New insights into the mechanism of protein-protein association

Association of a protein complex follows a two-step mechanism, with the first step being the formation of an encounter complex that evolves into the final complex. Here, we analyze recent experimental data of the association of TEM1-beta-lactamase with BLIP using theoretical calculations and simulation. We show that the calculated Debye-Hückel energy of interaction for a pair of proteins during association resembles an energy funnel, with the final complex at the minima. All attraction is lost at inter-protein distances of 20 A, or rotation angles of >60 degrees from the orientation of the final complex. For faster-associating protein complexes, the energy funnel deepens and its volume increases. Mutations with the largest impact on association (hotspots for association) have the largest effect on the size and depth of the energy funnel. Analyzing existing evidence, we suggest that the transition state along the association pathway is the formation of the final complex from the encounter complex. Consequently, pairs of proteins forming an encounter complex will tend to dissociate more readily than to evolve into the final complex. Increasing directional diffusion by increasing favorable electrostatic attraction results in a faster forming and slower dissociating encounter complex. The possible applicability of electrostatic calculations for protein-protein docking is discussed.     

Electrostatic contribution to the binding stability of protein-protein complexes

To investigate roles of electrostatic interactions in protein binding stability, electrostatic calculations were carried out on a set of 64 mutations over six protein-protein complexes. These mutations alter polar interactions across the interface and were selected for putative dominance of electrostatic contributions to the binding stability. Three protocols of implementing the Poisson-Boltzmann model were tested. In vdW4 the dielectric boundary between the protein low dielectric and the solvent high dielectric is defined as the protein van der Waals surface and the protein dielectric constant is set to 4. In SE4 and SE20, the dielectric boundary is defined as the surface of the protein interior inaccessible to a 1.4-A solvent probe, and the protein dielectric constant is set to 4 and 20, respectively. In line with earlier studies on the barnase-barstar complex, the vdW4 results on the large set of mutations showed the closest agreement with experimental data. The agreement between vdW4 and experiment supports the contention of dominant electrostatic contributions for the mutations, but their differences also suggest van der Waals and hydrophobic contributions. The results presented here will serve as a guide for future refinement in electrostatic calculation and inclusion of nonelectrostatic effects.     

Exploring the charge space of protein-protein association: a proteomic study

The rate of association of a protein complex is a function of an intrinsic basal rate and of the magnitude of electrostatic steering. In the present study we analyze the contribution of electrostatics towards the association rate of proteins in a database of 68 transient hetero-protein-protein complexes. Our calculations are based on an upgraded version of the computer algorithm PARE, which was shown to successfully predict the impact of mutations on k(on) by calculating the difference in Columbic energy of interaction of a pair of proteins. HyPare (http://bip.weizmann.ac.il/HyPare), automatically calculates the impact of mutations on a per-residue basis for all residues of a protein-protein interaction, achieving a precision similar to that of PARE. Our calculations show that electrostatics play a marginal role (<10 fold) in determining the rate of association for about half of the complexes in the database. Strong electrostatic steering, which results in an increase of over 100-fold in k(on), was calculated for about 25% of the complexes. Applying HyPare to all 68 complexes in the database shows that a small number of residues are hotspots for association. About 40% of the hotspots are calculated to increase the rate of association upon mutation, and thus increase binding affinity. This is a much higher ratio than found for hotspots for dissociation, where the large majority cause weaker binding. About 40% of the hotspots are located outside the physical boundary of the binding site, making them ideal candidates for protein engineering. Our data shows that a majority of protein-protein complexes are not optimized for fast association. Hotspots are not evenly distributed between all types of amino acids. About 75% of all hotspots are of charged residues. This is understandable, as a charge-reverse mutant changes the total charge by 2. The small number of hydrophobic residues that are hotspots upon mutation probably relates to their location and surrounding. For 18 out of the 68 complexes in the database, experimental values of k(on) are available. For these, a basal rate of association was calculated to be in the range of 10(4)M(-1)s(-1) to 10(7)M(-1)s(-1). Some of these rates were verified independently from experimental mutant data. The basal rates were correlated with the size of the proteins and the shape of the interface.     

