Simulation of the diffusional association of barnase and barstar.

The rate of protein association places an upper limit on the response time due to protein interactions, which, under certain circumstances, can be diffusion-controlled. Simulations of model proteins show that diffusion-limited association rates are approximately 10(6)-10(7) M-1 s-1 in the absence of long-range forces (Northrup, S. H., and H. P. Erickson. 1992. Kinetics of protein-protein association explained by Brownian dynamics computer simulations. Proc. Natl. Acad. Sci. U.S.A. 89:3338-3342). The measured association rates of barnase and barstar are 10(8)-10(9) M-1 s-1 at 50 mM ionic strength, and depend on ionic strength (Schreiber, G., and A. R. Fersht. 1996. Rapid, electrostatically assisted association of proteins. Nat. Struct. Biol. 3:427-431), implying that their association is electrostatically facilitated. We report Brownian dynamics simulations of the diffusional association of barnase and barstar to compute association rates and their dependence on ionic strength and protein mutation. Crucial to the ability to reproduce experimental rates is the definition of encounter complex formation at the endpoint of diffusional motion. Simple definitions, such as a required root mean square (RMS) distance to the fully bound position, fail to explain the large influence of some mutations on association rates. Good agreement with experiments could be obtained if satisfaction of two intermolecular residue contacts was required for encounter complex formation. In the encounter complexes, barstar tends to be shifted from its position in the bound complex toward the guanine-binding loop on barnase.     

Diffusional encounter of barnase and barstar

We present an analysis of trajectories from Brownian dynamics simulations of diffusional protein-protein encounter for the well-studied system of barnase and barstar. This analysis reveals details about the optimal association pathways, the regions of the encounter complex, possible differences of the pathways for dissociation and association, the coupling of translational and rotation motion, and the effect of mutations on the trajectories. We found that a small free-energy barrier divides the energetically most favorable region into a region of the encounter complex above the barnase binding interface and a region around a second energy minimum near the RNA binding loop. When entering the region of the encounter complex from the region near the RNA binding loop, barstar has to change its orientation to increase the electrostatic attraction between the proteins. By concentrating the analysis on the successful binding trajectories, we found that the region of the second minimum is not essential for the binding of barstar to barnase. Nevertheless, this region may be helpful to steer barstar into the region of the encounter complex. When applying the same analysis to several barnase mutants, we found that single mutations may drastically change the free-energy landscape and may significantly alter the population of the two minima. Therefore, certain protein-protein pairs may require careful adaptation of the positions of encounter and transition states when interpreting mutation effects on kinetic rates of association and/or dissociation.     

How optimal are the binding energetics of barnase and barstar?

The extracellular ribonuclease barnase and its intracellular inhibitor barstar bind fast and with high affinity. Although extensive experimental and theoretical studies have been carried out on this system, it is unclear what the relative importance of different contributions to the high affinity is and whether binding can be improved through point mutations. In this work, we first applied Poisson-Boltzmann electrostatic calculations to 65 barnase-barstar complexes with mutations in both barnase and barstar. The continuum electrostatic calculations with a van der Waals surface dielectric boundary definition result in the electrostatic interaction free energy providing the dominant contribution favoring barnase-barstar binding. The results show that the computed electrostatic binding free energy can be improved through mutations at W44/barstar and E73/barnase. Furthermore, the determinants of binding affinity were quantified by applying COMparative BINding Energy (COMBINE) analysis to derive quantitative structure-activity relationships (QSARs) for the 65 complexes. The COMBINE QSAR model highlights approximately 20 interfacial residue pairs as responsible for most of the differences in binding affinity between the mutant complexes, mainly due to electrostatic interactions. Based on the COMBINE model, together with Brownian dynamics simulations to compute diffusional association rate constants, several mutants were designed to have higher binding affinities than the wild-type proteins.     

