Cooperative Assembly of Hsp70 Subdomain Clusters

Many molecular chaperones exist as oligomeric complexes in their functional states, yet the physical determinants underlying such self-assembly behavior, as well as the role of oligomerization in the activity of molecular chaperones in inhibiting protein aggregation, have proven to be difficult to define. Here, we demonstrate direct measurements under native conditions of the changes in the average oligomer populations of a chaperone system as a function of concentration and time and thus determine the thermodynamic and kinetic parameters governing the self-assembly process. We access this self-assembly behavior in real time under native-like conditions by monitoring the changes in the micrometer-scale diffusion of the different complexes in time and space using a microfluidic platform. Using this approach, we find that the oligomerization mechanism of the Hsp70 subdomain occurs in a cooperative manner and involves structural constraints that limit the size of the species formed beyond the limits imposed by mass balance. These results illustrate the ability of microfluidic methods to probe polydisperse protein self-assembly in real time in solution and to shed light on the nature and dynamics of oligomerization processes.

M olecular chaperones play a crucial role in vivo not only in assisting in protein folding but also in regulating the formation of aberrant protein assemblies, including in particular those implicated in the onset and progression of neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. 1−9 Despite their important cellular roles, defining the microscopic mechanisms by which molecular chaperones can protect against pathogenic aggregation remains a substantial challenge to study as a result of the polydispersity of the systems involved. 10−13 Indeed, many molecular chaperones, including the 70 kDa heat shock proteins (Hsp70s) and small heat shock proteins such as αB-crystallin, are known to have the propensity to self-assemble into various oligomeric forms, and it has been thought that this serves as a control mechanism for storage of chaperones when they are not exerting their cellular functions. 12,14−29 Evaluating the intrinsic dynamics of molecular chaperones in the presence and absence of their interaction partners is therefore a key target in biophysical studies to begin to define the specific oligomeric species responsible for the suppression of protein aggregation.
A number of conventional biophysical techniques are currently available for probing the quaternary structure and oligomeric populations of proteins; these approaches, however, are typically more reliable for monodisperse solutions of isolated components. 14,30−32 Moreover, many of the techniques involve the interaction of the protein of interest with a surface or a matrix, which may influence the self-assembly behavior. It has recently become apparent, however, that microfluidic techniques offer a fruitful avenue for the characterization of the dynamics, interactions, and physical properties of biomolecules in solution. 8,9,16,33−39 These approaches include methods for the rapid sizing of biological complexes in solution by monitoring the spatiotemporal evolution of their diffusion through a microfluidic channel. 39−41 In this work, we have applied microfluidic diffusional sizing (MDS) to the study of the oligomerization of SBD641, the substrate binding subdomain (residues 384−641) of human Hsp70. Construct SBD641 consists of the hydrophobic linker, the substrate binding subdomain itself, and the helical lid, which are the regions that have been found to be critical for oligomerization in full-length Hsp70. 14 We show that the rapid nature of the microfluidic sizing measurements under native solution conditions makes this approach particularly important for quantitative studies of the kinetics as well as the thermodynamics of oligomerization processes. In particular, we demonstrate a robust method for determining the dissociation constant, oligomerization free energy, and association and dissociation rate constants of the self-assembly reaction and show that the assembly process is guided by specific structural constraints and is qualitatively different from unconstrained polymerization processes.

■ MATERIALS AND METHODS
Protein Expression and Purification. SBD641 was purified according to a protocol outlined previously. 42 In brief, N-hexa-His-tagged SBD641 was expressed recombinantly in Escherichia coli from the pET28b (Novagen) vector. The cells were then centrifuged, resuspended in buffer [50 mM Tris (pH 7.4)], and lysed using sonication. The expressed protein was collected using a Ni 2+ -NTA Superflow column (Qiagen, Manchester, U.K.) using standard washing procedures. The protein was further purified by size exclusion chromatography using a Superdex 75 26/60 column (GE Healthcare, Buckinghamshire, UK).
Labeling. Alexa Fluor 488 (Life Technologies, Paisley, UK) was added to SBD641 (10 mM Tris, pH 7.4) at a 1:2 Alexa:SBD641 molar ratio and degassed. The samples labeled at 1:2 and 1:5 ratios were used in the experiments for SBD641 concentrations below and above 3 μM, respectively. The mixture was left to incubate overnight in the dark at 4°C. The excess dye was removed after 24 h of incubation using a Zeba Spin desalting column 7 kDa (Thermo Scientific, Cramlington, UK) followed by size exclusion chromatography with a Superdex 10/300 GL column (GE Healthcare Life Sciences, Amersham). The protein was then divided into aliquots, flashfrozen, and stored at −80°C until further use.
