The free energy landscape of small molecule unbinding

Efficient Atomistic Simulation of Pathways and Calculation of Rate Constants for a Protein-Peptide Binding Process: Application to the MDM2 Protein and an Intrinsically Disordered p53 Peptide

The characterization of protein binding processes - with all of the key conformational changes - has been a grand challenge in the field of biophysics. Here, we have used the weighted ensemble path sampling strategy to orchestrate molecular dynamics simulations, yielding atomistic views of protein-peptide binding pathways involving the MDM2 oncoprotein and an intrinsically disordered p53 peptide. A total of 182 independent, continuous binding pathways were generated, yielding a kon that is in good agreement with experiment. These pathways were generated in 15 days using 3500 cores of a supercomputer, substantially faster than would be possible with "brute force" simulations. Many of these pathways involve the anchoring of p53 residue F19 into the MDM2 binding cleft when forming the metastable encounter complex, indicating that F19 may be a kinetically important residue. Our study demonstrates that it is now practical to generate pathways and calculate rate constants for protein binding processes using atomistic simulation on typical computing resources.

Exploration of gated ligand binding recognizes an allosteric site for blocking FABP4-protein interaction

Fatty acid binding protein 4 (FABP4), reversibly binding to fatty acids and other lipids with high affinities, is a potential target for treatment of cancers. The binding site of FABP4 is buried in an interior cavity and thereby ligand binding/unbinding is coupled with opening/closing of FABP4. It is a difficult task both experimentally and computationally to illuminate the entry or exit pathway, especially with the conformational gating. In this report we combine extensive computer simulations, clustering analysis, and the Markov state model to investigate the binding mechanism of FABP4 and troglitazone. Our simulations capture spontaneous binding and unbinding events as well as the conformational transition of FABP4 between the open and closed states. An allosteric binding site on the protein surface is recognized for the development of novel FABP4 inhibitors. The binding affinity is calculated and compared with the experimental value. The kinetic analysis suggests that ligand residence on the protein surface may delay the binding process. Overall, our results provide a comprehensive picture of ligand diffusion on the protein surface, ligand migration into the buried cavity, and the conformational change of FABP4 at an atomic level.

Product Release Pathways in Human and Plasmodium falciparum Phosphoribosyltransferase

Atomistic molecular dynamics (MD) simulations coupled with the metadynamics technique were carried out to delineate the product (PPi.2Mg and IMP) release mechanisms from the active site of both human (Hs) and Plasmodium falciparum (Pf) hypoxanthine-guanine-(xanthine) phosphoribosyltransferase (HG(X)PRT). An early movement of PPi.2Mg from its binding site has been observed. The swinging motion of the Asp side chain (D134/D145) in the binding pocket facilitates the detachment of IMP, which triggers the opening of flexible loop II, the gateway to the bulk solvent. In PfHGXPRT, PPi.2Mg and IMP are seen to be released via the same path in all of the biased MD simulations. In HsHGPRT too, the product molecules follow similar routes from the active site; however, an alternate but minor escape route for PPi.2Mg has been observed in the human enzyme. Tyr 104 and Phe 186 in HsHGPRT and Tyr 116 and Phe 197 in PfHGXPRT are the key residues that mediate the release of IMP, whereas the motion of PPi.2Mg away from the reaction center is guided by the negatively charged Asp and Glu and a few positively charged residues (Lys and Arg) that line the product release channels. Mutations of a few key residues present in loop II of Trypanosoma cruzi (Tc) HGPRT have been shown to reduce the catalytic efficiency of the enzyme. Herein, in silico mutation of corresponding residues in loop II of HsHGPRT and PfHGXPRT resulted in partial opening of the flexible loop (loop II), thus exposing the active site to bulk water, which offers a rationale for the reduced catalytic activity of these two mutant enzymes. Investigations of the product release from these HsHGPRT and PfHGXPRT mutants delineate the role of these important residues in the enzymatic turnover.

Adaptive Multilevel Splitting Method for Molecular Dynamics Calculation of Benzamidine-Trypsin Dissociation Time

Adaptive multilevel splitting (AMS) is a rare event sampling method that requires minimal parameter tuning and allows unbiased sampling of transition pathways of a given rare event. Previous simulation studies have verified the efficiency and accuracy of AMS in the calculation of transition times for simple systems in both Monte Carlo and molecular dynamics (MD) simulations. Now, AMS is applied for the first time to an MD simulation of protein-ligand dissociation, representing a leap in complexity from the previous test cases. Of interest is the dissociation rate, which is typically too low to be accessible to conventional MD. The present study joins other recent efforts to develop advanced sampling techniques in MD to calculate dissociation rates, which are gaining importance in the pharmaceutical field as indicators of drug efficacy. The system investigated here, benzamidine bound to trypsin, is an example common to many of these efforts. The AMS estimate of the dissociation rate was found to be (2.6 ± 2.4) × 10(2) s(-1), which compares well with the experimental value.

