Protein-protein association: investigation of factors influencing association rates by brownian dynamics simulations

Complementarity of structure ensembles in protein-protein binding

Protein-protein association is often accompanied by changes in receptor and ligand structure. This interplay between protein flexibility and protein-protein recognition is currently the largest obstacle both to our understanding of and to the reliable prediction of protein complexes. We performed two sets of molecular dynamics simulations for the unbound receptor and ligand structures of 17 protein complexes and applied shape-driven rigid body docking to all combinations of representative snapshots. The crossdocking of structure ensembles increased the likelihood of finding near-native solutions. The free ensembles appeared to contain multiple complementary conformations. These were in general not related to the bound structure. We suggest that protein-protein binding follows a three-step mechanism of diffusion, free conformer selection, and refolding. This model combines previously conflicting ideas and is in better agreement with the current data on interaction forces, time scales, and kinetics.

A docking analysis of the statistical physics of protein–protein recognition

We describe protein-protein recognition within the frame of the random energy model of statistical physics. We simulate, by docking the component proteins, the process of association of two proteins that form a complex. We obtain the energy spectrum of a set of protein-protein complexes of known three-dimensional structure by performing docking in random orientations and scoring the models thus generated. We use a coarse protein representation where each amino acid residue is replaced by its Voronoï cell, and derive a scoring function by applying the evolutionary learning program ROGER to a set of parameters measured on that representation. Taking the scores of the docking models to be interaction energies, we obtain energy spectra for the complexes and fit them to a Gaussian distribution, from which we derive physical parameters such as a glass transition temperature and a specificity transition temperature.

Electrostatics of Cytochrome-c assemblies

Electrostatic potentials along with computational mutagenesis are used to obtain atomic level insights into Cytochrome-c in order to design efficient bionanosensors. The electrostatic properties of wild type and mutant Cytochrome-c are examined in the context of their assembly, i.e. are examined in the absence and presence of neighboring molecules from the assembly. An intense increase in the positive potential ensues when the neighboring molecules are taken into account. This suggests that in the extrapolation of electric field effects upon the design of assemblies, considering the properties of only the central molecule may not be sufficient. Additionally, the influence of the uncharged residues becomes quite diminished when the molecule is considered in an assembly. This could pave the way for making mutants that might be more soluble in different media used in the construction of devices. [Figure: see text]. The electrostatic potential, calculated using the program DELPHI mapped on to the surface of Cytochrome-c when it is considered by itself (in the left column) and in the presence of the electrostatic field generated by the presence of the surrounding 4 molecules on the right. The potentials range from -10kT in red to +10kT in blue. The central figure shows the regions that have been mutated to positively charged residues by placing a unit positive charge at the terminal atom of the respective side chain. The figures range from the wild type in the first row, followed by the Gln12, Asn70, Asp50, Glu90 and Ala83 mutants.

Electrostatic Recognition and Induced Fit in the κ-PVIIA Toxin Binding to Shaker Potassium Channel

Brownian dynamics (BD) and molecular dynamics (MD) simulations and electrostatic calculations were performed to study the binding process of kappa-PVIIA to the Shaker potassium channel and the structure of the resulting complex. BD simulations, guided by electrostatic interactions, led to an initial alignment between the toxin and the channel protein. MD simulations were then carried out to allow for rearrangements from this initial structure. After approximately 4 ns, a critical "induced fit" process was observed to last for approximately 2 ns. In this process, the interface was reorganized, and side chains were moved so that favorable atomic contacts were formed or strengthened, while unfavorable contacts were eliminated. The final complex structure was stabilized through electrostatic interactions with the positively charged side chain of Lys7 of kappa-PVIIA deeply inserted into the channel pore and other hydrogen bonds and by hydrophobic interactions involving Phe9 and Phe23 of the toxin. The validity of the predicted structure for the complex was assessed by calculating the effects of mutating charged and polar residues of both the toxin and the channel protein, with the calculated effects correlating reasonably well with experimental data. The present study suggests a general binding mechanism, whereby proteins are pre-aligned in their diffusional encounter by long-range electrostatic attraction, and nanosecond-scale rearrangements within the initial complex then lead to a specifically bound complex.