Electrostatic properties of cowpea chlorotic mottle virus and cucumber mosaic virus capsids

Electrostatic properties of cowpea chlorotic mottle virus (CCMV) and cucumber mosaic virus (CMV) were investigated using numerical solutions to the Poisson-Boltzmann equation. Experimentally, it has been shown that CCMV particles swell in the absence of divalent cations when the pH is raised from 5 to 7. CMV, although structurally homologous, does not undergo this transition. An analysis of the calculated electrostatic potential confirms that a strong electrostatic repulsion at the calcium-binding sites in the CCMV capsid is most likely the driving force for the capsid swelling process during the release of calcium. The binding interaction between the encapsulated genome material (RNA) inside of the capsid and the inner capsid shell is weakened during the swelling transition. This probably aids in the RNA release process, but it is unlikely that the RNA is released through capsid openings due to unfavorable electrostatic interaction between the RNA and capsid inner shell residues at these openings. Calculations of the calcium binding energies show that Ca(2+) can bind both to the native and swollen forms of the CCMV virion. Favorable binding to the swollen form suggests that Ca(2+) ions can induce the capsid contraction and stabilize the native form.     

Ribosome motions modulate electrostatic properties

The electrostatic properties of the 70S ribosome of Thermus thermophilus were studied qualitatively by solving the Poisson-Boltzmann (PB) equation in aqueous solution and with physiological ionic strength. The electrostatic potential was calculated for conformations of the ribosome derived by recent normal mode analysis (Tama, F., et al. Proc Natl Acad Sci USA 2003 100, 9319-9323) of the ratchet-like reorganization that occurs during translocation (Frank, J.; Agrawal, R. K. Nature 2000 406, 318-322). To solve the PB equation, effective parameters (charges and radii), applicable to a highly charged backbone model of the ribosome, were developed. Regions of positive potential were found at the binding site of the elongation factors G and Tu, as well as where the release factors bind. Large positive potential areas are especially pronounced around the L11 and L6 proteins. The region around the L1 protein is also positively charged, supporting the idea that L1 may interact with the E-site tRNA during its release from the ribosome after translocation. Functional rearrangement of the ribosome leads to electrostatic changes which may help the translocation of the tRNAs during the elongation stage.     

Do electrostatic interactions destabilize protein–nucleic acid binding?

The negatively charged phosphates of nucleic acids are often paired with positively charged residues upon binding proteins. It was thus counter-intuitive when previous Poisson-Boltzmann (PB) calculations gave positive energies from electrostatic interactions, meaning that they destabilize protein-nucleic acid binding. Our own PB calculations on protein-protein binding have shown that the sign and the magnitude of the electrostatic component are sensitive to the specification of the dielectric boundary in PB calculations. A popular choice for the boundary between the solute low dielectric and the solvent high dielectric is the molecular surface; an alternative is the van der Waals (vdW) surface. In line with results for protein-protein binding, in this article, we found that PB calculations with the molecular surface gave positive electrostatic interaction energies for two protein-RNA complexes, but the signs are reversed when the vdW surface was used. Therefore, whether destabilizing or stabilizing effects are predicted depends on the choice of the dielectric boundary. The two calculation protocols, however, yielded similar salt effects on the binding affinity. Effects of charge mutations differentiated the two calculation protocols; PB calculations with the vdW surface had smaller deviations overall from experimental data.     

Electrostatic interaction between RNA and protein capsid in cowpea chlorotic mottle virus simulated by a coarse-grain RNA model and a Monte Carlo approach

Although many viruses have been crystallized and the protein capsid structures have been determined by x-ray crystallography, the nucleic acids often cannot be resolved. This is especially true for RNA viruses. The lack of information about the conformation of DNA/RNA greatly hinders our understanding of the assembly mechanism of various viruses. Here we combine a coarse-grain model and a Monte Carlo method to simulate the distribution of viral RNA inside the capsid of cowpea chlorotic mottle virus. Our results show that there is very strong interaction between the N-terminal residues of the capsid proteins, which are highly positive charged, and the viral RNA. Without these residues, the binding energy disfavors the binding of RNA by the capsid. The RNA forms a shell close to the capsid with the highest densities associated with the capsid dimers. These high-density regions are connected to each other in the shape of a continuous net of triangles. The overall icosahedral shape of the net overlaps with the capsid subunit icosahedral organization. Medium density of RNA is found under the pentamers of the capsid. These findings are consistent with experimental observations.     

