Diffusional encounter of barnase and barstar

Protein-Protein Interaction-Gaussian Accelerated Molecular Dynamics (PPI-GaMD): Characterization of Protein Binding Thermodynamics and Kinetics

Protein-protein interactions (PPIs) play key roles in many fundamental biological processes such as cellular signaling and immune responses. However, it has proven challenging to simulate repetitive protein association and dissociation in order to calculate binding free energies and kinetics of PPIs due to long biological timescales and complex protein dynamics. To address this challenge, we have developed a new computational approach to all-atom simulations of PPIs based on a robust Gaussian accelerated molecular dynamics (GaMD) technique. The method, termed "PPI-GaMD", selectively boosts interaction potential energy between protein partners to facilitate their slow dissociation. Meanwhile, another boost potential is applied to the remaining potential energy of the entire system to effectively model the protein's flexibility and rebinding. PPI-GaMD has been demonstrated on a model system of the ribonuclease barnase interactions with its inhibitor barstar. Six independent 2 μs PPI-GaMD simulations have captured repetitive barstar dissociation and rebinding events, which enable calculations of the protein binding thermodynamics and kinetics simultaneously. The calculated binding free energies and kinetic rate constants agree well with the experimental data. Furthermore, PPI-GaMD simulations have provided mechanistic insights into barstar binding to barnase, which involves long-range electrostatic interactions and multiple binding pathways, being consistent with previous experimental and computational findings of this model system. In summary, PPI-GaMD provides a highly efficient and easy-to-use approach for binding free energy and kinetics calculations of PPIs.

Challenges and frontiers of computational modelling of biomolecular recognition

Biomolecular recognition including binding of small molecules, peptides and proteins to their target receptors plays a key role in cellular function and has been targeted for therapeutic drug design. However, the high flexibility of biomolecules and slow binding and dissociation processes have presented challenges for computational modelling. Here, we review the challenges and computational approaches developed to characterise biomolecular binding, including molecular docking, molecular dynamics simulations (especially enhanced sampling) and machine learning. Further improvements are still needed in order to accurately and efficiently characterise binding structures, mechanisms, thermodynamics and kinetics of biomolecules in the future.

Membrane Binding of Antimicrobial Peptides Is Modulated by Lipid Charge Modification

Peptide interactions with lipid bilayers play a key role in a range of biological processes and depend on electrostatic interactions between charged amino acids and lipid headgroups. Antimicrobial peptides (AMPs) initiate the killing of bacteria by binding to and destabilizing their membranes. The multiple peptide resistance factor (MprF) provides a defense mechanism for bacteria against a broad range of AMPs. MprF reduces the negative charge of bacterial membranes through enzymatic conversion of the anionic lipid phosphatidyl glycerol (PG) to either zwitterionic alanyl-phosphatidyl glycerol (Ala-PG) or cationic lysyl-phosphatidyl glycerol (Lys-PG). The resulting change in the membrane charge is suggested to reduce the binding of AMPs to membranes, thus impeding downstream AMP activity. Using coarse-grained molecular dynamics to investigate the effects of these modified lipids on AMP binding to model membranes, we show that AMPs have substantially reduced affinity for model membranes containing Ala-PG or Lys-PG. More than 5000 simulations in total are used to define the relationship between lipid bilayer composition, peptide sequence (using five different membrane-active peptides), and peptide binding to membranes. The degree of interaction of a peptide with a membrane correlates with the membrane surface charge density. Free energy profile (potential of mean force) calculations reveal that the lipid modifications due to MprF alter the energy barrier to peptide helix penetration of the bilayer. These results will offer a guide to the design of novel peptides, which addresses the issue of resistance via MprF-mediated membrane modification.

The Transient Complex of Cytochrome c and Cytochrome c Peroxidase: Insights into the Encounter Complex from Multifrequency EPR and NMR Spectroscopy

We present a novel approach to study transient protein-protein complexes with standard, 9 GHz, and high-field, 95 GHz, electron paramagnetic resonance (EPR) and paramagnetic NMR at ambient temperatures and in solution. We apply it to the complex of yeast mitochondrial iso-1-cytochrome c (Cc) with cytochrome c peroxidase (CcP) with the spin label [1-oxyl-2,2,5,5-tetramethyl-Δ3-pyrroline-3-methyl)-methanethiosulfonate] attached at position 81 of Cc (SL-Cc). A dissociation constant KD of 20±4×10-6  M (EPR and NMR) and an equal amount of stereo-specific and encounter complex (NMR) are found. The EPR spectrum of the fully bound complex reveals that the encounter complex has a significant population (60 %) that shares important features, such as the Cc-interaction surface, with the stereo-specific complex.

Model of a Kinetically Driven Crosstalk between Paralogous Protein Encounter Complexes

Proteins interact with one another across a broad spectrum of affinities. Our understanding of the low end of this spectrum, as characterized by millimolar dissociation constants, relies on a handful of cases in which weak encounters have experimentally been identified. These weak interactions away from the specific target binding site can lead toward a higher-affinity complex. Recently, we detected weak encounters between two paralogous phosphotransferase pathways of Escherichia coli, which regulate various metabolic processes and stress responses. In addition to encounters that are known to occur between cognate proteins, i.e., those that can exchange phosphate groups with each other, surprisingly, encounters involving noncognates were also observed. It is not clear whether these "futile" encounters have a cooperative or competitive role. Using agent-based simulations, we find that the encounter complexes can be cooperative or competitive so as to increase or lower the effective binding affinity of the specific complex under different circumstances. This finding invites further questions into how organisms might exploit such low affinities to connect their signaling components.