Microfluidic Device Fabrication. The microfluidic devices used in this study were fabricated using standard softlithography techniques. 43 SU-8 3025 photoresist (3 mL, MicroChemCorp, Westborough, MA) was spin-coated onto a silicon wafer at 3000 rpm to create 25 μm height channels. After being baked at 96°C for 12 min, the wafers were covered with a photomask imprinted with a pattern of the device. The wafer was then exposed to ultraviolet (UV) radiation for 15 s at an intensity of 16 mW/cm 2 (OAI Instruments, San Jose, CA) and baked at 96°C for a further 5 min. This procedure allowed cross-linking of the photoresist in the regions exposed to UV light, and the residual photoresist was then removed with PGMEA (propylene glycol methyl ether acetate). The master was subsequently rinsed with IPA (isopropyl alcohol) and dried.
The PDMS (polydimethylsiloxane) curing agent and elastomer (Dow Corning) were thoroughly mixed in a 1:10 ratio. Carbon black nanopowder (Sigma-Aldrich, Dorset, U.K.) was added to the mixture, which was subsequently centrifuged for 5 min at 5000 rpm to spin down large clusters of carbon powder. The centrifuged black PDMS was then poured into a Petri dish containing the wafer, and the dish was placed in a vacuum desiccator for 30 min to eliminate air bubbles and then baked at 65°C for 3 h.
Diffusion Measurements. The microfluidic devices were plasma bonded to glass microscope slides using an Electronic Femto Plasma Bonder (Diener, Ebhausen, Germany) directly before use. The channels in the bonded device were filled from the outlet with the relevant buffer using a 250 or 500 μL glass syringe (Hamilton Robotics, Bonaduz, GR, Switzerland), needles (25 gauge, 0.5 mm × 16 mm) (Neolus Terumo, Bagshot, U.K.), and polyethene tubing (inner diameter of 0.38 mm, outer diameter of 1.09 mm). The sample and buffers were loaded into their respective device inlets using gel loading pipet tips.
Fluid flow through the device was controlled using neMESYS syringe pumps (Cetoni GmbH, Korbussen, Germany) at a flow rate of 100 or 160 μL/h. Once the system had equilibrated, the diffusion profiles were imaged using an inverted fluorescence microscope (Zeiss Axio Observer.D1) fitted with broadband white LED illumination (Cairn Research, Faversham, U.K.) and a 49002 GFP filter (Chroma Technology, Bellows Falls, VT). The microfluidic diffusion channels were imaged at 12 points along the channels using an Evolve 512 CCD camera (Photometrics, Tuscon, AZ) with a 10× objective and exposure times ranging from 1 to 10 s depending on the sample concentration.
Numerical Simulations and Data Analysis for Microfluidic Sizing Experiments. Fitting of the basis functions to the experimental data was performed as described previously. 39 The basis functions used in this analysis were simulated in the range of radii relevant to the samples, namely, 0.25−10 nm in 0.25 nm increments. 44 Fluidity One Measurements. In addition, we used a Fluidity One (Fluidic Analytics Ltd., Cambridge, U.K.), which is a self-contained instrument that enables microfluidic diffusional sizing measurements with post separation labeling using injection moulded disposable plastic chips, rather than PDMS. Four repeats were taken on 10 μL of unlabeled SBD641 at 0.3 μM on a prototype instrument.
Thermodynamic Models of SBD641 Oligomerization. Model with No Cooperativity. Assuming a single equilibrium constant K for the association and dissociation of monomers, the equilibrium concentration [A j ] of j-mers is given by 45 where the equilibrium monomer concentration [A 1 ] is linked to the total concentration of protein molecules [A] tot through mass conservation, yielding: Using eq 1, we obtain the average hydrodynamic radius at equilibrium [A ] where Li s (z) = ∑ k=1 ∞ z k /k s is the polylogarithm function of order s, R m is the size of the pure monomer, and d is the fractal Assuming an association−dissociation equilibrium constant K = K 0 /j, we obtain the following expression for the concentration of filaments of size j at equilibrium where a relationship between the equilibrium monomer concentration and the total concentration of protein molecules is given in terms of the Lambert W- . Thus, the dependence of the average hydrodynamic radius on the total protein concentration becomes Positive Cooperativity with a Size Limit. This model assumes a monomer−N equilibrium, with a very fast preequilibrium between intermediates. The overall equilibrium is a result of several distinct steps in a more detailed model in which monomers are sequentially added to N-mers. At low values of N, we note that intermediate populations can start to emerge. Using the equilibrium concentration of oligomers [A N ] = K[A 1 ] N , we obtain for the average hydrodynamic radius where the total concentration dependence of equilibrium monomer concentration [A 1 ] is found by inverting the mass balance equation Kinetics. These rate laws assume that N-mers are the largest oligomers formed and that the time evolution is given by where [A 1 ](t) and [A N ](t) are the monomer and N-mer concentrations at time t, respectively.