Protein Structural Memory Influences Ligand Binding Mode(s) and Unbinding Rates

The binding of small molecules (e.g., natural ligands, metabolites, and drugs) to proteins governs most biochemical pathways and physiological processes. Here, we use molecular dynamics to investigate the unbinding of dimethyl sulfoxide (DMSO) from two distinct states of a small rotamase enzyme, the FK506-binding protein (FKBP). These states correspond to the FKBP protein relaxed with and without DMSO in the active site. Since the time scale of ligand unbinding (2-20 ns) is faster than protein relaxation (100 ns), a novel methodology is introduced to relax the protein without having to introduce an artificial constraint. The simulation results show that the unbinding time is an order of magnitude longer for dissociation from the DMSO-bound state (holo-relaxed). That is, the actual rate of unbinding depends on the state of the protein, with the protein having a long-lived memory. The rate thus depends on the concentration of the ligand as the apo and holo states reflect low and high concentrations of DMSO, respectively. Moreover, there are multiple binding modes in the apo-relaxed state, while a single binding mode dominates the holo-relaxed state in which DMSO acts as hydrogen bond acceptor from the backbone NH of Ile56, as in the crystal structure of the DMSO/FKBP complex. The solvent relaxes very fast (∼1 ns) close to the NH of Ile56 and with the same time scale of the protein far away from the active site. These results have implications for high-throughput docking, which makes use of a rigid structure of the protein target.

Molecular Dynamics: New Frontier in Personalized Medicine

The field of drug discovery has witnessed infinite development over the last decade with the demand for discovery of novel efficient lead compounds. Although the development of novel compounds in this field has seen large failure, a breakthrough in this area might be the establishment of personalized medicine. The trend of personalized medicine has shown stupendous growth being a hot topic after the successful completion of Human Genome Project and 1000 genomes pilot project. Genomic variant such as SNPs play a vital role with respect to inter individual's disease susceptibility and drug response. Hence, identification of such genetic variants has to be performed before administration of a drug. This process requires high-end techniques to understand the complexity of the molecules which might bring an insight to understand the compounds at their molecular level. To sustenance this, field of bioinformatics plays a crucial role in revealing the molecular mechanism of the mutation and thereby designing a drug for an individual in fast and affordable manner. High-end computational methods, such as molecular dynamics (MD) simulation has proved to be a constitutive approach to detecting the minor changes associated with an SNP for better understanding of the structural and functional relationship. The parameters used in molecular dynamic simulation elucidate different properties of a macromolecule, such as protein stability and flexibility. MD along with docking analysis can reveal the synergetic effect of an SNP in protein-ligand interaction and provides a foundation for designing a particular drug molecule for an individual. This compelling application of computational power and the advent of other technologies have paved a promising way toward personalized medicine. In this in-depth review, we tried to highlight the different wings of MD toward personalized medicine.

Computational design of a time-dependent histone deacetylase 2 selective inhibitor

Development of isoform-selective histone deacetylase (HDAC) inhibitors is of great biological and medical interest. Among 11 zinc-dependent HDAC isoforms, it is particularly challenging to achieve isoform inhibition selectivity between HDAC1 and HDAC2 due to their very high structural similarities. In this work, by developing and applying a novel de novo reaction-mechanism-based inhibitor design strategy to exploit the reactivity difference, we have discovered the first HDAC2-selective inhibitor, β-hydroxymethyl chalcone. Our bioassay experiments show that this new compound has a unique time-dependent selective inhibition on HDAC2, leading to about 20-fold isoform-selectivity against HDAC1. Furthermore, our ab initio QM/MM molecular dynamics simulations, a state-of-the-art approach to study reactions in biological systems, have elucidated how the β-hydroxymethyl chalcone can achieve the distinct time-dependent inhibition toward HDAC2.

