Diffusion Coefficients in Simulations of Fluids and Lipid Membranes
      Vogele Martin; Hummer Gerhard
      The journal of physical chemistry. B (2016), 120 (33), 8722-32 ISSN:.
      We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with t ln t and t(3/2) components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments.
    53. 53
      Biercuk, M. J.; Monsma, D. J.; Marcus, C. M.; Becker, J. S.; Gordon, R. G. Low-Temperature Atomic-Layer-Deposition Lift-off Method for Microelectronic and Nanoelectronic Applications. Appl. Phys. Lett. 2003, 83 (12), 2405– 2407,  DOI: 10.1063/1.1612904
      53
      Low-temperature atomic-layer-deposition lift-off method for microelectronic and nanoelectronic applications
      Biercuk, M. J.; Monsma, D. J.; Marcus, C. M.; Becker, J. S.; Gordon, R. G.
      Applied Physics Letters (2003), 83 (12), 2405-2407CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      The authors report a method for depositing patterned dielec. layers with submicron features using at. layer deposition. The patterned films are superior to sputtered or evapd. films in continuity, smoothness, conformality, and min. feature size. Films were deposited at 100-150° using several different precursors and patterned using either electron-beam or photoresist. The low deposition temp. permits uniform film growth without significant outgassing or hardbaking of resist layers. A lift-off technique presented here gives sharp step edges with edge roughness as low as ∼10 nm. The authors also measure dielec. consts. (κ) and breakdown fields for the high-κ materials aluminum oxide (κ ∼ 8-9), hafnium oxide (κ ∼ 16-19), and zirconium oxide (κ ∼ 20-29), grown under similar low temp. conditions.
    54. 54
      Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P. R. Production of Large Unilamellar Vesicles by a Rapid Extrusion Procedure. Characterization of Size Distribution, Trapped Volume and Ability to Maintain a Membrane Potential. Biochim. Biophys. Acta, Biomembr. 1985, 812 (1), 55– 65,  DOI: 10.1016/0005-2736(85)90521-8
      54
      Production of large unilamellar vesicles by a rapid extrusion procedure. Characterization of size distribution, trapped volume and ability to maintain a membrane potential
      Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P. R.
      Biochimica et Biophysica Acta, Biomembranes (1985), 812 (1), 55-65CODEN: BBBMBS; ISSN:0005-2736.
      A technique for the rapid prodn. of large unilamellar vesicles by repeated extrusion under moderate pressures (≤500 lb/in2) of multilamellar vesicles through polycarbonate filters (100 nm pore size) is demonstrated. In combination with freeze-thaw protocols where required, this procedure results in unilamellar vesicles with diams. in the range 60-100 nm and with trapped vols. in the region of 1-3 μL/μmol phospholipid. Advantages of this technique include the absence of org. solvents or detergents, the high lipid concns. (up to 300 μmol/mL) that can be employed and the high trapping efficiencies (up to 30%) that can be achieved. Further, the procedure for generating these LUVET's (large unilamellar vesicles by extrusion techniques) is rapid (≤10 min prepn. time) and can be employed to generate large unilamellar vesicles from a wide variety of lipid species and mixts. As a particular illustration of the utility of this vesicle prepn., LUVET systems exhibiting a membrane potential (Δψ) in response to a transmembrane Na+/K+ gradient (K+ inside) have been characterized. By employing the lipophilic cation methyltriphenylphosphonium (MTPP+), a K+ diffusion potential (Δψ < -100 mV) forms rapidly in the presence of the K+ ionophore valinomycin for soya phosphatidylcholine LUVET's. The values of Δψ obtained correlate well with the K+ concn. gradient across the membrane, and it is demonstrated that the decay of Δψ with time depends on the flux of Na+ into the vesicles.
    55. 55
      Kučerka, N.; Nieh, M.-P.; Katsaras, J. Fluid Phase Lipid Areas and Bilayer Thicknesses of Commonly Used Phosphatidylcholines as a Function of Temperature. Biochim. Biophys. Acta, Biomembr. 2011, 1808 (11), 2761– 2771,  DOI: 10.1016/j.bbamem.2011.07.022
      55
      Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature
      Kucerka, Norbert; Nieh, Mu-Ping; Katsaras, John
      Biochimica et Biophysica Acta, Biomembranes (2011), 1808 (11), 2761-2771CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
      The structural parameters of fluid phase bilayers composed of phosphatidylcholines with fully satd., mixed, and branched fatty acid chains, at several temps., were detd. by simultaneously analyzing small-angle neutron and x-ray scattering data. Bilayer parameters, such as area per lipid and overall bilayer thickness were obtained in conjunction with intrabilayer structural parameters (e.g. hydrocarbon region thickness). The results have allowed one to assess the effect of temp. and hydrocarbon chain compn. on bilayer structure. For example, for all lipids there is, not surprisingly, an increase in fatty acid chain trans-gauche isomerization with increasing temp. Also, this increase in trans-gauche isomerization scales with fatty acid chain length in mixed chain lipids. However, in the case of lipids with satd. fatty acid chains, trans-gauche isomerization is increasingly tempered by attractive chain-chain van der Waals interactions with increasing chain length. Finally, the results confirm a strong dependence of lipid chain dynamics as a function of double bond position along fatty acid chains.
    56. 56
      Voce, N.; Stevenson, P. Vesicle Fusion on SiO2 Substrates. VERSION 22023.  DOI: 10.17504/protocols.io.36wgq3b4ylk5/v2 .
      There is no corresponding record for this reference.
    57. 57
      Pincet, F.; Adrien, V.; Yang, R.; Delacotte, J.; Rothman, J. E.; Urbach, W.; Tareste, D. FRAP to Characterize Molecular Diffusion and Interaction in Various Membrane Environments. PLoS One 2016, 11 (7), e0158457  DOI: 10.1371/journal.pone.0158457
      57
      FRAP to characterize molecular diffusion and interaction in various membrane environments
      Pincet, Frederic; Adrien, Vladimir; Yang, Rong; Delacotte, Jerome; Rothman, James E.; Urbach, Wladimir; Tareste, David
      PLoS One (2016), 11 (7), e0158457/1-e0158457/19CODEN: POLNCL; ISSN:1932-6203. (Public Library of Science)
      Fluorescence recovery after photobleaching (FRAP) is a std. method used to study the dynamics of lipids and proteins in artificial and cellular membrane systems. The advent of confocal microscopy two decades ago has made quant. FRAP easily available to most labs. Usually, a single bleaching pattern/area is used and the corresponding recovery time is assumed to directly provide a diffusion coeff., although this is only true in the case of unrestricted Brownian motion. Here, we propose some general guidelines to perform FRAP expts. under a confocal microscope with different bleaching patterns and area, allowing the experimentalist to establish whether the mols. undergo Brownian motion (free diffusion) or whether they have restricted or directed movements. Using in silico simulations of FRAP measurements, we further indicate the data acquisition criteria that have to be verified in order to obtain accurate values for the diffusion coeff. and to be able to distinguish between different diffusive species. Using this approach, we compare the behavior of lipids in three different membrane platforms (supported lipid bilayers, giant liposomes and sponge phases), and we demonstrate that FRAP measurements are consistent with results obtained using other techniques such as Fluorescence Correlation Spectroscopy (FCS) or Single Particle Tracking (SPT). Finally, we apply this method to show that the presence of the synaptic protein Munc18-1 inhibits the interaction between the synaptic vesicle SNARE protein, VAMP2, and its partner from the plasma membrane, Syn1A.
    58. 58
      Soumpasis, D. M. Theoretical Analysis of Fluorescence Photobleaching Recovery Experiments. Biophys. J. 1983, 41 (1), 95– 97,  DOI: 10.1016/S0006-3495(83)84410-5
      58
      Theoretical analysis of fluorescence photobleaching recovery experiments
      Soumpasis D M
      Biophysical journal (1983), 41 (1), 95-7 ISSN:0006-3495.
