Modest Protein−Crowder Attractive Interactions Can Counteract

ARTICLE pubs.acs.org/JPCB

Modest Protein-Crowder Attractive Interactions Can Counteract Enhancement of Protein Association by Intermolecular Excluded Volume Interactions Jonathan Rosen,† Young C. Kim,‡ and Jeetain Mittal*,† † ‡

Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, United States ABSTRACT: We study the effects of attractive interactions between spherical crowders and protein residues on the thermodynamics and structure of two weakly binding protein complexes: ubiquitin/UIM1 and cytochrome c/cytochrome c peroxidase. Systematic replica exchange Monte Carlo (REMC) simulations are performed over a range of attraction strengths and crowder packing fractions using a transferable coarsegrained protein binding model. We find that moderate attractive interactions (≈0.2 kcal/mol) between crowders and protein residues can destabilize protein association, and therefore counteract the stabilizing effect of excluded volume interactions. The destabilization of protein binding, as measured by an increase in binding free energy, increases with increasing crowder packing fraction. For a critical attraction strength value, which is found to be approximately independent of crowder packing fraction, the destabilization due to attractions is exactly canceled by the stabilization effect of excluded volume interactions. This results in a net zero change in binding free energy with respect to a crowder-free solution. Further, we find that attractive interactions between crowders and protein residues can favor transiently bound encounter complexes over the native specific complexes in the bound state. We propose a simple theoretical model based on the scaled particle theory augmented by a mean-field attraction term that can explain our simulation results semiquantitatively.

’ INTRODUCTION The high concentration of macromolecules found in the milieu of a cell can significantly alter the observed protein behavior, an effect commonly referred to as “macromolecular crowding”.1,2 The crowded environment is known to affect most of the biochemical reactions inside the cell such as protein folding,3-15 aggregation,16-20 protein-protein interactions,21-26 and protein allostery.27 Identifying crowding induced changes in these reactions is the key to bridge the gap in our understanding of biological processes from laboratory experiments performed under dilute conditions and actual in vivo conditions. Because of their physiological importance, these crowding induced changes have been the topic of several theoretical, computational, and experimental studies in recent years and have contributed significantly to advance our understanding of macromolecular crowding effects; the reader is referred to several recent review articles summarizing results from these studies.28-34 Most of the studies so far have focused on the entropic crowding effects arising from the excluded volume interactions as the crowding molecules occupy volume which is not accessible to proteins.35 This reduction in space available to proteins leads to a stabilizing effect toward protein conformations and multiprotein complexes which occupy a lesser volume.6,11,15,28 In the case of protein folding, this results in a folded state stabilization with respect to an expanded unfolded state. For protein-protein r 2011 American Chemical Society

interactions, bound complexes usually occupy a lesser volume than the combined volume occupied by the individual protein molecules in solution, and this leads to an increase in the binding affinity.26 Interestingly, we found that the specific complexes, owing to a much tighter fit between two proteins, can be stabilized at the expense of nonspecific encounter complexes in the presence of repulsive crowding particles.26 This suggests that the reaction mechanism observed under dilute conditions can be very different from that in a crowded solution. In addition to the excluded volume crowding effects, several additional effects arising due to electrostatic interactions, nonspecific attractive interactions (such as hydrophobic interactions), and hydrogen bonding may be important in a crowded cell. In very early models of macromolecular crowding developed by Minton, attractive interaction potentials were approximated by an effective hard-sphere potential.36 In such models, the effect of attractive protein-crowder interactions is implicitly included by tuning the repulsive potential. Later models included weakly attractive interactions between macromolecules and confining surfaces explicitly using a square-well potential and predicted that only a few kcal/mol surface

Received: January 20, 2011 Revised: February 1, 2011 Published: March 01, 2011 2683