Potential Regulatory Role of Competitive Encounter Complexes in Paralogous Phosphotransferase Systems

There are two paralogous Escherichia coli phosphotransferase systems, one for sugar import (PTS^sugar) and one for nitrogen regulation (PTS^Ntr), that utilize proteins enzyme I^sugar (EI^sugar) and HPr, and enzyme I^Ntr (EI^Ntr) and NPr, respectively. The enzyme I proteins have similar folds, as do their substrates HPr and NPr, yet they show strict specificity for their cognate partner both in stereospecific protein-protein complex formation and in reversible phosphotransfer. Here, we investigate the mechanism of specific EI^Ntr:NPr complex formation by the study of transient encounter complexes. NMR paramagnetic relaxation enhancement experiments demonstrated transient encounter complexes of EI^Ntr not only with the expected partner, NPr, but also with the unexpected partner, HPr. HPr occupies transient sites on EI^Ntr but is unable to complete stereospecific complex formation. By occupying the non-productive transient sites, HPr promotes NPr transient interaction to productive sites closer to the stereospecific binding site and actually enhances specific complex formation between NPr and EI^Ntr. The cellular level of HPr is approximately 150 times higher than that of NPr. Thus, our finding suggests a potential mechanism for cross-regulation of enzyme activity through formation of competitive encounter complexes.

Unbiased Atomistic Insight into the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation

Association and dissociation of proteins are fundamental processes in nature. Although simple to understand conceptually, the details of the underlying mechanisms and role of the solvent are poorly understood. Here, we investigate the dissociation of the hydrophilic β-lactoglobulin dimer by employing transition path sampling. Analysis of the sampled path ensembles reveals a variety of mechanisms: (1) a direct aligned dissociation (2) a hopping and rebinding transition followed by unbinding, and (3) a sliding transition before unbinding. Reaction coordinate and transition-state analysis predicts that, besides native contact and neighboring salt-bridge interactions, solvent degrees of freedom play an important role in the dissociation process. Bridging waters, hydrogen-bonded to both proteins, support contacts in the native state and nearby lying transition-state regions, whereas they exhibit faster dynamics in further lying transition-state regions, rendering the proteins more mobile and assisting in rebinding. Analysis of the structure and dynamics of the solvent molecules reveals that the dry native interface induces enhanced populations of both disordered hydration water near hydrophilic residues and tetrahedrally ordered hydration water nearby hydrophobic residues. Although not exhaustive, our sampling of rare unbiased reactive molecular dynamics trajectories enhances the understanding of protein dissociation via complex pathways including (multiple) rebinding events.

Protein-protein binding pathways and calculations of rate constants using fully-continuous, explicit-solvent simulations

A grand challenge in the field of biophysics has been the complete characterization of protein-protein binding processes at atomic resolution. This characterization requires the direct simulation of binding pathways starting from the initial, unbound state and proceeding through states that are too transient to be captured by experiment. Here, we applied the weighted ensemble path sampling strategy to orchestrate atomistic simulation of protein-protein binding pathways. Our simulation generated 203 fully-continuous and independent pathways along with rate constants for the binding process involving the barnase and barstar proteins. Results reveal multiple binding pathways along a "funnel-like" free energy landscape in which the formation of the "encounter complex" intermediate is rate-limiting followed by a relatively rapid rearrangement of the encounter complex to the bound state. Among all diffusional collisions, only ∼11% were productive. In the most probable binding pathways, the proteins rotated to a large extent (likely via electrostatic steering) in order to collide productively followed by "rolling" of the proteins along each other's binding interfaces to reach the bound state. Consistent with experiment, R59 was identified as the most kinetically important barnase residue for the binding process. Furthermore, protein desolvation occurs late in the binding process during the rearrangement of the encounter complex to the bound state. Notably, the positions of crystallographic water molecules that bridge hydrogen bonds between barnase and barstar are occupied in the bound-state ensemble. Our simulation was completed in a month using 1600 CPU cores at a time, demonstrating that it is now practical to carry out atomistic simulations of protein-protein binding.

Atomic-level characterization of protein-protein association

Most proteins associate with other proteins to function, forming complexes that are central to almost all physiological processes. Determining the structures of these complexes and understanding how they associate are problems of fundamental importance. Using long-timescale molecular dynamics simulations, some performed using a new enhanced sampling method, we observed spontaneous association and dissociation of five protein–protein systems to and from their experimentally determined native complexes. By analyzing the simulations of these five systems, which include members of diverse structural and functional classes, we are able to draw general mechanistic conclusions about protein association.