      We derive an exact closed formula for the fluorescence recovery curve measured in fluorescence photobleaching recovery experiments employing uniform circular laser beams. In contrast to the expression used currently, this result is very simple and free of mathematical drawbacks, thus facilitating the quantitative analysis of experimental data.
    59. 59
      Korlach, J.; Schwille, P.; Webb, W. W.; Feigenson, G. W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. PNAS 1999, 96 (15), 8461– 8466,  DOI: 10.1073/pnas.96.15.8461
      There is no corresponding record for this reference.
    60. 60
      Almeida, P. F. F.; Vaz, W. L. C.; Thompson, T. E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis. Biochemistry 1992, 31 (29), 6739– 6747,  DOI: 10.1021/bi00144a013
      151
      Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis
      Almeida, Paulo F. F.; Vaz, Winchil L. C.; Thompson, T. E.
      Biochemistry (1992), 31 (29), 6739-47CODEN: BICHAW; ISSN:0006-2960.
      Fluorescence recovery after photobleaching is used to perform an extensive study of the lateral diffusion of a phospholipid probe in the binary mixt. dimyristoylphosphatidylcholine/cholesterol, above the melting temp. of the phospholipid. In the regions of the phase diagram where a single liq. phase exists, diffusion can be quant. described by free vol. theory, using a modified Macedo-Litovitz hybrid equation. In the liq.-liq. immiscibility region, the temp. dependence of the diffusion coeff. is in excellent agreement with current theories of generalized diffusivities in composite two-phase media. A consistent interpretation of the diffusion data can be provided based essentially on the idea that the primary effect of cholesterol addn. to the bilayer is to occupy free vol. On this basis, a general interpretation of the phase behavior of this mixt. is also proposed.
    61. 61
      Jung, M.; Vogel, N.; Köper, I. Nanoscale Patterning of Solid-Supported Membranes by Integrated Diffusion Barriers. Langmuir 2011, 27 (11), 7008– 7015,  DOI: 10.1021/la200027e
      59
      Nanoscale Patterning of Solid-Supported Membranes by Integrated Diffusion Barriers
      Jung, Mathieu; Vogel, Nicolas; Koeper, Ingo
      Langmuir (2011), 27 (11), 7008-7015CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Ultraflat nanostructured substrates have been used as a template to create patterned solid-supported bilayer membranes with polymerizable tethered lipids acting as diffusion barriers. Patterns in the size range of 100 nm were successfully produced and characterized. The diffusion barriers were embedded directly into the phospholipid bilayer and could be used to control the fluidity of the membrane as well as to construct isolated membrane corrals. By using nanosphere lithog. to structure the templates it was possible to systematically adjust the lipid diffusion coeffs. in a range comparable to those obsd. in cellular membranes. Single colloids applied as mask in the patterning process yielded substrates for creation of isolated fluid membrane patches corralled by diffusion barriers. Numerous potential applications for this new model system can be envisioned, ranging from the study of cellular interactions or of mol. diffusion in confined geometries to biosensor arrays.
    62. 62
      Motegi, T.; Takiguchi, K.; Tanaka-Takiguchi, Y.; Itoh, T.; Tero, R. Physical Properties and Reactivity of Microdomains in Phosphatidylinositol-Containing Supported Lipid Bilayer. Membranes 2021, 11 (5), 339,  DOI: 10.3390/membranes11050339
      There is no corresponding record for this reference.
    63. 63
      Morigaki, K.; Kiyosue, K.; Taguchi, T. Micropatterned Composite Membranes of Polymerized and Fluid Lipid Bilayers. Langmuir 2004, 20 (18), 7729– 7735,  DOI: 10.1021/la049340e
      61
      Micropatterned composite membranes of polymerized and fluid lipid bilayers
      Morigaki, Kenichi; Kiyosue, Kazuyuki; Taguchi, Takahisa
      Langmuir (2004), 20 (18), 7729-7735CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Micropatterned composite membranes of polymd. and fluid lipid bilayers were constructed on solid substrates. Lithog. photopolymn. of a diacetylene-contg. phospholipid, 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DiynePC), and subsequent removal of nonreacted monomers by a detergent soln. (0.1 M sodium dodecyl sulfate (SDS)) yielded a patterned polymeric bilayer matrix on the substrate. Fluid lipid bilayers of phosphatidylcholine from egg yolk (egg-PC) were incorporated into the lipid-free wells surrounded by the polymeric bilayers through the process of fusion and reorganization of suspended small unilamellar vesicles. Spatial distribution of the fluid bilayers in the patterned bilayer depended on the degree of photopolymn. that in turn could be modulated by varying the applied UV irradn. dose. The polymeric bilayer domains blocked lateral diffusion of the fluid lipid bilayers and confined them in the defined areas (corrals), if the polymn. was conducted with a sufficiently large UV dose. On the other hand, lipid mols. of the fluid bilayers penetrated into the polymeric bilayer domains, if the UV dose was relatively small. A direct correlation was obsd. between the applied UV dose and the lateral diffusion coeff. of fluorescent marker mols. in the fluid bilayers embedded within the polymeric bilayer domains. Artificial control of lateral diffusion by polymeric bilayers may lead to the creation of complex and versatile biomimetic model membrane arrays.
    64. 64
      Gao, Y.; Zhong, Z.; Geng, M. L. Calibration of Probe Volume in Fluorescence Correlation Spectroscopy. Appl. Spectrosc. 2007, 61 (9), 956– 962,  DOI: 10.1366/000370207781745883
      There is no corresponding record for this reference.
    65. 65
      Majer, G.; Melchior, J. P. Characterization of the Fluorescence Correlation Spectroscopy (FCS) Standard Rhodamine 6G and Calibration of Its Diffusion Coefficient in Aqueous Solutions. J. Chem. Phys. 2014, 140, 094201,  DOI: 10.1063/1.4867096
      There is no corresponding record for this reference.
    66. 66
      Yu, L.; Lei, Y.; Ma, Y.; Liu, M.; Zheng, J.; Dan, D.; Gao, P. A Comprehensive Review of Fluorescence Correlation Spectroscopy. Front. Phys. 2021, 9, 644450,  DOI: 10.3389/fphy.2021.644450
      There is no corresponding record for this reference.
    67. 67
      Schaff, J.; Fink, C. C.; Slepchenko, B.; Carson, J. H.; Loew, L. M. A General Computational Framework for Modeling Cellular Structure and Function. Biophys. J. 1997, 73 (3), 1135– 1146,  DOI: 10.1016/S0006-3495(97)78146-3
      There is no corresponding record for this reference.
    68. 68
      Cowan, A. E.; Moraru, I. I.; Schaff, J. C.; Slepchenko, B. M.; Loew, L. M. Spatial Modeling of Cell Signaling Networks. Methods Cell Biol. 2012, 110, 195– 221,  DOI: 10.1016/B978-0-12-388403-9.00008-4
      66
      Spatial modeling of cell signaling networks
      Cowan Ann E; Moraru Ion I; Schaff James C; Slepchenko Boris M; Loew Leslie M
      Methods in cell biology (2012), 110 (), 195-221 ISSN:0091-679X.
      The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.
    69. 69
      Okazaki, T.; Inaba, T.; Tatsu, Y.; Tero, R.; Urisu, T.; Morigaki, K. Polymerized Lipid Bilayers on a Solid Substrate: Morphologies and Obstruction of Lateral Diffusion. Langmuir 2009, 25 (1), 345– 351,  DOI: 10.1021/la802670t
      67
      Polymerized Lipid Bilayers on a Solid Substrate: Morphologies and Obstruction of Lateral Diffusion
      Okazaki, Takashi; Inaba, Takehiko; Tatsu, Yoshiro; Tero, Ryugo; Urisu, Tsuneo; Morigaki, Kenichi
      Langmuir (2009), 25 (1), 345-351CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Substrate supported planar lipid bilayers (SPBs) are versatile models of the biol. membrane in biophys. studies and biomedical applications. The authors previously developed a methodol. for generating SPBs composed of polymeric and fluid phospholipid bilayers by using a photopolymerizable diacetylene phospholipid (DiynePC). Polymeric bilayers could be generated with micropatterns by conventional photolithog., and the d.p. could be controlled by modulating UV irradn. doses. After removing nonreacted monomers, fluid lipid membranes could be integrated with polymeric bilayers. Herein, the authors report on a quant. study of the morphol. of polymeric bilayer domains and their obstruction toward lateral diffusion of membrane-assocd. mols. At. force microscopy (AFM) observations revealed that polymd. DiynePC bilayers were formed as nanometer-sized domains. The ratio of polymeric and fluid bilayers could be modulated quant. by changing the UV irradn. dose for photopolymn. Lateral diffusion coeffs. of lipid mols. in fluid bilayers were measured by fluorescence recovery after photobleaching (FRAP) and correlated with the amt. of polymeric bilayer domains on the substrate. Controlled domain structures, lipid compns., and lateral mobility in the model membranes should allow the authors to fabricate model membranes that mimic complex features of biol. membranes with well-defined structures and physicochem. properties.
