Will molecular dynamics simulations of proteins ever reach equilibrium?

A trick of the tail: computing the entropic contribution to the energetics of quinone-protein unbindung

We estimate the entropic contributions to the free energy of quinone unbinding in bacterial and mitochondrial respiratory chains using molecular dynamics (MD) and Monte Carlo (MC) computer simulations. For a varying length of the isoprenoid side chain, MD simulations in lipid bilayers and in unpolar solvents are used to assess the dihedral angle distributions along the chain. These form the basis of a MC estimate of the number of molecular structures that do not exhibit steric self-overlap and that are confined to the bilayer. We obtain an entropy drive of TΔS = 1.4 kcal mol-1 for each isoprene unit, which in sum is comparable to the redox potential differences involved in respiratory chain electron transfer. We postulate an entropy-driven zipper for quinone unbinding and discuss it in the context of the bioenergetics and the structure of complex I, and we indicate possible consequences of our findings for MD-based free energy computations.

Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Critical Assessment of Self-Consistency Checks in the All-Atom Molecular Dynamics Simulation of Intrinsically Disordered Proteins

All atom simulations can be used to quantify conformational properties of Intrinsically Disordered Proteins (IDP). However, simulations must satisfy convergence checks to ensure observables computed from simulation are reliable and reproducible. While absolute convergence is purely a theoretical concept requiring infinitely long simulation, a more practical, yet rigorous, approach is to impose Self Consistency Checks (SCCs) to gain confidence in the simulated data. Currently there is no study of SCCs in IDPs, unlike their folded counterparts. In this paper, we introduce different criteria for self-consistency checks for IDPs. Next, we impose these SCCs to critically assess the performance of different simulation protocols using the N terminal domain of HIV Integrase and the linker region of SARS-CoV-2 Nucleoprotein as two model IDPs. All simulation protocols begin with all-atom implicit solvent Monte Carlo (MC) simulation and subsequent clustering of MC generated conformations to create the representative structures of the IDPs. These representative structures serve as the initial structure for subsequent molecular dynamics (MD) runs with explicit solvent. We conclude that generating multiple short (∼3 μs) MD simulation trajectories─all starting from the most representative MC generated conformation─and merging them is the protocol of choice due to (i) its ability to satisfy multiple SCCs, (ii) consistently reproducing experimental data, and (iii) the efficiency of running independent trajectories in parallel by harnessing multiple cores available in modern GPU clusters. Running one long trajectory (greater than 20 μs) can also satisfy the first two criteria but is less desirable due to prohibitive computation time. These findings help resolve the challenge of identifying a usable starting configuration, provide an objective measure of SCC, and establish rigorous criteria to determine the minimum length (for one long simulation) or number of trajectories needed in all-atom simulation of IDPs.

Computation-Aided Engineering of Cytochrome P450 for the Production of Pravastatin

CYP105AS1 is a cytochrome P450 from Amycolatopsis orientalis that catalyzes monooxygenation of compactin to 6-epi-pravastatin. For fermentative production of the cholesterol-lowering drug pravastatin, the stereoselectivity of the enzyme needs to be inverted, which has been partially achieved by error-prone PCR mutagenesis and screening. In the current study, we report further optimization of the stereoselectivity by a computationally aided approach. Using the CoupledMoves protocol of Rosetta, a virtual library of mutants was designed to bind compactin in a pro-pravastatin orientation. By examining the frequency of occurrence of beneficial substitutions and rational inspection of their interactions, a small set of eight mutants was predicted to show the desired selectivity and these variants were tested experimentally. The best CYP105AS1 variant gave >99% stereoselective hydroxylation of compactin to pravastatin, with complete elimination of the unwanted 6-epi-pravastatin diastereomer. The enzyme-substrate complexes were also examined by ultrashort molecular dynamics simulations of 50 × 100 ps and 5 × 22 ns, which revealed that the frequency of occurrence of near-attack conformations agreed with the experimentally observed stereoselectivity. These results show that a combination of computational methods and rational inspection could improve CYP105AS1 stereoselectivity beyond what was obtained by directed evolution. Moreover, the work lays out a general in silico framework for specificity engineering of enzymes of known structure.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Effect of the Force Field on Molecular Dynamics Simulations of the Multidrug Efflux Protein P-Glycoprotein