Electrostatic steering enhances the rate of cAMP binding to phosphodiesterase: Brownian dynamics modeling

Signaling in cells often involves co‐localization of the signaling molecules. Most experimental evidence has shown that intracellular compartmentalization restricts the range of action of the second messenger, 3'‐5'‐cyclic adenosine monophosphate (cAMP), which is degraded by phosphodiesterases (PDEs). The objective of this study is to understand the details of molecular encounter that may play a role in efficient operation of the cAMP signaling apparatus. The results from electrostatic potential calculations and Brownian dynamics simulations suggest that positive potential of the active site from PDE enhances capture of diffusing cAMP molecules. This electrostatic steering between cAMP and the active site of a PDE plays a major role in the enzyme‐substrate encounter, an effect that may be of significance in sequestering cAMP released from a nearby binding site or in attracting more freely diffusing cAMP molecules.     

Modelling the three-dimensional structure and electrostatic potential field of the two Cu,Zn superoxide dismutase variants from Xenopus laevis

The crystallographic structure of bovine superoxide dismutase has been used as a template for the graphic reconstruction of the three-dimensional structures of the two Xenopus laevis variants (Schininà, M.E. et al. Arch. Biochem. Biophys. 272:507-515, 1989). In these models the structure-essential residues maintain their position and their structural role, and the interactions between the subunits and the close packing within the beta-barrel are maintained with conservative substitutions and even increased with "aromatic pairs." Because of the same topological motif and surface location of charges, arising from the model building of the two variants with respect to the bovine enzyme, we have calculated the electrostatic potential fields around the models of the two Xenopus laevis variants by numerically solving the Poisson-Boltzmann equation. We show that conservation of a specific space-relationship of charges maintains the potential field pattern already observed in the bovine enzyme, where a negative potential field surrounds the protein surface and specific positive regions wrap up the copper center active site. This electrostatic potential field distribution supports the idea that electrostatic interactions control, like in the bovine enzyme, the mechanism of enzyme-substrate recognition in the Xenopus laevis Cu,Zn superoxide dismutases, suggesting that coordinated mutation of charged residues has occurred in the evolution of this enzyme.     

Protein–protein association rates captured in a single geometric parameter

Understanding factors that drive protein–protein association is of fundamental importance. We show that a single geometric parameter in crystal structures of protein–protein complexes, the angle between the electric dipole of one subunit and the partner‐generated electric field at the same subunit, linearly correlates with experimentally determined protein–protein association rates. Imprint of a dynamic kinetic process in a single static geometric parameter, associated with mutual electrostatic orientation of subunits in protein–protein complexes, is elegant and demonstrates the universality of electrostatic steering in attenuating protein–protein association rates. That the essence of a complex phenomenon could be captured by properties of the final crystal structure of the complex implies that the electrostatic orientations of protein subunits in crystal structures and the associated transition states are nearly identical. Further, the cosine of the angle, alone, is shown to be sufficient in predicting association rate constants, with accuracies comparable to currently available predictors that use more intricate methodologies. Our results offer mechanistic insights and could be useful in development of coarse‐grained models. Proteins 2015; 83:1557–1562. © 2015 Wiley Periodicals, Inc.     