Despite the biological importance of protein–protein complexes, determining their structures and association mechanisms remains an outstanding challenge. Here, we report the results of atomic-level simulations in which we observed five protein–protein pairs repeatedly associate to, and dissociate from, their experimentally determined native complexes using a molecular dynamics (MD)–based sampling approach that does not make use of any prior structural information about the complexes. To study association mechanisms, we performed additional, conventional MD simulations, in which we observed numerous spontaneous association events. A shared feature of native association for these five structurally and functionally diverse protein systems was that if the proteins made contact far from the native interface, the native state was reached by dissociation and eventual reassociation near the native interface, rather than by extensive interfacial exploration while the proteins remained in contact. At the transition state (the conformational ensemble from which association to the native complex and dissociation are equally likely), the protein–protein interfaces were still highly hydrated, and no more than 20% of native contacts had formed.

re-TAMD: exploring interactions between H3 peptide and YEATS domain using enhanced sampling

BACKGROUND

Analysis of preferred binding regions of a ligand on a protein is important for detecting cryptic binding pockets and improving the ligand selectivity.

RESULT

The enhanced sampling approach TAMD has been adapted to allow a ligand to unbind from its native binding site and explore the protein surface. This so-called re-TAMD procedure was then used to explore the interaction between the N terminal peptide of histone H3 and the YEATS domain. Depending on the length of the peptide, several regions of the protein surface were explored. The peptide conformations sampled during the re-TAMD correspond to peptide free diffusion around the protein surface.

CONCLUSIONS

The re-TAMD approach permitted to get information on the relative influence of different regions of the N terminal peptide of H3 on the interaction between H3 and YEATS.

Synthesis meets theory: Past, present and future of rational chemistry

Chemical synthesis has its roots in the empirical approach of alchemy. Nonetheless, the birth of the scientific method, the technical and technological advances (exploiting revolutionary discoveries in physics) and the improved management and sharing of growing databases greatly contributed to the evolution of chemistry from an esoteric ground into a mature scientific discipline during these last 400 years. Furthermore, thanks to the evolution of computational resources, platforms and media in the last 40 years, theoretical chemistry has added to the puzzle the final missing tile in the process of “rationalizing” chemistry. The use of mathematical models of chemical properties, behaviors and reactivities is nowadays ubiquitous in literature. Theoretical chemistry has been successful in the difficult task of complementing and explaining synthetic results and providing rigorous insights when these are otherwise unattainable by experiment. The first part of this review walks the reader through a concise historical overview on the evolution of the “model” in chemistry. Salient milestones have been highlighted and briefly discussed. The second part focuses more on the general description of recent state-of-the-art computational techniques currently used worldwide by chemists to produce synergistic models between theory and experiment. Each section is complemented by key-examples taken from the literature that illustrate the application of the technique discussed therein.

Hydrodynamic Steering in Protein Association Revisited: Surprisingly Minuscule Effects of Considerable Torques

We investigate the previously postulated hydrodynamic steering phenomenon, resulting from complication of molecular shapes, its magnitude and possible relevance for protein-ligand and protein-protein diffusional encounters, and the kinetics of diffusion-controlled association. We consider effects of hydrodynamic interactions in a prototypical model system consisting of a cleft enzyme and an elongated substrate, and real protein-protein complexes, that of barnase and barstar, and human growth hormone and its binding protein. The kinetics of diffusional encounters is evaluated on the basis of rigid-body Brownian dynamics simulations in which hydrodynamic interactions between molecules are modeled using the bead-shell method for detailed description of molecular surfaces, and the first-passage-time approach. We show that magnitudes of steering torques resulting from the hydrodynamic coupling of associating molecules, evaluated for the studied systems on the basis of the Stokes-Einstein type relations for arbitrarily shaped rigid bodies, are comparable with magnitudes of torques resulting from electrostatic interactions of binding partners. Surprisingly, however, unlike in the case of electrostatic torques that strongly affect the diffusional encounter, overall effects of hydrodynamic steering torques on the association kinetics, while clearly discernible in Brownian dynamics simulations, are rather minute. We explain this result as a consequence of the thermal agitation of the binding partners. Our finding is relevant for the general understanding of a wide spectrum of molecular processes in solution but there is also a more practical aspect to it if one considers the low level of shape detail of models that are usually employed to evaluate hydrodynamic interactions in particle-based Stokesian and Brownian dynamics simulations of multicomponent biomolecular systems. Results described in the current work justify, in part at least, such a low-resolution description.

Multiscale Simulation of Receptor-Drug Association Kinetics: Application to Neuraminidase Inhibitors

A detailed understanding of the drug-receptor association process is of fundamental importance for drug design. Due to the long time scales of typical binding kinetics, the atomistic simulation of the ligand traveling from bulk solution into the binding site is still computationally challenging. In this work, we apply a multiscale approach of combined Molecular Dynamics (MD) and Brownian Dynamics (BD) simulations to investigate association pathway ensembles for the two prominent H1N1 neuraminidase inhibitors oseltamivir and zanamivir. Including knowledge of the approximate binding site location allows for the selective confinement of detailed but expensive MD simulations and application of less demanding BD simulations for the diffusion controlled part of the association pathway. We evaluate a binding criterion based on the residence time of the inhibitor in the binding pocket and compare it to geometric criteria that require prior knowledge about the binding mechanism. The method ranks the association rates of both inhibitors in qualitative agreement with experiment and yields reasonable absolute values depending, however, on the reaction criteria. The simulated association pathway ensembles reveal that, first, ligands are oriented in the electrostatic field of the receptor. Subsequently, a salt bridge is formed between the inhibitor's carboxyl group and neuraminidase residue Arg368, followed by adopting the native binding mode. Unexpectedly, despite oseltamivir's higher overall association rate, the rate into the intermediate salt-bridge state was found to be higher for zanamivir. The present methodology is intrinsically parallelizable and, although computationally demanding, allows systematic binding rate calculation on selected sets of potential drug molecules.