Brownian dynamics simulation of the association of Bacillus amyloliquefaciens ribonuclease (barnase) and Bacillus intermedius ribonuclease (binase) with barstar

A comparative study of the association of two ribonucleases, barnase and binase, with the polypeptide inhibitor barstar has been performed by the Brownian dynamics simulation method. It was shown that the method adequately reproduced the dependence of the association rate on pH and ionic strength of solution and the influence of mutations of some ribonuclease amino acids. Two types of energetically favorable complexes of binase-barstar encounter were determined. In the type I complex, the amino acids of binase active center take part in the complex formation. In the second complex, the active center is free. It was supposed that the temporary binding of barstar into complex of type II is competitive relative to the inhibition reaction. This can partially explain the decrease in the rate of binase inhibition as compared with the corresponding reaction of barnase.     

A comparative study of the interaction of Bacillus amyloliquefaciens ribonuclease (barnase) and Bacillus intermedius ribonuclease (binase) with barstar by brownian dynamics simulation

A comparative study of the interaction of two RNases (binase and barnase) with the polypeptide inhibitor barstar was performed by Brownian dynamics simulation. It was demonstrated that this method adequately reproduced the dependence of the association rate on the pH of solution as well as the effect of mutations at individual amino acid residues on the inhibition of barnase by barstar. Two types of energy-favorable binase-barstar encounter complexes were found. In type I complex, the amino acid residues of the binase active center are involved in formation of the complex; in type II complex, the active center remains free. It is suggested that temporary binding of free barstar into type II complex competes with the inhibition reaction. Presumably, this explains the decrease in the rate of binase inhibition by barstar as compared with the analogous reaction of barnase.     

Biomolecular diffusional association

The primary method for the computational study of biomolecular diffusional association is Brownian dynamics. Recent work has seen advances in the efficiency of computing association rates and in the accuracy of simulation models. New areas to which Brownian dynamics has been applied include protein polymerisation and protein adsorption to a surface. There has recently been particularly intense study of protein-protein association, and Brownian dynamics, together with other theoretical and experimental approaches, has led to new insights into the determinants of protein-protein binding kinetics.     

Association and dissociation kinetics of bobwhite quail lysozyme with monoclonal antibody HyHEL-5

The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and its complexes with various species-variant and mutant lysozymes have been the subject of considerable experimental and theoretical investigation. The affinity of HyHEL-5 for bobwhite quail lysozyme (BWQL) is over 1000-fold lower than its affinity for the original antigen, hen egg lysozyme (HEL). This difference is believed to arise almost entirely from the replacement in BWQL of the structural and energetic epitope residue Arg68 by lysine. In this study, the association and dissociation kinetics of BWQL with HyHEL-5 were investigated under a variety of conditions and compared with previous results for HEL. HyHEL-5-BWQL association follows a bimolecular mechanism and the dissociation of the antibody-antigen complex is a first-order process. Changes in ionic strength (from 27 to 500 mM) and pH (from 6.0 to 10.0) produced about a 2-fold change in the association and dissociation rates. The effect of viscosity modifiers on the association reaction was also studied. The large difference in the HEL and BWQL affinities for HyHEL-5 is essentially due to differences in the dissociation rate constant.     

Dissection of binding interactions in the complex between the anti-lysozyme antibody HyHEL-63 and its antigen