Electrostatic contributions to protein-protein interactions: fast energetic filters for docking and their physical basis

The methods of continuum electrostatics are used to calculate the binding free energies of a set of protein-protein complexes including experimentally determined structures as well as other orientations generated by a fast docking algorithm. In the native structures, charged groups that are deeply buried were often found to favor complex formation (relative to isosteric nonpolar groups), whereas in nonnative complexes generated by a geometric docking algorithm, they were equally likely to be stabilizing as destabilizing. These observations were used to design a new filter for screening docked conformations that was applied, in conjunction with a number of geometric filters that assess shape complementarity, to 15 antibody-antigen complexes and 14 enzyme-inhibitor complexes. For the bound docking problem, which is the major focus of this paper, native and near-native solutions were ranked first or second in all but two enzyme-inhibitor complexes. Less success was encountered for antibody-antigen complexes, but in all cases studied, the more complete free energy evaluation was able to identify native and near-native structures. A filter based on the enrichment of tyrosines and tryptophans in antibody binding sites was applied to the antibody-antigen complexes and resulted in a native and near-native solution being ranked first and second in all cases. A clear improvement over previously reported results was obtained for the unbound antibody-antigen examples as well. The algorithm and various filters used in this work are quite efficient and are able to reduce the number of plausible docking orientations to a size small enough so that a final more complete free energy evaluation on the reduced set becomes computationally feasible.     

Effect of crowding on protein-protein association rates: fundamental differences between low and high mass crowding agents

Physiological media constitutes a crowded environment that serves as the field of action for protein-protein interaction in vivo. Measuring protein-protein interaction in crowded solutions can mimic this environment. In this work we follow the process of protein-protein association and its rate constants (k(on)) of the beta-lactamase (TEM)-beta-lactamase inhibitor protein (BLIP) complex in crowded solution using both low and high molecular mass crowding agents. In all crowded solutions (0-40% (w/w) of ethylene glycol (EG), poly(ethylene glycol) (PEG) 200, 1000, 3350, 8000 Da Ficoll-70 and Haemaccel the measured absolute k(on), but not k(off) values, were found to be slower as compared to buffer. However, there is a fundamental difference between low and high mass crowding agents. In the presence of low mass crowding agents and Haemaccel k(on) depends inversely on the solution viscosity. In high mass polymer solutions k(on) changes only slightly, even at viscosities 12-fold higher than water. The border between low and high molecular mass polymers is sharp and is dictated by the ratio between the polymer length (L) and its persistence length (Lp). Polymers that are long enough to form a flexible coil (L/Lp > 2) behave as high molecular mass polymers and those who are unable to do so (L/Lp < 2) behave as low molecular mass polymers. We concluded that although polymers solution are crowded, this property is not uniform; i.e. there are areas in the solution that contain bulk water, and in these areas proteins can diffuse and associate almost as if they were in diluted environment. This porous medium may be taken as mimicking some aspects of the cellular environment, where many of the macromolecules are organized along membranes and the cytoskeleton. To determine the contribution of electrostatic attraction between proteins in crowded milieu, we followed k(on) of wt-TEM and three BLIP analogs with up to 100-fold increased values of k(on) due to electrostatic steering. Faster associating BLIP variants keep their relative advantage in all crowded solutions, including Haemaccel. This result suggests that faster associating protein complexes keep their advantage also in complex environment.     

The kinetics of protein-protein recognition

We examine a simple kinetic model for association that incorporates the basic features of protein-protein recognition within the rigid body approximation, that is, when no large conformation change occurs. Association starts with random collision at the rate k_coll predicted by the Einstein-Smoluchowski equation. This creates an encounter pair that can evolve into a stable complex if and only if the two molecules are correctly oriented and positioned, which has a probability p_r. In the absence of long-range interactions, the bimolecular rate of association is p_r k_coll. Long-range electrostatic interactions affect both k_coll and p_r. The collision rate is multiplied by q_t, a factor larger than 1 when the molecules carry net charges of opposite sign as coulombic attraction makes collisions more frequent, and less than 1 in the opposite case. The probability p_r is multiplied by a factor q_r that represents the steering effect of electric dipoles, which preorient the molecules before they collide. The model is applied to experimental data obtained by Schreiber and Fersht (Nat. Struct. Biol. 3:427–431, 1996) on the kinetics of barnase-barstar association. When long-range electrostatic interactions are fully screened or mutated away, q_tq_r ≈1, and the observed rate of productive collision is p_r k_coll ≈10⁵ M⁻¹ · s⁻¹. Under these conditions, p_r ≈1.5 · 10⁻⁵ is determined by geometric constraints corresponding to a loss of rotational freedom. Its value is compatible with computer docking simulations and implies a rotational entropy loss ΔS_rot ≈ 22 e.u. in the transition state. At low ionic strength, long-range electrostatic interactions accelerate barnase-barstar association by a factor q_tq_rof up to 10⁵ as favorable charge-charge and charge-dipole interactions work together to make it much faster than free diffusion would allow. Proteins 28:153–161, 1997. © 1997 Wiley-Liss Inc.     