Floppy but not sloppy: Interaction mechanism of FG-nucleoporins and nuclear transport receptors

The nuclear pore complex (NPC) forms a permeability barrier between the nucleus and the cytoplasm. Molecules that are able to cross this permeability barrier encounter different disordered phenylalanine glycine rich nucleoporins (FG-Nups) that act as a molecular filter and regulate the selective NPC crossing of biomolecules. In this review, we provide a current overview regarding the interaction mechanism between FG-Nups and the carrier molecules that recognize and enable the transport of cargoes through the NPC aiming to understand the general molecular mechanisms that facilitate the nucleocytoplasmic transport.

Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling

Protein-protein association is fundamental to many life processes. However, a microscopic model describing the structures and kinetics during association and dissociation is lacking on account of the long lifetimes of associated states, which have prevented efficient sampling by direct molecular dynamics (MD) simulations. Here we demonstrate protein-protein association and dissociation in atomistic resolution for the ribonuclease barnase and its inhibitor barstar by combining adaptive high-throughput MD simulations and hidden Markov modelling. The model reveals experimentally consistent intermediate structures, energetics and kinetics on timescales from microseconds to hours. A variety of flexibly attached intermediates and misbound states funnel down to a transition state and a native basin consisting of the loosely bound near-native state and the tightly bound crystallographic state. These results offer a deeper level of insight into macromolecular recognition and our approach opens the door for understanding and manipulating a wide range of macromolecular association processes.

The conformational feasibility for the formation of reaching dimer in ASV and HIV integrase: a molecular dynamics study

Retroviral integrases are reported to form alternate dimer assemblies like the core-core dimer and reaching dimer. The core-core dimer is stabilized predominantly by an extensive interface between two catalytic core domains. The reaching dimer is stabilized by N-terminal domains that reach to form intermolecular interfaces with the other subunit's core and C-terminal domains (CTD), as well as CTD-CTD interactions. In this study, molecular dynamics (MD), Brownian dynamics (BD) simulations, and free energy analyses, were performed to elucidate determinants for the stability of the reaching dimer forms of full-length Avian Sarcoma Virus (ASV) and Human Immunodeficiency Virus (HIV) IN, and to examine the role of the C-tails (the last ~16-18 residues at the C-termini) in their structural dynamics. The dynamics of an HIV reaching dimer derived from small angle X-ray scattering and protein crosslinking data, was compared with the dynamics of a core-core dimer model derived from combining the crystal structures of two-domain fragments. The results showed that the core domains in the ASV reaching dimer express free dynamics, whereas those in the HIV reaching dimer are highly stable. BD simulations suggest a higher rate of association for the HIV core-core dimer than the reaching dimer. The predicted stability of these dimers was therefore ranked in the following order: ASV reaching dimer < HIV reaching dimer < composite core-core dimer. Analyses of MD trajectories have suggested residues that are critical for intermolecular contacts in each reaching dimer. Tests of these predictions and insights gained from these analyses could reveal a potential pathway for the association and dissociation of full-length IN multimers.

Influence of pH and ionic strength on electrostatic properties of ferredoxin, FNR, and hydrogenase and the rate constants of their interaction

Ferredoxin (Fd) protein transfers electrons from photosystem I (PSI) to ferredoxin:NADP⁺-reductase (FNR) in the photosynthetic electron transport chain, as well as other metabolic pathways. In some photosynthetic organisms including cyanobacteria and green unicellular algae under anaerobic conditions Fd transfers electrons not only to FNR but also to hydrogenase-an enzyme which catalyzes reduction of atomic hydrogen to H₂. One of the questions posed by this competitive relationship between proteins is which characteristics of thylakoid stroma media allow switching of the electron flow between the linear path PSI-Fd-FNR-NADP⁺ and the path PSI-Fd-hydrogenase-H₂. The study was conducted using direct multiparticle simulation approach. In this method protein molecules are considered as individual objects that experience Brownian motion and electrostatic interaction with the surrounding media and each other. Using the model we studied the effects of pH and ionic strength (I) upon complex formation between ferredoxin and FNR and ferredoxin and hydrogenase. We showed that the rate constant of Fd-FNR complex formation is constant in a wide range of physiologically significant pH values. Therefore it can be argued that regulation of FNR activity doesn't involve pH changes in stroma. On the other hand, in the model rate constant of Fd-hydrogenase interaction dramatically depends upon pH: in the range 7-9 it increases threefold. It may seem that because hydrogenase reduces protons it should be more active when pH is acidic. Apparently, regulation of hydrogenase's affinity to both her reaction partners (H⁺ and Fd) is carried out by changes in its electrostatic properties. In the dark, the protein is inactive and in the light it is activated and starts to interact with both Fd and H⁺. Therefore, we can conclude that in chloroplasts the rate of hydrogen production is regulated by pH through the changes in the affinity between hydrogenase and ferredoxin.