Alanine-scanning mutagenesis, X-ray crystallography, and double mutant cycles were used to characterize the interface between the anti-hen egg white lysozyme (HEL) antibody HyHEL-63 and HEL. Eleven HEL residues in contact with HyHEL-63 in the crystal structure of the antigen-antibody complex, and 10 HyHEL-63 residues in contact with HEL, were individually truncated to alanine in order to determine their relative contributions to complex stabilization. The residues of HEL (Tyr20, Lys96, and Lys97) most important for binding HyHEL-63 (Delta G(mutant) - Delta G(wild type) > 3.0 kcal/mol) form a contiguous patch at the center of the surface contacted by the antibody. Hot spot residues of the antibody (Delta Delta G > 2.0 kcal/mol) are organized in two clusters that juxtapose hot spot residues of HEL, resulting in energetic complementarity across the interface. All energetically critical residues are centrally located, shielded from solvent by peripheral residues that contribute significantly less to the binding free energy. Although HEL hot spot residues Lys96 and Lys97 make similar interactions with antibody in the HyHEL-63/HEL complex, alanine substitution of Lys96 results in a nearly 100-fold greater reduction in affinity than the corresponding mutation in Lys97. To understand the basis for this marked difference, we determined the crystal structures of the HyHEL-63/HEL Lys96Ala and HyHEL-63/HEL Lys97Ala complexes to 1.80 and 1.85 A resolution, respectively. Whereas conformational changes in the proteins and differences in the solvent networks at the mutation sites appear too small to explain the observed affinity difference, superposition of free HEL in different crystal forms onto bound HEL in the wild type and mutant HyHEL-63/HEL complexes reveals that the side-chain conformation of Lys96 is very similar in the various structures, but that the Lys97 side chain displays considerable flexibility. Accordingly, a greater entropic penalty may be associated with quenching the mobility of the Lys97 than the Lys96 side chain upon complex formation, reducing binding. To further dissect the energetics of specific interactions in the HyHEL-63/HEL interface, double mutant cycles were constructed to measure the coupling of 13 amino acid pairs, 11 of which are in direct contact in the crystal structure. A large coupling energy, 3.0 kcal/mol, was found between HEL residue Lys97 and HyHEL-63 residue V(H)Asp32, which form a buried salt bridge surrounded by polar residues of the antigen. Thus, in contrast to protein folding where buried salt bridges are generally destabilizing, salt bridges in protein-protein interfaces, whose residual composition is more hydrophilic than that of protein interiors, may contribute significantly to complex stabilization.     

Association and dissociation kinetics of anti-hen egg lysozyme monoclonal antibodies HyHEL-5 and HyHEL-10.

The immunoglobulin G1 (IgG1) kappa antibodies HyHEL-5 and HyHEL-10 interact with nonoverlapping epitopes on hen egg lysozyme (HEL); the HyHEL-5/HEL interface has two energetically and structurally important salt links, whereas the HyHEL-10/HEL interface involves predominantly hydrogen bonds and van der Waals interactions. The kinetics of association and dissociation of antibodies HyHEL-5 and HyHEL-10 with HEL under a variety of conditions were investigated in this study. The association of each antibody with HEL follows second-order kinetics. The association process is significantly diffusion-limited, as indicated by the viscosity dependence of the interaction of both antibodies with HEL, although detailed energetics suggest that the association process may be more complex. The association rate constant for the HyHEL-5/HEL system is within a factor of 2 of the modified Smoluchowski estimate for proteins of this size, whereas HyHEL-10 interacts with HEL with an association rate an order of magnitude lower. The association reactions are insensitive to ionic strength, showing only a twofold decrease in the association rate constant when the ionic strength was increased from 27 mM to 500 mM. Interestingly, the association rate constant for the interaction of HyHEL-5 with HEL varies with pH in the range 6.0-10.0, whereas HyHEL-10/HEL association is not affected by pH in the same range. The dissociation of the HyHEL-5/HEL and HyHEL-10/HEL complexes follow first-order kinetics with half-lives at 25 degrees C of approximately 3,150 s and approximately 21,660 s, respectively.     

Involvement of water molecules in the association of monoclonal antibody HyHEL-5 with bobwhite quail lysozyme.

Fluorescence polarization spectroscopy and isothermal titration calorimetry were used to study the influence of osmolytes on the association of the anti-hen egg lysozyme (HEL) monoclonal antibody HyHEL-5 with bobwhite quail lysozyme (BWQL). BWQL is an avian species variant with an Arg-->Lys mutation in the HyHEL-5 epitope, as well as three other mutations outside the HyHEL-5 structural epitope. This mutation decreases the equilibrium association constant of HyHEL-5 for BWQL by over 1000-fold as compared to HEL. The three-dimensional structure of this complex has been obtained recently. Fluorescein-labeled BWQL, obtained by labeling at pH 7.5 and purified by hydrophobic interaction chromatograpy, bound HyHEL-5 with an equilibrium association constant close to that determined for unlabeled BWQL by isothermal titration calorimetry. Fluorescence titration, stopped-flow kinetics, and isothermal titration calorimetry experiments using various concentrations of the osmolytes glycerol, ethylene glycol, and betaine to perturb binding gave a lower limit of the uptake of approximately 6-12 water molecules upon formation of the HyHEL-5/BWQL complex.     