Simulation of Electron Transfer between Cytochrome c2 and the Bacterial Photosynthetic Reaction Center: Brownian Dynamics Analysis of the Native Proteins and Double Mutants

Electron transfer is essential for bacterial photosynthesis which converts light energy into chemical energy. This paper theoretically studies the interprotein electron transfer from cytochrome c(2) of Rhodobacter capsulatus to the photosynthetic reaction center of Rhodobacter sphaeroides in native and mutated systems. Brownian dynamics is used with an exponential distance-dependent electron-transfer rate model to compute bimolecular rate constants, which are consistent with experimental data when reasonable prefactors and decay constants are used. Interestingly, switching of the reaction mechanism from the diffusion-controlled limit in the native proteins to the activation-controlled limit in one of the mutants (DK(L261)/KE(C99)) was found. We also predict that the second-order rate for the native reaction center/cytochrome c(2) system will decrease with increasing ionic strength, a characteristic of electrostatically controlled docking.

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 study of cytochrome f interactions with cytochrome c6 and plastocyanin in Chlamydomonas reinhardtii plastocyanin, and cytochrome c6 mutants

Using Brownian dynamics simulations, all of the charged residues in Chlamydomonas reinhardtii cytochrome c(6) (cyt c(6)) and plastocyanin (PC) were mutated to alanine and their interactions with cytochrome f (cyt f) were modeled. Systematic mutation of charged residues on both PC and cyt c(6) confirmed that electrostatic interactions (at least in vitro) play an important role in bringing these proteins sufficiently close to cyt f to allow hydrophobic and van der Waals interactions to form the final electron transfer-active complex. The charged residue mutants on PC and cyt c(6) displayed similar inhibition classes. Our results indicate a difference between the two acidic clusters on PC. Mutations D44A and E43A of the lower cluster showed greater inhibition than do any of the mutations of the upper cluster residues. Replacement of acidic residues on cyt c(6) that correspond to the PC's lower cluster, particularly E70 and E69, was observed to be more inhibitory than those corresponding to the upper cluster. In PC residues D42, E43, D44, D53, D59, D61, and E85, and in cyt c(6) residues D2, E54, K57, D65, R66, E70, E71, and the heme had significant electrostatic contacts with cyt f charged residues. PC and cyt c(6) showed different binding sites and orientations on cyt f. As there are no experimental cyt c(6) mutation data available for algae, our results could serve as a good guide for future experimental work on this protein. The comparison between computational values and the available experimental data (for PC-cyt f interactions) showed overall good agreement, which supports the predictive power of Brownian dynamics simulations in mutagenesis studies.

A structural perspective on protein-protein interactions

Structures of macromolecular complexes are necessary for a mechanistic description of biochemical and cellular processes. They can be solved by experimental methods, such as X-ray crystallography, NMR spectroscopy and electron microscopy, as well as by computational protein structure prediction, docking and bioinformatics. Recent advances and applications of these methods emphasize the need for hybrid approaches that combine a variety of data to achieve better efficiency, accuracy, resolution and completeness.

Finite element solution of the steady-state Smoluchowski equation for rate constant calculations

This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.

The impact of protein flexibility on protein-protein docking

Accounting for protein flexibility in protein-protein docking algorithms is challenging, and most algorithms therefore treat proteins as rigid bodies or permit side-chain motion only. While the consequences are obvious when there are large conformational changes upon binding, the situation is less clear for the modest conformational changes that occur upon formation of most protein-protein complexes. We have therefore studied the impact of local protein flexibility on protein-protein association by means of rigid body and torsion angle dynamics simulation. The binding of barnase and barstar was chosen as a model system for this study, because the complexation of these 2 proteins is well-characterized experimentally, and the conformational changes accompanying binding are modest. On the side-chain level, we show that the orientation of particular residues at the interface (so-called hotspot residues) have a crucial influence on the way contacts are established during docking from short protein separations of approximately 5 A. However, side-chain torsion angle dynamics simulations did not result in satisfactory docking of the proteins when using the unbound protein structures. This can be explained by our observations that, on the backbone level, even small (2 A) local loop deformations affect the dynamics of contact formation upon docking. Complementary shape-based docking calculations confirm this result, which indicates that both side-chain and backbone levels of flexibility influence short-range protein-protein association and should be treated simultaneously for atomic-detail computational docking of proteins.

A Brownian dynamics study of the interaction of Phormidium laminosum plastocyanin with Phormidium laminosum cytochrome f