Binding Kinetics in Drug Discovery

Over the last years, researchers have increasingly become interested in measuring and understanding drugs' binding kinetics, namely the time in which drug and its target associate and dissociate. Historically, drug discovery programs focused on the optimization of target affinity as a proxy of in-vivo efficacy. However, often the efficacy of a ligand is not appropriately described by the in-vitro measured drug-receptor affinity, but rather depends on the lifetime of the in-vivo drug-receptor interaction. In this review we review recent works that highlight the importance of binding kinetics, molecular determinants for rational optimization and the recent emergence of computational methods as powerful tools in measuring and understanding binding kinetics.

Electrostatic Steering Accelerates C3d:CR2 Association

Electrostatic effects are ubiquitous in protein interactions and are found to be pervasive in the complement system as well. The interaction between complement fragment C3d and complement receptor 2 (CR2) has evolved to become a link between innate and adaptive immunity. Electrostatic interactions have been suggested to be the driving factor for the association of the C3d:CR2 complex. In this study, we investigate the effects of ionic strength and mutagenesis on the association of C3d:CR2 through Brownian dynamics simulations. We demonstrate that the formation of the C3d:CR2 complex is ionic strength-dependent, suggesting the presence of long-range electrostatic steering that accelerates the complex formation. Electrostatic steering occurs through the interaction of an acidic surface patch in C3d and the positively charged CR2 and is supported by the effects of mutations within the acidic patch of C3d that slow or diminish association. Our data are in agreement with previous experimental mutagenesis and binding studies and computational studies. Although the C3d acidic patch may be locally destabilizing because of unfavorable Coulombic interactions of like charges, it contributes to the acceleration of association. Therefore, acceleration of function through electrostatic steering takes precedence to stability. The site of interaction between C3d and CR2 has been the target for delivery of CR2-bound nanoparticle, antibody, and small molecule biomarkers, as well as potential therapeutics. A detailed knowledge of the physicochemical basis of C3d:CR2 association may be necessary to accelerate biomarker and drug discovery efforts.

Dissociation of a Dynamic Protein Complex Studied by All-Atom Molecular Simulations

The process of protein complex dissociation remains to be understood at the atomic level of detail. Computers now allow microsecond timescale molecular-dynamics simulations, which make the visualization of such processes possible. Here, we investigated the dissociation process of the EphA2-SHIP2 SAM-SAM domain heterodimer complex using unrestrained all-atom molecular-dynamics simulations. Previous studies on this system have shown that alternate configurations are sampled, that their interconversion can be fast, and that the complex is dynamic by nature. Starting from different NMR-derived structures, mutants were designed to stabilize a subset of configurations by swapping ion pairs across the protein-protein interface. We focused on two mutants, K956D/D1235K and R957D/D1223R, with attenuated binding affinity compared with the wild-type proteins. In contrast to calculations on the wild-type complexes, the majority of simulations of these mutants showed protein dissociation within 2.4 μs. During the separation process, we observed domain rotation and pivoting as well as a translation and simultaneous rolling, typically to alternate and weaker binding interfaces. Several unsuccessful recapturing attempts occurred once the domains were moderately separated. An analysis of protein solvation suggests that the dissociation process correlates with a progressive loss of protein-protein contacts. Furthermore, an evaluation of internal protein dynamics using quasi-harmonic and order parameter analyses indicates that changes in protein internal motions are expected to contribute significantly to the thermodynamics of protein dissociation. Considering protein association as the reverse of the separation process, the initial role of charged/polar interactions is emphasized, followed by changes in protein and solvent dynamics. The trajectories show that protein separation does not follow a single distinct pathway, but suggest that the mechanism of dissociation is common in that it initially involves transitions to surfaces with fewer, less favorable contacts compared with those seen in the fully formed complex.

Exploring the unbinding of Leishmania (L.) amazonensis CPB derived-epitopes from H2 MHC class I proteins

New strategies to control Leishmania disease demand an extensive knowledge about several aspects of infection including the understanding of its molecular events. In murine models, cysteine proteinase B from Leishmania amazonensis promotes regulation of immune response, and fragments from its C-terminus extension (cyspep) can play a decisive role in the host-parasite interaction. The interaction between cyspep-derived peptides and major histocompatibility complex (MHC) proteins is a crucial factor in Leishmania infections. Seven cyspep-derived peptides, previously identified as capable of interacting with H-2 (murine) MHC class I proteins, were studied in this work. We established a protocol to simulate the unbinding of these peptides from the cleft of H-2 receptors. From the simulations, we estimated the corresponding free energy of dissociation (ΔGd ) and described the molecular events that occur during the exit of peptides from the cleft. To test the reliability of this method, we first applied it to a calibration set of four crystallographic MHC/peptide complexes. Next, we explored the unbinding of the seven complexes mentioned above. Results were consistent with ΔGd values obtained from surface plasmon resonance (SPR) experiments. We also identified some of the primary interactions between peptides and H-2 receptors, and we detected three regions of influence for the interaction. This pattern was systematically observed for the peptides and helped determine a minimum distance for the real interaction between peptides and H-2 proteins occurring at ∼ 25 Å.

