Brownian dynamics simulation of protein association

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Classification of protein-protein association rates based on biophysical informatics

BACKGROUND

Proteins form various complexes to carry out their versatile functions in cells. The dynamic properties of protein complex formation are mainly characterized by the association rates which measures how fast these complexes can be formed. It was experimentally observed that the association rates span an extremely wide range with over ten orders of magnitudes. Identification of association rates within this spectrum for specific protein complexes is therefore essential for us to understand their functional roles.

RESULTS

To tackle this problem, we integrate physics-based coarse-grained simulations into a neural-network-based classification model to estimate the range of association rates for protein complexes in a large-scale benchmark set. The cross-validation results show that, when an optimal threshold was selected, we can reach the best performance with specificity, precision, sensitivity and overall accuracy all higher than 70%. The quality of our cross-validation data has also been testified by further statistical analysis. Additionally, given an independent testing set, we can successfully predict the group of association rates for eight protein complexes out of ten. Finally, the analysis of failed cases suggests the future implementation of conformational dynamics into simulation can further improve model.

CONCLUSIONS

In summary, this study demonstrated that a new modeling framework that combines biophysical simulations with bioinformatics approaches is able to identify protein-protein interactions with low association rates from those with higher association rates. This method thereby can serve as a useful addition to a collection of existing experimental approaches that measure biomolecular recognition.

Understanding the Impacts of Conformational Dynamics on the Regulation of Protein-Protein Association by a Multiscale Simulation Method

Complexes formed among diverse proteins carry out versatile functions in nearly all physiological processes. Association rates which measure how fast proteins form various complexes are of fundamental importance to characterize their functions. The association rates are not only determined by the energetic features at binding interfaces of a protein complex but also influenced by the intrinsic conformational dynamics of each protein in the complex. Unfortunately, how this conformational effect regulates protein association has never been calibrated on a systematic level. To tackle this problem, we developed a multiscale strategy to incorporate the information on protein conformational variations from Langevin dynamic simulations into a kinetic Monte Carlo algorithm of protein-protein association. By systematically testing this approach against a large-scale benchmark set, we found the association of a protein complex with a relatively rigid structure tends to be reduced by its conformational fluctuations. With specific examples, we further show that higher degrees of structural flexibility in various protein complexes can facilitate the searching and formation of intermolecular interactions and thereby accelerate their associations. In general, the integration of conformational dynamics can improve the correlation between experimentally measured association rates and computationally derived association probabilities. Finally, we analyzed the statistical distributions of different secondary structural types on protein-protein binding interfaces and their preference to the change of association rates. Our study, to the best of our knowledge, is the first computational method that systematically estimates the impacts of protein conformational dynamics on protein-protein association. It throws lights on the molecular mechanisms of how protein-protein recognition is kinetically modulated.

Using Coarse-Grained Simulations to Characterize the Mechanisms of Protein-Protein Association

The formation of functionally versatile protein complexes underlies almost every biological process. The estimation of how fast these complexes can be formed has broad implications for unravelling the mechanism of biomolecular recognition. This kinetic property is traditionally quantified by association rates, which can be measured through various experimental techniques. To complement these time-consuming and labor-intensive approaches, we developed a coarse-grained simulation approach to study the physical processes of protein–protein association. We systematically calibrated our simulation method against a large-scale benchmark set. By combining a physics-based force field with a statistically-derived potential in the simulation, we found that the association rates of more than 80% of protein complexes can be correctly predicted within one order of magnitude relative to their experimental measurements. We further showed that a mixture of force fields derived from complementary sources was able to describe the process of protein–protein association with mechanistic details. For instance, we show that association of a protein complex contains multiple steps in which proteins continuously search their local binding orientations and form non-native-like intermediates through repeated dissociation and re-association. Moreover, with an ensemble of loosely bound encounter complexes observed around their native conformation, we suggest that the transition states of protein–protein association could be highly diverse on the structural level. Our study also supports the idea in which the association of a protein complex is driven by a “funnel-like” energy landscape. In summary, these results shed light on our understanding of how protein–protein recognition is kinetically modulated, and our coarse-grained simulation approach can serve as a useful addition to the existing experimental approaches that measure protein–protein association rates.

