Diffusional encounter of barnase and barstar

Transient protein-protein interaction of the SH3-peptide complex via closely located multiple binding sites

Protein-protein interactions play an essential role in cellular processes. Certain proteins form stable complexes with their partner proteins, whereas others function by forming transient complexes. The conventional protein-protein interaction model describes an interaction between two proteins under the assumption that a protein binds to its partner protein through a single binding site. In this study, we improved the conventional interaction model by developing a Multiple-Site (MS) model in which a protein binds to its partner protein through closely located multiple binding sites on a surface of the partner protein by transiently docking at each binding site with individual binding free energies. To test this model, we used the protein-protein interaction mediated by Src homology 3 (SH3) domains. SH3 domains recognize their partners via a weak, transient interaction and are therefore promiscuous in nature. Because the MS model requires large amounts of data compared with the conventional interaction model, we used experimental data from the positionally addressable syntheses of peptides on cellulose membranes (SPOT-synthesis) technique. From the analysis of the experimental data, individual binding free energies for each binding site of peptides were extracted. A comparison of the individual binding free energies from the analysis with those from atomistic force fields gave a correlation coefficient of 0.66. Furthermore, application of the MS model to 10 SH3 domains lowers the prediction error by up to 9% compared with the conventional interaction model. This improvement in prediction originates from a more realistic description of complex formation than the conventional interaction model. The results suggested that, in many cases, SH3 domains increased the protein complex population through multiple binding sites of their partner proteins. Our study indicates that the consideration of general complex formation is important for the accurate description of protein complex formation, and especially for those of weak or transient protein complexes.

Clustering of HIV-1 Subtypes Based on gp120 V3 Loop electrostatic properties

BACKGROUND

The V3 loop of the glycoprotein gp120 of HIV-1 plays an important role in viral entry into cells by utilizing as coreceptor CCR5 or CXCR4, and is implicated in the phenotypic tropisms of HIV viruses. It has been hypothesized that the interaction between the V3 loop and CCR5 or CXCR4 is mediated by electrostatics. We have performed hierarchical clustering analysis of the spatial distributions of electrostatic potentials and charges of V3 loop structures containing consensus sequences of HIV-1 subtypes.

RESULTS

Although the majority of consensus sequences have a net charge of +3, the spatial distribution of their electrostatic potentials and charges may be a discriminating factor for binding and infectivity. This is demonstrated by the formation of several small subclusters, within major clusters, which indicates common origin but distinct spatial details of electrostatic properties. Some of this information may be present, in a coarse manner, in clustering of sequences, but the spatial details are largely lost. We show the effect of ionic strength on clustering of electrostatic potentials, information that is not present in clustering of charges or sequences. We also make correlations between clustering of electrostatic potentials and net charge, coreceptor selectivity, global prevalence, and geographic distribution. Finally, we interpret coreceptor selectivity based on the N6X7T8|S8X9 sequence glycosylation motif, the specific positive charge location according to the 11/24/25 rule, and the overall charge and electrostatic potential distribution.

CONCLUSIONS

We propose that in addition to the sequence and the net charge of the V3 loop of each subtype, the spatial distributions of electrostatic potentials and charges may also be important factors for receptor recognition and binding and subsequent viral entry into cells. This implies that the overall electrostatic potential is responsible for long-range recognition of the V3 loop with coreceptors CCR5/CXCR4, whereas the charge distribution contributes to the specific short-range interactions responsible for the formation of the bound complex. We also propose a scheme for coreceptor selectivity based on the sequence glycosylation motif, the 11/24/25 rule, and net charge.

Electrostatically biased binding of kinesin to microtubules

An electrostatic field rotates, slides, and guides the kinesin head to bind the microtubule at a site a short distance ahead, thus determining the direction of movement of the motor.

The minimum motor domain of kinesin-1 is a single head. Recent evidence suggests that such minimal motor domains generate force by a biased binding mechanism, in which they preferentially select binding sites on the microtubule that lie ahead in the progress direction of the motor. A specific molecular mechanism for biased binding has, however, so far been lacking. Here we use atomistic Brownian dynamics simulations combined with experimental mutagenesis to show that incoming kinesin heads undergo electrostatically guided diffusion-to-capture by microtubules, and that this produces directionally biased binding. Kinesin-1 heads are initially rotated by the electrostatic field so that their tubulin-binding sites face inwards, and then steered towards a plus-endwards binding site. In tethered kinesin dimers, this bias is amplified. A 3-residue sequence (RAK) in kinesin helix alpha-6 is predicted to be important for electrostatic guidance. Real-world mutagenesis of this sequence powerfully influences kinesin-driven microtubule sliding, with one mutant producing a 5-fold acceleration over wild type. We conclude that electrostatic interactions play an important role in the kinesin stepping mechanism, by biasing the diffusional association of kinesin with microtubules.