    70. 70
      Groves, J. T.; Ulman, N.; Boxer, S. G. Micropatterning Fluid Lipid Bilayers on Solid Supports. Science 1997, 275 (5300), 651– 653,  DOI: 10.1126/science.275.5300.651
      68
      Micropatterning fluid lipid bilayers on solid supports
      Groves, Jay T.; Ulman, Nick; Boxer, Steven G.
      Science (Washington, D. C.) (1997), 275 (5300), 651-653CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Lithog. patterned grids of photoresist, aluminum oxide, or gold on oxidized silicon substrates were used to partition supported lipid bilayers into micrometer-scale arrays of isolated fluid membrane corrals. Fluorescently labeled lipids were obsd. to diffuse freely within each membrane corral but were confined by the micropatterned barriers. The concns. of fluorescent probe mols. in individual corrals were altered by selective photobleaching to create arrays of fluid membrane patches with differing compns. Application of an elec. field parallel to the surface induced steady-state concn. gradients of charged membrane components in the corrals. In addn. to producing patches of membrane with continuously varying compn., these gradients provide an intrinsically parallel means of acquiring information about mol. properties such as the diffusion coeff. in individual corrals.
    71. 71
      Kung, L. A.; Kam, L.; Hovis, J. S.; Boxer, S. G. Patterning Hybrid Surfaces of Proteins and Supported Lipid Bilayers. Langmuir 2000, 16 (17), 6773– 6776,  DOI: 10.1021/la000653t
      69
      Patterning Hybrid Surfaces of Proteins and Supported Lipid Bilayers
      Kung, Li A.; Kam, Lance; Hovis, Jennifer S.; Boxer, Steven G.
      Langmuir (2000), 16 (17), 6773-6776CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Two methods for patterning surfaces with supported lipid bilayers and immobilized protein are described. First, proteins are used to fabricate corrals for supported lipid bilayers. Poly(dimethylsiloxane) stamps are used to deposit arbitrarily shaped patterns of thin layers of immobilized protein onto glass surfaces. This is followed by vesicle fusion into the regions that are not coated with proteins. Second, supported bilayer membranes are blotted to remove patterned regions of the membrane,1 and the blotted regions are filled in or caulked with protein from soln. In both cases, the lipid bilayer regions exhibit lateral fluidity, but each region is confined or corralled by the protein. These two methods can be combined and used iteratively to create arrays with increasing lateral complexity in both the fixed protein and mobile-supported membrane regions for biophys. studies or cell-based assays.
    72. 72
      Morigaki, K.; Baumgart, T.; Offenhäusser, A.; Knoll, W. Patterning Solid-Supported Lipid Bilayer Membranes by Lithographic Polymerization of a Diacetylene Lipid. Angew. Chem., Int. Ed. 2001, 40 (1), 172– 174,  DOI: 10.1002/1521-3773(20010105)40:1<172::AID-ANIE172>3.0.CO;2-G
      70
      Patterning solid-supported lipid bilayer membranes by lithographic polymerization of diacetylene lipid
      Morigaki, Kenichi; Baumgart, Tobias; Offenhausser, Andreas; Knoll, Wolfgang
      Angewandte Chemie, International Edition (2001), 40 (1), 172-174CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH)
      The authors report a novel approach for creating patterned bilayers on solid supports. The basic idea is to imprint a pattern within the lipid bilayer by photochem. polymn. of the lipids.
    73. 73
      Hovis, J. S.; Boxer, S. G. Patterning Barriers to Lateral Diffusion in Supported Lipid Bilayer Membranes by Blotting and Stamping. Langmuir 2000, 16 (3), 894– 897,  DOI: 10.1021/la991175t
      71
      Patterning Barriers to Lateral Diffusion in Supported Lipid Bilayer Membranes by Blotting and Stamping
      Hovis, Jennifer S.; Boxer, Steven G.
      Langmuir (2000), 16 (3), 894-897CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Two new methods are introduced for patterning fluid lipid bilayer membranes on solid supports. These methods are based on the observation that supported membranes undergo self-limiting lateral expansion when bilayer material is removed from the surface or when it is deposited in a pattern on a surface. Spatially selective (patterned) removal of bilayer material can be achieved by using a poly(dimethylsiloxane) (PDMS) stamp. Following slight lateral expansion into the bilayer-free region created by this blotting process, stable barriers to lateral diffusion are formed. Inspection of the barrier regions indicates that nearly all of the bilayer material is removed, implying that it has been transferred to the stamp. As a consequence, it also proves possible to transfer the lifted material from the stamp onto a fresh surface. The transferred material retains the original pattern from the stamp and is also laterally mobile, and the mobility is confined to the printed region. Alternatively, bilayers assembled on a PDMS stamp can be printed onto fresh surfaces. Together these methods constitute a simple and powerful approach for prepg. patterned fluid bilayers in nearly any geometry.
    74. 74
      Hovis, J. S.; Boxer, S. G. Patterning and Composition Arrays of Supported Lipid Bilayers by Microcontact Printing. Langmuir 2001, 17 (11), 3400– 3405,  DOI: 10.1021/la0017577
      72
      Patterning and composition arrays of supported lipid bilayers by microcontact printing
      Hovis, Jennifer S.; Boxer, Steven G.
      Langmuir (2001), 17 (11), 3400-3405CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Fluid-supported lipid bilayers self-assemble on glass and SiO2 surfaces. We have found that it is also possible to assemble fluid bilayers on plasma-oxidized polydimethyl siloxane (PDMS) surfaces. Furthermore, it is possible to transfer or print the supported bilayer from raised PDMS surfaces, such as are typically used for microcontact printing, to fresh glass surfaces creating a supported bilayer membrane replica of the patterned PDMS surface on glass. These patterned islands of bilayer are fully fluid and indefinitely stable under water. The pattern is erased upon addn. of more vesicles leaving a continuous bilayer surface. By printing membrane islands of various sizes onto a glass surface that is prepatterned with a material that forms permanent barriers to lateral diffusion and then backfilling the open region with vesicles, it is possible to create arbitrary concn. or compn. arrays of membrane-assocd. components. These arrays may be useful for studies of membrane biophysics, for high throughput screening of compds. that target membrane components, and for probing and possibly controlling living cell-synthetic membrane interactions.