Structural consequences of mutations in interfacial Tyr residues of a protein antigen-antibody complex. The case of HyHEL-10-HEL

Tyrosine is an important amino acid in protein-protein interaction hot spots. In particular, many Tyr residues are located in the antigen-binding sites of antibodies and endow high affinity and high specificity to these antibodies. To investigate the role of interfacial Tyr residues in protein-protein interactions, we performed crystallographic studies and thermodynamic analyses of the interaction between hen egg lysozyme (HEL) and the anti-HEL antibody HyHEL-10 Fv fragment. HyHEL-10 has six Tyr residues in its antigen-binding site, which were systematically mutated to Phe and Ala using site-directed mutagenesis. The crystal structures revealed several critical roles for these Tyr residues in the interaction between HEL and HyHEL-10 as follows: 1) the aromatic ring of Tyr-50 in the light chain (LTyr-50) was important for the correct ternary structure of variable regions of the immunoglobulin light chain and heavy chain and of HEL; 2) deletion of the hydroxyl group of Tyr-50 in the heavy chain (HTyr-50) resulted in structural changes in the antigen-antibody interface; and 3) the side chains of HTyr-33 and HTyr-53 may help induce fitting of the antibody to the antigen. Hot spot Tyr residues may contribute to the high affinity and high specificity of the antigen-antibody interaction through a diverse set of structural and thermodynamic interactions.     

Downhill binding energy surface of the barnase–barstar complex

We have employed biased molecular dynamics simulations in explicit solvent to characterize the one‐dimensional potential of mean force for the dissociation process of the barnase–barstar protein–protein complex. Unbinding of barstar from wild‐type barnase was compared with dissociation from four charge‐deletion mutants of barnase. Interestingly, we find in all cases that unbinding of barnase and barstar is an uphill process on a smooth, tilted energy landscape. The total free energy difference between the dissociated and bound state was similar for wild‐type barnase–barstar and for the R87A mutant of barnase. The values for the three other mutant barnase mutants K27A, R59A, and R83Q were only about half as much. Besides, we have analyzed the conformational dynamics of important residues at the barnase–barstar interface. In the bound state, their conformational fluctuations are reduced relatively to the free state because of the formation of intermolecular contacts. Interestingly, we find that some residues also show decreased mobility at intermediate stages of the unbinding process suggesting that these residues may be involved in the first contacts being formed on binding. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 977–985, 2010.     

Brownian dynamics study of the association between the 70S ribosome and elongation factor G

Protein synthesis on the ribosome involves a number of external protein factors that bind at its functional sites. One key factor is the elongation factor G (EF-G) that facilitates the translocation of transfer RNAs between their binding sites, as well as advancement of the messenger RNA by one codon. The details of the EF-G/ribosome diffusional encounter and EF-G association pathway still remain unanswered. Here, we applied Brownian dynamics methodology to study bimolecular association in the bacterial EF-G/70S ribosome system. We estimated the EF-G association rate constants at 150 and 300 mM monovalent ionic strengths and obtained reasonable agreement with kinetic experiments. We have also elucidated the details of EF-G/ribosome association paths and found that positioning of the L11 protein of the large ribosomal subunit is likely crucial for EF-G entry to its binding site.     