Insights into Protein-Ligand Interactions: Mechanisms, Models, and Methods

Molecular recognition, which is the process of biological macromolecules interacting with each other or various small molecules with a high specificity and affinity to form a specific complex, constitutes the basis of all processes in living organisms. Proteins, an important class of biological macromolecules, realize their functions through binding to themselves or other molecules. A detailed understanding of the protein–ligand interactions is therefore central to understanding biology at the molecular level. Moreover, knowledge of the mechanisms responsible for the protein-ligand recognition and binding will also facilitate the discovery, design, and development of drugs. In the present review, first, the physicochemical mechanisms underlying protein–ligand binding, including the binding kinetics, thermodynamic concepts and relationships, and binding driving forces, are introduced and rationalized. Next, three currently existing protein-ligand binding models—the “lock-and-key”, “induced fit”, and “conformational selection”—are described and their underlying thermodynamic mechanisms are discussed. Finally, the methods available for investigating protein–ligand binding affinity, including experimental and theoretical/computational approaches, are introduced, and their advantages, disadvantages, and challenges are discussed.

Plasticity of an ultrafast interaction between nucleoporins and nuclear transport receptors

The mechanisms by which intrinsically disordered proteins engage in rapid and highly selective binding is a subject of considerable interest and represents a central paradigm to nuclear pore complex (NPC) function, where nuclear transport receptors (NTRs) move through the NPC by binding disordered phenylalanine-glycine-rich nucleoporins (FG-Nups). Combining single-molecule fluorescence, molecular simulations, and nuclear magnetic resonance, we show that a rapidly fluctuating FG-Nup populates an ensemble of conformations that are prone to bind NTRs with near diffusion-limited on rates, as shown by stopped-flow kinetic measurements. This is achieved using multiple, minimalistic, low-affinity binding motifs that are in rapid exchange when engaging with the NTR, allowing the FG-Nup to maintain an unexpectedly high plasticity in its bound state. We propose that these exceptional physical characteristics enable a rapid and specific transport mechanism in the physiological context, a notion supported by single molecule in-cell assays on intact NPCs.

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Integrative structural biology reveals the basis of rapid nuclear transport

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Transient binding of disordered nucleoporins leaves their plasticity unaffected

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Multiple minimalistic low-affinity binding motifs create a polyvalent complex

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A highly reactive and dynamic surface permits an ultrafast binding mechanism

Toward understanding allosteric activation of thrombin: a conjecture for important roles of unbound Na(+) molecules around thrombin

We shed light on important roles of unbound Na(+) molecules in enzymatic activation of thrombin. Molecular mechanism of Na(+)-activation of thrombin has been discussed in the context of allostery. However, the recent challenge to redesign K(+)-activated thrombin revealed that the allosteric interaction is insufficient to explain the mechanism. Under these circumstances, we have examined the roles of unbound Na(+) molecule in maximization of thrombin-substrate association reaction rate. We performed all-atomic molecular dynamics (MD) simulations of thrombin in the presence of three different cations; Li(+), Na(+), and Cs(+). Although these cations are commonly observed in the vicinity of the S1-pocket of thrombin, smaller cations are distributed more densely and extensively than larger ones. This suggests the two observation rules: (i) thrombin surrounded by Na(+) is at an advantage in the initial step of association reaction, namely, the formation of an encounter complex ensemble, and (ii) the presence of Na(+) molecules does not necessarily have an advantage in the final step of association reaction, namely, the formation of the stereospecific complex. In conclusion, we propose a conjecture that unbound Na(+) molecules also affect the maximization of rate constant of thrombin-substrate association reaction through optimally forming an encounter complex ensemble.

Poisson-Boltzmann versus Size-Modified Poisson-Boltzmann Electrostatics Applied to Lipid Bilayers

Mean-field methods, such as the Poisson–Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson–Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

Energy landscape of all-atom protein-protein interactions revealed by multiscale enhanced sampling

Protein-protein interactions are regulated by a subtle balance of complicated atomic interactions and solvation at the interface. To understand such an elusive phenomenon, it is necessary to thoroughly survey the large configurational space from the stable complex structure to the dissociated states using the all-atom model in explicit solvent and to delineate the energy landscape of protein-protein interactions. In this study, we carried out a multiscale enhanced sampling (MSES) simulation of the formation of a barnase-barstar complex, which is a protein complex characterized by an extraordinary tight and fast binding, to determine the energy landscape of atomistic protein-protein interactions. The MSES adopts a multicopy and multiscale scheme to enable for the enhanced sampling of the all-atom model of large proteins including explicit solvent. During the 100-ns MSES simulation of the barnase-barstar system, we observed the association-dissociation processes of the atomistic protein complex in solution several times, which contained not only the native complex structure but also fully non-native configurations. The sampled distributions suggest that a large variety of non-native states went downhill to the stable complex structure, like a fast folding on a funnel-like potential. This funnel landscape is attributed to dominant configurations in the early stage of the association process characterized by near-native orientations, which will accelerate the native inter-molecular interactions. These configurations are guided mostly by the shape complementarity between barnase and barstar, and lead to the fast formation of the final complex structure along the downhill energy landscape.