    75. 75
      Etoc, F.; Balloul, E.; Vicario, C.; Normanno, D.; Liße, D.; Sittner, A.; Piehler, J.; Dahan, M.; Coppey, M. Non-Specific Interactions Govern Cytosolic Diffusion of Nanosized Objects in Mammalian Cells. Nat. Mater. 2018, 17 (8), 740– 746,  DOI: 10.1038/s41563-018-0120-7
      73
      Non-specific interactions govern cytosolic diffusion of nanosized objects in mammalian cells
      Etoc, Fred; Balloul, Elie; Vicario, Chiara; Normanno, Davide; Lisse, Domenik; Sittner, Assa; Piehler, Jacob; Dahan, Maxime; Coppey, Mathieu
      Nature Materials (2018), 17 (8), 740-746CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
      The diffusivity of macromols. in the cytoplasm of eukaryotic cells varies over orders of magnitude and dictates the kinetics of cellular processes. However, a general description that assocs. the Brownian or anomalous nature of intracellular diffusion to the architectural and biochem. properties of the cytoplasm has not been achieved. Here we measure the mobility of individual fluorescent nanoparticles in living mammalian cells to obtain a comprehensive anal. of cytoplasmic diffusion. We identify a correlation between tracer size, its biochem. nature and its mobility. Inert particles with size equal or below 50 nm behave as Brownian particles diffusing in a medium of low viscosity with negligible effects of mol. crowding. Increasing the strength of non-specific interactions of the nanoparticles within the cytoplasm gradually reduces their mobility and leads to subdiffusive behavior. These exptl. observations and the transition from Brownian to subdiffusive motion can be captured in a minimal phenomenol. model.
    76. 76
      Stylianopoulos, T.; Poh, M.-Z.; Insin, N.; Bawendi, M. G.; Fukumura, D.; Munn, L. L.; Jain, R. K. Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions. Biophys. J. 2010, 99 (5), 1342– 1349,  DOI: 10.1016/j.bpj.2010.06.016
      74
      Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions
      Stylianopoulos, Triantafyllos; Poh, Ming-Zher; Insin, Numpon; Bawendi, Moungi G.; Fukumura, Dai; Munn, Lance L.; Jain, Rakesh K.
      Biophysical Journal (2010), 99 (5), 1342-1349CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Diffusive transport of macromols. and nanoparticles in charged fibrous media is of interest in many biol. applications, including drug delivery and sepn. processes. Exptl. findings have shown that diffusion can be significantly hindered by electrostatic interactions between the diffusing particle and charged components of the extracellular matrix. The implications, however, were not analyzed rigorously. Here, the authors present a math. framework to study the effect of charge on the diffusive transport of macromols. and nanoparticles in the extracellular matrix of biol. tissues. The model takes into account steric, hydrodynamic, and electrostatic interactions. The authors show that when the fiber size is comparable to the Debye length, electrostatic forces between the fibers and the particles result in slowed diffusion. However, as the fiber diam. increases the repulsive forces become less important. The authors' results explain the exptl. observations that neutral particles diffuse faster than charged particles. Taken together, the authors conclude that optimal particles for delivery to tumors should be initially cationic to target the tumor vessels and then change to neutral charge after exiting the blood vessels.
    77. 77
      Ando, T.; Skolnick, J. Crowding and Hydrodynamic Interactions Likely Dominate in Vivo Macromolecular Motion. Proc. Natl. Acad. Sci. U. S. A. 2010, 107 (43), 18457– 18462,  DOI: 10.1073/pnas.1011354107
      There is no corresponding record for this reference.
    78. 78
      Lizana, L.; Bauer, B.; Orwar, O. Controlling the Rates of Biochemical Reactions and Signaling Networks by Shape and Volume Changes. Proc. Natl. Acad. Sci. U. S. A. 2008, 105 (11), 4099– 4104,  DOI: 10.1073/pnas.0709932105
      76
      Controlling the rates of biochemical reactions and signaling networks by shape and volume changes
      Lizana, L.; Bauer, B.; Orwar, O.
      Proceedings of the National Academy of Sciences of the United States of America (2008), 105 (11), 4099-4104CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      In biol. systems, chem. activity takes place in micrometer and nanometer-sized compartments that constantly change in shape and vol. These ever-changing cellular compartments embed chem. reactions, and we demonstrate that the rates of such incorporated reactions are directly affected by the ongoing shape reconfigurations. First, we show that the rate of product formation in an enzymic reaction can be regulated by simple vol. contraction-dilation transitions. The results suggest that mitochondria may regulate the dynamics of interior reaction path-ways (e.g., the Krebs cycle) by vol. changes. We then show the effect of shape changes on reactions occurring in more complex and structured systems by using biomimetic networks composed of micrometer-sized compartments joined together by nanotubes. Chem. activity was measured by implementing an enzymic reaction-diffusion system. During ongoing reactions, the network connectivity is changed suddenly (similar to the dynamic tube formations found inside Golgi stacks, for example), and the effect on the reaction is registered. We show that spatiotemporal properties of the reaction-diffusion system are extremely sensitive to sudden changes in network topol. and that chem. reactions can be initiated, or boosted, in certain nodes as a function of connectivity.
    79. 79
      Eggeling, C.; Ringemann, C.; Medda, R.; Schwarzmann, G.; Sandhoff, K.; Polyakova, S.; Belov, V. N.; Hein, B.; Von Middendorff, C.; Schönle, A.; Hell, S. W. Direct Observation of the Nanoscale Dynamics of Membrane Lipids in a Living Cell. Nature 2009, 457 (7233), 1159– 1162,  DOI: 10.1038/nature07596
      77
      Direct observation of the nanoscale dynamics of membrane lipids in a living cell
      Eggeling, Christian; Ringemann, Christian; Medda, Rebecca; Schwarzmann, Guenter; Sandhoff, Konrad; Polyakova, Svetlana; Belov, Vladimir N.; Hein, Birka; von Middendorff, Claas; Schoenle, Andreas; Hell, Stefan W.
      Nature (London, United Kingdom) (2009), 457 (7233), 1159-1162CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Cholesterol-mediated lipid interactions are thought to have a functional role in many membrane-assocd. processes such as signaling events. Although several expts. indicate their existence, lipid nanodomains (rafts') remain controversial owing to the lack of suitable detection techniques in living cells. The controversy is reflected in their putative size of 5-200 nm, spanning the range between the extent of a protein complex and the resoln. limit of optical microscopy. Here we demonstrate the ability of stimulated emission depletion (STED) far-field fluorescence nanoscopy to detect single diffusing (lipid) mols. in nanosized areas in the plasma membrane of living cells. Tuning of the probed area to spot sizes ∼70-fold below the diffraction barrier reveals that unlike phosphoglycerolipids, sphingolipids and glycosylphosphatidylinositol-anchored proteins are transiently (∼10-20 ms) trapped in cholesterol-mediated mol. complexes dwelling within <20-nm diam. areas. The non-invasive optical recording of mol. time traces and fluctuation data in tunable nanoscale domains is a powerful new approach to study the dynamics of biomols. in living cells.
    80. 80
      Garcia-Fandino, R.; Pineiro, A.; Trick, J. L.; Sansom, M. S. P. Lipid Bilayer Membrane Perturbation by Embedded Nanopores: A Simulation Study. ACS Nano 2016, 2016 (10), 3693– 3701,  DOI: 10.1021/acsnano.6b00202
      There is no corresponding record for this reference.
    81. 81
      Niemelä, P. S.; Miettinen, M. S.; Monticelli, L.; Hammaren, H.; Bjelkmar, P.; Murtola, T.; Lindahl, E.; Vattulainen, I. Membrane Proteins Diffuse as Dynamic Complexes with Lipids. J. Am. Chem. Soc. 2010, 132 (22), 7574– 7575,  DOI: 10.1021/ja101481b
      79
      Membrane Proteins Diffuse as Dynamic Complexes with Lipids
      Niemela, Perttu S.; Miettinen, Markus S.; Monticelli, Luca; Hammaren, Henrik; Bjelkmar, Par; Murtola, Teemu; Lindahl, Erik; Vattulainen, Ilpo
      Journal of the American Chemical Society (2010), 132 (22), 7574-7575CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      We describe how membrane proteins diffuse laterally in the membrane plane together with the lipids surrounding them. We find a no. of intriguing phenomena. The lateral displacements of the protein and the lipids are strongly correlated, as the protein and the neighboring lipids form a dynamical protein-lipid complex, consisting of ∼50-100 lipids. The diffusion of the lipids in the complex is much slower compared to the rest of the lipids. We also find a strong directional correlation between the movements of the protein and the lipids in its vicinity. The results imply that in crowded membrane environments there are no "free" lipids, as they are all influenced by the protein structure and dynamics. Our results indicate that, in studies of cell membranes, protein and lipid dynamics have to be considered together.