Animal and plant cells contain a molecular-scale “railway” network, in which the tracks, called microtubules, radiate out from the cell centre and locomotive proteins, called kinesins, haul their molecular cargoes along the microtubule tracks. This railway system transports many different cargoes to where they are needed, so it is crucial for the cell's organization and function. Breakdowns in this transport system can cause diseases like Alzheimer's, and drugs that temporarily halt transport make powerful anti-cancer agents. Precisely how kinesin motor proteins move along their microtubule tracks is an important question in biology. We know that some kinesins have twin “heads” that alternately bind to and step along microtubules in a coordinated walking action. But more usually, kinesins have only one head. How single-headed kinesins produce force and movement is poorly understood. In this study, we address this question and show that electrical attraction between single kinesin heads and microtubules is a critical factor deciding the direction of movement: each time the head approaches a microtubule, it slides forwards by the electrical attraction between the engine and the track.

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.

Ionic strength dependence of F-actin and glycolytic enzyme associations: a Brownian dynamics simulations approach

The association of glycolytic enzymes with F-actin is proposed to be one mechanism by which these enzymes are compartmentalized, and, as a result, may possibly play important roles for: regulation of the glycolytic pathway, potential substrate channeling, and increasing glycolytic flux. Historically, in vitro experiments have shown that many enzyme/actin interactions are dependent on ionic strength. Herein, Brownian dynamics (BD) examines how ionic strength impacts the energetics of the association of F-actin with the glycolytic enzymes: lactate dehydrogenase (LDH), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), fructose-1,6-bisphosphate aldolase (aldolase), and triose phosphate isomerase (TPI). The BD simulations are steered by electrostatics calculated by Poisson-Boltzmann theory. The BD results confirm experimental observations that the degree of association diminishes as ionic strength increases but also suggest that these interactions are significant, at physiological ionic strengths. Furthermore, BD agrees with experiments that muscle LDH, aldolase, and GAPDH interact significantly with F-actin whereas TPI does not. BD indicates similarities in binding regions for aldolase and LDH among the different species investigated. Furthermore, the residues responsible for salt bridge formation in stable complexes persist as ionic strength increases. This suggests the importance of the residues determined for these binary complexes and specificity of the interactions. That these interactions are conserved across species, and there appears to be a general trend among the enzymes, support the importance of these enzyme-F-actin interactions in creating initial complexes critical for compartmentation.

Exploring sparsely populated states of macromolecules by diamagnetic and paramagnetic NMR relaxation

Sparsely populated states of macromolecules, characterized by short lifetimes and high free-energies relative to the predominant ground state, often play a key role in many biological, chemical, and biophysical processes. In this review, we briefly summarize various new developments in NMR spectroscopy that permit these heretofore invisible, sparsely populated states to be detected, characterized, and in some instances visualized. Relaxation dispersion spectroscopy yields detailed kinetic information on processes involving species characterized by distinct chemical shifts with lifetimes in the ∼50 μs-10 ms range and populations as low as 0.5%. In the fast exchange regime (time scale less than ∼250-500 μs), the footprint of sparsely populated states can be observed on paramagnetic relaxation enhancement profiles measured on the resonances of the major species, thereby yielding structural information that is directly related to paramagnetic center-nuclei distances from which it is possible, under suitable circumstances, to compute a structure or ensemble of structures for the minor species. Finally, differential transverse relaxation measurements can be used to detect lifetime broadening effects that directly reflect the unidirectional rates for the conversion of NMR-visible into high-molecular weight NMR-invisible species. Examples of these various approaches are presented.

Mechanisms of protein-ligand association and its modulation by protein mutations

Protein-ligand interactions are essential for nearly all biological processes, and yet the biophysical mechanism that enables potential binding partners to associate before specific binding occurs remains poorly understood. Fundamental questions include which factors influence the formation of protein-ligand encounter complexes, and whether designated association pathways exist. To address these questions, we developed a computational approach to systematically analyze the complete ensemble of association pathways. Here, we use this approach to study the binding of a phosphate ion to the Escherichia coli phosphate-binding protein. Various mutants of the protein are considered, and their effects on binding free-energy profiles, association rates, and association pathway distributions are quantified. The results reveal the existence of two anion attractors, i.e., regions that initially attract negatively charged particles and allow them to be efficiently screened for phosphate, which is subsequently specifically bound. Point mutations that affect the charge on these attractors modulate their attraction strength and speed up association to a factor of 10 of the diffusion limit, and thus change the association pathways of the phosphate ligand. It is demonstrated that a phosphate that prebinds to such an attractor neutralizes its attraction effect to the environment, making the simultaneous association of a second phosphate ion unlikely. This study suggests ways in which structural properties can be used to tune molecular association kinetics so as to optimize the efficiency of binding, and highlights the importance of kinetic properties.