General principles of binding between cell surface receptors and multi-specific ligands: A computational study

The interactions between membrane receptors and extracellular ligands control cell-cell and cell-substrate adhesion, and environmental responsiveness by representing the initial steps of cell signaling pathways. These interactions can be spatial-temporally regulated when different extracellular ligands are tethered. The detailed mechanisms of this spatial-temporal regulation, including the competition between distinct ligands with overlapping binding sites and the conformational flexibility in multi-specific ligand assemblies have not been quantitatively evaluated. We present a new coarse-grained model to realistically simulate the binding process between multi-specific ligands and membrane receptors on cell surfaces. The model simplifies each receptor and each binding site in a multi-specific ligand as a rigid body. Different numbers or types of ligands are spatially organized together in the simulation. These designs were used to test the relation between the overall binding of a multi-specific ligand and the affinity of its cognate binding site. When a variety of ligands are exposed to cells expressing different densities of surface receptors, we demonstrated that ligands with reduced affinities have higher specificity to distinguish cells based on the relative concentrations of their receptors. Finally, modification of intramolecular flexibility was shown to play a role in optimizing the binding between receptors and ligands. In summary, our studies bring new insights to the general principles of ligand-receptor interactions. Future applications of our method will pave the way for new strategies to generate next-generation biologics.

In order to adapt to surrounding environments, multiple signaling pathways have been evolved in cells. The first step of these pathways is to detect external stimuli, which is conducted by the dynamic interactions between cell surface receptors and extracellular ligands. As a result, recognition of extracellular ligands by cell surface receptors is an indispensable component of many physiological or pathological activities. In both natural selection and drug design, the presence of multiple binding sites in extracellular ligand complexes (so-called multi-specific ligands) is a common strategy to target different receptors on surface of the same cell. Such spatial organization of ligand binding sites can elaborately modulate the downstream signaling pathways. However, our understanding to the interactions between multi-specific ligands and membrane receptors is largely limited by the fact that these interactions are difficult to quantify and they have only been successfully measured in a very small number of cases in vivo. Using a simple computational model, we can realistically simulate the binding process between specially designed multi-specific ligands and membrane receptors on cell surfaces. This study therefore provides a useful pathway to unravel basic mechanisms of ligand-receptor interactions and design principles for new drug candidates.

Predicting Protein-protein Association Rates using Coarse-grained Simulation and Machine Learning

Protein–protein interactions dominate all major biological processes in living cells. We have developed a new Monte Carlo-based simulation algorithm to study the kinetic process of protein association. We tested our method on a previously used large benchmark set of 49 protein complexes. The predicted rate was overestimated in the benchmark test compared to the experimental results for a group of protein complexes. We hypothesized that this resulted from molecular flexibility at the interface regions of the interacting proteins. After applying a machine learning algorithm with input variables that accounted for both the conformational flexibility and the energetic factor of binding, we successfully identified most of the protein complexes with overestimated association rates and improved our final prediction by using a cross-validation test. This method was then applied to a new independent test set and resulted in a similar prediction accuracy to that obtained using the training set. It has been thought that diffusion-limited protein association is dominated by long-range interactions. Our results provide strong evidence that the conformational flexibility also plays an important role in regulating protein association. Our studies provide new insights into the mechanism of protein association and offer a computationally efficient tool for predicting its rate.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Linking 3D and 2D binding kinetics of membrane proteins by multiscale simulations

Membrane proteins are among the most functionally important proteins in cells. Unlike soluble proteins, they only possess two translational degrees of freedom on cell surfaces, and experience significant constraints on their rotations. As a result, it is currently challenging to characterize the in situ binding of membrane proteins. Using the membrane receptors CD2 and CD58 as a testing system, we developed a multiscale simulation framework to study the differences of protein binding kinetics between 3D and 2D environments. The association and dissociation processes were implemented by a coarse-grained Monte-Carlo algorithm, while the dynamic properties of proteins diffusing on lipid bilayer were captured from all-atom molecular dynamic simulations. Our simulations show that molecular diffusion, linker flexibility and membrane fluctuations are important factors in adjusting binding kinetics. Moreover, by calibrating simulation parameters to the measurements of 3D binding, we derived the 2D binding constant which is quantitatively consistent with the experimental data, indicating that the method is able to capture the difference between 3D and 2D binding environments. Finally, we found that the 2D dissociation between CD2 and CD58 is about 100-fold slower than the 3D dissociation. In summary, our simulation framework offered a generic approach to study binding mechanisms of membrane proteins.

Molecular modelling and simulations in cancer research

The complexity of cancer and the vast amount of experimental data available have made computer-aided approaches necessary. Biomolecular modelling techniques are becoming increasingly easier to use, whereas hardware and software are becoming better and cheaper. Cross-talk between theoretical and experimental scientists dealing with cancer-research from a molecular approach, however, is still uncommon. This is in contrast to other fields, such as amyloid-related diseases, where molecular modelling studies are widely acknowledged. The aim of this review paper is therefore to expose some of the more common approaches in molecular modelling to cancer scientists in simple terms, illustrating success stories while also revealing the limitations of computational studies at the molecular level.