    82. 82
      Długosz, M.; Trylska, J. Diffusion in Crowded Biological Environments: Applications of Brownian Dynamics. BMC Biophys. 2011, 4 (1), 3,  DOI: 10.1186/2046-1682-4-3
      There is no corresponding record for this reference.
    83. 83
      Netz, P. A.; Dorfmüller, T. Computer Simulation Studies of Diffusion in Gels: Model Structures. J. Chem. Phys. 1997, 107 (21), 9221– 9233,  DOI: 10.1063/1.475214
      There is no corresponding record for this reference.
    84. 84
      Saxton, M. J. Anomalous Diffusion Due to Obstacles: A Monte Carlo Study. Biophys. J. 1994, 66 (2), 394– 401,  DOI: 10.1016/S0006-3495(94)80789-1
      There is no corresponding record for this reference.
    85. 85
      Saxton, M. J. Lateral Diffusion in an Archipelago. The Effect of Mobile Obstacles. Biophys. J. 1987, 52 (6), 989– 997,  DOI: 10.1016/S0006-3495(87)83291-5
      There is no corresponding record for this reference.
    86. 86
      Modica, K. J.; Xi, Y.; Takatori, S. C. Porous Media Microstructure Determines the Diffusion of Active Matter: Experiments and Simulations. Front. Phys. 2022, 10, 869175,  DOI: 10.3389/fphy.2022.869175
      There is no corresponding record for this reference.
    87. 87
      He, K.; Babaye Khorasani, F.; Retterer, S. T.; Thomas, D. K.; Conrad, J. C.; Krishnamoorti, R. Diffusive Dynamics of Nanoparticles in Arrays of Nanoposts. ACS Nano 2013, 7 (6), 5122– 5130,  DOI: 10.1021/nn4007303
      85
      Diffusive Dynamics of Nanoparticles in Arrays of Nanoposts
      He, Kai; Babaye Khorasani, Firoozeh; Retterer, Scott T.; Thomas, Darrell K.; Conrad, Jacinta C.; Krishnamoorti, Ramanan
      ACS Nano (2013), 7 (6), 5122-5130CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      The diffusive dynamics of dil. dispersions of nanoparticles of diam. 200-400 nm were studied in microfabricated arrays of nanoposts using differential dynamic microscopy and single particle tracking. Posts of diam. 500 nm and height 10 μm were spaced by 1.2-10 μm on a square lattice. As the spacing between posts was decreased, the dynamics of the nanoparticles slowed. The dynamics at all length scales were best represented by a stretched exponential rather than a simple exponential. Both the relative diffusivity and the stretching exponent decreased linearly with increased confinement and, equivalently, with decreased void vol. The slowing of the overall diffusive dynamics and the broadening distribution of nanoparticle displacements with increased confinement are consistent with the onset of dynamic heterogeneity and the approach to vitrification.
    88. 88
      Macháň, R.; Foo, Y. H.; Wohland, T. On the Equivalence of FCS and FRAP: Simultaneous Lipid Membrane Measurements. Biophys. J. 2016, 111 (1), 152– 161,  DOI: 10.1016/j.bpj.2016.06.001
      86
      On the Equivalence of FCS and FRAP: Simultaneous Lipid Membrane Measurements
      Machan, Radek; Foo, Yong Hwee; Wohland, Thorsten
      Biophysical Journal (2016), 111 (1), 152-161CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP) are widely used methods to det. diffusion coeffs. However, they often do not yield the same results. With the advent of camera-based imaging FCS, which measures the diffusion coeff. in each pixel of an image, and proper bleaching corrections, it is now possible to measure the diffusion coeff. by FRAP and FCS in the exact same images. The authors thus performed simultaneous FCS and FRAP measurements on supported lipid bilayers and live cell membranes to test how far the two methods differ in their results and whether the methodol. differences, in particular the high bleach intensity in FRAP, the bleach corrections, and the fitting procedures in the two methods explain obsd. differences. Overall, the FRAP bleach intensity does not measurably influence the diffusion in the samples, but bleach correction and fitting introduce large uncertainties in FRAP. The authors confirm the authors' results by simulations.
    89. 89
      Stasevich, T. J.; Mueller, F.; Michelman-Ribeiro, A.; Rosales, T.; Knutson, J. R.; McNally, J. G. Cross-Validating FRAP and FCS to Quantify the Impact of Photobleaching on In Vivo Binding Estimates. Biophys. J. 2010, 99 (9), 3093– 3101,  DOI: 10.1016/j.bpj.2010.08.059
      87
      Cross-Validating FRAP and FCS to Quantify the Impact of Photobleaching on In Vivo Binding Estimates
      Stasevich, Timothy J.; Mueller, Florian; Michelman-Ribeiro, Ariel; Rosales, Tilman; Knutson, Jay R.; McNally, James G.
      Biophysical Journal (2010), 99 (9), 3093-3101CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Binding can now be quantified in live cells, but the accuracy of such measurements remains uncertain. To address this uncertainty, the authors compare fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS) measurements of the binding kinetics of a transcription factor, the glucocorticoid receptor, in the nuclei of live cells. The authors find that the binding residence time measured by FRAP is 15 times longer than that obtained by FCS. The authors show that this discrepancy is not likely due to the significant differences in concns. typically used for FRAP and FCS, nor is it likely due to spatial heterogeneity of the nucleus, improper calibration of the FCS focal vol., or the intentional FRAP photobleach. Instead, the authors' data indicate that photobleaching of bound mols. in FCS is mainly responsible. When this effect is minimized, FRAP and FCS measurements nearly agree, although cross-validation by other approaches is now required to rule out mutual errors. The authors' results demonstrate the necessity of a photobleach correction for FCS measurements of GFP-tagged mols. that are bound for >0.25 s, and represent an important step forward in establishing a gold std. for in vivo binding measurements.
    90. 90
      Reitan, N. K.; Juthajan, A.; Lindmo, T.; de Lange Davies, C. Macromolecular Diffusion in the Extracellular Matrix Measured by Fluorescence Correlation Spectroscopy. J. Biomed. Opt. 2008, 13 (5), 054040,  DOI: 10.1117/1.2982530
      There is no corresponding record for this reference.
    91. 91
      Mazza, D.; Abernathy, A.; Golob, N.; Morisaki, T.; McNally, J. G. A Benchmark for Chromatin Binding Measurements in Live Cells. Nucleic Acids Res. 2012, 40, e119  DOI: 10.1093/nar/gks701
      89
      A benchmark for chromatin binding measurements in live cells
      Mazza, Davide; Abernathy, Alice; Golob, Nicole; Morisaki, Tatsuya; McNally, James G.
      Nucleic Acids Research (2012), 40 (15), e119CODEN: NARHAD; ISSN:0305-1048. (Oxford University Press)
      Live-cell measurement of protein binding to chromatin allows probing cellular biochem. in physiol. conditions, which are difficult to mimic in vitro. However, different studies have yielded widely discrepant predictions, and so it remains uncertain how to make the measurements accurately. To establish a benchmark the authors measured binding of the transcription factor p53 to chromatin by three approaches: fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS) and single-mol. tracking (SMT). Using new procedures to analyze the SMT data and to guide the FRAP and FCS anal., all three approaches yield similar ests. for both the fraction of p53 mols. bound to chromatin (only ∼20%) and the residence time of these bound mols. (∼1.8 s). The authors also apply these procedures to mutants in p53 chromatin binding. The authors' results support the model that p53 locates specific sites by first binding at sequence-independent sites.
    92. 92
      Goksu, E. I.; Nellis, B. A.; Lin, W.-C.; Jr, J. H. S.; Groves, J. T.; Risbud, S. H.; Longo, M. L. Effect of Support Corrugation on Silica Xerogel–Supported Phase-Separated Lipid Bilayers. Langmuir 2009, 25, 3713– 3717,  DOI: 10.1021/la803851b
      90
      Effect of Support Corrugation on Silica Xerogel-Supported Phase-Separated Lipid Bilayers
      Goksu, Emel I.; Nellis, Barbara A.; Lin, Wan-Chen; Satcher, Joe H.; Groves, Jay T.; Risbud, Subhash H.; Longo, Marjorie L.