Bayesian framework for modeling diffusion processes with nonlinear drift based on nonlinear and incomplete observations

Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.

Automated computational framework for the analysis of electrostatic similarities of proteins

Charge plays an important role in protein-protein interactions. In the case of excessively charged proteins, their electrostatic potentials contribute to the processes of recognition and binding with other proteins or ligands. We present an automated computational framework for determining the contribution of each charged amino acid to the electrostatic properties of proteins, at atomic resolution level. This framework involves computational alanine scans, calculation of Poisson-Boltzmann electrostatic potentials, calculation of electrostatic similarity distances (ESDs), hierarchical clustering analysis of ESDs, calculation of solvation free energies of association, and visualization of the spatial distributions of electrostatic potentials. The framework is useful to classify families of mutants with similar electrostatic properties and to compare them with the parent proteins in the complex. The alanine scan mutants introduce perturbations in the local electrostatic properties of the proteins and aim in delineating the contribution of each mutated amino acid in the spatial distribution of electrostatic potential, and in biological function when electrostatics is a dominant contributing factor in protein-protein interactions. The framework can be used to design new proteins with tailored electrostatic properties, such as immune system regulators, inhibitors, and vaccines, and in guiding experimental studies. We present an example for the interaction of the immune system protein C3d (the d-fragment of complement protein C3) with its receptor CR2, and we discuss our data in view of a binding site controversy.

Cholera toxin B subunits assemble into pentamers--proposition of a fly-casting mechanism

The cholera toxin B pentamer (CtxB₅), which belongs to the AB₅ toxin family, is used as a model study for protein assembly. The effect of the pH on the reassembly of the toxin was investigated using immunochemical, electrophoretic and spectroscopic methods. Three pH-dependent steps were identified during the toxin reassembly: (i) acquisition of a fully assembly-competent fold by the CtxB monomer, (ii) association of CtxB monomer into oligomers, (iii) acquisition of the native fold by the CtxB pentamer. The results show that CtxB₅ and the related heat labile enterotoxin LTB₅ have distinct mechanisms of assembly despite sharing high sequence identity (84%) and almost identical atomic structures. The difference can be pinpointed to four histidines which are spread along the protein sequence and may act together. Thus, most of the toxin B amino acids appear negligible for the assembly, raising the possibility that assembly is driven by a small network of amino acids instead of involving all of them.

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.

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Visualization of macromolecular structures

Structural biology is rapidly accumulating a wealth of detailed information about protein function, binding sites, RNA, large assemblies and molecular motions. These data are increasingly of interest to a broader community of life scientists, not just structural experts. Visualization is a primary means for accessing and using these data, yet visualization is also a stumbling block that prevents many life scientists from benefiting from three-dimensional structural data. In this review, we focus on key biological questions where visualizing three-dimensional structures can provide insight and describe available methods and tools.

Mechanistic details of a protein-protein association pathway revealed by paramagnetic relaxation enhancement titration measurements

Protein-protein association generally proceeds via the intermediary of a transient, lowly populated, encounter complex ensemble. The mechanism whereby the interacting molecules in this ensemble locate their final stereospecific structure is poorly understood. Further, a fundamental question is whether the encounter complex ensemble is an effectively homogeneous population of nonspecific complexes or whether it comprises a set of distinct structural and thermodynamic states. Here we use intermolecular paramagnetic relaxation enhancement (PRE), a technique that is exquisitely sensitive to lowly populated states in the fast exchange regime, to characterize the mechanistic details of the transient encounter complex interactions between the N-terminal domain of Enzyme I (EIN) and the histidine-containing phosphocarrier protein (HPr), two major bacterial signaling proteins. Experiments were conducted at an ionic strength of 150 mM NaCl to eliminate any spurious nonspecific associations not relevant under physiological conditions. By monitoring the dependence of the intermolecular transverse PRE (Gamma(2)) rates measured on (15)N-labeled EIN on the concentration of paramagnetically labeled HPr, two distinct types of encounter complex configurations along the association pathway are identified and dissected. The first class, which is in equilibrium with and sterically occluded by the specific complex, probably involves rigid body rotations and small translations near or at the active site. In contrast, the second class of encounter complex configurations can coexist with the specific complex to form a ternary complex ensemble, which may help EIN compete with other HPr binding partners in vivo by increasing the effective local concentration of HPr even when the active site of EIN is occupied.