Dynamic nature of the protein-protein interactions is an important element of cellular processes such as metabolic reactions and signal transduction, but its atomistic details are still unclear. Computational survey using molecular dynamics simulation is a straightforward method to elucidate these atomistic protein-protein interaction processes. However, a sufficient configurational sampling of the large system containing the atomistic protein complex model and explicit solvent remains a great challenge due to the long timescale involved. Here, we demonstrate that the multiscale enhanced sampling (MSES) successfully captured the atomistic details of the association/dissociation processes of a barnase-barstar complex covering the sampled space from the native complex structure to fully non-native configurations. The landscape derived from the simulation indicates that the association process is funnel-like downhill, analogously to the funnel landscape of fast-folding proteins. The funnel was found to be originated from near-native orientations guided by the shape complementarity between barnase and barstar, accelerating the formation of native inter-molecular interactions to complete the final complex structure.

Visualising intrinsic disorder and conformational variation in protein ensembles

Intrinsically disordered regions (IDRs) in proteins are still not well understood, but are increasingly recognised as important in key biological functions, as well as in diseases. IDRs often confound experimental structure determination-however, they are present in many of the available 3D structures, where they exhibit a wide range of conformations, from ill-defined and highly flexible to well-defined upon binding to partner molecules, or upon post-translational modifications. Analysing such large conformational variations across ensembles of 3D structures can be complex and difficult; our goal in this paper is to improve this situation by augmenting traditional approaches (molecular graphics and principal components) with methods from human-computer interaction and information visualisation, especially parallel coordinates. We present a new tool integrating these approaches, and demonstrate how it can dissect ensembles to reveal functional insights into conformational variation and intrinsic disorder.

Free-energy landscape of protein oligomerization from atomistic simulations

In the realm of protein-protein interactions, the assembly process of homooligomers plays a fundamental role because the majority of proteins fall into this category. A comprehensive understanding of this multistep process requires the characterization of the driving molecular interactions and the transient intermediate species. The latter are often short-lived and thus remain elusive to most experimental investigations. Molecular simulations provide a unique tool to shed light onto these complex processes complementing experimental data. Here we combine advanced sampling techniques, such as metadynamics and parallel tempering, to characterize the oligomerization landscape of fibritin foldon domain. This system is an evolutionarily optimized trimerization motif that represents an ideal model for experimental and computational mechanistic studies. Our results are fully consistent with previous experimental nuclear magnetic resonance and kinetic data, but they provide a unique insight into fibritin foldon assembly. In particular, our simulations unveil the role of nonspecific interactions and suggest that an interplay between thermodynamic bias toward native structure and residual conformational disorder may provide a kinetic advantage.

Formation of transient protein complexes

The encounter complex of two proteins is a dynamic intermediate state that guides proteins to their binding site, thus enhancing the rate of complex formation. It is particularly useful for complexes that must balance a biological requirement for high turnover with the need for specific binding, such as electron transfer complexes. Here, we describe the current methods for studying and visualizing encounter complexes. We discuss recent developments in mapping the energy landscapes, the role of hydrophobic interactions during encounter complex formation and the discovery of futile encounter complexes. These studies have not only provided insight into encounter complexes of electron transfer proteins, but also opened up new questions and approaches for studying encounter complexes in other weakly associated proteins.

Efficient determination of protein-protein standard binding free energies from first principles

Characterizing protein-protein association quantitatively has been a longstanding challenge for computer simulations. Here, a theoretical framework is put forth that addresses this challenge on the basis of detailed all-atom molecular dynamics simulations with explicit solvent. The proposed methodology relies upon independent potential of mean force (PMF) free-energy calculations carried out sequentially, wherein the biological objects are restrained in the conformation, position and orientation of the bound state, using adequately chosen biasing potentials. These restraints systematically narrow down the configurational entropy available to the system and effectively guarantee that the relevant network of interactions is properly sampled as the two proteins reversibly associate. Decomposition of the binding process into consecutive, well-delineated stages, for both the protein complex and the individual, unbound partners, offers a rigorous definition of the standard state, from which the absolute binding free energy can be determined. The method is applied to the difficult case of the extracellular ribonuclease barnase binding to its intracellular inhibitor barstar. The calculated binding free energy is -21.0 ± 1.4 kcal/mol, which compares well with the experimental value of -19.0 ± 0.2 kcal/mol. The relatively small statistical error reflects the precision and convergence afforded by the PMF-based simulation methodology. In addition to providing an accurate reproduction of the standard binding free energy, the proposed strategy offers a detailed picture of the protein-protein interface, illuminating the thermodynamic forces that underlie reversible association. The application of the present formal framework to barnase:barstar binding provides a foundation for tackling nearly any protein-protein complex.