      Langmuir (2009), 25 (6), 3713-3717CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Lipid bilayers supported by substrates with nanometer-scale surface corrugations hold interest in understanding both nanoparticle-membrane interactions and the challenges of constructing models of cell membranes on surfaces with desirable properties, e.g., porosity. Here, the authors successfully form a two-phase (gel-fluid) lipid bilayer supported by nanoporous silica xerogel. Surface topol., lateral diffusion coeff., and lipid d. in comparison to mica-supported lipid bilayers were characterized by at. force microscopy, fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), and quant. fluorescence microscopy, resp. The authors found that the two-phase lipid bilayer follows the silica xerogel surface contours. The corrugation imparted on the lipid bilayer results in a lipid d. that is twice that on a flat mica surface in the fluid regions. In direct agreement with the doubling of actual bilayer area in a projected area, the authors find that the lateral diffusion coeff. (D) of fluid lipids on silica xerogel (∼1.7 μm2/s) is lower than on mica (∼3.9 μm2/s) by both FRAP and FCS techniques. Furthermore, the gel-phase domains on silica xerogel compared to mica were larger and less numerous. Overall, the authors' results suggest the presence of a relatively defect-free continuous two-phase lipid bilayer that penetrates approx. midway into the first layer of ∼50 nm silica xerogel beads.
    93. 93
      Pastor, I.; Vilaseca, E.; Madurga, S.; Garcés, J. L.; Cascante, M.; Mas, F. Diffusion of α-Chymotrypsin in Solution-Crowded Media. A Fluorescence Recovery after Photobleaching Study. J. Phys. Chem. B 2010, 114 (11), 4028– 4034,  DOI: 10.1021/jp910811j
      91
      Diffusion of α-Chymotrypsin in Solution-Crowded Media. A Fluorescence Recovery after Photobleaching Study
      Pastor, Isabel; Vilaseca, Eudald; Madurga, Sergio; Garces, Josep Lluis; Cascante, Marta; Mas, Francesc
      Journal of Physical Chemistry B (2010), 114 (11), 4028-4034CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      Fluorescence recovery after photobleaching (FRAP) is one of the most powerful and widely-used techniques for the study of diffusion processes of macromols. in membranes or in bulk. Here, we study the diffusion of α-chymotrypsin in different crowded (Dextran) in vitro solns. using a confocal laser scanning microscope. Under these exptl. conditions, confocal FRAP images could be analyzed applying the uniform circular disk approxn. described for a nonscanning microscope generalized to take into account anomalous diffusion. Considering the slow diffusion of macromols. in crowded media, we compare the fitting of confocal FRAP curves analyzed with the equations provided by the Gaussian and the uniform circular disk profile models for nonscanning microscopes. As the fitted parameter variation with the size and concn. of crowders is qual. similar for both models, the use of the uniform circular disk or the Gaussian model is justified for these expts. Moreover, in our exptl. conditions, α-chymotrypsin shows anomalous diffusion (α < 1), depending on the size and concn. of Dextran mols., until a high concn. and high size of crowding agent are achieved. This result indicates a range of validity of the idealized fitting expressions used, beyond which other phys. phenomena must be considered.
    94. 94
      Wawrezinieck, L.; Rigneault, H.; Marguet, D.; Lenne, P.-F. Fluorescence Correlation Spectroscopy Diffusion Laws to Probe the Submicron Cell Membrane Organization. Biophys. J. 2005, 89 (6), 4029– 4042,  DOI: 10.1529/biophysj.105.067959
      There is no corresponding record for this reference.
    95. 95
      Calizo, R. C.; Scarlata, S. Discrepancy between Fluorescence Correlation Spectroscopy and Fluorescence Recovery after Photobleaching Diffusion Measurements of G-Protein-Coupled Receptors. Anal. Biochem. 2013, 440 (1), 40– 48,  DOI: 10.1016/j.ab.2013.04.033
      There is no corresponding record for this reference.
    96. 96
      Müller, K. P.; Erdel, F.; Caudron-Herger, M.; Marth, C.; Fodor, B. D.; Richter, M.; Scaranaro, M.; Beaudouin, J.; Wachsmuth, M.; Rippe, K. Multiscale Analysis of Dynamics and Interactions of Heterochromatin Protein 1 by Fluorescence Fluctuation Microscopy. Biophys. J. 2009, 97 (11), 2876– 2885,  DOI: 10.1016/j.bpj.2009.08.057
      94
      Multiscale analysis of dynamics and interactions of heterochromatin protein 1 by fluorescence fluctuation microscopy
      Mueller, Katharina P.; Erdel, Fabian; Caudron-Herger, Maiwen; Marth, Caroline; Fodor, Barna D.; Richter, Mario; Scaranaro, Manuela; Beaudouin, Joel; Wachsmuth, Malte; Rippe, Karsten
      Biophysical Journal (2009), 97 (11), 2876-2885CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
      Heterochromatin protein 1 (HP1) is a central factor in establishing and maintaining the repressive heterochromatin state. To elucidate its mobility and interactions, we conducted a comprehensive anal. on different time and length scales by fluorescence fluctuation microscopy in mouse cell lines. The local mobility of HP1α and HP1β was investigated in densely packed pericentric heterochromatin foci and compared with other bona fide euchromatin regions of the nucleus by fluorescence bleaching and correlation methods. A quant. description of HP1α/β in terms of its concn., diffusion coeff., kinetic binding, and dissocn. rate consts. was derived. Three distinct classes of chromatin-binding sites with av. residence times tres ≤ 0.2 s (class I, dominant in euchromatin), 7 s (class II, dominant in heterochromatin), and ∼2 min (class III, only in heterochromatin) were identified. HP1 was present at low micromolar concns. at heterochromatin foci, and required histone H3 lysine 9 methylases Suv39h1/2 for two- to fourfold enrichment at these sites. These findings impose a no. of constraints for the mechanism by which HP1 is able to maintain a heterochromatin state.
    97. 97
      Adkins, E. M.; Samuvel, D. J.; Fog, J. U.; Eriksen, J.; Jayanthi, L. D.; Vaegter, C. B.; Ramamoorthy, S.; Gether, U. Membrane Mobility and Microdomain Association of the Dopamine Transporter Studied with Fluorescence Correlation Spectroscopy and Fluorescence Recovery after Photobleaching. ACS Biochem. 2007, 46, 10484– 10497,  DOI: 10.1021/bi700429z
      There is no corresponding record for this reference.
    98. 98
      Renz, M.; Langowski, J. Dynamics of the CapG Actin-Binding Protein in the Cell Nucleus Studied by FRAP and FCS. Chromosome Res. 2008, 16 (3), 427– 437,  DOI: 10.1007/s10577-008-1234-6
      96
      Dynamics of the CapG actin-binding protein in the cell nucleus studied by FRAP and FCS
      Renz, Malte; Langowski, Joerg
      Chromosome Research (2008), 16 (3), 427-437CODEN: CRRSEE; ISSN:0967-3849. (Springer)
      FRAP (fluorescence recovery after photobleaching) and FCS (fluorescence correlation spectroscopy) are spectroscopic methods for monitoring the dynamic distribution of proteins inside the nucleus of living cells. As an example we report our studies on the intracellular mobility of the actin-binding protein CapG in live breast cancer cells. This Gelsolin-related protein is a putative oncogene. It appears to be overexpressed esp. in metastasizing breast cancer. Furthermore, the CapG protein is known to be involved in the motility control of non-muscle benign cells. Its increased expression triggers an increase in cell motility of benign cells. Thus it can be expected that in cancer cells overexpressing the CapG protein, motility, invasiveness and metastasis might be particularly promoted. Since the nuclear CapG fraction seems to be pivotal to the increase in cell motility, we focused our studies on the CapG mobility in cell nuclei of live breast cancer cells. Using FCS and FRAP we showed that the eGFP-tagged CapG is monomeric and characterized its diffusional properties on the microsecond to minute timescale. This information about the mobility and compartmentalization of CapG might help to provide insight into its function within the cell nucleus and give clues about its altered cellular function in malignant dedifferentiation.
