Influence of Temperature on Molecular Adsorption and Transport at Liposome Surfaces Studied by Molecular Dynamics Simulations and Second Harmonic Generation Spectroscopy

A fundamental understanding of the kinetics and thermodynamics of chemical interactions at the phospholipid bilayer interface is crucial for developing potential drug-delivery applications. Here we use molecular dynamics (MD) simulations and surface-sensitive second harmonic generation (SHG) spectroscopy to study the molecular adsorption and transport of a small organic cation, malachite green (MG), at the surface of 1,2-dioleoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (DOPG) liposomes in water at different temperatures. The temperature-dependent adsorption isotherms, obtained by SHG measurements, provide information on adsorbate concentration, free energy of adsorption, and associated changes in enthalpy and entropy, showing that the adsorption process is exothermic, resulting in increased overall entropy. Additionally, the molecular transport kinetics are found to be more rapid under higher temperatures. Corresponding MD simulations are used to calculate the free energy profiles of the adsorption and the molecular orientation distributions of MG at different temperatures, showing excellent agreement with the experimental results.

The 1,2-dioleoyl-sn-glycero-3phospho-(1'rac-glycerol) (DOPG) liposome formation protocol has been reported previously. [1][2][3] For determination of the lipid concentration, perchloric acid was used to convert phospholipids to inorganic phosphates. The addition of ammonium molybdate in an acidic condition leads to the formation of phosphor-molybdic acid, which was then reduced by Fiske-Subbarow agent, producing a blue solution for absorbance measurements at 800 nm (Bartlett assay). Absorption measurements were done using a UV−vis spectrometer from PerkinElmer, Boston, MA, U.S.A. The calibration curve for the Bartlett assay, as shown in Figure S1, is fit with a linear equation with a slope of 0.00300 ± 0.00004, a y-intercept of −0.002 ± 0.003, and an R 2 value of 0.999 for the fit. The dynamic light scattering (DLS) size distribution is shown in Figure   S2 with a size of 137 ± 42 nm and a polydispersity index of 0.07 for the DOPG liposomes in 5 mM citrate buffer with pH 4.0. The molecular structure of DOPG is shown in Figure S3.   shows a strong SHG signal centered at 400 nm with a full width at half maximum of 4.5 nm. The small signal at wavelengths greater than 410 nm is due to two-photon fluorescence from MG, 2,4 and is clearly separated spectroscopically from the SHG signal. Here, the SHG intensity is enhanced by approximately 2.5 times in comparison to the hyper-Raleigh scattering (HRS) signal generated from free dye molecules alone, 5,6 confirming molecular adsorption of MG to the liposome surface. In contrast, the SHG signal from the liposomes alone is much lower, in agreement with our previous studies. 2,3 For a direct comparison, all SHG intensities are normalized with respect to the DOPG liposomes upon addition of 15 µM MG at 25 °C. Figure S4b displays the SHG spectra of DOPG liposomes immediately after the addition of 15 µM MG under different temperatures ranging from 25 °C to 40 °C. The SHG intensity is found to decrease as temperature is increased, which is primarily attributed to the change in the orientational distribution of the dipole moment of the adsorbed MG dye molecules at the liposome interface, 7 as discussed in greater detail in the paper and later in the Supporting Information using results obtained from molecular dynamics (MD) simulations. The determined rate constants ( −1 ) for different temperatures are plotted as a function of MG concentration at different temperatures, as shown in Figure S5, with corresponding linear fits for each temperature. The slopes of obtained rate constants from Figure S5 are plotted as a function of temperature and are displayed in Figure S6. SHG from a colloidal nanoparticle sample is understood to be a coherent process from each individual nanoparticle, while the overall SHG signal is the incoherent summation of an ensemble of nanoparticles at the laser focus, along with background signals from hyper Raleigh scattering. 5,8,9 Fitting the time traces using ( ) = 0 + 1 − / , as described in the paper, properly accounts for these coherent and incoherent signals. The transport times are tabulated in Table S1. The fitting parameters 0 and 1 are listed in Tables S2 and S3, respectively. The HRS intensities obtained for different MG concentrations in 5 mM citrate buffer with pH 4.0 at 25 °C and 40 °C are shown in Figure S7 with corresponding linear fits. The HRS signal is from incoherent second-order scattering which arises from orientational and density fluctuations of molecules in the bulk solutions. 5 The HRS signal has the      Figure  force between the positively-charged amine group of MG and the negatively-charged sulfate group at the PSSP surface. 9,10 The SHG adsorption isotherms for this system are studied as a function of temperature, with the results shown in Figure S8 for temperatures of 20 °C, 30 °C, 40 °C, 50 °C, and 60 °C. The experimentally obtained isotherms are fit using the modified Langmuir model, as described previously. The fitting parameters obtained from the modified Langmuir fits are listed in Table S2. The obtained equilibrium constant is a measure of the electrostatic interaction between the charged dye and microparticle interface. However, the value of the equilibrium constant does not change to within the experimental uncertainty for the temperature range studied here. The obtained adsorption equilibrium constants for 20 °C, 30 °C, 40 °C, 50 °C, and 60 °C are (2.37 ± 0.32) × 10 9 , (1.9 ± 0.53) × 10 9 , (2.49 ± 0.32) × 10 9 , (2.81 ± 0.32) × 10 9 , and (2.27 ± 0.54) × 10 9 , respectively. In comparison to the liposome results presented in the manuscript, the obtained adsorption equilibrium constants are larger in magnitude indicating a stronger interaction between MG and PSSPs, in agreement with the previous studies. 3,11 The free energy of adsorption, obtained from ∆ = − ln , is plotted as a function of temperature, as shown in Figure S9. Here, the results are fit to a line with ∆ = ∆ − ∆ to provide the thermodynamic properties of the molecular adsorption, where is the change in adsorption enthalpy, is the change in adsorption entropy, and is the temperature. The calculated ∆ from the y-intercept is 0.45 ± 1.00 kcal/mol, indicating that the net change in adsorption enthalpy is approximately zero to within experimental uncertainty. The calculated from the linear slope is 0.044 ± 0.003 kcal/K·mol. This change in entropy is a full accounting of the adsorption process, including the change in entropy of the adsorbate molecules and the solvated microparticle surface. The adsorption process is described by free dye molecules adsorbing to "empty" adsorption sites, which are then converted to "filled" adsorption sites. 2,4,8 The molecular S10 adsorption of the MG adsorbates alone should have negative entropy as these MG molecules are more ordered when adsorbed to the nanoparticle surface. However, the adsorbate MG molecules are replacing water molecules and counterions that were originally at the nanoparticle surface.
Since each MG adsorbate molecule will replace numerous water molecules and counterions due to their relative sizes, an overall increase of entropy occurs upon adsorption, when given a full account. For this particular case, where is approximately equal to zero to within the experimental uncertainty, the overall condition is ∆ ≈ − ∆ , so the molecular adsorption process is expected to be spontaneous at all aqueous temperatures.  Figure S8. SHG-determined adsorption isotherms for MG with 1 μm polystyrene sulfate particles (PSSPs) in water at different temperatures.