Molecular dynamics (MD) simulations have been used extensively to study P-glycoprotein (P-gp), a flexible multidrug transporter that is a key player in the development of multidrug resistance to chemotherapeutics. A substantial body of literature has grown from simulation studies that have employed various simulation conditions and parameters, including AMBER, CHARMM, OPLS, GROMOS, and coarse-grained force fields, drawing conclusions from simulations spanning hundreds of nanoseconds. Each force field is typically parametrized and validated on different data and observables, usually of small molecules and peptides; there have been few comparisons of force field performance on large protein-membrane systems. Here we compare the conformational ensembles of P-gp embedded in a POPC/cholesterol bilayer generated over 500 ns of replicate simulation with five force fields from popular biomolecular families: AMBER 99SB-ILDN, CHARMM 36, OPLS-AA/L, GROMOS 54A7, and MARTINI. We find considerable differences among the ensembles with little conformational overlap, although they correspond to similar extents to structural data obtained from electron paramagnetic resonance and cross-linking studies. Moreover, each trajectory was still sampling new conformations at a high rate after 500 ns of simulation, suggesting the need for more sampling. This work highlights the need to consider known limitations of the force field used (e.g., biases toward certain secondary structures) and the simulation itself (e.g., whether sufficient sampling has been achieved) when interpreting accumulated results of simulation studies of P-gp and other transport proteins.

On the Use of Interaction Entropy and Related Methods to Estimate Binding Entropies

Molecular mechanics combined with Poisson-Boltzmann or generalized Born and solvent-accessible area solvation energies (MM/PBSA and MM/GBSA) are popular methods to estimate the free energy for the binding of small molecules to biomacromolecules. However, the estimation of the entropy has been problematic and time-consuming. Traditionally, normal-mode analysis has been used to estimate the entropy, but more recently, alternative approaches have been suggested. In particular, it has been suggested that exponential averaging of the electrostatic and Lennard-Jones interaction energies may provide much faster and more accurate entropies, the interaction entropy (IE) approach. In this study, we show that this exponential averaging is extremely poorly conditioned. Using stochastic simulations, assuming that the interaction energies follow a Gaussian distribution, we show that if the standard deviation of the interaction energies (σIE) is larger than 15 kJ/mol, it becomes practically impossible to converge the interaction entropies (more than 10 million energies are needed, and the number increases exponentially). A cumulant approximation to the second order of the exponential average shows a better convergence, but for σIE > 25 kJ/mol, it gives entropies that are unrealistically large. Moreover, in practical applications, both methods show a steady increase in the entropy with the number of energies considered.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Thermosensitive Hydration of Four Acrylamide-Based Polymers in Coil and Globule Conformations

To characterize the thermosensitive coil–globule transition in atomistic detail, the conformational dynamics of linear polymer chains of acrylamide-based polymers have been investigated at multiple temperatures. Therefore, molecular dynamic simulations of 30mers of polyacrylamide (AAm), poly-N-methylacrylamide (NMAAm), poly-N-ethylacrylamide (NEAAm), and poly-N-isopropylacrylamide (NIPAAm) have been performed at temperatures ranging from 250 to 360 K for 2 μs. While two of the polymers are known to exhibit thermosensitivity (NEAAm, NIPAAm), no thermosensitivity is observed for AAm and NMAAm in aqueous solution. Our computer simulations consistently reproduce these properties. To understand the thermosensitivity of the respective polymers, the conformational ensembles at different temperatures have been separated according to the coil–globule transition. The coil and globule conformational ensembles were exhaustively analyzed in terms of hydrogen bonding with the solvent, the change of the solvent accessible surface, and enthalpic contributions. Surprisingly, independent of different thermosensitive properties of the four polymers, the surface affinity to water of coil conformations is higher than for globule conformations. Therefore, polymer–solvent interactions stabilize coil conformations at all temperatures. Nevertheless, the enthalpic contributions alone cannot explain the differences in thermosensitivity. This clearly implies that entropy is the distinctive factor for thermosensitivity. With increasing side chain length, the lifetime of the hydrogen bonds between the polymer surface and water is extended. Thus, we surmise that a longer side chain induces a larger entropic penalty due to immobilization of water molecules.