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The Journal of Physical Chemistry B attraction per monomer may result in a large increase in self- or heteroassociation as well as native state deformation.37 Cheung and Thirumalai have shown that, for proteins confined in restricted spaces, nanopore-protein interactions can have a dramatic effect on protein stability.38 They found that these interactions can stabilize intermediate states during protein folding, resulting in a more rugged protein folding landscape as compared to bulk (dilute) conditions. In another computational study, Jewett and Shea found that loose binding of a protein to a model cageless chaperone can enhance protein folding yield.39 In a recent study, McGuffee and Elcock14 showed that favorable interactions between proteins and their cytoplasmic neighbors could counterbalance stabilizing the excluded-volume effect. The strength of attraction in their model is adjusted to reproduce protein diffusion in cells. Most of the experimental studies have utilized model crowding agents, such as Ficoll or Dextran, which are expected to have minimal attractive interactions with proteins and can therefore be modeled appropriately as repulsive particles and therefore expected to have excluded volume-type effects only.32 Interestingly, results obtained from a commonly used crowding agent in experiments, polyethylene glycol (PEG), have not always been found to conform to the excluded-volume-based theoretical models.25 There is now experimental evidence that PEG actually interacts with protein surfaces.40 A theoretical model of accumulated results on PEG as a crowding agent will require additional contributions due to attractive proteincrowder interactions. Very recently, the effect of temperature on crowding induced changes was used to identify the presence of attractive interactions41 or soft repulsive interactions42 between proteins and crowders, which can counter the stabilizing excluded-volume effect on protein folding and protein-protein interactions. Here, we present a systematic study to understand the effect of varying ubiquitous protein-crowder attractive interactions on the thermodynamics of protein-protein interactions. To model protein-protein interactions, we use a transferable coarse grained model that reproduces the binding affinity of weakly interacting protein complexes,43 correct binding interface, as well as the presence of nonspecific encounter complexes in agreement with NMR paramagnetic relaxation enhancement experiments.44 To model attractive protein-crowder interactions, we use a Lennard-Jones (LJ)-type potential with varying particle size and interaction strength. With this study, we hope to provide a more comprehensive picture of protein-protein interactions in the cell, extending the utility of previous observations on the role of attractive protein-crowder interactions.14,41 We find that, in contrast to excluded volume repulsive interactions, the attractive protein-crowder interactions destabilize a bound complex to maximize favorable interactions between crowder particles and protein residues. For low enough attraction strength, the effect of stabilizing excluded volume interactions is still stronger than destabilizing attractions, and therefore the protein binding free energy is still lower than that in the absence of crowders. For a critical attraction strength, the stabilizing effect of excluded volume interactions is counterbalanced by the destabilizing effect, resulting in net zero bindingfree-energy change with respect to a crowder-free solution. Surprisingly, the critical attraction strength is found to be largely independent of the crowder packing fraction for all the cases studied here. Any experiment around this value of attraction strength will therefore predict that crowding has no effect on

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protein binding affinity. For a higher attraction strength than this critical value, the destabilization effect is dominating and the unbound state is stabilized as compared to the dilute condition. Consistent with this destabilization, loosely bound nonspecific encounter complexes become more favorable as the attraction strength increases, since these complexes interact more favorably with a larger number of crowders. Finally, we provide a simple theoretical model based on scaled particle theory augmented with a mean-field attraction term that is in semiquantitative agreement with our simulation results.

’ MODEL AND METHODS Coarse-Grained Model of Protein-Protein Interactions. In the coarse-grained model used here, protein-protein interactions are specified at the residue level. Each amino acid residue is represented by a spherical bead centered at the corresponding CR atom. The interaction potential, jij(r), between two residues, i and j, is given by LJ

jij ðrÞ ¼ jij ðrÞ þ jelij ðrÞ

ð1Þ

where jLJ ij (r) is the Lennard-Jones (LJ)-type potential while jelij (r) is the electrostatic interaction contribution. For LJ-type interactions, we employ both longer range attractive and repulsive interactions depending on the amino acid pair type ij. This enables one to include the interactions with the solvent implicitly. For example, longer-range repulsive interactions are used for amino acid pairs that interact less favorably with each other than with the solvent. For a pair of residues ij that experiences an attractive interaction (εij < 0), we use the usual form of the LJ potential given by LJ

jij ðrÞ ¼ 4jεij j½ðσ ij =rÞ12 - ðσij =rÞ6 

ð2Þ

Here, σij = (σi þ σj)/2, where σi is the diameter of a sphere with the van der Waals volume of residue i.43 For a pair of residues experiencing repulsive interactions (εij > 0), the potential energy function is given by 8 < 4εij ½ðσij =rÞ12 - ðσij =rÞ6  þ 2εij , if r < r 0 ij LJ ð3Þ jij ðrÞ ¼ : -4εij ½ðσ ij =rÞ12 - ðσ ij =rÞ6 , if r g rij0 where r0ij = 21/6σij. Note that at r = r0ij the attractive and repulsive functions have an equal magnitude of the interactions, i.e., 0 jLJ ij (rij) = εij. The details of εij are given below. The electrostatic interaction potential is given by a simple Debye-H€uckel potential jelij ðrÞ ¼ qi qj expð - r=ξÞ=4πDr