The effect of different force applications on the protein-protein complex Barnase-Barstar

Steered molecular dynamics simulations are a tool to examine the energy landscape of protein-protein complexes by applying external forces. Here, we analyze the influence of the velocity and geometry of the probing forces on a protein complex using this tool. With steered molecular dynamics, we probe the stability of the protein-protein complex Barnase-Barstar. The individual proteins are mechanically labile. The Barnase-Barstar binding site is more stable than the folds of the individual proteins. By using different force protocols, we observe a variety of responses of the system to the applied tension.

Fruitful and futile encounters along the association reaction between proteins

The association reaction between pairs of proteins proceeds through an encounter complex that develops into the final complex. Here, we combined Brownian dynamics simulations with experimental studies to analyze the structures of the encounter complexes along the association reaction between TEM1-beta-lactamase and its inhibitor, beta-lactamase-inhibitor protein. The encounter complex can be considered as an ensemble of short-lived low free-energy states that are stabilized primarily by electrostatic forces and desolvation. For the wild-type, the simulation showed two main encounter regions located outside the physical binding site. One of these regions was located near the experimentally determined transition state. To validate whether these encounters are fruitful or futile, we examined three groups of mutations that altered the encounter. The first group consisted of mutations that increased the experimental rate of association through electrostatic optimization. This resulted in an increase in the size of the encounter region located near the experimentally determined transition state, as well as a decrease in the energy of this region and an increase in the number of successful trajectories (i.e., encounters that develop into complex). A second group of mutations was specifically designed to either increase or decrease the size and energy of the second encounter complex, but either way it did not affect k(on). A third group of mutations consisted of residues that increased k(on) without significantly affecting the encounter complexes. These results indicate that the size and energy of the encounter regions are only two of several parameters that lead to fruitful association, and that electrostatic optimization is a major driving force in fast association.

Association and electrostatic steering of alpha-lactalbumin-lysozyme heterodimers

The salt and pH dependent association of hen egg white lysozyme with alpha-lactalbumin whey proteins has been studied using molecular level Monte Carlo simulations. A highly uneven charge distribution of alpha-lactalbumin leads to strongly ordered heterodimers that may facilitate the formation of structured, mesoscopic aggregates. This electrostatic steering gives rise to 80% alignment at 5 mM 1 : 1 salt which, due to screening, diminishes to 60% at 100 mM salt. The free energy of interaction minima, dominated by electrostatics, ranges between -9 kT at 1 mM salt to -2 kT at 100 mM (neutral pH). Calculated osmotic second virial cross coefficients indicate complexation in the pH interval 6-10. Multivalent ions are found to effectively destabilize the protein complex and, at constant ionic strength, the order is La(3+) > Ca(2+) > Mg(2+) > Na(+). Upon binding of calcium to alpha-lactalbumin both the interaction and orientational alignment with lysozyme are reduced due to induced changes in the whey protein charge distribution. This potentially explains the experimentally observed absence of supramolecular structuring for the calcium loaded holo alpha-lactalbumin. Where available, good agreement is found with experimental data.

Association of cytochrome c with membrane-bound cytochrome c oxidase proceeds parallel to the membrane rather than in bulk solution

Electron transfer between the water-soluble cytochrome c and the integral membrane protein cytochrome c oxidase (COX) is the terminal reaction in the respiratory chain. The first step in this reaction is the diffusional association of cytochrome c toward COX, and it is still not completely clear whether cytochrome c diffuses in the bulk solution while encountering COX, or whether it prefers to diffuse laterally on the membrane surface. This is a rather crucial question, since in the latter case the association would be strongly dependent on the lipid composition and the presence of additional membrane proteins. We applied Brownian dynamics simulations to investigate the effect of an atomistically modeled dipalmitoyl phosphatidylcholine membrane on the association behavior of cytochrome c toward COX from Paracoccus denitrificans. We studied the negatively charged, physiological electron-transfer partner of COX, cytochrome c(552), and the positively charged horse-heart cytochrome c. As expected, both cytochrome c species prefer diffusion in bulk solution while associating toward COX embedded in a membrane, where the partial charges of the lipids were switched off, and the corresponding optimal association pathways largely overlap with the association toward fully solvated COX. Remarkably, after switching on the lipid partial charges, both cytochrome c species were strongly attracted by the inhomogeneous charge distribution caused by the zwitterionic lipid headgroups. This effect is particularly enhanced for horse-heart cytochrome c and is stronger at lower ionic strength. We therefore conclude that in the presence of a polar or even a charged membrane, cytochrome c diffuses laterally rather than in three dimensions.