The interaction of Phormidium laminosum plastocyanin (PC) with P. laminosum cytochrome f (cyt f) was studied using Brownian dynamics (BD) simulations. Few complexes and a low rate of electron transfer were observed for wild-type PC. Increasing the positive electrostatic field on PC by the addition of a Zn(2+) ion in the neighborhood of D44 and D45 on PC (as found in crystal structure of plastocyanin) increased the number of complexes formed and the calculated rates of electron transfer as did PC mutations D44A, D45A, E54A, and E57A. Mutations of charged residues on Phormidium PC and Phormidium cyt f were used to map binding sites on both proteins. In both the presence and absence of the Zn(2+) ion, the following residues on PC interact with cyt f: D44, D45, K6, D79, R93, and K100 that lie in a patch just below H92 and Y88 and D10, E17, and E70 located on the upper portion of the PC molecule. In the absence of the Zn(2+) ion, K6 and K35 on the top of the PC molecule also interact with cyt f. Cyt f residues involved in binding PC, in the absence of the Zn(2+) ion, include E165, D187, and D188 that are located on the small domain of cyt f. The orientation of PC in the complexes was quite random in accordance with NMR results. In the presence of the Zn(2+) ion, K53 and E54 in the lower patch of the PC molecule also interact with cyt f and PC interacts with E86, E95, and E123 on the large domain of cyt f. Also, the orientation of PC in the complexes was much more uniform than in the absence of the Zn(2+) ion. The difference may be due to both the larger electrostatic field and the greater asymmetry of the charge distribution on PC observed in the presence of the Zn(2+) ion. Hydrophobic interactions were also observed suggesting a model of cyt f-PC interactions in which electrostatic forces bring the two molecules together but hydrophobic interactions participate in stabilizing the final electron-transfer-active dock.

A Brownian dynamics study: the effect of a membrane environment on an electron transfer system

During the past few years, three-dimensional crystal structures of many of the important integral membrane proteins responsible for the bioenergetic processes of photosynthesis and respiration have been determined. Moreover, a few crystal structures of protein-protein complexes have become available that characterize the interaction between those membrane proteins and the electron carrier protein cytochrome c. Here, we address the association kinetics for binding of cytochrome c to cytochrome c oxidase (COX) from Paracoccus denitrificans by Brownian dynamics simulations. The effects of ionic strength and protein mutations were studied for two different cytochrome c species: the positively charged, dipolar horse heart cytochrome c and the negatively charged physiological electron transfer partner cytochrome c(552). We studied association toward "naked" COX and toward membrane-embedded COX where the membrane is represented as an uncharged DPPC bilayer modeled in atomistic detail. For the nonnatural association toward "naked" COX, the association rates are >100 times larger for horse heart cytochrome c than for cytochrome c(552). Interestingly, the presence of the lipid bilayer leads to a dramatic decrease of the association rate of horse heart cytochrome c, but slightly enhances association of cytochrome c(552), leading to very similar association rates of both proteins to membrane-embedded COX. This finding from computational modeling studies may reflect the optimization of surface patches and of the total net charge on electron transfer pairs in nature.

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.

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.

Dynamic Docking and Electron-Transfer between Cytochrome b5 and a Suite of Myoglobin Surface-Charge Mutants. Introduction of a Functional-Docking Algorithm for Protein−Protein Complexes

Horse myoglobin (Mb) provides a convenient "workbench" for probing the effects of electrostatics on binding and reactivity in the dynamic [Mb, cytochrome b(5)] electron-transfer (ET) complex. We have combined mutagenesis and heme neutralization to prepare a suite of six Mb surface-charge variants: the [S92D]Mb and [V67R]Mb mutants introduce additional charges on the "front" face, and incorporation of the heme di-ester into each of these neutralizes the charge on the heme propionates which further increases the positive charge on the "front" face. For this set of mutants, the nominal charge of Mb changes by -1 to +3 units relative to that for native Mb. For each member of this set, we have measured the bimolecular quenching rate constant (k(2)) for the photoinitiated (3)ZnDMb --> Fe(3+)b(5) ET reaction as a function of ionic strength. We find: (i) a dramatic decoupling of binding and reactivity, in which k(2) varies approximately 10(3)-fold within the suite of Mbs without a significant change in binding affinity; (ii) the ET reaction occurs within the "thermodynamic" or "rapid exchange" limit of the "Dynamic Docking" model, in which a large ensemble of weakly bound protein-protein configurations contribute to binding, but only a few are reactive, as shown by the fact that the zero-ionic-strength bimolecular rate constant varies exponentially with the net charge on Mb; (iii) Brownian dynamic docking profiles allow us to visualize the microscopic basis of dynamic docking. To describe these results we present a new theoretical approach which mathematically combines PATHWAY donor/acceptor coupling calculations with Poisson-Boltzmann-based electrostatics estimates of the docking energetics in a Monte Carlo (MC) sampling framework that is thus specially tailored to the intermolecular ET problem. This procedure is extremely efficient because it targets only the functionally active complex geometries by introducing a "reactivity filter" into the computations themselves, rather than as a subsequent step. This efficiency allows us to employ more computationally expensive and accurate methods to describe the relevant intermolecular interaction energies and the protein-mediated donor/acceptor coupling interactions. It is employed here to compute the changes in the bimolecular rate constant for ET between Mb and cyt b(5) upon variations in the myoglobin surface charge, pH, and ionic strength.