STEREODYNAMICS, MASS EFFECT AND DOCKING FROM O(3P) + HD → OH + D AT Ecol = 0.4–1.0eV AND O(3P) + HD → OD + H AT Ecol = 0.5–1.0eV

Quasiclassical Trajectory (QCT) calculation for O(3P) + HD → OH + D and O(3P) + HD → OD + H at E col = 0.4–1.0 eV and 0.5–1.0 eV, respectively, on the lowest PES 1 3A″ of Kuppermann et al. has been done. Distribution p(ϑr) of azimuthal angles between the relative velocity k of the reactants and rotational angular momentum vector j′ of either OH or OD , p(φr) of polar as well as dihedral angles correlating k - k′ -j′, p(ϑr, φr), and PDDCS dependent upon the scattering angle ϑt of either OH , or OD between k and k′ of the reactants and products, respectively, are presented and discussed. The stereodynamics and isotopic mass effects at the smallest possible collision energies 0.4 eV and 0.5 eV for OH and OD , respectively, are significantly different. The significant mass effect with quotient 1/2 of H/D, at the corresponding collision threshold may be applied for the investigation of docking mechanism, drug modification and delivery.

Electron transfer interactome of cytochrome C

Lying at the heart of many vital cellular processes such as photosynthesis and respiration, biological electron transfer (ET) is mediated by transient interactions among proteins that recognize multiple binding partners. Accurate description of the ET complexes – necessary for a comprehensive understanding of the cellular signaling and metabolism – is compounded by their short lifetimes and pronounced binding promiscuity. Here, we used a computational approach relying solely on the steric properties of the individual proteins to predict the ET properties of protein complexes constituting the functional interactome of the eukaryotic cytochrome c (Cc). Cc is a small, soluble, highly-conserved electron carrier protein that coordinates the electron flow among different redox partners. In eukaryotes, Cc is a key component of the mitochondrial respiratory chain, where it shuttles electrons between its reductase and oxidase, and an essential electron donor or acceptor in a number of other redox systems. Starting from the structures of individual proteins, we performed extensive conformational sampling of the ET-competent binding geometries, which allowed mapping out functional epitopes in the Cc complexes, estimating the upper limit of the ET rate in a given system, assessing ET properties of different binding stoichiometries, and gauging the effect of domain mobility on the intermolecular ET. The resulting picture of the Cc interactome 1) reveals that most ET-competent binding geometries are located in electrostatically favorable regions, 2) indicates that the ET can take place from more than one protein-protein orientation, and 3) suggests that protein dynamics within redox complexes, and not the electron tunneling event itself, is the rate-limiting step in the intermolecular ET. Further, we show that the functional epitope size correlates with the extent of dynamics in the Cc complexes and thus can be used as a diagnostic tool for protein mobility.

A number of vital cellular processes such as respiration, photosynthesis, and multifarious metabolic conversions rely on a long-range electron transfer (ET) among protein molecules. Full understanding of the biological ET requires accurate description of the redox protein complexes, which is hampered by their pronounced mobility and short lifetimes. Here we used a simple computational approach to predict the ET properties of the physiological protein complexes of cytochrome c (Cc) – a small electron carrier that coordinates the electron flow among different redox partners. By performing extensive conformational sampling of the possible binding geometries, we mapped out functional epitopes in the Cc complexes and assessed their ET properties. Our study suggests that protein dynamics within redox complexes is the rate-limiting step in the intermolecular ET and indicates that the functional epitope size correlates with the extent of dynamics in the Cc complexes. We believe that the latter finding can be used as a diagnostic tool for protein mobility and expect that this work will engender future studies of the intermolecular ET in biological networks.

A Brownian dynamics study of the interactions of the luminal domains of the cytochrome b6f complex with plastocyanin and cytochrome c6: the effects of the Rieske FeS protein on the interactions

The availability of the structures of the cytochrome b6f complex (cyt b6f), plastocyanin (PC), and cytochrome c6 (cyt c6) from Chlamydomonas reinhardtii allowed us, for the first time, to model electron transfer interactions between the luminal domains of this complex (including cyt f and the Rieske FeS protein) and its redox partners in the same species. We also generated a model structure in which the FeS center of the Rieske protein was positioned closer to the heme of cyt f than observed in the crystal structure and studied its interactions with both PC and cyt c6. Our data showed that the Rieske protein in both the original crystal structure and in our modeled structure of the cyt b6f complex did not physically interfere with binding position or orientation of PC or cyt c6 on cyt f. PC docked on cyt f with the same orientation in the presence or the absence of the Rieske protein, which matched well with the previously reported NMR structures of complexes between cyt f and PC. When the FeS center of the Rieske protein was moved close to the heme of cyt f, it even enhanced the interaction rates. Studies using a cyt f modified in the 184-191 loop showed that the cyt f structure is a more important factor in determining the rate of complex formations than is the presence or the absence of the Rieske protein or its position with respect to cyt f.