    99. 99
      Rossetti, F. F.; Bally, M.; Michel, R.; Textor, M.; Reviakine, I. Interactions between Titanium Dioxide and Phosphatidyl Serine-Containing Liposomes: Formation and Patterning of Supported Phospholipid Bilayers on the Surface of a Medically Relevant Material. Langmuir 2005, 21 (14), 6443– 6450,  DOI: 10.1021/la0509100
      97
      Interactions between Titanium Dioxide and Phosphatidyl Serine-Containing Liposomes: Formation and Patterning of Supported Phospholipid Bilayers on the Surface of a Medically Relevant Material
      Rossetti, Fernanda F.; Bally, Marta; Michel, Roger; Textor, Marcus; Reviakine, Ilya
      Langmuir (2005), 21 (14), 6443-6450CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Titanium is widely used in biomedical applications. Its mech. properties and biocompatibility, conferred by a layer of oxide present on its surface, make titanium the material of choice for various implants (artificial hip and knee joints, dental prosthetics, vascular stents, heart valves). Furthermore, the high refractive index of titanium oxide is advantageous in biosensor applications based on optical detection methods. In both of the above fields of application, novel surface modification strategies leading to biointeractive interfaces (that trigger specific responses in biol. systems) are continuously sought. In this report, we investigate the interactions between TiO2 and phosphatidyl serine-contg. liposomes, present a novel approach for prepg. supported phospholipid bilayers (SPBs) of various compns. on TiO2, and use the unique ability of liposomes to distinguish between different surfaces to create SPB corrals on SiO2/TiO2 structured substrates. These results represent an important first step toward the design of biointeractive interfaces on titanium oxide surfaces that are based on a cell membrane-like environment.
    100. 100
      Groves, J. T.; Ulman, N.; Cremer, P. S.; Boxer, S. G. Substrate–Membrane Interactions: Mechanisms for Imposing Patterns on a Fluid Bilayer Membrane. Langmuir 1998, 14 (12), 3347– 3350,  DOI: 10.1021/la9711701
      98
      Substrate-Membrane Interactions: Mechanisms for Imposing Patterns on a Fluid Bilayer Membrane
      Groves, Jay T.; Ulman, Nick; Cremer, Paul; Boxer, Steven G.
      Langmuir (1998), 14 (12), 3347-3350CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      A variety of new techniques are emerging that require the use of a patterned substrate to impose micropartitions on a supported fluid bilayer membrane. The barrier-forming characteristics of aluminum oxide, indium-tin oxide (ITO), chrome, and gold patterns on silica substrates have been examd. All four materials form effective barriers to lateral diffusion within the supported membrane; however, two distinctly different mechanisms were obsd. Aluminum oxide inhibits vesicle fusion, thus restricting membrane formation to the exposed silica surface. In contrast, vesicles will fuse with ITO, chrome, and, to some extent, gold; however, the resulting membrane is effectively immobile over the time scale of several hours. These materials partition the supported membrane by selectively immobilizing membrane that adsorbs to their surface. The two mechanisms of membrane partitioning described here provide addnl. flexibility in the design and application of micropatterned membranes.
    101. 101
      Mager, M. D.; Almquist, B.; Melosh, N. A. Formation and Characterization of Fluid Lipid Bilayers on Alumina. Langmuir 2008, 24 (22), 12734– 12737,  DOI: 10.1021/la802726u
      99
      Formation and Characterization of Fluid Lipid Bilayers on Alumina
      Mager, Morgan D.; Almquist, Benjamin; Melosh, Nicholas A.
      Langmuir (2008), 24 (22), 12734-12737CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Fluid lipid bilayers were deposited on alumina substrates with the use of bubble collapse deposition (BCD). Previous studies using vesicle rupture have required the use of charged lipids or surface functionalization to induce bilayer formation on alumina, but these modifications are not necessary with BCD. Photobleaching expts. reveal that the diffusion coeff. of POPC on alumina is 0.6 μm2/s, which is much lower than the 1.4-2.0 μm2/s reported on silica. Systematically accounting for roughness, immobile regions and membrane viscosity shows that pinning sites account for about half of this drop in diffusivity. The remainder of the difference is attributed to a more tightly bound water state on the alumina surface, which induces a larger drag on the bilayer.
    102. 102
      Jackman, J. A.; Tabaei, S. R.; Zhao, Z.; Yorulmaz, S.; Cho, N.-J. Self-Assembly Formation of Lipid Bilayer Coatings on Bare Aluminum Oxide: Overcoming the Force of Interfacial Water. ACS Appl. Mater. Interfaces 2015, 7 (1), 959– 968,  DOI: 10.1021/am507651h
      100
      Self-Assembly Formation of Lipid Bilayer Coatings on Bare Aluminum Oxide: Overcoming the Force of Interfacial Water
      Jackman, Joshua A.; Tabaei, Seyed R.; Zhao, Zhilei; Yorulmaz, Saziye; Cho, Nam-Joon
      ACS Applied Materials & Interfaces (2015), 7 (1), 959-968CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      Simple and robust strategies to form fluidic lipid bilayers on aluminum oxide are identified. The fabrication of a single lipid bilayer coating was achieved by two methods, vesicle fusion under acidic conditions and solvent-assisted lipid bilayer (SALB) formation under near-physiol. pH conditions. Importantly, quartz crystal microbalance with dissipation (QCM-D) monitoring measurements detd. that the hydration layer of a supported lipid bilayer on aluminum oxide is appreciably thicker than that of a bilayer on silicon oxide. Fluorescence recovery after photobleaching (FRAP) anal. indicated that the diffusion coeff. of lateral lipid mobility was up to 3-fold greater on silicon oxide than on aluminum oxide. In spite of this hydrodynamic coupling, the diffusion coeff. on aluminum oxide, but not silicon oxide, was sensitive to the ionic strength condition. Extended-DLVO model calcns. estd. the thermodn. of lipid-substrate interactions on aluminum oxide and silicon oxide, and predict that the range of the repulsive hydration force is greater on aluminum oxide, which in turn leads to an increased equil. sepn. distance. Hence, while a strong hydration force likely contributes to the difficulty of bilayer fabrication on aluminum oxide, it also confers advantages by stabilizing lipid bilayers with thicker hydration layers due to confined interfacial water. Such knowledge provides the basis for improved surface functionalization strategies on aluminum oxide, underscoring the practical importance of surface hydration.
    103. 103
      Tabaei, S. R.; Vafaei, S.; Cho, N. J. Fabrication of Charged Membranes by the Solvent-Assisted Lipid Bilayer (SALB) Formation Method on SiO2 and Al2O3. Phys. Chem. Chem. Phys. 2015, 17 (17), 11546– 11552,  DOI: 10.1039/C5CP01428J
      101
      Fabrication of charged membranes by the solvent-assisted lipid bilayer (SALB) formation method on SiO2 and Al2O3
      Tabaei, Seyed R.; Vafaei, Setareh; Cho, Nam-Joon
      Physical Chemistry Chemical Physics (2015), 17 (17), 11546-11552CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Solvent-assisted lipid bilayer (SALB) formation method was used to fabricate charged membranes on solid supports. The SALB formation method exploits a ternary mixt. of lipid-alc.-aq. buffer to deposit lamellar phase structures on solid supports upon gradual increase of the buffer fraction. Using the quartz crystal microbalance with dissipation (QCM-D) technique, the authors investigated the formation of neg. and pos. charged membranes via the SALB formation method and directly compared with the vesicle fusion method on two different oxide films. Bilayers contg. an increasing fraction of neg. charged DOPS lipid mols. were formed on both SiO2 and Al2O3 substrates using the SALB formation method at physiol. pH (7.5). In contrast, the vesicle fusion method did not support bilayer formation on Al2O3 and those contg. more than 10% DOPS ruptured on SiO2 only under acidic conditions (pH 5). Characterization of the fraction of neg. charge DOPS by in situ annexin 5A binding assay revealed that the fraction of DOPS lipid mols. in the bilayers formed on Al2O3 is significantly higher than that formed on SiO2. This suggests that the SALB self-assembly of charged membranes is predominantly governed by the electrostatic interaction. These findings indicate that when multicomponent lipid mixts. are used, the relative fraction of lipids in the bilayer may differ from the fraction of lipids in the precursor mixt.