Brownian dynamics simulations of simplified cytochrome c molecules in the presence of a charged surface

Simulations were performed for up to 150 simplified spherical horse heart cytochrome c molecules in the presence of a charged surface, which serves as an approximate model for a lipid membrane. Screened electrostatic and short-ranged attractive as well as repulsive van der Waals forces for interparticle and particle-membrane interactions are utilized in the simulations. At a distance from the membrane, where particle-membrane interactions are negligible, the simulation is coupled to a noninteraction continuum analogous to a heat bath [Geyer et al., J. Chem. Phys. 120, 4573 (2004)]. From the particles' density profiles perpendicular to the planar surface binding isotherms are derived and compared to experimental results [Heimburg et al. (1999)]. Using a negatively charged structureless membrane surface a saturation effect was found for relatively large particle concentrations. Since biological membranes often contain membrane proteins, we also studied the influence of additional charges on our model membrane mimicking bacterial reaction centers. We find that the onset of the saturation occurs for much lower concentrations and is sensitive to the detailed implementation. Therefore we suggest that local distortion of membrane planarity (undulation), or lipid demixing, or the presence of charged integral membrane proteins create preferential binding sites on the membrane. Only then do we observe saturation at physiological concentrations.

Identification of Protein–Protein Interaction Sites from Docking Energy Landscapes

Protein recognition is one of the most challenging and intriguing problems in structural biology. Despite all the available structural, sequence and biophysical information about protein-protein complexes, the physico-chemical patterns, if any, that make a protein surface likely to be involved in protein-protein interactions, remain elusive. Here, we apply protein docking simulations and analysis of the interaction energy landscapes to identify protein-protein interaction sites. The new protocol for global docking based on multi-start global energy optimization of an all-atom model of the ligand, with detailed receptor potentials and atomic solvation parameters optimized in a training set of 24 complexes, explores the conformational space around the whole receptor without restrictions. The ensembles of the rigid-body docking solutions generated by the simulations were subsequently used to project the docking energy landscapes onto the protein surfaces. We found that highly populated low-energy regions consistently corresponded to actual binding sites. The procedure was validated on a test set of 21 known protein-protein complexes not used in the training set. As much as 81% of the predicted high-propensity patch residues were located correctly in the native interfaces. This approach can guide the design of mutations on the surfaces of proteins, provide geometrical details of a possible interaction, and help to annotate protein surfaces in structural proteomics.

Continuum Electrostatic Model for the Binding of Cytochrome c2 to the Photosynthetic Reaction Center from Rhodobacter sphaeroides

Electrostatic interactions are important for protein-protein association. In this study, we examined the electrostatic interactions between two proteins, cytochrome c(2) (cyt c(2)) and the reaction center (RC) from the photosynthetic bacterium Rhodobacter sphaeroides, that function in intermolecular electron transfer in photosynthesis. Electrostatic contributions to the binding energy for the cyt c(2)-RC complex were calculated using continuum electrostatic methods based on the recent cocrystal structure [Axelrod, H. L., et al. (2002) J. Mol. Biol. 319, 501-515]. Calculated changes in binding energy due to mutations of charged interface residues agreed with experimental results for a protein dielectric constant epsilon(in) of 10. However, the electrostatic contribution to the binding energy for the complex was close to zero due to unfavorable desolvation energies that compensate for the favorable Coulomb attraction. The electrostatic energy calculated as a function of displacement of the cyt c(2) from the bound position showed a shallow minimum at a position near but displaced from the cocrystal configuration. These results show that although electrostatic steering is present, other short-range interactions must be present to contribute to the binding energy and to determine the structure of the complex. Calculations made to model the experimental data on association rates indicate a solvent-separated transition state for binding in which the cyt c(2) is displaced approximately 8 A above its position in the bound complex. These results are consistent with a two-step model for protein association: electrostatic docking of the cyt c(2) followed by desolvation to form short-range van der Waals contacts for rapid electron transfer.

Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations

A major problem in mathematical modeling of the dynamics of complex biological systems is the frequent lack of knowledge of kinetic parameters. Here, we apply Brownian dynamics simulations, based on protein three-dimensional structures, to estimate a previously undetermined kinetic parameter, which is then used in biochemical network simulations. The peroxidase-oxidase reaction involves many elementary steps and displays oscillatory dynamics important for immune response. Brownian dynamics simulations were performed for three different peroxidases to estimate the rate constant for one of the elementary steps crucial for oscillations in the peroxidase-oxidase reaction, the association of superoxide with peroxidase. Computed second-order rate constants agree well with available experimental data and permit prediction of rate constants at physiological conditions. The simulations show that electrostatic interactions depress the rate of superoxide association with myeloperoxidase, bringing it into the range necessary for oscillatory behavior in activated neutrophils. Such negative electrostatic steering of enzyme-substrate association presents a novel control mechanism and lies in sharp contrast to the electrostatically-steered fast association of superoxide and Cu/Zn superoxide dismutase, which is also simulated here. The results demonstrate the potential of an integrated and concerted application of structure-based simulations and biochemical network simulations in cellular systems biology.

Brownian dynamics simulations of the interaction of Chlamydomonas cytochrome f with plastocyanin and cytochrome c6

The interaction of Chlamydomonas cytochrome f (cyt f) with either Chlamydomonas plastocyanin (PC) or Chlamydomonas cytochrome c(6) (cyt c(6)) was studied using Brownian dynamics simulations. The two electron acceptors (PC and cyt c(6)) were found to be essentially interchangeable despite a lack of sequence homology and different secondary structures (beta-sheet for PC and alpha-helix for cyt c(6)). Simulations using PC and cyt c(6) interacting with cyt f showed approximately equal numbers of successful complexes and calculated rates of electron transfer. Cyt f-PC and cyt f-cyt c(6) showed the same types of interactions. Hydrophobic residues surrounding the Y1 ligand to the heme on cyt f interacted with hydrophobic residues on PC (surrounding the H87 ligand to the Cu) or cyt c(6) (surrounding the heme). Both types of complexes were stabilized by electrostatic interactions between K65, K188, and K189 on cyt f and conserved anionic residues on PC (E43, D44, D53, and E85) or cyt c(6) (E2, E70, and E71). Mutations on cyt f had identical effects on its interaction with either PC or cyt c(6). K65A, K188A, and K189A showed the largest effects whereas residues such as K217A, R88A, and K110A, which are located far from the positive patch on cyt f, showed very little inhibition. The effect of mutations observed in Brownian dynamics simulations paralleled those observed in experiments.

Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar

The contributions of electrostatic interactions to the binding stability of barnase and barstar were studied by the Poisson-Boltzmann model with three different protocols: a), the dielectric boundary specified as the van der Waals (vdW) surface of the protein along with a protein dielectric constant (epsilon (p)) of 4; b), the dielectric boundary specified as the molecular (i.e., solvent-exclusion (SE)) surface along with epsilon (p) = 4; and c), "SE + epsilon (p) = 20." The "vdW + epsilon (p) = 4" and "SE + epsilon (p) = 20" protocols predicted an overall electrostatic stabilization whereas the "SE + epsilon (p) = 4" protocol predicted an overall electrostatic destabilization. The "vdW + epsilon (p) = 4" protocol was most consistent with experiment. It quantitatively reproduced the observed effects of 17 mutations neutralizing charged residues lining the binding interface and the measured coupling energies of six charge pairs across the interface and reasonably rationalized the experimental ionic strength and pH dependences of the binding constant. In contrast, the "SE + epsilon (p) = 4" protocol predicted significantly larger coupling energies of charge pairs whereas the "SE + epsilon (p) = 20" protocol did not predict any pH dependence. This study calls for further scrutiny of the different Poisson-Boltzmann protocols and demonstrates potential danger in drawing conclusions on electrostatic contributions based on a particular calculation protocol.

How FMN binds to anabaena apoflavodoxin: a hydrophobic encounter at an open binding site

Molecular recognition begins when two molecules approach and establish interactions of certain strength. The mechanisms of molecular recognition reactions between biological molecules are not well known, and few systems have been analyzed in detail. We investigate here the reaction between an apoprotein and its physiological cofactor (apoflavodoxin and flavin mononucleotide) that binds reversibly to form a non-covalent complex (flavodoxin) involved in electron transfer reactions. We have analyzed the fast binding reactions between the FMN cofactor (and shorter analogs) and wild type (and nine mutant apoflavodoxins where residues interacting with FMN in the final complex have been replaced). The x-ray structures of two such mutants are reported that show the mutations are well tolerated by the protein. From the calculated microscopic binding rate constants we have performed a Phi analysis of the transition state of complex formation that indicates that the binding starts by interaction of the isoalloxazine-fused rings in FMN with residues of its hydrophobic binding site. In contrast, the phosphate in FMN, known to contribute most to the affinity of the final holoflavodoxin complex, is not bound in the transition state complex. Both the effects of ionic strength and of phosphate concentration on the wild type complex rate constant agree with this scenario. As suggested previously by nmr data, it seems that the isoalloxazine-binding site may be substantially open in solution. Interestingly, although FMN is a charged molecule, electrostatic interactions seem not to play a role in directing the binding, unlike what has been reported for other biological complexes. The binding can thus be best described as a hydrophobic encounter at an open binding site.