A Brownian dynamics study of the effects of cytochrome f structure and deletion of its small domain in interactions with cytochrome c6 and plastocyanin in Chlamydomonas reinhardtii

The availability of seven different structures of cytochrome f (cyt f) from Chlamydomonas reinhardtii allowed us, using Brownian dynamics simulations, to model interactions between these molecules and their redox partners, plastocyanin (PC) and cytochrome c6 (cyt c6) in the same species to study the effect of cyt f structure on its function. Our results showed that different cyt f structures, which are very similar, produced different reaction rates in interactions with PC and cyt c6. We were able to attribute this to structural differences among these molecules, particularly to a small flexible loop between A-184 and G-191 (which has some of the highest crystallographic temperature factors in all of the cyt f structures) on the cyt f small domain. We also showed that deletion of the cyt f small domain affected cyt c6 more than PC, due to their different binding positions on cyt f. One function of the small domain in cyt f may be to guide PC or cyt c6 to a uniform dock with cyt f, especially due to electrostatic interactions with K-188 and K-189 on this domain. Our results could serve as a good guide for future experimental work on these proteins to understand better the electron transfer process between them. Also, these results demonstrated the sensitivity and the power of the Brownian dynamics simulations in the study of molecular interactions.

Theoretical study of interactions between muscle aldolase and F-actin: Insight into different species

Interactions of the glycolytic enzyme, fructose-1,6-bisphosphate aldolase (aldolase), with F-actin may be one mechanism for the colocalization of glycolytic enzymes. Examination of these interactions in different animal species tests this hypothesis by observing whether binding sites are conserved across species. Brownian dynamics (BD) simulations provide descriptions of such protein-protein interactions with the muscle isoforms of zebra fish and human aldolase. The results are compared with previous results obtained for rabbit muscle and yeast. The aldolase binding groove previously determined in rabbit muscle is conserved in both the human and fish muscle isoforms. The nonspecific radial free energies of interaction are similar with fish being slightly weaker than human and rabbit: human, -2.27 +/- 0.05 kcal/mol; rabbit, -2.0 +/- 0.04 kcal/mol; and fish, -1.5 +/- 0.03 kcal/mol. BD results show a large Boltzmann population of complexes formed around the A/D and B/C grooves of aldolase with the most feasible binding mode comprising two aldolase subunits to subdomain I region of the actin subunits. These results show that the location of the important residues and binding site for fish and human aldolase is very similar to that in rabbit and that in different animals the binding site is conserved. This suggests that the binding interaction between aldolase and F-actin is general in animal muscles and is rendered possible and energetically favorable through the conservation of this binding site.

Glycolytic enzyme interactions with yeast and skeletal muscle F-actin

Interaction of glycolytic enzymes with F-actin is suggested to be a mechanism for compartmentation of the glycolytic pathway. Earlier work demonstrates that muscle F-actin strongly binds glycolytic enzymes, allowing for the general conclusion that "actin binds enzymes", which may be a generalized phenomenon. By taking actin from a lower form, such as yeast, which is more deviant from muscle actin than other higher animal forms, the generality of glycolytic enzyme interactions with actin and the cytoskeleton can be tested and compared with higher eukaryotes, e.g., rabbit muscle. Cosedimentation of rabbit skeletal muscle and yeast F-actin with muscle fructose-1,6-bisphosphate aldolase (aldolase) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH) followed by Scatchard analysis revealed a biphasic binding, indicating high- and low-affinity domains. Muscle aldolase and GAPDH showed low-affinity for binding yeast F-actin, presumably because of fewer acidic residues at the N-terminus of yeast actin; this difference in affinity is also seen in Brownian dynamics computer simulations. Yeast GAPDH and aldolase showed low-affinity binding to yeast actin, which suggests that actin-glycolytic enzyme interactions may also occur in yeast although with lower affinity than in higher eukaryotes. The cosedimentation results were supported by viscometry results that revealed significant cross-linking at lower concentrations of rabbit muscle enzymes than yeast enzymes. Brownian dynamics simulations of yeast and muscle aldolase and GAPDH with yeast and muscle actin compared the relative association free energy. Yeast aldolase did not specifically bind to either yeast or muscle actin. Yeast GAPDH did bind to yeast actin although with a much lower affinity than when binding muscle actin. The binding of yeast enzymes to yeast actin was much less site specific and showed much lower affinities than in the case with muscle enzymes and muscle actin.

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.

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.

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.