Hydrodynamic effects on the relative rotational velocity of associating proteins

Hydrodynamic steering effects on the barnase-barstar association were studied through the analysis of the relative rotational velocity of the proteins. We considered the two proteins approaching each other in response to their electrostatic attraction and employed a method that accounts for the long-range and many-body character of the hydrodynamic interactions, as well as the complicated shapes of the proteins. Hydrodynamic steering effects were clearly seen when attractive forces were applied to the geometric centers of the proteins (resulting in zero torques) and the attraction acted along the line that connects centers of geometry of proteins in their crystallographic complex. When we rotated barstar relative to barnase around this line by an angle in the range from -90° to 60°, the rotational velocity arising solely from hydrodynamic interactions restored the orientation of the proteins in the crystal structure. However, because, in reality, both electrostatic forces and torques act on the proteins and these forces and torques depend on the protein-protein distance and the relative orientation of the binding partners, we also investigated more realistic situations employing continuum electrostatics calculations based on atomistic protein models. Overall, we conclude that hydrodynamic interactions aid barnase and barstar in assuming a proper relative orientation upon complex formation.

Ligand Binding Pathway Elucidation for Cryptophane Host-Guest Complexes

Modeling binding pathways can provide insight into molecular recognition, including kinetic mechanisms, barriers to binding, and gating effects. This work represents a novel computational approach, Hopping Minima, for the determination of conformational transitions of single molecules as well as binding pathways for molecular complexes. The method begins by thoroughly sampling a set of conformational minima for a molecular system. The natural motions of the system are modeled using the normal modes of the sampled minima. The natural motions are utilized to connect conformational minima and are finally combined to form association/binding pathways in the case of molecular complexes. We provide an implementation and example application of the method using alanine dipeptide and a set of chemical host-guest systems: two cryptophane hosts with two guest cations, trimethylammonium and tetramethylammonium. Our results demonstrate that conformational transitions can be modeled and extended to find binding pathways as well as energetic information relevant to the minimum conformations involved. This approach has advantages over simulation-based methods for studying systems with slow binding processes and can help design molecules with preferred binding kinetics.

Evolving the [myoglobin, cytochrome b(5)] complex from dynamic toward simple docking: charging the electron transfer reactive patch

We describe photoinitiated electron transfer (ET) from a suite of Zn-substituted myoglobin (Mb) variants to cytochrome b(5) (b(5)). An electrostatic interface redesign strategy has led to the introduction of positive charges into the vicinity of the heme edge through D/E → K charge-reversal mutation combinations at "hot spot" residues (D44, D60, and E85), augmented by the elimination of negative charges from Mb or b(5) by neutralization of heme propionates. These variations create an unprecedentedly large range in the product of the ET partners' total charges (-5 < -q(Mb)q(b(5)) < 40). The binding affinity (K(a)) increases 1000-fold as -q(Mb)q(b(5)) increases through this range and exhibits a surprisingly simple, exponential dependence on -q(Mb)q(b(5)). This is explained in terms of electrostatic interactions between a "charged reactive patch" (crp) on each partner's surface, defined as a compact region around the heme edge that (i) contains the total protein charge of each variant and (ii) encompasses a major fraction of the "reactive region" (Rr) comprising surface atoms with large matrix elements for electron tunneling to the heme. As -q(Mb)q(b(5)) increases, the complex undergoes a transition from fast to slow-exchange dynamics on the triplet ET time scale, with a correlated progression in the rate constants for intracomplex (k(et)) and bimolecular (k(2)) ET. This progression is analyzed by integrating the crp and Rr descriptions of ET into the textbook steady-state treatment of reversible binding between partners that undergo intracomplex ET and found to encompass the full range of behaviors predicted by the model. The generality of this approach is demonstrated by its application to the extensive body of data for the ET complex between the photosynthetic reaction center and cytochrome c(2). Deviations from this model also are discussed.

Do we have to explicitly model the ions in brownian dynamics simulations of proteins?

Brownian dynamics (BD) is a very efficient coarse-grained simulation technique which is based on Einstein's explanation of the diffusion of colloidal particles. On these length scales well beyond the solvent granularity, a treatment of the electrostatic interactions on a Debye-Hückel (DH) level with its continuous ion densities is consistent with the implicit solvent of BD. On the other hand, since many years BD is being used as a workhorse simulation technique for the much smaller biological proteins. Here, the assumption of a continuous ion density, and therefore the validity of the DH electrostatics, becomes questionable. We therefore investigated for a few simple cases how far the efficient DH electrostatics with point charges can be used and when the ions should be included explicitly in the BD simulation. We find that for large many-protein scenarios or for binary association rates, the conventional continuum methods work well and that the ions should be included explicitly when detailed association trajectories or protein folding are investigated.

EMMA: A Software Package for Markov Model Building and Analysis

The study of folding and conformational changes of macromolecules by molecular dynamics simulations often requires the generation of large amounts of simulation data that are difficult to analyze. Markov (state) models (MSMs) address this challenge by providing a systematic way to decompose the state space of the molecular system into substates and to estimate a transition matrix containing the transition probabilities between these substates. This transition matrix can be analyzed to reveal the metastable, i.e., long-living, states of the system, its slowest relaxation time scales, and transition pathways and rates, e.g., from unfolded to folded, or from dissociated to bound states. Markov models can also be used to calculate spectroscopic data and thus serve as a way to reconcile experimental and simulation data. To reduce the technical burden of constructing, validating, and analyzing such MSMs, we provide the software framework EMMA that is freely available at https://simtk.org/home/emma .

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.