ð4Þ

where qi is the charge of residue i located at the center of the corresponding bead, ξ is the Debye screening length, and D is the dielectric constant of the solvent medium. Here, we set D = 80 equivalent to the dielectric constant of water and ξ = 10 Å corresponding to the physiological salt concentration of 100 mM. Residue charges are set for pH 7, so that qi = þe for Lys and Arg, -e for Asp and Glu, and þ0.5e for His, where e is the elementary charge of a proton. The LJ interaction strengths εij are adapted from the knowledge-based contact potentials derived by Miyazawa and Jernigan (MJ).45 The MJ contact potentials are scaled according to the 2684

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known electrostatic interactions and the second virial coefficient of lysozyme. Specifically, we set εij ¼ λðeij - e0 Þ

ð5Þ

where eij( 0). For both of the crowder sizes, such effects are seen for modest crowder-protein attraction strengths, as shown in Figure 3. A theoretical model based on repulsive interactions such as the effective hard sphere approximation model36 cannot capture this trend even qualitatively. One must introduce the effect of attractive protein-crowder interactions explicitly in a theoretical model. We propose a simple theoretical model as shown below: ΔΔFb ðrc , φ, εa Þ ¼ ΔΔFbSPT ðrc , φÞ þ ΔΔFbatt ðrc , φ, εa Þ

ð9Þ

We note that a similar model was also introduced recently to interpret experimental data on protein association equilibria.41 The stabilizing effect of excluded volume interactions ΔΔFSPT b on protein binding equilibria can be predicted quantitatively by a scaled particle theory (SPT) model without any fit parameters, as we have shown recently.26 This SPT model is based on the assumption that the individual proteins and the bound complex can be represented as spherical objects with an appropriate effective radius. The effective radius reff is calculated on the basis of the protein (complex) volume inaccessible to crowders (see Model and Methods). The predictions of this SPT model were found to be in remarkable agreement with simulated binding affinities over a large range of φ and rc values. The predictions of this model (which are valid for purely repulsive crowding particles) are shown by solid lines in Figure 3. To account for the destabilizing effect of protein-crowder attractions, we augment the SPT model with a mean-field free

is proportional to the number density of crowders, where while κ is a constant which depends on rc and ΔS is the change in accessible protein surface area to crowder particles in going from unbound proteins to a bound protein complex. The term ΔS is expected to account for the difference in the buried surface area for different protein complexes, thereby making the fit parameter κ approximately independent of the complex under study.41 The predictions of this modified SPT (mSPT) model are shown in Figure 3 by dashed lines with the fitted κ/Å = 4.92 (rc = 8 Å) and 7.48 (rc = 16 Å). It appears that κ may have a weak dependence on εa and φ, as predictions of our model utilizing a single value of κ for each crowder size are not in complete quantitative agreement with all the simulation data. Furthermore, for larger εa, the second-order term (µφ2) seems to play a bigger role, judging from the change in the curvature of the binding data. Nonetheless, we find it remarkable that a single fit parameter value (dependent only on rc) can make semiquantitative predictions of crowding induced changes in binding free energy from easily available information about protein complexes. To find out how the critical attraction, εca, for which ΔΔFb = 0, may depend on φ and rc, we plot ΔΔFb as a function of εa in Figure 4. We find that the dependence of ΔΔFb on εa is approximately linear, as shown by the fits (solid lines) to the simulation data (symbols). Further, we notice that, even though ΔΔFb changes with φ, all the constant φ curves converge approximately to a single εa point at which ΔΔFb = 0. This suggests that the critical εa value is independent of the crowder packing fraction. This observation may be used as a marker to find out if in a given experimental system protein-crowder attractive interactions are such that the two competing crowding effects are canceled with each other and in fact may have been observed in previous experiments.25 We note that this observed behavior can also be thought of as an enthalpy-entropy compensation, leading to a net zero crowding effect, because excluded volume interactions are entropic in origin and protein-crowder attractive interactions are mostly enthalpic in nature. Such an enthalpy-entropy compensation due to crowding was first predicted by Douglas and co-workers47 and later confirmed by the experimental work of Jiao et al.41 The critical attraction, εca, can be obtained approximately from the geometry of proteins and protein complexes by linearizing eq 8 and combining with eqs 9 and 10. One can then easily write εca 