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.

On the evaluation and optimization of protein X-ray structures for pKa calculations

The calculation of the physical properties of a protein from its X-ray structure is of importance in virtually every aspect of modern biology. Although computational algorithms have been developed for calculating everything from the dynamics of a protein to its binding specificity, only limited information is available on the ability of these methods to give accurate results when used with a particular X-ray structure. We examine the ability of a pKa calculation algorithm to predict the proton-donating residue in the catalytic mechanism of hen egg white lysozyme. We examine the correlation between the ability of the pKa calculation method to obtain the correct result and the overall characteristics of 41 X-ray structures such as crystallization conditions, resolution, and the output of structure validation software. We furthermore examine the ability of energy minimizations (EM), molecular dynamics (MD) simulations, and structure-perturbation methods to optimize the X-ray structures such that these give correct results with the pKa calculation algorithm. We propose a set of criteria for identifying the proton donor in a catalytic mechanism, and demonstrate that the application of these criteria give highly accurate prediction results when using unmodified X-ray structures. More specifically, we are able to successfully identify the proton donor in 85% of the X-ray structures when excluding structures with crystal contacts near the active site. Neither the use of the overall characteristics of the X-ray structures nor the optimization of the structure by EM, MD, or other methods improves the results of the pKa calculation algorithm. We discuss these results and their implications for the design of structure-based energy calculation algorithms in general.

Differences in electrostatic properties at antibody-antigen binding sites: implications for specificity and cross-reactivity

Antibodies HyHEL8, HyHEL10, and HyHEL26 (HH8, HH10, and HH26, respectively) recognize highly overlapping epitopes on hen egg-white lysozyme (HEL) with similar affinities, but with different specificities. HH8 binding to HEL is least sensitive toward mutations in the epitope and thus is most cross-reactive, HH26 is most sensitive, whereas the sensitivity of HH10 lies in between HH8 and HH26. Here we have investigated intra- and intermolecular interactions in three antibody-protein complexes: theoretical models of HH8-HEL and HH26-HEL complexes, and the x-ray crystal structure of HH10-HEL complex. Our results show that HH8-HEL has the lowest number and HH26-HEL has the highest number of intra- and intermolecular hydrogen bonds. The number of salt bridges is lowest in HH8-HEL and highest in HH26-HEL. The binding site salt bridges in HH8-HEL are not networked, and are weak, whereas, in HH26-HEL, an intramolecular salt-bridge triad at the binding site is networked to an intermolecular triad to form a pentad. The pentad and each salt bridge of this pentad are exceptionally stabilizing. The number of binding-site salt bridges and their strengths are intermediate in HH10-HEL, with an intramolecular triad. Our further calculations show that the electrostatic component contributes the most to binding energy of HH26-HEL, whereas the hydrophobic component contributes the most in the case of HH8-HEL. A "hot-spot" epitope residue Lys-97 forms an intermolecular salt bridge in HH8-HEL, and participates in the intermolecular pentad in the HH26-HEL complex. Mutant modeling and surface plasmon resonance (SPR) studies show that this hot-spot epitope residue contributes significantly more to the binding than an adjacent epitope residue, Lys-96, which does not form a salt bridge in any of the three HH-HEL complexes. Furthermore, the effect of mutating Lys-97 is most severe in HH26-HEL. Lys-96, being a charged residue, also contributes the most in HH26-HEL among the three complexes. The SPR results on these mutants also highlight that the apparent "electrostatic steering" on net on rates actually act at post-collision level stabilization of the complex. The significance of this work is the observed variations in electrostatic interactions among the three complexes. Our work demonstrates that higher electrostatics, both as a number of short-range electrostatic interactions and their contributions, leads to higher binding specificity. Strong salt bridges, their networking, and electrostatically driven binding, limit flexibilities through geometric constrains. In contrast, hydrophobic driven binding and low levels of electrostatic interactions are associated with conformational flexibility and cross-reactivity.