Markov state models of biomolecular conformational dynamics

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

Network visualization of conformational sampling during molecular dynamics simulation

Effective data reduction methods are necessary for uncovering the inherent conformational relationships present in large molecular dynamics (MD) trajectories. Clustering algorithms provide a means to interpret the conformational sampling of molecules during simulation by grouping trajectory snapshots into a few subgroups, or clusters, but the relationships between the individual clusters may not be readily understood. Here we show that network analysis can be used to visualize the dominant conformational states explored during simulation as well as the connectivity between them, providing a more coherent description of conformational space than traditional clustering techniques alone. We compare the results of network visualization against 11 clustering algorithms and principal component conformer plots. Several MD simulations of proteins undergoing different conformational changes demonstrate the effectiveness of networks in reaching functional conclusions.

Mechanism and Kinetics of Acetyl-Lysine Binding to Bromodomains

Bromodomains are four-helix bundle proteins that specifically recognize acetylation of lysine side chains on histones. The available X-ray structures of bromodomain/histone tail complexes show that the conserved Asn residue in the loop between helices B and C is involved in a hydrogen bond with the acetyl-lysine side chain. Here we analyze the spontaneous binding of acetyl-lysine to the bromodomain TAF1(2) by the first molecular dynamics simulations of histone mark binding to an epigenetic reader protein. Multiple events of reversible association sampled along the unbiased simulations allow us to determine the pathway and kinetics of binding. The simulations show that acetyl-lysine has two major binding modes in TAF1(2) one of which corresponds to the available crystal structures and is stabilized by a hydrogen bond to the conserved Asn side chain. The other major binding mode is more buried than in the crystal structures and is stabilized by two hydrogen bonds with conserved residues of the loop between helices Z and A. In the more buried binding conformation, three of the six structured water molecules at the bottom of the binding pocket are displaced by the acetyl-lysine side chain. The kinetic analysis shows that the two binding modes interconvert on a faster time scale with respect to the association/dissociation process. The atomic-level description of the binding pathway and binding modes is useful for the design of small molecule modulators of histone binding to bromodomains.

Structured water molecules in the binding site of bromodomains can be displaced by cosolvent

Bromodomains are α-helical bundles of approximately 110 residues that recognize acetylated lysine side chains mainly on histone tails. Bromodomains are known to play an important role in cancer and inflammation, and as such, significant efforts are being made to identify small-molecule inhibitors of these epigenetic reader proteins. Here, explicit solvent molecular dynamics (MD) simulations of two bromodomains (BAZ2B and CREBBP) are used to analyze the water molecules that seem to be conserved at the bottom of the acetyl-lysine binding site in most crystal structures of bromodomains. The MD runs suggest that the occupancy of the structured water molecules is influenced by conformational transitions of the loop that connects helices Z and A. Additional simulations in the presence of 50 molecules of cosolvent (i.e., 440 mM of dimethylsulfoxide, methanol, or ethanol) indicate that some of the structured water molecules can be displaced transiently. The residence time in the acetyl-lysine binding site is calculated to be about 1 ns, 2-5 ns, and 10-30 ns for methanol, ethanol, and dimethylsulfoxide, respectively, while the affinity of the three cosolvents for BAZ2B and CREBBP is in the range of 50-500 mM. The results described have implications for ligand design, suggesting that only structured water molecules that do not exchange with cosolvent should be maintained in crystal structures used for docking campaigns, and that hydroxy substituents should be incorporated in the ligand so as to map the structured water molecules replaced by (m)ethanol.

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.

GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit

MOTIVATION

Molecular simulation has historically been a low-throughput technique, but faster computers and increasing amounts of genomic and structural data are changing this by enabling large-scale automated simulation of, for instance, many conformers or mutants of biomolecules with or without a range of ligands. At the same time, advances in performance and scaling now make it possible to model complex biomolecular interaction and function in a manner directly testable by experiment. These applications share a need for fast and efficient software that can be deployed on massive scale in clusters, web servers, distributed computing or cloud resources.

RESULTS

Here, we present a range of new simulation algorithms and features developed during the past 4 years, leading up to the GROMACS 4.5 software package. The software now automatically handles wide classes of biomolecules, such as proteins, nucleic acids and lipids, and comes with all commonly used force fields for these molecules built-in. GROMACS supports several implicit solvent models, as well as new free-energy algorithms, and the software now uses multithreading for efficient parallelization even on low-end systems, including windows-based workstations. Together with hand-tuned assembly kernels and state-of-the-art parallelization, this provides extremely high performance and cost efficiency for high-throughput as well as massively parallel simulations.