Role of the Electrostatic Interactions in Pre-orientation of Subunits in the Formation of Protein-protein Complexes

Theoretical estimation of contribution of the electrostatic interactions to pre-orientation of ribonuclease subunits in process of complex formation was carried out. The subunit was considered as a multipole consisting of partial charges of all atoms of the molecule. The object of investigation was a system of two subunits with their centers of gravity fixed at some distance in vacuum. It was proposed that each subunit independently could rotate freely around its fixed center of gravity. The relative orientation states of the subunits in such system were searched at which the system has electrostatic energy minima (equilibrium states). In first approximation the equilibrium states were found using especially designed approximate method for electrostatic interaction energy calculation, which permitted to calculate and compare the energies of the system in 24(5) (approximately 8 10(6)) states with different mutual orientation of subunits. The angular coordinates of the found equilibrium states were further specified by calculation with gradient sliding method. Angular coordinates of the equilibrium states and the shapes of energy surface cuts along each coordinate angle were calculated also for the intersubunits distances diminished down to 50 angstroms. The dispersions of the angular coordinates of equilibrium states caused by heat movement (at T=300 degrees) and their changes with shortening the distance between centers of gravity of subunits were estimated. Mutual orientation of subunits in the equilibrium states of the system under consideration was found to be similar to their mutual orientations in complex. Also it was found that relaxation time of the system, caused by electrostatic interaction of subunits, after removing the system from an equilibrium state, is much less in vacuum than the mean time between their Brownian collisions at room temperature. It follows from these results that in the case of ribonuclease in vacuum the electrostatic interactions of its subunits must be strong enough to realize the effective pre-orientation of subunits during their Brownian approach from distances of the order 100 angstroms. Preliminary consideration taking into account the effect of surrounding water molecules on the electrostatic interactions of ribonuclease subunits showed that weakening of the interaction must be much less than in the case when one uses in its calculation the macroscopic dielectric permeability value equal to 80. So the results obtained for vacuum seem to be true for water solution also. More strict theoretical analysis of this problem will be carried out in the following publication.

Brownian dynamics of interactions between glyceraldehyde-3-phosphate dehydrogenase (GAPDH) mutants and F-actin

Brownian dynamics simulations of computer models of GAPDH mutants interacting with F-actin emphasized the electrostatic nature of such interactions, and confirmed the importance of four previously identified lysine residues on the GAPDH structure in these interactions. Mutants were GAPDH models in which one or more of the previously identified lysines had been replaced with alanine. Simulations showed reduced binding of these mutants to F-actin compared to wild-type GAPDH. Binding was significantly reduced by mutating the four lysines; the specific electrostatic interaction energy of the quadruple mutant was -7.3 +/- 1.0 compared to -11.4 +/- 0.5 kcal/mol for the wild enzyme. The BD simulations also reaffirmed the importance of quaternary structure for GAPDH binding F-actin.

Brownian dynamics simulations of glycolytic enzyme subsets with F-actin

Previous Brownian dynamics (BD) simulations identified specific basic residues on fructose-1,6-bisphophate aldolase (aldolase) (I. V. Ouporov et al., Biophysical Journal, 1999, Vol. 76, pp. 17-27) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH) (I. V. Ouporov et al., Journal of Molecular Recognition, 2001, Vol. 14, pp. 29-41) involved in binding F-actin, and suggested that the quaternary structure of the enzymes may be important. Herein, BD simulations of F-actin binding by enzyme dimers or peptides matching particular sequences of the enzyme and the intact enzyme triose phosphate isomerase (TIM) are compared. BD confirms the experimental observation that TIM has little affinity for F-actin. For aldolase, the critical residues identified by BD are found in surface grooves, formed by subunits A/D and B/C, where they face like residues of the neighboring subunit enhancing their electrostatic potentials. BD simulations between F-actin and aldolase A/D dimers give results similar to the native tetramer. Aldolase A/B dimers form complexes involving residues that are buried in the native structure and are energetically weaker; these results support the importance of quaternary structure for aldolase. GAPDH, however, placed the critical residues on the corners of the tetramer so there is no enhancement of the electrostatic potential between the subunits. Simulations using GAPDH dimers composed of either S/H or G/H subunits show reduced binding energetics compared to the tetramer, but for both dimers, the sets of residues involved in binding are similar to those found for the native tetramer. BD simulations using either aldolase or GAPDH peptides that bind F-actin experimentally show complex formation. The GAPDH peptide bound to the same F-actin domain as did the intact tetramer; however, unlike the tetramer, the aldolase peptide lacked specificity for binding a single F-actin domain.

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.

Brownian dynamics of interactions between aldolase mutants and F-actin

Previous Brownian dynamics (BD) simulations (Ouporov IG, Knull HR and Thomasson KA 1999. Biophys. J. 76: 17-27) of complex formation between rabbit aldolase and F-actin have identified three lysine residues (K288, K293 and K341) on aldolase and acidic residues (DEDE) at the N-terminus of actin as important to binding. BD simulations of computer models of aldolase mutants with any of these lysine residues replaced by alanine show reduced binding energy; the greatest effect of a single substitution is for K341A, and replacement of all three lysines greatly reduces binding. BD simulations of wild-type rabbit aldolase vs altered F-actin show that binding is decreased if any one of the four N-terminal acidic residues is replaced by alanine and binding is greatly reduced if three or more of the N-terminal acidic residues are replaced; none of the four actin residues appear more critical for binding than the others.