Visualizing lowly-populated regions of the free energy landscape of macromolecular complexes by paramagnetic relaxation enhancement

Many biological macromolecular interactions proceed via lowly-populated, highly transient species that arise from rare excursions between the minimum free energy configuration and other local minima of the free energy landscape. Little is known about the structural properties of such lowly-occupied states since they are difficult to trap and hence inaccessible to conventional structural and biophysical techniques. Yet these states play a crucial role in a variety of dynamical processes including molecular recognition and binding, allostery, induced-fit and self-assembly. Here we highlight recent progress in paramagnetic nuclear magnetic resonance to detect, visualize and characterize lowly-populated transient species at equilibrium. The underlying principle involves the application of paramagnetic relaxation enhancement (PRE) in the fast exchange regime. Under these conditions the footprint of the minor species can be observed in the PRE profiles measured for the major species, providing distances between the paramagnetic label and protons of interest are shorter in the minor species than the major one. Ensemble simulated annealing refinement directly against the PRE data permits one to obtain structural data on the minor species. We have used the PRE (a) to detect and characterize the stochastic target search process whereby a sequence-specific transcription factor (the Hox-D9 homeodomain) binds to non-cognate DNA sites as a means of enhancing the rate of specific association via intramolecular sliding and intermolecular translocation; (b) to directly visualize the distribution of non-specific transient encounter complexes involved in the formation of stereospecific protein-protein complexes; (c) to detect and visualize ultra-weak self-association of a protein, a process that is relevant to early nucleation events involved in the formation of higher order structures; and (d) to determine the structure of a minor species for a multidomain protein (maltose binding protein) where large interdomain motions are associated with ligand binding, thereby shedding direct light on the fundamental question of allostery versus induced fit in this system. The PRE offers unique opportunities to directly probe and explore in structural terms lowly-populated regions of the free energy landscape and promises to yield fundamental new insights into biophysical processes.

Replica exchange simulations of transient encounter complexes in protein-protein association

Recent paramagnetic relaxation enhancement (PRE) studies on several weakly interacting protein complexes have unequivocally demonstrated the existence of transient encounter complexes. Here, we present a computational method to study protein-protein binding by creating equilibrium ensembles that include both specific and nonspecific protein complexes. In a joint analysis of simulation and experiment we explore the physical nature and underlying physicochemical characteristics of encounter complexes involving three protein-protein interactions of the bacterial phosphotransferase system. Replica exchange Monte Carlo simulations using a coarse-grained energy function recover the structures of the specific complexes and produce binding affinities in good agreement with experiment. Together with the specific complex, a relatively small number of distinct nonspecific complexes largely accounts for the measured PRE data. The combined relative population of the latter is less than approximately 10%. The binding interfaces of the specific and nonspecific complexes differ primarily in size but exhibit similar amino acid compositions. We find that the overall funnel-shaped energy landscape of complex formation is dominated by the specific complex, a small number of structured nonspecific complexes, and a diffuse cloud of loosely bound complexes connecting the specific and nonspecific binding sites with each other and the unbound state. Nonspecific complexes may not only accelerate the binding kinetics by enhancing the rate of success of random diffusional encounters but also play a role in protein function as alternative binding modes.

Brownian dynamics and molecular dynamics study of the association between hydrogenase and ferredoxin from Chlamydomonas reinhardtii

The [FeFe] hydrogenase from the green alga Chlamydomonas reinhardtii can catalyze the reduction of protons to hydrogen gas using electrons supplied from photosystem I and transferred via ferredoxin. To better understand the association of the hydrogenase and the ferredoxin, we have simulated the process over multiple timescales. A Brownian dynamics simulation method gave an initial thorough sampling of the rigid-body translational and rotational phase spaces, and the resulting trajectories were used to compute the occupancy and free-energy landscapes. Several important hydrogenase-ferredoxin encounter complexes were identified from this analysis, which were then individually simulated using atomistic molecular dynamics to provide more details of the hydrogenase and ferredoxin interaction. The ferredoxin appeared to form reasonable complexes with the hydrogenase in multiple orientations, some of which were good candidates for inclusion in a transition state ensemble of configurations for electron transfer.

Crystal structural analysis of protein-protein interactions drastically destabilized by a single mutation

The complex of barnase (bn) and barstar (bs), which has been widely studied as a model for quantitative analysis of protein-protein interactions, is significantly destabilized by a single mutation, namely, bs Asp39 --> Ala, which corresponds to a change of 7.7 kcal x mol(-1) in the free energy of binding. However, there has been no structural information available to explain such a drastic destabilization. In the present study, we determined the structure of the mutant complex at 1.58 A resolution by X-ray crystallography. The complex was similar to the wild-type complex in terms of overall and interface structures; however, the hydrogen bond network mediated by water molecules at the interface was significantly different. Several water molecules filled the cavity created by the mutation and consequently caused rearrangement of the hydrated water molecules at the interface. The water molecules were redistributed into a channel-like structure that penetrated into the complex. Furthermore, molecular dynamics simulations showed that the mutation increased the mobility of water molecules at the interface. Since such a drastic change in hydration was not observed in other mutant complexes of bn and bs, the significant destabilization of the interaction may be due to this channel-like structure of hydrated water molecules.