AVAILABILITY

GROMACS is an open source and free software available from http://www.gromacs.org.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Accounting for the kinetics in order parameter analysis: lessons from theoretical models and a disordered peptide

Molecular simulations as well as single molecule experiments have been widely analyzed in terms of order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive, mounting evidence showed that such descriptions are inaccurate, leading to ambiguous definitions of states and wrong kinetics. To overcome these limitations a framework making use of order parameter fluctuations in conjunction with complex network analysis is investigated. Derived from recent advances in the analysis of single molecule time traces, this approach takes into account the fluctuations around each time point to distinguish between states that have similar values of the order parameter but different dynamics. Snapshots with similar fluctuations are used as nodes of a transition network, the clusterization of which into states provides accurate Markov-state-models of the system under study. Application of the methodology to theoretical models with a noisy order parameter as well as the dynamics of a disordered peptide illustrates the possibility to build accurate descriptions of molecular processes on the sole basis of order parameter time series without using any supplementary information.

Free energy landscape for the binding process of Huperzine A to acetylcholinesterase

Drug-target residence time (t = 1/k(off), where k(off) is the dissociation rate constant) has become an important index in discovering better- or best-in-class drugs. However, little effort has been dedicated to developing computational methods that can accurately predict this kinetic parameter or related parameters, k(off) and activation free energy of dissociation (ΔG(off)≠). In this paper, energy landscape theory that has been developed to understand protein folding and function is extended to develop a generally applicable computational framework that is able to construct a complete ligand-target binding free energy landscape. This enables both the binding affinity and the binding kinetics to be accurately estimated. We applied this method to simulate the binding event of the anti-Alzheimer's disease drug (-)-Huperzine A to its target acetylcholinesterase (AChE). The computational results are in excellent agreement with our concurrent experimental measurements. All of the predicted values of binding free energy and activation free energies of association and dissociation deviate from the experimental data only by less than 1 kcal/mol. The method also provides atomic resolution information for the (-)-Huperzine A binding pathway, which may be useful in designing more potent AChE inhibitors. We expect this methodology to be widely applicable to drug discovery and development.

On the interaction mechanisms of a p53 peptide and nutlin with the MDM2 and MDMX proteins: a Brownian dynamics study

The interaction of p53 with its regulators MDM2 and MDMX plays a major role in regulating the cell cycle. Inhibition of this interaction has become an important therapeutic strategy in oncology. Although MDM2 and MDMX share a very high degree of sequence/structural similarity, the small-molecule inhibitor nutlin appears to be an efficient inhibitor only of the p53-MDM2 interaction. Here, we investigate the mechanism of interaction of nutlin with these two proteins and contrast it with that of p53 using Brownian dynamics simulations. In contrast to earlier attempts to examine the bound states of the partners, here we locate initial reaction events in these interactions by identifying the regions of space around MDM2/MDMX, where p53/nutlin experience associative encounters with prolonged residence times relative to that in bulk solution. We find that the initial interaction of p53 with MDM2 is long-lived relative to nutlin, but, unlike nutlin, it takes place at the N- and C termini of the MDM2 protein, away from the binding site, suggestive of an allosteric mechanism of action. In contrast, nutlin initially interacts with MDM2 directly at the clefts of the binding site. The interaction of nutlin with MDMX, however, is very short-lived compared with MDM2 and does not show such direct initial interactions with the binding site. Comparison of the topology of the electrostatic potentials of MDM2 and MDMX and the locations of the initial encounters with p53/nutlin in tandem with structure-based sequence alignment revealed that the origin of the diminished activity of nutlin toward MDMX relative to MDM2 may stem partly from the differing topologies of the electrostatic potentials of the two proteins. Glu25 and Lys51 residues underpin these topological differences and appear to collectively play a key role in channelling nutlin directly toward the binding site on the MDM2 surface and are absent in MDMX. The results, therefore, provide new insight into the mechanism of p53/nutlin interactions with MDM2 and MDMX and could potentially have a broader impact on anticancer drug optimization strategies.

Automation of the CHARMM General Force Field (CGenFF) I: bond perception and atom typing

Molecular mechanics force fields are widely used in computer-aided drug design for the study of drug-like molecules alone or interacting with biological systems. In simulations involving biological macromolecules, the biological part is typically represented by a specialized biomolecular force field, while the drug is represented by a matching general (organic) force field. In order to apply these general force fields to an arbitrary drug-like molecule, functionality for assignment of atom types, parameters, and charges is required. In the present article, which is part I of a series of two, we present the algorithms for bond perception and atom typing for the CHARMM General Force Field (CGenFF). The CGenFF atom typer first associates attributes to the atoms and bonds in a molecule, such as valence, bond order, and ring membership among others. Of note are a number of features that are specifically required for CGenFF. This information is then used by the atom typing routine to assign CGenFF atom types based on a programmable decision tree. This allows for straightforward implementation of CGenFF's complicated atom typing rules and for equally straightforward updating of the atom typing scheme as the force field grows. The presented atom typer was validated by assigning correct atom types on 477 model compounds including in the training set as well as 126 test-set molecules that were constructed to specifically verify its different components. The program may be utilized via an online implementation at https://www.paramchem.org/ .