Molecular Dynamics Simulations
The initial lipid bilayer with 72 DOPG molecules is built using the CHARMM-GUI Membrane Å away from the average membrane surface is used. In order to obtain the water number density, the number of water molecules in a water layer with 1 Å thickness in the z-direction is counted and binned.

Canonical Simulations
Prior to the umbrella sampling simulations, 20 ns of canonical simulations are performed. Figure   S10 shows the distance in the z-direction between the COM of the MG molecule and the COM of the DOPG membrane for the canonical simulations for the two different temperatures. The average surface of the DOPG membrane is determined using the average z-coordinates of the oxygen atom of each DOPG's furthest hydroxyl group on one side of the membrane and the interfacial region is determined using the normalized water number density. S15 Figure S10. The distance in the z-direction between the COM of the MG molecule and the COM of the DOPG membrane for 303 K and 313 K temperature for the canonical simulations. The horizontal dotted lines represent the average interface for 303 K (black) and 313 K (red). The dashed lines represent the normalized water number density for 303 K (black) and 313 K (red).
According to results in Figure S10, the MG molecule gets adsorbed more rapidly to the DOPG membrane at the higher temperature compared to the lower temperature simulation. Figure   S11 shows a representative snapshot of the MG molecule adsorbed on to the DOPG membrane during the canonical simulation at 313 K temperature. The MG molecule at the lower temperature takes much longer to reach the interface and does not readily penetrate the membrane, unlike in the higher temperature case. This indicates that the higher energy barrier at the lower temperature S16 simulation hinders the adsorption process of the MG molecule as compared to the higher temperature simulation. Figure S11. A representative snapshot of the MG molecule adsorbed on to the DOPG membrane during the canonical simulation under 313 K temperature (on the left) and a magnified view of the snapshot (on the right).