Electrostatic rate enhancement and transient complex of protein-protein association

The association of two proteins is bounded by the rate at which they, via diffusion, find each other while in appropriate relative orientations. Orientational constraints restrict this rate to approximately 10(5)-10(6) M(-1) s(-1). Proteins with higher association rates generally have complementary electrostatic surfaces; proteins with lower association rates generally are slowed down by conformational changes upon complex formation. Previous studies (Zhou, Biophys J 1997;73:2441-2445) have shown that electrostatic enhancement of the diffusion-limited association rate can be accurately modeled by $k_{\bf D}$ = $k_{D}0\ {exp} ( - \langle U_{el} \rangle;{\star}/k_{B} T),$ where k(D) and k(D0) are the rates in the presence and absence of electrostatic interactions, respectively, U(el) is the average electrostatic interaction energy in a "transient-complex" ensemble, and k(B)T is the thermal energy. The transient-complex ensemble separates the bound state from the unbound state. Predictions of the transient-complex theory on four protein complexes were found to agree well with the experiment when the electrostatic interaction energy was calculated with the linearized Poisson-Boltzmann (PB) equation (Alsallaq and Zhou, Structure 2007;15:215-224). Here we show that the agreement is further improved when the nonlinear PB equation is used. These predictions are obtained with the dielectric boundary defined as the protein van der Waals surface. When the dielectric boundary is instead specified as the molecular surface, electrostatic interactions in the transient complex become repulsive and are thus predicted to retard association. Together these results demonstrate that the transient-complex theory is predictive of electrostatic rate enhancement and can help parameterize PB calculations.

Association of aminoglycosidic antibiotics with the ribosomal A-site studied with Brownian dynamics

Brownian dynamics methodology was applied to simulate the encounter of aminoglycosidic antibiotics with the ribosomal A-site RNA. Studied antibiotics included neamine, neomycin, ribostamycin and paromomycin which differ in chemical structure, the number of pseudo-sugar rings and the net charge. The influence of structural, electrostatic and hydrodynamic properties of antibiotics on the kinetics of their association with the ribosomal A-site was analyzed. The computed diffusion limited rates of association are of the order of 10(10)[Formula: see text] and they weakly depend on ionic strength. Prior to binding antibiotics often slide along the RNA groove with the time scale of approximately 10 ns per base pair in case of neamine. We observed that upon forming the encounter complex aminoglycosides displace from the binding pocket up to two Mg(2+) ions.

Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm

We present a general-purpose model for biomolecular simulations at the molecular level that incorporates stochasticity, spatial dependence, and volume exclusion, using diffusing and reacting particles with physical dimensions. To validate the model, we first established the formal relationship between the microscopic model parameters (timestep, move length, and reaction probabilities) and the macroscopic coefficients for diffusion and reaction rate. We then compared simulation results with Smoluchowski theory for diffusion-limited irreversible reactions and the best available approximation for diffusion-influenced reversible reactions. To simulate the volumetric effects of a crowded intracellular environment, we created a virtual cytoplasm composed of a heterogeneous population of particles diffusing at rates appropriate to their size. The particle-size distribution was estimated from the relative abundance, mass, and stoichiometries of protein complexes using an experimentally derived proteome catalog from Escherichia coli K12. Simulated diffusion constants exhibited anomalous behavior as a function of time and crowding. Although significant, the volumetric impact of crowding on diffusion cannot fully account for retarded protein mobility in vivo, suggesting that other biophysical factors are at play. The simulated effect of crowding on barnase-barstar dimerization, an experimentally characterized example of a bimolecular association reaction, reveals a biphasic time course, indicating that crowding exerts different effects over different timescales. These observations illustrate that quantitative realism in biosimulation will depend to some extent on mesoscale phenomena that are not currently well understood.

Computational methods for biomolecular electrostatics

An understanding of intermolecular interactions is essential for insight into how cells develop, operate, communicate, and control their activities. Such interactions include several components: contributions from linear, angular, and torsional forces in covalent bonds, van der waals forces, as well as electrostatics. Among the various components of molecular interactions, electrostatics are of special importance because of their long range and their influence on polar or charged molecules, including water, aqueous ions, and amino or nucleic acids, which are some of the primary components of living systems. Electrostatics, therefore, play important roles in determining the structure, motion, and function of a wide range of biological molecules. This chapter presents a brief overview of electrostatic interactions in cellular systems, with a particular focus on how computational tools can be used to investigate these types of interactions.

Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II

We have developed a computational approach for predicting protein-protein association rates (Alsallaq and Zhou, Structure 2007, 15, 215). Here we expand the range of applicability of this approach to protein-RNA binding and report the first results for protein-RNA binding rates predicted from atomistic modeling. The system studied is the U1A protein and stem/loop II of the U1 small nuclear RNA. Experimentally it was observed that the binding rate is significantly reduced by increasing salt concentration while the dissociation changes little with salt concentration, and charges distant from the binding site make marginal contribution to the binding rate. These observations are rationalized. Moreover, predicted effects of salt and charge mutations are found to be in quantitative agreement with experimental results.

Coarse-grained models for simulations of multiprotein complexes: application to ubiquitin binding

We develop coarse-grained models and effective energy functions for simulating thermodynamic and structural properties of multiprotein complexes with relatively low binding affinity (K(d) >1 microM) and apply them to binding of Vps27 to membrane-tethered ubiquitin. Folded protein domains are represented as rigid bodies. The interactions between the domains are treated at the residue level with amino-acid-dependent pair potentials and Debye-Hückel-type electrostatic interactions. Flexible linker peptides connecting rigid protein domains are represented as amino acid beads on a polymer with appropriate stretching, bending, and torsion-angle potentials. In simulations of membrane-attached protein complexes, interactions between amino acids and the membrane are described by residue-dependent short-range potentials and long-range electrostatics. We parameterize the energy functions by fitting the osmotic second virial coefficient of lysozyme and the binding affinity of the ubiquitin-CUE complex. For validation, extensive replica-exchange Monte Carlo simulations are performed of various protein complexes. Binding affinities for these complexes are in good agreement with the experimental data. The simulated structures are clustered on the basis of distance matrices between two proteins and ranked according to cluster population. In approximately 70% of the complexes, the distance root-mean-square is less than 5 A from the experimental structures. In approximately 90% of the complexes, the binding interfaces on both proteins are predicted correctly, and in all other cases at least one interface is correct. Transient and nonspecifically bound structures are also observed. With the validated model, we simulate the interaction between the Vps27 multiprotein complex and a membrane-tethered ubiquitin. Ubiquitin is found to bind preferentially to the two UIM domains of Vps27, but transient interactions between ubiquitin and the VHS and FYVE domains are observed as well. These specific and nonspecific interactions are found to be positively cooperative, resulting in a substantial enhancement of the overall binding affinity beyond the approximately 300 microM of the specific domains. We also find that the interactions between ubiquitin and Vps27 are highly dynamic, with conformational rearrangements enabling binding of Vps27 to diverse targets as part of the multivesicular-body protein-sorting pathway.

Elucidating transient macromolecular interactions using paramagnetic relaxation enhancement

Recent advances in the use of paramagnetic relaxation enhancement (PRE) in structure refinement and in the analysis of transient dynamic processes involved in macromolecular complex formation are presented. In the slow exchange regime, we show, using the SRY/DNA complex as an example, that the PRE provides a powerful tool that can lead to significant increases in the reliability and accuracy of NMR structure determinations. Refinement necessitates the use of an ensemble representation of the paramagnetic center and a model-free extension of the Solomon-Bloembergen equations. In the fast exchange regime, the PRE provides insight into dynamic processes and the existence of transient, low population intermediate species. The PRE allows one to characterize dynamic nonspecific binding of a protein to DNA; to directly demonstrate that the search process whereby a transcription factor locates its specific DNA target site involves both intramolecular (sliding) and intermolecular (hopping and intersegment transfer) translocation; and to detect and visualize the distribution of an ensemble of transient encounter complexes in protein-protein association.

qPIPSA: relating enzymatic kinetic parameters and interaction fields

Background

The simulation of metabolic networks in quantitative systems biology requires the assignment of enzymatic kinetic parameters. Experimentally determined values are often not available and therefore computational methods to estimate these parameters are needed. It is possible to use the three-dimensional structure of an enzyme to perform simulations of a reaction and derive kinetic parameters. However, this is computationally demanding and requires detailed knowledge of the enzyme mechanism. We have therefore sought to develop a general, simple and computationally efficient procedure to relate protein structural information to enzymatic kinetic parameters that allows consistency between the kinetic and structural information to be checked and estimation of kinetic constants for structurally and mechanistically similar enzymes.

Results

We describe qPIPSA: quantitative Protein Interaction Property Similarity Analysis. In this analysis, molecular interaction fields, for example, electrostatic potentials, are computed from the enzyme structures. Differences in molecular interaction fields between enzymes are then related to the ratios of their kinetic parameters. This procedure can be used to estimate unknown kinetic parameters when enzyme structural information is available and kinetic parameters have been measured for related enzymes or were obtained under different conditions. The detailed interaction of the enzyme with substrate or cofactors is not modeled and is assumed to be similar for all the proteins compared. The protein structure modeling protocol employed ensures that differences between models reflect genuine differences between the protein sequences, rather than random fluctuations in protein structure.