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 .

Free Energy Guided Sampling

A free energy-guided sampling (FEGS) method is proposed for accelerating exploration of conformational space in unbiased molecular dynamics. Using the cut-based free energy profile and Markov state models, FEGS speeds up sampling of the canonical ensemble by iteratively restarting multiple short simulations in parallel from regions of the free energy surface visited rarely. This exploration stage is followed by a refinement stage in which multiple independent runs are initiated from Boltzmann distributed conformations. Notably, FEGS does not require either collective variables or reaction coordinates and can control the kinetic distance from the starting conformation. We applied FEGS to the alanine dipeptide, which has a human-comprehensible two-dimensional free energy landscape, and a three-stranded antiparallel β-sheet peptide of 20 residues whose folding/unfolding process is governed by a delicate interplay of enthalpy and entropy. For these two systems, FEGS speeds up the exploration of conformational space by 1 to 2 orders of magnitude with respect to conventional sampling and preserves the basins and barriers on the free energy profile.

Characterization of the Ligand Receptor Encounter Complex and Its Potential for in Silico Kinetics-Based Drug Development

The study of drug-receptor interactions has largely been framed in terms of the equilibrium thermodynamic binding affinity, an in vitro measure of the stability of the drug-receptor complex that is commonly used as a proxy measure of in vivo biological activity. In response to the growing realization of the importance of binding kinetics to in vivo drug activity we present a computational methodology for the kinetic characterization of drug-receptor interactions in terms of the encounter complex. Using trajectory data from multiple Brownian dynamics simulations of ligand diffusion, we derive the spatial density of the ligand around the receptor and show how it can be quantitatively partitioned into different basins of attraction. Numerical integration of the ligand densities within the basins can be used to estimate the residence time of the ligand within these diffusive binding sites. Simulations of two structurally similar inhibitors of Hsp90 exhibit diffusive binding sites with similar spatial structure but with different ligand residence times. In contrast, a pair of structurally dissimilar inhibitors of MDM2, a peptide and a small molecule, exhibit spatially distinct basins of attraction around the receptor, which in turn reveal differences in ligand orientational order. Thus, our kinetic approach provides microscopic details of drug-receptor dynamics that provide novel insight into the observed differences in the thermodynamic binding affinities for the two inhibitors, such as the differences in the entropic contributions to binding. The characterization of the encounter complex, in terms of the structure, topology, and dynamics of diffusive binding sites, offers a new perspective on ligand-receptor interactions and the potential for greater insight into drug action. The method, which requires no prior knowledge of the bound state, is a first step toward the incorporation of ligand kinetics into in silico drug development protocols.

Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations

The understanding of protein-ligand binding is of critical importance for biomedical research, yet the process itself has been very difficult to study because of its intrinsically dynamic character. Here, we have been able to quantitatively reconstruct the complete binding process of the enzyme-inhibitor complex trypsin-benzamidine by performing 495 molecular dynamics simulations of free ligand binding of 100 ns each, 187 of which produced binding events with an rmsd less than 2 Å compared to the crystal structure. The binding paths obtained are able to capture the kinetic pathway of the inhibitor diffusing from solvent (S0) to the bound (S4) state passing through two metastable intermediate states S2 and S3. Rather than directly entering the binding pocket the inhibitor appears to roll on the surface of the protein in its transition between S3 and the final binding pocket, whereas the transition between S2 and the bound pose requires rediffusion to S3. An estimation of the standard free energy of binding gives ΔG° = -5.2 ± 0.4 kcal/mol (cf. the experimental value -6.2 kcal/mol), and a two-states kinetic model k(on) = (1.5 ± 0.2) × 10(8) M(-1) s(-1) and k(off) = (9.5 ± 3.3) × 10(4) s(-1) for unbound to bound transitions. The ability to reconstruct by simple diffusion the binding pathway of an enzyme-inhibitor binding process demonstrates the predictive power of unconventional high-throughput molecular simulations. Moreover, the methodology is directly applicable to other molecular systems and thus of general interest in biomedical and pharmaceutical research.