Orientation Calculations
To gain a molecular level understanding of the change of SHG intensities at different temperatures, the orientation angle ( Figure S12a) between the dipole moment vector of the MG molecule and the vector normal to the membrane surface pointing to the solvent side, with the MG molecule at different distances in the z-direction from the COM of the membrane is calculated.
The results from this analysis are shown in Figure S12. This specific type of orientational distribution has been used to gain an understanding of molecular ordering at interfaces in previous MD studies. 30 Figure S12b shows that the dipole vector of the MG molecule always forms a narrow distribution at an angle greater than 90°, with the two amine groups of the MG molecule directed towards the membrane, at the lower temperature. This demonstrates that the orientation of the MG molecule is well ordered at the aqueous solution-membrane interface at the lower temperature, S17 thereby enhancing the intensity of the SHG signal. In contrast, at the higher temperature, the angular distribution is much broader with a wider range of angles indicating a less-ordered interfacial structure due to the weakened interaction between the MG and the DOPG molecules, as shown in Figure S12c. This contributes to the lower observed SHG intensity at higher temperatures. It should be noted that adsorbate-adsorbate interactions and additional interactions with added salt and buffer molecules are present in the experimental studies, but are not included in the MD studies. The MD simulations are also used to study the displacement of the water solvent molecules caused by the MG molecular adsorption, as explained in greater detail in the section below. According to the results shown in Figure S13, approximately 50 -70 water molecules are displaced when MG adsorbs to the DOPG membrane at both 303 K and 313 K. This is also in agreement with the SHG experimental results, where a positive change in entropy is observed due to adsorption from a large number of interfacial water molecules being displaced from every singular MG molecular adsorption event that occurs.

Water and Potassium Ion Displacement Calculations
To analyze the displacement of water molecules as the MG molecule adsorbs to the DOPG membrane, the change in the number of interfacial water molecules is calculated. This interfacial water layer is defined as the water molecules which are within 3.5 Å along the z-direction from the average surface of the membrane. The average surface of the DOPG membrane is determined using the z-coordinates of the oxygen atom of each DOPG's furthest hydroxyl group on one side of the membrane. Figure S13 shows the number of water molecules in the layer within 3.5 Å from the average surface of the membrane for different umbrella sampling windows calculated as a function of the separation in the z-direction between the MG molecule and COM of the membrane.
According to these results, the number of water molecules decreases more rapidly at the higher

Membrane Surface
temperature as the MG molecule approaches the membrane, as compared to the lower temperature case. This is consistent with the orientation angle distributions observed for the dye at two temperatures. For the higher temperature the orientation angle distribution is much broader and more random while it is more ordered in the lower temperature simulations. Since the dipole vector distribution is broader at higher temperature, the MG molecule clearly shows greater orientational variability during adsorption to the membrane, which results in more water molecules being displaced near the membrane surface at the higher temperature. Figure S13. The number of water molecules in the first solvation layer of the membrane, when the MG molecule is at different separation distances in the z-direction from the COM of the DOPG membrane for temperatures of 303 K and 313 K. The vertical dotted lines represent the average interface for 303 K (black) and 313 K (red). The dashed lines represent the normalized water number density change for 303 K (black) and 313 K (red).

S20
The number of water molecules displaced by MG adsorption is also consistent with a computational study of monatomic ion adsorption at the air-water interface. 31  For comparison, the displacement of K + ions is also calculated as the MG molecule approaches the DOPG membrane. The number of interfacial K + ions is calculated as a function of distance in the z-direction of the MG molecule from the COM of the membrane. This interfacial K + ion layer is defined as the K + ions which are within 3.5 Å along the z-direction from the average surface of the membrane. Figure S14 shows the number of K + ions in the layer within 3.5 Å from the average surface of the membrane for different umbrella sampling windows calculated as a function of the separation in the z-direction between the MG molecule and COM of the membrane.
According to these results, the change in the number of K + ions as the MG molecule approaches the membrane is minimal, fluctuating between an average number of 33 and 40, with a net S21 difference of approximately 1 or 2 (changing from approximately 40 to 39 at 313 K, and changing from approximately 39 to 37 at 303 K). This result shows that the number of K + ions displaced (~1) is much less than the number of water molecules displaced (~70) as the MG molecule adsorbs to the DOPG membrane. Figure S14. The number of K + in the first solvation layer of the membrane, when the MG molecule is at different separation distances in the z-direction from the COM of the DOPG membrane for temperatures of 303 K and 313 K. The vertical dotted lines represent the average interface for 303 K (black) and 313 K (red). The dashed lines represent the normalized water number density change for 303 K (black) and 313 K (red).

Error Analysis of Fits
The R 2 -values obtained for time-dependent exponential fits of the SHG results from Figure   2 are summarized in Table S4. Similarly, the R 2 -values obtained for the modified Langmuir fits of the SHG results for the liposomes and PSSPs are shown in Tables S6 and S7, respectively.