Computation of FRAP recovery times for linker histone – chromatin binding on the basis of Brownian dynamics simulations

BackgroundFluorescence recovery after photobleaching (FRAP) studies can provide kinetic information about proteins in cells. Single point mutations can significantly affect the binding kinetics of proteins and result in variations in the recovery half time (t₅₀) measured in FRAP experiments. FRAP measurements of linker histone (LH) proteins in the cell nucleus have previously been reported by Brown et al. (2006) and Lele et al. (2006).MethodsWe performed Brownian dynamics (BD) simulations of the diffusional association of the wild-type and 38 single or double point mutants of the globular domain of mouse linker histone H1.0 (gH1.0) to a nucleosome. From these simulations, we calculated the bimolecular association rate constant (k_on), the Gibbs binding free energy (ΔG) and the dissociation rate constant (k_off) related to formation of a diffusional encounter complex between the nucleosome and the gH1.0.ResultsWe used these parameters, after application of a correction factor to account for the effects of the crowded environment of the nucleus, to compute FRAP recovery times and curves that are in good agreement with previously published, experimentally measured FRAP recovery time courses.ConclusionsOur computational analysis suggests that BD simulations can be used to predict the relative effects of single point mutations on FRAP recovery times related to protein binding.General SignificanceBD simulations assist in providing a detailed molecular level interpretation of FRAP data.     

Protein-protein docking by simulating the process of association subject to biochemical constraints

We present a computational procedure for modeling protein-protein association and predicting the structures of protein-protein complexes. The initial sampling stage is based on an efficient Brownian dynamics algorithm that mimics the physical process of diffusional association. Relevant biochemical data can be directly incorporated as distance constraints at this stage. The docked configurations are then grouped with a hierarchical clustering algorithm into ensembles that represent potential protein-protein encounter complexes. Flexible refinement of selected representative structures is done by molecular dynamics simulation. The protein-protein docking procedure was thoroughly tested on 10 structurally and functionally diverse protein-protein complexes. Starting from X-ray crystal structures of the unbound proteins, in 9 out of 10 cases it yields structures of protein-protein complexes close to those determined experimentally with the percentage of correct contacts >30% and interface backbone RMSD <4 A. Detailed examination of all the docking cases gives insights into important determinants of the performance of the computational approach in modeling protein-protein association and predicting of protein-protein complex structures.     

Interaction energy decomposition in protein-protein association: a quantum mechanical study of barnase-barstar complex

Protein-protein interactions are very important in the function of a cell. Computational studies of these interactions have been of interest, but often they have utilized classical modelling techniques. In recent years, quantum mechanical (QM) treatment of entire proteins has emerged as a powerful approach to study biomolecular systems. Herein, we apply a semi-empirical divide and conquer (DC) methodology coupled with a dielectric continuum model for the solvent, to explore the contribution of electrostatics, polarization and charge transfer to the interaction energy between barnase and barstar in their complex form. Molecular dynamic (MD) simulation was performed to account for the dynamic behavior of the complex. The results show that electrostatics, charge transfer and polarization favor the formation of the complex. Our study shows that electrostatics dominates the interaction between barnase and barstar ( approximately 73%), while charge transfer and polarization are approximately 21% and approximately 6%, respectively. Close inspection of the polarization and charge-transfer effects on the charge distribution of the complex reveals the existence of two, well localized, regions in barstar. The first region includes the residues between P27 and Y47 and the second region is between N65 and D83. Since no such regions could be detected in barnase clearly suggests that barstar is well optimized for efficiently binding barnase. Furthermore, using our interaction energy decomposition scheme, we were able to identify all residues that have been experimentally determined to be important for the complex formation and to suggest other residues never have been investigated. This suggests that our approach will be useful as an aid in further understanding protein-protein contacts for the ultimate goal to produce successful inhibitors for protein complexes.     

Computer modeling of electrostatic steering and orientational effects in antibody-antigen association.