Yeast cytochrome c peroxidase: mechanistic studies via protein engineering

Cytochrome c peroxidase (CcP) is a yeast mitochondrial enzyme that catalyzes the reduction of hydrogen peroxide to water by ferrocytochrome c. It was the first heme enzyme to have its crystallographic structure determined and, as a consequence, has played a pivotal role in developing ideas about structural control of heme protein reactivity. Genetic engineering of the active site of CcP, along with structural, spectroscopic, and kinetic characterization of the mutant proteins has provided considerable insight into the mechanism of hydrogen peroxide activation, oxygen-oxygen bond cleavage, and formation of the higher-oxidation state intermediates in heme enzymes. The catalytic mechanism involves complex formation between cytochrome c and CcP. The cytochrome c/CcP system has been very useful in elucidating the complexities of long-range electron transfer in biological systems, including protein-protein recognition, complex formation, and intracomplex electron transfer processes.

Crowding by trisaccharides and the 2:1 cytochrome c-cytochrome c peroxidase complex

Proteins are designed to function under crowded conditions where the solute concentration can reach 400 g/L, but they are almost always studied in dilute solutions. To address this discrepancy, we have undertaken a series of studies to determine the effects of high solute concentrations on the thermodynamics of protein equilibria. Recently, we used isothermal titration calorimetry (ITC) to show that high concentrations of mono-, di-, and tetrasaccharides have a small stabilizing effect on the crystallographically defined cytochrome c binding site on yeast ferricytochrome c peroxidase [Morar, A. S., Wang, X., and Pielak, G. J. (2001) Biochemistry 40, 281-285]. Here, we use this technique to show that trisaccharides increase the apparent thermodynamic binding constants for both cytochrome c binding sites on the peroxidase. Mutagenesis studies confirm that the second site includes Asp 148 on the peroxidase. Binding of both cytochrome c molecules is exothermic. The data are interpreted by assuming either the presence or absence of intersite interactions.

Brownian dynamics simulations of aldolase binding glyceraldehyde 3-phosphate dehydrogenase and the possibility of substrate channeling

Brownian dynamics (BD) simulations test for channeling of the substrate, glyceraldehyde 3-phosphate (GAP), as it passes between the enzymes fructose-1,6-bisphosphate aldolase (aldolase) and glyceraldehyde 3-phosphate dehydrogenase (GAPDH). First, BD simulations determined the favorable complexes between aldolase and GAPDH; two adjacent subunits of GAPDH form salt bridges with two subunits of aldolase. These intermolecular contacts provide a strong electrostatic interaction between the enzymes. Second, BD simulates GAP moving out of the active site of the A or D aldolase subunit and entering any of the four active sites of GAPDH. The efficiency of transfer is determined as the relative number of BD trajectories that reached any active site of GAPDH. The distribution functions of the transfer time were calculated based on the duration of successful trajectories. BD simulations of the GAP binding from solution to aldolase/GAPDH complex were compared to the channeling simulations. The efficiency of transfer of GAP within an aldolase/GAPDH complex was 2 to 3% compared to 1.3% when GAP was binding to GAPDH from solution. There is a preference for GAP channeling between aldolase and GAPDH when compared to binding from solution. However, this preference is not large enough to be considered as a theoretical proof of channeling between these proteins.

Interactions of glyceraldehyde-3-phosphate dehydrogenase with G- and F-actin predicted by Brownian dynamics

Brownian dynamics (BD) was used to simulate the binding of glyceraldehyde-3-phosphate dehydrogenase (GAPDH) to G- and F-actin. High-resolution three-dimensional models (X-ray and homology built) of the proteins were used in the simulations. The electrostatic potential about each protein was predicted by solving the linearized Poisson-Boltzmann equation for use in BD simulations. The BD simulations resulted in complexes of GAPDH with G- or F-actin involving positively charged surface patches on GAPDH (Lyses 24, 69, 110 and 114) and negatively charged residues of the N- and C-termini (Asps 1, 25 and 363 and Glus 2, 4, 224 and 364) of actin. The actin residues all belong to subdomain 1. Although the positively charged surface patches of GAPDH are not close enough to each other to enhance their electrostatic potential, occasionally two subunits of the GAPDH tetramer may simultaneously interact with two neighboring monomers of F-actin. These results are different from those of fructose-1,6-bisphosphate aldolase, where quaternary structure directly influenced binding by two subunits combining their electrostatic potentials (see previous study, Ouporov et al., 1999, Biophys. J. 76: 17-27). Instead, GAPDH uses its quaternary structure to span the distance between two different actin subunits so that it can interact with two different actin subunits simultaneously.