ð1 þ YAB - YA - YB Þrc 3 kΔS

ð11Þ

where the subscripts AB, A, and B represent a complex AB and individual A and B proteins, while Y ¼ 3y þ 3y2 þ y3

ð12Þ

εca/kBT

Using Table 1, one obtains = 0.19 (rc = 8 Å) and 0.23 (rc16 Å) for Ubq/UIM1 and 0.19 (rc = 8 Å) and 0.24 (rc = 16 Å) for Cc/CcP complexes, respectively. These values are shown by vertical magenta dashed lines in Figure 4 and are similar to those observed from a convergence in simulation data fits. In addition to the change in binding free energy, crowding can also have some subtle biological effects on the specificity of the protein binding within the bound states. In our previous work on repulsive crowding, we found that the specific bound complexes 2687

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Figure 5. Crowding enhances the fraction of nonspecific bound complexes. Cumulative distributions of bound complexes are shown as a function of dRMS from the experimental structure for Ubq-UIM1 (top panel) and Cc-CcP (bottom panel). Randomly selected specific (dRMS < 5 Å) and nonspecific (dRMS > 10 Å) bound structures are shown with red-green and red-yellow combinations, respectively. The native bound structures are shown with red-blue combination for easy comparison.

are stabilized with respect to transient encounter complexes.26 This is a direct consequence of the larger volume occupied by nonspecific complexes as compared to tightly bound specific complexes. As attractive interactions between protein residues and crowder particles will tend to maximize contact between the two, the bound complex in this case is expected to be stabilized toward nonspecific type, which typically has a larger surface area exposed to crowders. Figure 5 shows the cumulative dRMS distribution as a function of dRMS for bound complexes. dRMS is the measure of similarity between experimental and simulated structures. We also show simulation snapshots of experimentallike (less than 5 Å dRMS) and encounter complexes (10 Å < dRMS < 15 Å) in Figure 5. To facilitate the comparison, native bound structures are shown by blue-red combination and the simulation structures are shown by red-green (specific complexes) and red-yellow (nonspecific complexes). The structures with a dRMS less than 5 Å are very similar to their native structure and are referred to as specific. Complexes with a DRMS greater than 5 Å are very different from their native structure and are said to be nonspecific. At lower εa values, the effect of the crowding is stabilizing, and we observe a slight increase in the population of specific complexes (data not shown), as expected from our previous work on repulsive crowders.26 For εa higher than the critical value for which ΔΔFb > 0, we observe an increase in the population of nonspecific encounter complexes with increasing φ, as shown in Figure 5 for both Ubq/UIM1 and Cc/CcP complexes. As discussed earlier, a decrease in system enthalpy due to protein solvation by attractive crowders favors unbound and less tightly bound structures.

’ CONCLUSIONS The effects of attractive crowder-protein interactions on thermodynamics and structures of protein binding are studied via replica exchange Monte Carlo simulations. Proteins are

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represented at residue level with a transferable energy function developed previously for weakly binding protein complexes,43,44,48,49 while spherical crowders attract residues uniformly but repel other crowders. While the repulsive part of the crowder-protein interactions stabilizes the protein binding which can be described entirely by a scaled particle theory (SPT) model, the attractive interactions destabilize the protein binding which is consistent with previous work.41,50 The competing nature of these interactions results in a critical protein-crowder attraction strength for which the binding free energy becomes identical to that for crowder-free solution. At the attractive strength below the critical attraction, the binding free energy is still lower than that of the crowder-free solution, while above the critical value the effect of attraction dominates the binding events, thereby destabilizing the protein binding. The critical attraction is observed to be mostly independent of the crowder packing fraction over the range studied here. We also observe that the transiently bound encounter complexes are more favored by crowders than the specific complexes owing to their larger exposed surface area. Even though the uniform attractive interactions between spherical crowders and protein residues considered here is a simplification for representing actual protein-crowder interactions, this work presents a detailed study of the effects of attractive protein-crowder interactions on the protein-binding affinity and specificity.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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