Entropy of Proteins Using Multiscale Cell Correlation

A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.

Impact of HEC72702 chirality on the selective inhibition of hepatitis B virus capsid dimer: A dynamics-structure-energetics perspective

Chirality in drug design has been attracting wide interests and attention over the years based on its innate potentials of enhancing the selectivity and prowess of therapeutic molecules. This approach was fundamental to the recent design of two inhibitors, where (R,R)-HEC72702 exhibited higher potency inhibition against hepatitis B virus capsid (HBVC) than (R,S)-HEC72702. Nevertheless, the detailed molecular mechanism has remained unresolved. Here, we apply multiple computational approaches to explore, validate, and differentiate the binding modes of (R,R) and (R,S)-HEC72702 and to explain the systematic roles mediated by chirality on the distinctive inhibition of HBVC dimer (HBVCd). Our findings revealed that chirality change from R,S to R,R engenders variations in the position of the propanoic acid group of HEC72702 toward the α5' and C-TER' region of HBVCd chain B which could explain the higher inhibitory affinity of (R,R)-HEC72702. Estimated binding free energies revealed a good correlation with bioactivity data. Moreover, analysis of energy decomposition revealed the prominent effects of van der Waals interactions in the binding process of both compounds to HBVCd. Furthermore, hierarchical clustering of residue-based energetic contributions suggested two hot-spot residues W125´ and F156´ play crucial roles in the systematic motions of the propanoic acid group toward chain B.

Elucidating the influence of linker histone variants on chromatosome dynamics and energetics

Linker histones are epigenetic regulators that bind to nucleosomes and alter chromatin structures and dynamics. Biophysical studies have revealed two binding modes in the linker histone/nucleosome complex, the chromatosome, where the linker histone is either centered on or askew from the dyad axis. Each has been posited to have distinct effects on chromatin, however the molecular and thermodynamic mechanisms that drive them and their dependence on linker histone compositions remain poorly understood. We present molecular dynamics simulations of chromatosomes with the globular domain of two linker histone variants, generic H1 (genGH1) and H1.0 (GH1.0), to determine how their differences influence chromatosome structures, energetics and dynamics. Results show that both unbound linker histones adopt a single compact conformation. Upon binding, DNA flexibility is reduced, resulting in increased chromatosome compaction. While both variants enthalpically favor on-dyad binding, energetic benefits are significantly higher for GH1.0, suggesting that GH1.0 is more capable than genGH1 of overcoming the large entropic reduction required for on-dyad binding which helps rationalize experiments that have consistently demonstrated GH1.0 in on-dyad states but that show genGH1 in both locations. These simulations highlight the thermodynamic basis for different linker histone binding motifs, and details their physical and chemical effects on chromatosomes.

Variance of Atomic Coordinates as a Dynamical Metric to Distinguish Proteins and Protein-Protein Interactions in Molecular Dynamics Simulations

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.