Computer simulations of glycolytic enzyme interactions with F-actin

Muscle actin and fructose-1,6-bisphosphate aldolase (aldolase) were chemically crosslinked to produce an 80 kDa product representing one subunit of aldolase linked to one subunit of actin. Hydroxylamine digestion of the crosslinked product resulted in two 40.5 kDa fragments, one that was aldolase linked to the 12 N-terminal residues of actin. Brownian dynamics simulations of muscle aldolase and GAPDH with F-actin (muscle, yeast, and various mutants) estimated the association free energy. Mutations of residues 1-4 of muscle actin to Ala individually or two in combination of the first four residues reduced the estimated binding free energy. Simulations showed that muscle aldolase binds with the same affinity to the yeast actin as to the double mutated muscle actin; these mutations make the N-terminal of muscle actin identical to yeast, supporting the conclusion that the actin N-terminus participates in binding. Because the depth of free energy wells for yeast and the double mutants is less than for native rabbit actin, the simulations support experimental findings that muscle aldolase and GAPDH have a higher affinity for muscle actin than for yeast actin. Furthermore, Brownian dynamics revealed that the lower affinity of yeast actin for aldolase and GAPDH compared to muscle actin, was directly related to the acidic residues at the N-terminus of actin.

Brownian dynamics simulations of interactions between aldolase and G- or F-actin

Compartmentation of proteins in cells is important to proper cell function. Interactions of F-actin and glycolytic enzymes is one mechanism by which glycolytic enzymes can compartment. Brownian dynamics (BD) simulations of the binding of the muscle form of the glycolytic enzyme fructose-1,6-bisphosphate aldolase (aldolase) to F- or G-actin provide first-encounter snapshots of these interactions. Using x-ray structures of aldolase, G-actin, and three-dimensional models of F-actin, the electrostatic potential about each protein was predicted by solving the linearized Poisson-Boltzmann equation for use in BD simulations. The BD simulations provided solution complexes of aldolase with F- or G-actin. All complexes demonstrate the close contacts between oppositely charged regions of the protein surfaces. Positively charged surface regions of aldolase (residues Lys 13, 27, 288, 293, and 341 and Arg 257) are attracted to the negatively charged amino terminus (Asp 1 and Glu 2 and 4) and other patches (Asp 24, 25, and 363 and Glu 361, 364, 99, and 100) of actin subunits. According to BD results, the most important factor for aldolase binding to actin is the quaternary structure of aldolase and actin. Two pairs of adjacent aldolase subunits greatly add to the positive electrostatic potential of each other creating a region of attraction for the negatively charged subdomain 1 of the actin subunit that is exposed to solvent in the quaternary F-actin structure.

Dynamics of protein-protein docking: cytochrome c and cytochrome c peroxidase revisited

The dynamics of the docking step in the electron transfer reaction between yeast cytochrome c peroxidase and iso-1-cytochrome c has been studied using the Brownian dynamics method. In particular we have calculated the bimolecular rate constant at which a specific complex, the xray crystalline complex, can form in solution by translational and rotational diffusion in a field of force. Complexation criteria have been assessed based on the simultaneous alignment of three atom-atom contacts, as well as alternative criteria. The proteins are able to align one or two contacts at remarkably high rates, in fact, at rates approaching the diffusion-controlled limit for two spheres reactive over their entire surfaces. Three contacts may align, and hence the specific complex may dock, at rates on the order of 10(8) M(-1) s(-1), which is quite representative of the experimental association rate constant for ET-competent complex(es). The formation of the specific complex is strongly influenced by the favorable electrostatic interaction between these proteins. It is striking that a specific protein-protein complex can form within one order of magnitude as fast as two spherical proteins can touch at any orientation. It remains plausible that the high ET tunneling rate in this system can take place through a single highly favorable specific complex using a single high efficiency pathway. Still the contribution from a nonspecific set of complexes is not ruled out, particularly considering the marginal reproduction of the ionic strength dependence in the formation of the xray complex.

N epsilon,N epsilon-dimethyl-lysine cytochrome c as an NMR probe for lysine involvement in protein-protein complex formation

The reductively dimethylated derivatives of horse and yeast iso-1-ferricytochromes c have been prepared and characterized for use as NMR probes of the complexes formed by cytochrome c with bovine liver cytochrome b5 and yeast cytochrome c peroxidase. The electrostatic properties and structures of the derivatized cytochromes are not significantly perturbed by the modifications; neither are the electrostatics of protein-protein complex formation or rates of interprotein electron transfer. Two-dimensional 1H-13C NMR spectroscopy of the complexes formed by the derivatized cytochromes with cytochrome b5 and cytochrome c peroxidase has been used to investigate the number and identity of lysine residues of cytochrome c that are involved in interprotein interactions of cytochrome c. The NMR data are incompatible with simple static models proposed previously for the complexes formed by these proteins, but are consistent with the presence of multiple, interconverting complexes of comparable stability, consistent with studies employing Brownian dynamics to model the complexes. The NMR characteristics of the Nepsilon,Nepsilon-dimethyl-lysine groups, their chemical shift dispersion, oxidation state and temperature dependences and the possibility of chemical exchange phenomena are discussed with relevance to the utility of Nepsilon, Nepsilon-dimethyl-lysine's being a generally useful derivative for characterizing protein-protein complexes.