The time evolution of the hydrodynamic radius, then, is obtained from a mole-fraction weighted average of the radius of each species: Note that the kinetic equations (eqs 7 and 8) emerge from a steady-state approximation of a more detailed model that assumes N-mers to be formed by the addition of individual monomers in sequence with rate constant k + (i) : The connection between association rate constant k a entering eqs 7 and 8 and the geometrically averaged elongation rate ] 1/3 , assuming size-independent dissociation rate constants, is given by (for N = 4) Using the measured values for k a and equilibrium constant K= (⟨k + ⟩/k − ) 3 = k a /k − , we could determine the elongation rate constant to be approximately ⟨k + ⟩ = 2.0 ± 1.2 M −1 s −1 . This elongation rate corresponds to an association reaction whose barrier is the arithmetic mean of those for dimer, trimer, and tetramer formation through monomer addition, assuming similar diffusive prefactors for all.
Data Fitting. We assumed in all cases that R m = 1.7 nm, the R h value obtained at the lowest concentration of SBD641 measured.
In the case of the fits to models without and with negative cooperativity, we minimized the ] 2 between the thermodynamic data and each model with respect to the parameters α = d −1 and the relevant equilibrium constant. Here y i is the measured hydrodynamic radius corresponding to initial concentration x i , and p is a vector of the parameters. We took as a constant estimate for the error σ i the average non-zero standard deviation of hydrodynamic radii, averaged over all the initial concentrations.
For the two-state model, we performed a global fit to the thermodynamic and kinetic data simultaneously by minimizing the sum of kinetic and thermodynamic contributions to total χ 2 with respect to the elements of parameter vector p = (α,K,k a ). The errors in each kinetic data point were taken as 20% of the measured values. The derivation of the target function to minimize can be found in the Supporting Information. Note that off rate k − was constrained by k a and the association constant K̃by applying detailed balance: K̃= k a /k − . To sample rate constant space exponentially, the exponent (base 10) of the on rate constant k a was fitted.
In practice, all fits were performed by using the basinhopping algorithm of Python's scipy module, which involves several minimization steps interspersed by random moves in parameter space and effectively samples glassy fitting landscapes by removing barriers between local and global minima. 46 The minimization scheme was an L-BFGS-B algorithm implemented in Python's scipy.minimize module. 47 To avoid nonphysical regimes, the parameters of the no-or negativecooperativity models were constrained to the regions 0 ≤ α ≤ 1 and K ≥ 0. For the two-state fits, the imposed bounds were k a ≥ 0, K̃≥ 1, and 0 ≤ α ≤ 1 × 10 −18 .

Article
Errors in the fitted parameters were estimated by building an approximate covariance matrix of χ 2 and propagated to the fits as described in the Supporting Information. 48 Following minimization, α was converted to scaling exponent d, using the equation d = α −1 , with errors propagated in the standard way.

■ RESULTS
Multidimensional Microfluidic Diffusion Measurements. We measured the diffusion coefficients of SBD641 in solution by monitoring lateral diffusion under steady-state laminar flow in a microfluidic channel using a device shown schematically in Figure 1a. 39 The cysteine residues of SBD641 were conjugated to an AlexaFluor488 dye for visualization of the sample diffusion profiles, and images were taken at 12 different positions under steady-state flow conditions using the experimental procedure shown in Figure 1b. The diffusion profiles acquired in this way were then fitted to a linear combination of simulated basis functions calculated for ideal monodisperse solutions 44 (Figure 1c), yielding the average diffusion coefficients of the particles in the solution. 37,39,49 Thermodynamics of Oligomerization of the Hsp70 Substrate Binding Subdomain. To explore the thermodynamic determinants of SBD641 self-assembly, we determined the average hydrodynamic radius R h of the SBD641 construct in solution at 12 different monomer concentrations between 0.3 and 50 μM using the microfluidic diffusion approach described above. Each measurement was repeated two to four times at flow rates of 100 and 160 μL/h in at least two devices fabricated independently. We found that the average R h values increased significantly with concentration, from 1.8 ± 0.2 nm at 0.3 μM to 3.41 ± 0.15 nm at 12 μM, at which concentration the radius appeared to plateau (Figure 2a). The increase in the radius indicates an elevated population of higher-order oligomers with an increasing SBD641 concentration, in accordance with results from bulk experiments. 14 In addition, to verify that the fluorescent label does not affect the measured hydrodynamic radii of SBD641, we performed sizing measurements at 0.3 μM unlabeled protein using a Fluidic Analytics Fluidity One instrument. This approach for microfluidic diffusional sizing is based on postseparation labeling. 38 We found the radius of unlabeled SBD641 at 0.3 μM [10 mM sodium phosphate buffer (pH 7.4)] to be 1.89 ± 0.25 nm, in agreement with our labeled construct ( Figure 2, blue data point).