    104. 104
      Tero, R.; Ujihara, T.; Urisu, T. Lipid Bilayer Membrane with Atomic Step Structure: Supported Bilayer on a Step-and-Terrace TiO2(100) Surface. Langmuir 2008, 24 (20), 11567– 11576,  DOI: 10.1021/la801080f
      102
      Lipid Bilayer Membrane with Atomic Step Structure: Supported Bilayer on a Step-and-Terrace TiO2(100) Surface
      Tero, Ryugo; Ujihara, Toru; Urisu, Tsuneo
      Langmuir (2008), 24 (20), 11567-11576CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The formation of a supported planar lipid bilayer (SPLB) and its morphol. on step-and-terrace rutile TiO2(100) surfaces were investigated by fluorescence microscopy and at. force microscopy. The TiO2(100) surfaces consisting of at. steps and flat terraces were formed on a rutile TiO2 single-crystal wafer by a wet treatment and annealing under a flow of oxygen. An intact vesicular layer formed on the TiO2(100) surface when the surface was incubated in a sonicated vesicle suspension under the condition that a full-coverage SPLB forms on SiO2, as reported in previous studies. However, a full-coverage, continuous, fluid SPLB was obtained on the step-and-terrace TiO2(100) depending on the lipid concn., incubation time, and vesicle size. The SPLB on the TiO2(100) also has step-and-terrace morphol. following the substrate structure precisely even though the SPLB is in the fluid phase and an ∼1-nm-thick water layer exists between the SPLB and the substrate. This membrane distortion on the at. scale affects the phase-sepn. structure of a binary bilayer of micrometer order. The interaction energy calcd. including DLVO and non-DLVO factors shows that a lipid membrane on the TiO2(100) gains 20 times more energy than on SiO2. This specifically strong attraction on TiO2 makes the fluid SPLB precisely follow the substrate structure of angstrom order.
    105. 105
      Rossetti, F. F.; Textor, M.; Reviakine, I. Asymmetric Distribution of Phosphatidyl Serine in Supported Phospholipid Bilayers on Titanium Dioxide. Langmuir 2006, 22 (8), 3467– 3473,  DOI: 10.1021/la053000r
      103
      Asymmetric Distribution of Phosphatidyl Serine in Supported Phospholipid Bilayers on Titanium Dioxide
      Rossetti, Fernanda F.; Textor, Marcus; Reviakine, Ilya
      Langmuir (2006), 22 (8), 3467-3473CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Supported phospholipid bilayers (SPBs) are useful for studying cell adhesion, cell-cell interactions, protein-lipid interactions, protein crystn., and applications in biosensor and biomaterial areas. We have recently reported that SPBs could be formed on titanium dioxide, an important biomaterial, from vesicles contg. anionic phospholipid phosphatidylserine (PS) in the presence of calcium. Here, we show that the mobility of the fluorescently labeled PS present in these bilayers is severely restricted, whereas that of the zwitterionic phosphatidylcholine (PC) is not affected. Removal of calcium alleviated the restriction on the mobility of PS. Both components were found to be mobile in SPBs of identical compns. prepd. in the presence of calcium on silica. To explain these results, we propose that on TiO2, PS is trapped in the proximal leaflet of the bilayers. This proposal is supported by the results of protein adsorption expts. carried out on bilayers contg. various amts. of PS prepd. on silica and titania.
    106. 106
      Reimhult, E.; Höök, F.; Kasemo, B. Intact Vesicle Adsorption and Supported Biomembrane Formation from Vesicles in Solution: Influence of Surface Chemistry, Vesicle Size, Temperature, and Osmotic Pressure. Langmuir 2003, 19 (5), 1681– 1691,  DOI: 10.1021/la0263920
      104
      Intact Vesicle Adsorption and Supported Biomembrane Formation from Vesicles in Solution: Influence of Surface Chemistry, Vesicle Size, Temperature, and Osmotic Pressure
      Reimhult, Erik; Hoeoek, Fredrik; Kasemo, Bengt
      Langmuir (2003), 19 (5), 1681-1691CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      The adsorption kinetics of small unilamellar egg-yolk phosphatidylcholine vesicles was investigated by the quartz crystal microbalance-dissipation (QCM-D) technique, as a function of surface chem. (on SiO2, Si3N4, Au, TiO2, and Pt), temp. (273-303 K), vesicle size (25-200 nm), and osmotic pressure. On SiO2 and Si3N4, the vesicles adsorb intact at low coverage, followed by transformation to a bilayer at a crit. coverage. On TiO2, oxidized Pt, and oxidized Au, the vesicles adsorb intact at all coverages and all studied temps. Variation of vesicle size does not change the qual. behavior on any of the surfaces, but the quant. differences provide important information about surface-induced vesicle deformation. In the low-coverage regime (where vesicles adsorb intact on all surfaces), the deformation is much larger on SiO2 than on the surfaces where bilayer formation does not occur. This is attributed to stronger vesicle-surface interaction on SiO2. The bilayer formation is thermally activated with an apparent activation energy of 63-78 kJ/mol. Osmotic pressure promotes bilayer formation, esp. when the external salt concn. is higher than the internal one. Depending on prepn. conditions, a varying amt. of nonruptured vesicles are trapped in the satd. bilayer on SiO2, but the fraction can be efficiently reduced to below the detection level using elevated temp. and/or high osmotic stress.
    107. 107
      Mangeat, M.; Guérin, T.; Dean, D. S. Effective Diffusivity of Brownian Particles in a Two Dimensional Square Lattice of Hard Disks. J. Chem. Phys. 2020, 152, 234109,  DOI: 10.1063/5.0009095
      There is no corresponding record for this reference.
    108. 108
      Holcman, D.; Schuss, Z. Diffusion through a Cluster of Small Windows and Flux Regulation in Microdomains. Phys. Lett. A 2008, 372 (21), 3768– 3772,  DOI: 10.1016/j.physleta.2008.02.076
      There is no corresponding record for this reference.
    109. 109
      Jóhannesson, H.; Halle, B. Solvent Diffusion in Ordered Macrofluids: A Stochastic Simulation Study of the Obstruction Effect. J. Chem. Phys. 1996, 104 (17), 6807– 6817,  DOI: 10.1063/1.471347
      There is no corresponding record for this reference.
    110. 110
      Singer, A.; Schuss, Z.; Holcman, D. Narrow Escape, Part II: The Circular Disk. J. Stat. Phys. 2006, 122 (3), 465– 489,  DOI: 10.1007/s10955-005-8027-5
      There is no corresponding record for this reference.
    111. 111
      Holcman, D.; Schuss, Z. Control of Flux by Narrow Passages and Hidden Targets in Cellular Biology. Rep. Prog. Phys. 2013, 76 (7), 074601,  DOI: 10.1088/0034-4885/76/7/074601
      There is no corresponding record for this reference.
    112. 112
      Meiser, E.; Mohammadi, R.; Vogel, N.; Holcman, D.; Fenz, S. F. Experiments in Micro-Patterned Model Membranes Support the Narrow Escape Theory. Commun. Phys. 2023, 6 (1), 330,  DOI: 10.1038/s42005-023-01443-2
      There is no corresponding record for this reference.

  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.3c07388

    • Additional information regarding the substrate preparation (Figures S1 and S2), FCS setup (Figure S3), appropriateness of FRAP fit (Figures S4 and S5), comparison between FRAP measurements for all TiO2 and Al2O3 geometries (Figure S6), and numerical simulations (Figures S7 and S8) (PDF)


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