Conclusion

Provided that the experimental conditions and the protein structural models refer to the same protein state or conformation, correlations between interaction fields and kinetic parameters can be established for sets of related enzymes. Outliers may arise due to variation in the importance of different contributions to the kinetic parameters, such as protein stability and conformational changes. The qPIPSA approach can assist in the validation as well as estimation of kinetic parameters, and provide insights into enzyme mechanism.

Brownian dynamics simulation of the competitive reactions: binase dimerization and the association of binase and barstar

A comparative study of the competitive reactions-the association reaction of binase with polypeptide inhibitor barstar and the reaction of binase dimerization-has been performed by the Brownian dynamics simulation method. It was shown that three types of the binase dimers could be formed and the dimerization reaction could compete with the inhibition reaction. The first type of the dimers leaves the active centre of binase free. During the formation of the dimers of the second and the third types the active centre of one or both binase molecules is blocked and ribonuclease becomes partially or fully inactive. Brownian dynamics simulation shown, that the ratio of competitive reaction rates depends on pH and ionic strength of solution.

In silico screening of mutational effects on enzyme-proteic inhibitor affinity: a docking-based approach

Background

Molecular recognition between enzymes and proteic inhibitors is crucial for normal functioning of many biological pathways. Mutations in either the enzyme or the inhibitor protein often lead to a modulation of the binding affinity with no major alterations in the 3D structure of the complex.

Results

In this study, a rigid body docking-based approach has been successfully probed in its ability to predict the effects of single and multiple point mutations on the binding energetics in three enzyme-proteic inhibitor systems. The only requirement of the approach is an accurate structural model of the complex between the wild type forms of the interacting proteins, with the assumption that the architecture of the mutated complexes is almost the same as that of the wild type and no major conformational changes occur upon binding. The method was applied to 23 variants of the ribonuclease inhibitor-angiogenin complex, to 15 variants of the barnase-barstar complex, and to 8 variants of the bovine pancreatic trypsin inhibitor-β Trypsin system, leading to thermodynamic and kinetic estimates consistent with in vitro data. Furthermore, simulations with and without explicit water molecules at the protein-protein interface suggested that they should be included in the simulations only when their positions are well defined both in the wild type and in the mutants and they result to be relevant for the modulation of mutational effects on the association process.

Conclusion

The correlative models built in this study allow for predictions of mutational effects on the thermodynamics and kinetics of association of three substantially different systems, and represent important extensions of our computational approach to cases in which it is not possible to estimate the absolute free energies. Moreover, this study is the first example in the literature of an extensive evaluation of the correlative weights of the single components of the ZDOCK score on the thermodynamics and kinetics of binding of protein mutants compared to the native state.

Finally, the results of this study corroborate and extend a previously developed quantitative model for in silico predictions of absolute protein-protein binding affinities spanning a wide range of values, i.e. from -10 up to -21 kcal/mol.

The computational approach is simple and fast and can be used for structure-based design of protein-protein complexes and for in silico screening of mutational effects on protein-protein recognition.

On the dynamic nature of the transition state for protein-protein association as determined by double-mutant cycle analysis and simulation

The process of protein-protein association starts with their random collision, which may develop into an encounter complex followed by a transition state and final complex formation. Here we aim to experimentally characterize the nature of the transition state of protein-protein association for three different protein-protein interactions; Barnase-Barstar, TEM1-BLIP and IFNalpha2-IFNAR2, and use the data to model the transition state structures. To model the transition state, we determined inter-protein distance-constraints of the activated complex by using double mutant cycles (DMC) assuming that interacting residues are spatially close. Significant DeltaDeltaG(double dagger)(int) values were obtained only between residues on Barnase and Barstar. However, introducing specific mutations that optimize the charge complementarity between BLIP and TEM1 resulted in the introduction of significant DeltaDeltaG(double dagger)(int) values also between residues of these two proteins. While electrostatic interactions make major contributions towards stabilizing the transition state, we show two examples where steric hindrance exerts an effect on the transition state as well. To model the transition-state structures from the experimental DeltaDeltaG(double dagger)(int) values, we introduced a method for structure perturbation, searching for those inter-protein orientations that best support the experimental DeltaDeltaG(double dagger)(int) values. Two types of transition states were found, specific as observed for Barnase-Barstar and the electrostatically optimized TEM1-BLIP mutants, and diffusive as shown for wild-type TEM1-BLIP and IFNalpha2-IFNAR2. The specific transition states are characterized by defined inter-protein orientations, which cannot be modeled for the diffusive transition states. Mutations introduced through rational design can change the transition state from diffusive to specific. Together, these data provide a structural view of the mechanism allowing rates of association to differ by five orders of magnitude between different protein complexes.