On the protein–protein diffusional encounter complex

When two proteins diffuse together to form a bound complex, an intermediate is formed at the end‐point of diffusional association which is called the encounter complex. Its characteristics are important in determining association rates, yet its structure cannot be directly observed experimentally. Here, we address the problem of how to construct the ensemble of three‐dimensional structures which constitute the protein–protein diffusional encounter complex using available experimental data describing the dependence of protein association rates on mutation and on solvent ionic strength and viscosity. The magnitude of the association rates is fitted well using a variety of definitions of encounter complexes in which the two proteins are located at up to about 17 Å root‐mean‐squared distance from their relative arrangement in the bound complex. Analysis of the ionic strength dependence of bimolecular association rates shows that this is determined to a greater extent by the (protein charge) – (salt ion) separation distance than by the protein–protein charge separation distance. Consequently, ionic strength dependence of association rates provides little information about the geometry of the encounter complex. On the other hand, experimental data on electrostatic rate enhancement, mutation and viscosity dependence suggest a model of the encounter complex in which the two proteins form a subset of the contacts present in the bound complex and are significantly desolvated. Copyright © 1999 John Wiley & Sons, Ltd.     

Association and dissociation kinetics of colicin E3 and immunity protein 3: convergence of theory and experiment

The rapid binding of cytotoxic colicin E3 by its cognate immunity protein Im3 is essential in safeguarding the producing cell. The X-ray structure of the E3/Im3 complex shows that the Im3 molecule interfaces with both the C-terminal ribonuclease (RNase) domain and the N-terminal translocation domain of E3. The association and dissociation rates of the RNase domain and Im3 show drastically different sensitivities to ionic strength, as previously rationalized for electrostatically enhanced diffusion-limited protein-protein associations. Relative to binding to the RNase domain, binding to full-length E3 shows a comparable association rate but a significantly lower dissociation rate. This outcome is just what was anticipated by a theory for the binding of two linked domains to a protein. The E3/Im3 system thus provides a powerful paradigm for the interplay of theory and experiment.     

Structural characterisation and functional significance of transient protein-protein interactions

Protein-protein complexes that dissociate and associate readily, often depending on the physiological condition or environment, play an important role in many biological processes. In order to characterise these "transient" protein-protein interactions, two sets of complexes were collected and analysed. The first set consists of 16 experimentally validated "weak" transient homodimers, which are known to exist as monomers and dimers at physiological concentration, with dissociation constants in the micromolar range. A set of 23 functionally validated transient (i.e. intracellular signalling) heterodimers comprise the second set. This set includes complexes that are more stable, with nanomolar binding affinities, and require a molecular trigger to form and break the interaction. In comparison to more stable homodimeric complexes, the weak homodimers demonstrate smaller contact areas between protomers and the interfaces are more planar and polar on average. The physicochemical and geometrical properties of these weak homodimers more closely resemble those of non-obligate hetero-oligomeric complexes, whose components can exist either as monomers or as complexes in vivo. In contrast to the weak transient dimers, "strong" transient dimers often undergo large conformational changes upon association/dissociation and are characterised with larger, less planar and sometimes more hydrophobic interfaces. From sequence alignments we find that the interface residues of the weak transient homodimers are generally more conserved than surface residues, consistent with being constrained to maintain the protein-protein interaction during evolution. Protein families that include members with different oligomeric states or structures are identified, and found to exhibit a lower sequence conservation at the interface. The results are discussed in terms of the physiological function and evolution of protein-protein interactions.     

Hydrophobic folding units at protein-protein interfaces: implications to protein folding and to protein-protein association.