Brownian dynamics simulations are performed to investigate the role of long-range electrostatic forces in the association of the monoclonal antibody HyHEL-5 with hen egg lysozyme. The electrostatic field of the antibody is obtained from a solution of the nonlinear Poisson-Boltzmann using the x-ray crystal coordinates of this protein. The lysozyme is represented as an asymmetric dumbell consisting of two spheres of unequal size, an arrangement that allows for the modeling of the orientational requirements for docking. Calculations are done with the wild-type antibody and several point mutants at different ionic strengths. Changes in the charge distribution of the lysozyme are also considered. Results are compared with experiment and a simpler model in which the lysozyme is approximately by a single charged sphere.     

Realistic protein-protein association rates from a simple diffusional model neglecting long-range interactions, free energy barriers, and landscape ruggedness

We develop a simple but rigorous model of protein-protein association kinetics based on diffusional association on free energy landscapes obtained by sampling configurations within and surrounding the native complex binding funnels. Guided by results obtained on exactly solvable model problems, we transform the problem of diffusion in a potential into free diffusion in the presence of an absorbing zone spanning the entrance to the binding funnel. The free diffusion problem is solved using a recently derived analytic expression for the rate of association of asymmetrically oriented molecules. Despite the required high steric specificity and the absence of long-range attractive interactions, the computed rates are typically on the order of 10(4)-10(6) M(-1) sec(-1), several orders of magnitude higher than rates obtained using a purely probabilistic model in which the association rate for free diffusion of uniformly reactive molecules is multiplied by the probability of a correct alignment of the two partners in a random collision. As the association rates of many protein-protein complexes are also in the 10(5)-10(6) M(-1) sec(-1) range, our results suggest that free energy barriers arising from desolvation and/or side-chain freezing during complex formation or increased ruggedness within the binding funnel, which are completely neglected in our simple diffusional model, do not contribute significantly to the dynamics of protein-protein association. The transparent physical interpretation of our approach that computes association rates directly from the size and geometry of protein-protein binding funnels makes it a useful complement to Brownian dynamics simulations.     

Implicit solvent models for flexible protein-protein docking by molecular dynamics simulation

The suitability of three implicit solvent models for flexible protein-protein docking by procedures using molecular dynamics simulation is investigated. The three models are (i) the generalized Born (GB) model implemented in the program AMBER6.0; (ii) a distance-dependent dielectric (DDD) model; and (iii) a surface area-dependent model that we have parameterized and call the NPSA model. This is a distance-dependent dielectric model modified by neutralizing the ionizable side-chains and adding a surface area-dependent solvation term. These solvent models were first tested in molecular dynamics simulations at 300 K of the native structures of barnase, barstar, segment B1 of protein G, and three WW domains. These protein structures display a range of secondary structure contents and stabilities. Then, to investigate the performance of the implicit solvent models in protein docking, molecular dynamics simulations of barnase/barstar complexation, as well as PIN1 WW domain/peptide complexation, were conducted, starting from separated unbound structures. The simulations show that the NPSA model has significant advantages over the DDD and GB models in maintaining the native structures of the proteins and providing more accurate docked complexes.     

Brownian dynamics simulations of molecular recognition in an antibody-antigen system.

The crystal structure for an antibody-antigen system, that of the anti-hen egg lysozyme monoclonal antibody HyHEL-5 complexed to lysozyme, is used as the starting point for computer simulations of diffusional encounters between the two proteins. The investigation consists of two parts: first, the linearized Poisson-Boltzmann equation is solved to determine the long-range electrostatic forces between antibody and antigen, and then, the relative motion as influenced by these forces is modeled within Brownian motion theory. The effects of various point mutations on the calculated reaction rate are considered. It is found that charged residues close to the binding site exert the greatest influence in steering the proteins into a configuration favorable for their binding, while more distant mutations are qualitatively described by the Smoluchowski model for the mutual diffusion of two uniformly charged spheres. The antibody residues involved in forming salt links with the lysozyme, Glu-H35 and Glu-H50, appear to be particularly important in electrostatic steering, as neutralization of both of them yields reaction rates that are two to three orders of magnitude below those of wild-type rates. The relative rates obtained from the simulations can be tested through kinetic measurements on mutant protein complexes. Kinetically efficient partners can also be designed and constructed through directed mutagenesis.