Delineating elastic properties of kinesin linker and their sensitivity to point mutations

We analyze free energy estimators from simulation trials mimicking single-molecule pulling experiments on a neck linker of a kinesin motor. For that purpose, we have performed a version of steered molecular dynamics (SMD) calculations. The sample trajectories have been analyzed to derive distribution of work done on the system. In order to induce stretching of the linker, we have applied a constant pulling force to the molecule and allowed for a subsequent relaxation of its structure. The use of fluctuation relations (FR) relevant to non-equilibrium systems subject to thermal fluctuations allows us to assess the difference in free energy between stretched and relaxed conformations. To further understand effects of potential mutations on elastic properties of the linker, we have performed similar in silico studies on a structure formed of a polyalanine sequence (Ala-only) and on three other structures, created by substituting selected types of amino acid residues in the linker’s sequence with alanine (Ala) ones. The results of SMD simulations indicate a crucial role played by the Asparagine (Asn) and Lysine (Lys) residues in controlling stretching and relaxation properties of the linker domain of the motor.

Water structure in solution and crystal molecular dynamics simulations compared to protein crystal structures

The function of proteins is influenced not only by the atomic structure but also by the detailed structure of the solvent surrounding it. Computational studies of protein structure also critically depend on the water structure around the protein. Herein we compare the water structure obtained from molecular dynamics (MD) simulations of galectin-3 in complex with two ligands to crystallographic water molecules observed in the corresponding crystal structures. We computed MD trajectories both in a water box, which mimics a protein in solution, and in a crystallographic unit cell, which mimics a protein in a crystal. The calculations were compared to crystal structures obtained at both cryogenic and room temperature. Two types of analyses of the MD simulations were performed. First, the positions of the crystallographic water molecules were compared to peaks in the MD density after alignment of the protein in each snapshot. The results of this analysis indicate that all simulations reproduce the crystallographic water structure rather poorly. However, if we define the crystallographic water sites based on their distances to nearby protein atoms and follow these sites throughout the simulations, the MD simulations reproduce the crystallographic water sites much better. This shows that the failure of MD simulations to reproduce the water structure around proteins in crystal structures observed both in this and previous studies is caused by the problem of identifying water sites for a flexible and dynamic protein (traditionally done by overlaying the structures). Our local clustering approach solves the problem and shows that the MD simulations reasonably reproduce the water structure observed in crystals. Furthermore, analysis of the crystal MD simulations indicates a few water molecules that are close to unmodeled electron density peaks in the crystal structures, suggesting that crystal MD could be used as a complementary tool for identifying and modelling water in protein crystallography.

Molecular dynamics simulations can reproduce the water structure around proteins in crystal structure only if a local clustering is performed.

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Structure and Function of an Inflammatory Cytokine, Interleukin-2, Analyzed Using the Bioinformatic Approach

The inflammatory cytokine, interleukin-2 (IL-2), is an important regulator of cellular functions. This relatively less studied member of the interleukin protein family is responsible for multiple immuno-modulatory and immuno-stimulatory tasks, like T cell activation, triggering of natural killer cells, inflammation, as well as proliferation and progression of autoimmune diseases and cancers. In this communication we report the temporally variant structural aspects of the IL-2 ligand and its receptor interfaces, based on the available crystal structures. The intended goal of this effort is to generate simulated results that could potentially aid the designs of novel structure based therapeutics.

Revealing the distinct mechanistic binding and activity of 5-(1-(3,5-dichloropyridin-4-yl)ethoxy)-3-(5-(4-methylpiperazin-1-yl)-1H-benzo[d]imidazol-2-yl)-1H-indazole enantiomers against FGFR1

The concept of chirality has become prominent over the years, particularly with regards to the design of therapeutic molecules.

The irony of chirality – unveiling the distinct mechanistic binding and activities of 1-(3-(4-amino-5-(7-methoxy-5-methylbenzo[b]thiophen-2-yl)-7H-pyrrolo[2,3-d]pyrimidin-7-yl)pyrrolidin-1-yl)prop-2-en-1-one enantiomers as irreversible covalent FGFR4 inhibitors

Theoretical investigation of the effect of chirality on inhibitors is providing essential insights for drug design.

Are crystallographic B-factors suitable for calculating protein conformational entropy?

It is not possible to obtain reliable entropy estimates from crystallographic B-factors even with re-refined or room-temperature crystal structures.