To evaluate the thermodynamic parameters governing the oligomerization process, we explored the extent to which the experimental data could be described by different equilibrium models with varying levels of cooperativity (details of each model can be found in Materials and Methods) (Figure 2). The average hydrodynamic radius obtained in the experimental measurements was converted to the number of monomers (j) in individual oligomeric species by means of the relationship where R j is the hydrodynamic radius of an oligomer with j subunits, R 0 is the hydrodynamic radius of the monomeric species, and d indicates the dimensionality of the cluster (see the Supporting Information).
To understand the role of cooperativity in the assembly of these truncated Hsp70 clusters, we first considered the Oosawa model of equilibrium linear polymerization. 45,51,52 This model does not display any cooperativity because the polymerization reaction is assumed to proceed through simple addition and removal of individual subunits to existing aggregates; moreover, a single equilibrium constant K describes monomer association and dissociation at each polymerization step. Figure 2a shows the best fit of our thermodynamic data to this simple model. Evidently, this model does not account for the key features of the experimental data set; in particular, the fit fails to capture  (Figure 2a).
Because a simple polymerization model without cooperativity is unable to describe the data, we next investigated whether, at the next level of complexity, a polymerization model in which the formation of larger oligomers becomes increasingly less favorable as the size increases could result in a greater level of agreement between the simulation and the experimental data. We therefore examined a model for negative cooperativity in which the dissociation rate of larger clusters increases in proportion to their size, 50 yielding a limit to oligomer size. As for the Oosawa model, the negative cooperativity model assumes that aggregation proceeds by the addition and removal of single subunits, but the equilibrium constant varies with the number of subunits (j) in an oligomer in proportion to K j = K 0 /j for j > 1, thus making the formation of larger oligomers less favorable. Despite a slight improvement in the residuals of the fit, this model also fails to capture accurately the behavior of the experimental data under these conditions (Figure 2b).
Because the Oosawa and negative cooperativity models are incapable of capturing the sharp increase in the average R h values observed in the experiments, we explored a positive cooperativity model by allowing for a higher-than-linear dependence of the rate of oligomer formation on monomer concentration. In the simplest scenario, this effect can be captured by assuming the formation of oligomers of a maximal size of N = 4 subunits, which is the largest oligomeric assembly reported in the literature, 14 from the interaction of multiple monomers. Figure 2c shows that the best fit of the experimental data to this positive cooperativity model yields overall good agreement, demonstrating the necessity of a higher-than-linear monomer concentration dependence of oligomer formation to explain the observed sharp increase in R h . Similar thermodynamic models in which the subunits demonstrate high positive cooperativity with a limiting oligomer size have been shown to describe protein self-assembly very well in systems that exhibit strong structural constraints, such as the assembly of viral capsids. 53 The best fit to our data under our experimental conditions yields a value for the association constant K̃of 0.035 ± 0.011 μM −3 , i.e., an effective dissociation constant K D = K̃− 1/3 = 3.1 ± 0.3 μM. The effective K D value determined in this study is broadly consistent with the value reported in the literature, 5−10 μM, for SBD641. 14 We find, moreover, from the measurement of the equilibrium constants that the oligomerization process is thermodynamically favorable with a standard free energy change (ΔG assembly ⊖ ) of −95.0 ± 0.8 kJ/mol under standard conditions. Our results show therefore that the assembly process of the SBD641 oligomers is highly cooperative with a limit to the maximum size. Moreover, our analysis shows that the limit in the oligomer size at high concentrations is unlikely to originate from purely kinetic constraints, as is the case for instance with linear protein aggregation, 54 but rather appears to have an origin in structural  50 where the formation of larger oligomers is limited by the increasing rates of dissociation of the monomer from oligomeric clusters of increasing subunit numbers. The following parameters were obtained from the fit: K 0 = 1.7 ± 0.6 μM −1 , and d = 1.80 ± 0.13. (c) Positive cooperativity model, in which the largerst oligomer is capped to N = 4 subunits and a monomer−tetramer equilibrium is assumed (see Materials and Methods). The following parameters were obtained in the best fit: K̃= 0.035 ± 0.011 μM −3 , and d = 1.69 ± 0.06.