The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology

Electrostatics plays a fundamental role in virtually all processes involving biomolecules in solution. The Poisson-Boltzmann equation constitutes one of the most fundamental approaches to treat electrostatic effects in solution. The theoretical basis of the Poisson-Boltzmann equation is reviewed and a wide range of applications is presented, including the computation of the electrostatic potential at the solvent-accessible molecular surface, the computation of encounter rates between molecules in solution, the computation of the free energy of association and its salt dependence, the study of pKa shifts and the combination with classical molecular mechanics and dynamics. Theoretical results may be used for rationalizing or predicting experimental results, or for suggesting working hypotheses. An ever-increasing body of successful applications proves that the Poisson-Boltzmann equation is a useful tool for structural biology and complementary to other established experimental and theoretical methodologies.

Analysis of coupled bimolecular reaction kinetics and diffusion by two-color fluorescence correlation spectroscopy: enhanced resolution of kinetics by resonance energy transfer

In two-color fluorescence correlation spectroscopy (TCFCS), the fluorescence intensities of two fluorescently-labeled species are cross-correlated over time and can be used to identify static and dynamic interactions. Generally, fluorophore labels are chosen that do not undergo Förster resonance energy transfer (FRET). Here, a general TCFCS theory is presented that accounts for the possibility of FRET between reactants in the reversible bimolecular reaction, [reaction: see text] where k(f) and k(b) are forward and reverse rate constants, respectively (dissociation constant K(d) = k(b)/k(f)). Using this theory, we systematically investigated the influence on the correlation function of FRET, reaction rates, reactant concentrations, diffusion, and component visibility. For reactants of comparable size and an energy-transfer efficiency of approximately 90%, experimentally measurable cross-correlation functions should be sensitive to reaction kinetics for K(d) > 10(-8) M and k(f) >or= approximately 10(7) M(-1)s(-1). Measured auto-correlation functions corresponding to donor and acceptor labels are generally less sensitive to reaction kinetics, although for the acceptor, this sensitivity increases as the visibility of the donor increases relative to the acceptor. In the absence of FRET or a significant hydrodynamic difference between reactant species, there is little effect of reaction kinetics on the shape of auto- and cross-correlation functions. Our results suggest that a subset of biologically relevant association-dissociation kinetics can be measured by TCFCS and that FRET can be advantageous in enhancing these effects.

Computational simulation of the docking of Prochlorothrix hollandica plastocyanin to potosystem I: modeling the electron transfer complex

We have used several docking algorithms (GRAMM, FTDOCK, DOT, AUTODOCK) to examine protein-protein interactions between plastocyanin (Pc)/photosystem I (PSI) in the electron transfer reaction. Because of the large size and complexity of this system, it is faster and easier to use computer simulations than conduct x-ray crystallography or nuclear magnetic resonance experiments. The main criterion for complex selection was the distance between the copper ion of Pc and the P700 chlorophyll special pair. Additionally, the unique tyrosine residue (Tyr(12)) of the hydrophobic docking surface of Prochlorothrix hollandica Pc yields a specific interaction with the lumenal surface of PSI, thus providing the second constraint for the complex. The structure that corresponded best to our criteria was obtained by the GRAMM algorithm. In this structure, the solvent-exposed histidine that coordinates copper in Pc is at the van der Waals distance from the pair of stacked tryptophans that separate the chlorophylls from the solvent, yielding the shortest possible metal-to-metal distance. The unique tyrosine on the surface of the Prochlorothrix Pc hydrophobic patch also participates in a hydrogen bond with the conserved Asn(633) of the PSI PsaB polypeptide (numbering from the Synechococcus elongatus crystal structure). Free energy calculations for complex formation with wild-type Pc, as well as the hydrophobic patch Tyr(12)Gly and Pro(14)Leu Pc mutants, were carried out using a molecular mechanics Poisson-Boltzman, surface area approach (MM/PBSA). The results are in reasonable agreement with our experimental studies, suggesting that the obtained structure can serve as an adequate model for P. hollandica Pc-PSI complex that can be extended for the study of other cyanobacterial Pc/PSI reaction pairs.

Atomistic simulations of competition between substrates binding to an enzyme

Although the idea that electrostatic potentials generated by enzymes can guide substrates to active sites is well established, it is not always appreciated that the same potentials can also promote the binding of molecules other than the intended substrate, with the result that such enzymes might be sensitive to the presence of competing molecules. To provide a novel means of studying such "electrostatic competition" effects, computer simulation methodology has been developed to allow the diffusion and association of many solute molecules around a single enzyme to be simulated. To demonstrate the power of the methodology, simulations have been conducted on an artificial fusion protein of citrate synthase (CS) and malate dehydrogenase (MDH) to assess the chances of oxaloacetate being channeled between the MDH and CS active sites. The simulations demonstrate that the probability of channeling is strongly dependent on the concentration of the initial substrate (malate) in the solution. In fact, the high concentrations of malate used in experiments appear high enough to abolish any channeling of oxaloacetate. The simulations provide a resolution of a serious discrepancy between previous simulations and experiments and raise important questions relating to the observability of electrostatically mediated substrate channeling in vitro and in vivo.