Electrostatic field around cytochrome c: theory and energy transfer experiment

Energy transfer in the "rapid diffusion" limit from electronically excited terbium(III) chelates in three different charge states to horse heart ferricytochrome c was measured as a function of ionic strength. Theoretical rate constants calculated by numerical integration of the Forster integral (containing the Poisson-Boltzmann-generated protein electrostatic potential) were compared with the experimental data to evaluate the accuracy of protein electrostatic field calculations at the protein/solvent interface. Two dielectric formalisms were used: a simple coulombic/Debye-Hückel procedure and a finite difference method [Warwicker, J. & Watson, H. C. (1982) J. Mol. Biol. 157, 671-679] that accounts for the low-dielectric protein interior and the irregular protein/solvent boundary. Good agreement with experiment was obtained and the ionic-strength dependence of the reaction was successfully reproduced. The sensitivity of theoretical rate constants to the choices of effective donor sphere size and the energy transfer distance criterion was analyzed. Electrostatic potential and rate-constant calculations were carried out on sets of structures collected along two molecular dynamics trajectories of cytochrome c. Protein conformational fluctuations were shown to produce large variations in the calculated energy transfer rate constant. We conclude that protein fluctuations and the resulting transient structures can play significant roles in biological or catalytic activities that are not apparent from examination of a static structure. For calculating protein electrostatics, large-scale low-frequency conformational fluctuations, such as charged side-chain reorientation, are established to be as important as the computational method for incorporating dielectric boundary effects.

Membrane electrostatics

In conclusion, charged membrane together with their adjacent electrolyte solution form a thermodynamic and physico-chemical entity. Their surfaces represent an exceptionally complicated interfacial system owing to intrinsic membrane complexity, as well as to the polarity and often large thickness of the interfacial region. Despite this, charged membranes can be described reasonably accurately within the framework of available theoretical models, provided that the latter are chosen on the basis of suitable criteria, which are briefly discussed in Section A. Interion correlations are likely to be important for the regular and/or rigid, thin membrane-solution interfaces. Lateral distribution of the structural membrane charge is seldom and charge distribution perpendicular to the membranes is nearly always electrostatically important. So is the interfacial hydration, which to a large extent determines the properties of the innermost part of the interfacial region, with a thickness of 2-3 nm. Fine structure of the ion double-layer and the interfacial smearing of the structural membrane charge decrease whilst the surface hydration increases the calculated value of the electrostatic membrane potential relative to the result of common Gouy-Chapman approximation. In some cases these effects partly cancel-out; simple electrostatic models are then fairly accurate. Notwithstanding this, it is at present difficult to draw detailed molecular conclusions from a large part of the published data, mainly owing to the lack of really stringent controls or calibrations. Ion binding to the membrane surface is a complicated process which involves charge-charge as well as charge-solvent interactions. Its efficiency normally increases with the ion valency and with the membrane charge density, but it is also strongly dependent on the physico-chemical and thermodynamic state of the membrane. Except in the case of the stereospecific ion binding to a membrane, the relatively easily accessible phosphate and carboxylic groups on lipids and integral membrane proteins are the main cation binding sites. Anions bind preferentially to the amine groups, even on zwitterionic molecules. Membrane structure is apt to change upon ion binding but not always in the same direction: membranes with bound ions can either expand or become more condensed, depending on the final hydrophilicity (polarity) of the membrane surface. The more polar membranes, as a rule, are less tightly packed and more fluid. Diffusive ion flow across a membrane depends on the transmembrane potential and concentration gradients, but also on the coulombic and hydration potentials at the membrane surface.(ABSTRACT TRUNCATED AT 400 WORDS)

Brownian dynamics of cytochrome c and cytochrome c peroxidase association

Brownian dynamics computer simulations of the diffusional association of electron transport proteins cytochrome c (cyt c) and cytochrome c peroxidase (cyt c per) were performed. A highly detailed and realistic model of the protein structures and their electrostatic interactions was used that was based on an atomic-level spatial description. Several structural features played a role in enhancing and optimizing the electron transfer efficiency of this reaction. Favorable electrostatic interactions facilitated long-lived nonspecific encounters between the proteins that allowed the severe orientational criteria for reaction to be overcome by rotational diffusion during encounters. Thus a "reduction-in-dimensionality" effect operated. The proteins achieved plausible electron transfer orientations in a multitude of electrostatically stable encounter complexes, rather than in a single dominant complex.