Biochemistry
Article constraints that counterbalance the thermodynamic driving force for forming larger aggregates at higher concentrations.
Kinetics of Oligomerization of the Hsp70 Substrate Binding Subdomain. We next demonstrate that the microfluidics-based strategy presented here allows us to probe directly the kinetics of self-assembly processes. To this effect, we probed SBD641 oligomerization by measuring the time taken for a purely monomeric sample to re-establish completely the dynamic equilibrium distributions of monomers and oligomers; an aliquot of the monomeric SBD641 was therefore purified by size exclusion chromatography, and the variation in average hydrodynamic radius as a function of time was monitored using MDS at different time points. The cooperativity of the oligomerization process meant that the reassembly started immediately after the fraction of monomers eluted from the column. We conducted measurements for monomeric SBD641 at concentrations of 3.9 and 11.6 μM in 10 mM Tris-HCl buffer (pH 7.4) and found that in both cases the average R h value of SBD641 increases with time, indicating that the SBD641 oligomerization process is reversible on the time scales of this experiment and that the monomers are able to reassemble into higher-order oligomers (Figure 3), in accord with previous experiments performed in bulk. 14 We fitted the microfluidic data obtained at two different initial chaperone concentrations (3.9 and 11.6 μM) to the integrated rate law that captures the kinetics of the positive cooperative aggregation model that was found to describe this system most effectively in our thermodynamic study. Details of the fitting can be found in Materials and Methods. Using this approach, for the self-assembly of the substrate binding subdomain of Hsp70, we obtained an association rate constant k a of (2.1 ± 1.2) × 10 11 M −3 s −1 and a dissociation rate constant k − of (6 ± 4) × 10 −6 s −1 . The association rate constant can be further decomposed into an average elongation rate constant per monomer addition step of ⟨k + ⟩ = 2.0 ± 1.2 M −1 s −1 (see Materials and Methods).

■ DISCUSSION
Using the results of the kinetic fit, we compared the value of the average elongation rate constant ⟨k + ⟩ obtained here for this truncated molecular chaperone system to that of a variety of self-assembling biomolecular systems, as shown in Figure 4 and Table S2. The self-assembly of the proteins shown in the graph has a variety of biological effects, including proteins such as actin and tubulin that have evolved to aggregate as a part of their function (magenta), 55−57 the molecular chaperone αBcrystallin that is known to form native quaternary structures (green), and non-evolved proteins whose filamentous forms are associated with pathological aggregation such as Aβ 40 , Aβ 42 , αsynuclein, insulin, hemoglobin, and the yeast prion protein Ure2p (cyan). 57−64 We find that the geometrically averaged elongation rate constant of the substrate binding subdomain of Hsp70 (red) is much lower than that of most other proteins of biological interest that are known to self-assemble, and that the average elongation rate obtained for our system compares well with that of αB-crystallin, another ubiquitous molecular chaperone, which also forms oligomers ( Figure 4 and Table  S2). This fits with the trend that is apparent from Figure 4, in which the aggregation rates of nonfilamentous (red and green) structures that form native quaternary assemblies do so more slowly than misfolded, filamentous proteins do (magenta and cyan). The slow average rate of monomer addition of the labeled subdomain of Hsp70 suggests that at least one of the reactions on pathway to aggregate formation is highly unfavorable, and that there is a high activation barrier in the self-assembly process.

■ CONCLUSIONS
In this study, we have developed a microfluidic approach for determining the values of the thermodynamic parameters governing the oligomerization of proteins under native solution conditions, in particular the dissociation constant and free energy of oligomerization, and have shown that these results can provide novel molecular insights into the mechanisms of the self-assembly process. For the system of truncated human Hsp70 studied here, the analysis of the thermodynamic data reveals that there are strong structural constraints on the size of the oligomers, which are most likely to be determined by specific molecular interaction modes at the oligomerization interface.
In addition, we took advantage of the short analysis times afforded by our microfluidic diffusion measurements, a feature that is crucial for determining the characteristic time scales associated with the rapid assembly of proteins, to show that this method can also be used to determine the overall association rate constant of oligomerization and extract the maximum assembly size. We have shown that the solution-state measurements ensure that we can observe the self-assembly behavior of proteins without compromising oligomer assembly by the interference of a surface as in many other techniques. We anticipate that the approach discussed in this work will provide the opportunity for further quantitative real-time studies of the structure and oligomerization of other selfassembling protein systems of key physiological relevance under native solution conditions.