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.

Role of electrostatics in the interaction between cytochrome f and plastocyanin of the cyanobacterium Phormidium laminosum

The role of charged residues on the surface of plastocyanin from the cyanobacterium Phormidium laminosum in the reaction with soluble cytochrome f in vitro was studied using site-directed mutagenesis. The charge on each of five residues on the eastern face of plastocyanin was neutralized and/or inverted, and the effect of the mutation on midpoint potentials was determined. The dependence of the overall rate constant of reaction, k(2), on ionic strength was investigated using stopped-flow spectrophotometry. Removing negative charges (D44A or D45A) accelerated the reaction and increased the dependence on ionic strength, whereas removing positive charges slowed it down. Two mutations (K46A, K53A) each almost completely abolished any influence of ionic strength on k(2), and three mutations (R93A, R93Q, R93E) each converted electrostatic attraction into repulsion. At low ionic strength, wild type and all mutants showed an inhibition which might be due to changes in the interaction radius as a consequence of ionic strength dependence of the Debye length or to effects on the rate constant of electron transfer, k(et). The study shows that the electrostatics of the interaction between plastocyanin and cytochrome f of P. laminosum in vitro are not optimized for k(2). Whereas electrostatics are the major contributor to k(2) in plants [Kannt, A., et al. (1996) Biochim. Biophys. Acta 1277, 115-126], this role is taken by nonpolar interactions in the cyanobacterium, leading to a remarkably high rate at infinite ionic strength (3.2 x 10(7) M(-1) s(-1)).

Protein-protein association kinetics and protein docking

Rigid body protein docking methods frequently yield false positive structures that have good surface complementarity, but are far from the native complex. The main reason for this is the uncertainty of the protein structures to be docked, including the positions of solvent-exposed sidechains. Substantial efforts have been devoted to finding near-native structures by rescoring the docked conformations and employing various filters. An alternative approach emulates the process of protein-protein association, that is, first finding the region in which binding is likely to occur and then refining the complex while allowing for flexibility.

Prediction of protein-protein interactions by docking methods

Recently, developments have been made in predicting the structure of docked complexes when the coordinates of the components are known. The process generally consists of a stage during which the components are combined rigidly and then a refinement stage. Several rapid new algorithms have been introduced in the rigid docking problem and promising refinement techniques have been developed, based on modified molecular mechanics force fields and empirical measures of desolvation, combined with minimisations that switch on the short-range interactions gradually. There has also been progress in developing a benchmark set of targets for docking and a blind trial, similar to the trials of protein structure prediction, has taken place.

Kinetic studies of protein-protein interactions

The structure of a protein-protein interaction, its affinity and thermodynamic characteristics depict a 'frozen' state of a complex. This picture ignores the kinetic nature of complex formation and dissociation, which are of major biological and biophysical interest. This review highlights recent advances in deciphering the kinetic pathway of protein-protein complexation, the nature of the encounter complex, transition state and intermediate along the reaction, and the effects of mutation, viscosity, pH and salt on association.

Electrostatic analysis and Brownian dynamics simulation of the association of plastocyanin and cytochrome f

The oxidation of cytochrome f by the soluble cupredoxin plastocyanin is a central reaction in the photosynthetic electron transfer chain of all oxygenic organisms. Here, two different computational approaches are used to gain new insights into the role of molecular recognition and protein-protein association processes in this redox reaction. First, a comparative analysis of the computed molecular electrostatic potentials of seven single and multiple point mutants of spinach plastocyanin (D42N, E43K, E43N, E43Q/D44N, E59K/E60Q, E59K/E60Q/E43N, Q88E) and the wt protein was carried out. The experimentally determined relative rates (k(2)) for the set of plastocyanin mutants are found to correlate well (r(2) = 0.90 - 0.97) with the computed measure of the similarity of the plastocyanin electrostatic potentials. Second, the effects on the plastocyanin/cytochrome f association rate of these mutations in the plastocyanin "eastern site" were evaluated by simulating the association of the wild type and mutant plastocyanins with cytochrome f by Brownian dynamics. Good agreement between the computed and experimental relative rates (k(2)) (r(2) = 0.89 - 0.92) was achieved for the plastocyanin mutants. The results obtained by applying both computational techniques provide support for the fundamental role of the acidic residues at the plastocyanin eastern site in the association with cytochrome f and in the overall electron-transfer process.