A hydrophobic folding unit cutting algorithm, originally developed for dissecting single-chain proteins, has been applied to a dataset of dissimilar two-chain protein-protein interfaces. Rather than consider each individual chain separately, the two-chain complex has been treated as a single chain. The two-chain parsing results presented in this work show hydrophobicity to be a critical attribute of two-state versus three-state protein-protein complexes. The hydrophobic folding units at the interfaces of two-state complexes suggest that the cooperative nature of the two-chain protein folding is the outcome of the hydrophobic effect, similar to its being the driving force in a single-chain folding. In analogy to the protein-folding process, the two-chain, two-state model complex may correspond to the formation of compact, hydrophobic nuclei. On the other hand, the three-state model complex involves binding of already folded monomers, similar to the association of the hydrophobic folding units within a single chain. The similarity between folding entities in protein cores and in two-state protein-protein interfaces, despite the absence of some chain connectivities in the latter, indicates that chain linkage does not necessarily affect the native conformation. This further substantiates the notion that tertiary, non-local interactions play a critical role in protein folding. These compact, hydrophobic, two-chain folding units, derived from structurally dissimilar protein-protein interfaces, provide a rich set of data useful in investigations of the role played by chain connectivity and by tertiary interactions in studies of binding and of folding. Since they are composed of non-contiguous pieces of protein backbones, they may also aid in defining folding nuclei.     

Internal dynamics and ionization states of the macrophage migration inhibitory factor: comparison between wild-type and mutant forms

The macrophage migration inhibitory factor (MIF) is a cytokine that shares a common structural architecture and catalytic strategy with three isomerases: 4-oxalocrotonate tautomerase, 5-carboxymethyl-2-hydroxymuconate isomerase, and D-dopachrome tautomerase. A highly conserved N-terminal proline acts as a base-acid during the proton transfer reaction catalyzed by these enzymes. Such unusual catalytic strategy appears to be possible only due to the N-terminal proline pK(a) shifted to 5.0-6.0 units. Mutations of this residue result in a significant decrease of the catalytic activity of MIF. Two hypotheses have been proposed to explain the catalytic inefficiency of MIF: the lower basicity of primary amines with regard to secondary ones and the increased flexibility resulting from the replacement of a proline by residues like glycine. To investigate that, we have performed molecular dynamics simulations of MIF wild-type and its mutant P1G, as well as calculated the protonation properties of several mutant forms. It was found that the N-terminal glycine does not show larger fluctuations compared to proline, but the former residue is more exposed to the solvent throughout the simulations. The apparent pK(a) of these residues displays very little change (as expected from the structural rigidity of MIF) and is not significantly affected by the surrounding ionizable residues. Instead, the hydrophobic character of the active site seems to be the main factor in determining the pKa of the N-terminal residue and the catalytic efficiency of MIF.     

Predicting kinetic constants of protein-protein interactions based on structural properties

Elucidating kinetic processes of protein–protein interactions (PPI) helps to understand how basic building blocks affect overall behavior of living systems. In this study, we used structure‐based properties to build predictive models for kinetic constants of PPI. A highly diverse PPI dataset, protein–protein kinetic interaction data and structures (PPKIDS), was built. PPKIDS contains 62 PPI with complex structures and kinetic constants measured experimentally. The influence of structural properties on kinetics of PPI was studied using 35 structure‐based features, describing different aspects of complex structures. Linear models for the prediction of kinetic constants were built by fitting with selected subsets of structure‐based features. The models gave correlation coefficients of 0.801, 0.732, and 0.770 for k_off, k_on, and K_d, respectively, in leave‐one‐out cross validations. The predictive models reported here use only protein complex structures as input and can be generally applied in PPI studies as well as systems biology modeling. Our study confirmed that different properties play different roles in the kinetic process of PPI. For example, k_on was affected by overall structural features of complexes, such as the composition of secondary structures, the change of translational and rotational entropy, and the electrostatic interaction; while k_off was determined by interfacial properties, such as number of contacted atom pairs per 100 Ų. This information provides useful hints for PPI design. Proteins 2010;79:720–734. © 2010 Wiley‐Liss, Inc.