Exploring the flap dynamics of the South African HIV subtype C protease in presence of FDA-approved inhibitors: MD study

HIV-1 protease (HIV PR) is considered as one of the most attractive targets for the treatment of HIV and the impact of flap dynamics of HIV PR on the binding affinities of protease inhibitors (PIs) is a crucial ongoing research field. Recently, our research group evaluated the binding affinities of different FDA approved PIs against the South African HIV-1 subtype C (C-SA) protease (PR). The CSA-HIV PR displayed weaker binding affinity for most of the clinical PIs compared to HIV-1 B subtype for West and Central Europe, the Americas. In the current work, the flap dynamics of four different systems of HIV-1 C-SA PR complexed to FDA approved second generation PIs and its impact on binding was explored over the molecular dynamic trajectories. It was observed that the interactions of the selected drugs with the binding site residues of the protease may not be the major contributor for affinity towards PIs. Various post-MD analyses were performed, also entropic contributions, solvation free energies and hydrophobic core formation interactions were studied to assess how the flap dynamics of C-SA PR which is affected by such factors. From these contributions, large van der Waals interactions and low solvation free energies were found to be major factors for the higher activity of ATV against C-SA HIV PR. Furthermore, a comparatively stable hydrophobic core may be responsible for higher stability of the PR flaps of the ATV complex. The outcome of this study provides significant guidance to how the flap dynamics of C-SA PR is affected by various factors as a result of the binding affinity of various protease inhibitors. It will also assist with the design of potent inhibitors against C-SA HIV PR that apart from binding in the active site of PR can interacts with the flaps to prevent opening of the flaps resulting in inactivation of the protease.

Focused conformational sampling in proteins

A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.

Assessing the performance of MM/PBSA and MM/GBSA methods. 7. Entropy effects on the performance of end-point binding free energy calculation approaches

Entropy effects play an important role in drug-target interactions, but the entropic contribution to ligand-binding affinity is often neglected by end-point binding free energy calculation methods, such as MM/GBSA and MM/PBSA, due to the expensive computational cost of normal mode analysis (NMA). Here, we systematically investigated entropy effects on the prediction power of MM/GBSA and MM/PBSA using >1500 protein-ligand systems and six representative AMBER force fields. Two computationally efficient methods, including NMA based on truncated structures and the interaction entropy approach, were used to estimate the entropic contributions to ligand-target binding free energies. In terms of the overall accuracy, we found that, for the minimized structures, in most cases the inclusion of the conformational entropies predicted by truncated NMA (enthalpynmode_min_9Å) compromises the overall accuracy of MM/GBSA and MM/PBSA compared with the enthalpies calculated based on the minimized structures (enthalpymin). However, for the MD trajectories, the binding free energies can be improved by the inclusion of the conformation entropies predicted by either truncated-NMA for a relatively high dielectric constant (εin = 4) or the interaction entropy method for εin = 1-4. In terms of reproducing the absolute binding free energies, the binding free energies estimated by including the truncated-NMA entropies based on the MD trajectories (ΔGnmode_md_9Å) give the lowest average absolute deviations against the experimental data among all the tested strategies for both MM/GBSA and MM/PBSA. Although the inclusion of the truncated NMA based on the MD trajectories (ΔGnmode_md_9Å) for a relatively high dielectric constant gave the overall best result and the lowest average absolute deviations against the experimental data (for the ff03 force field), it needs too much computational time. Alternatively, considering that the interaction entropy method does not incur any additional computational cost and can give comparable (at high dielectric constant, εin = 4) or even better (at low dielectric constant, εin = 1-2) results than the truncated-NMA entropy (ΔGnmode_md_9Å), the interaction entropy approach is recommended to estimate the entropic component for MM/GBSA and MM/PBSA based on MD trajectories, especially for a diverse dataset. Furthermore, we compared the predictions of MM/GBSA with six different AMBER force fields. The results show that the ff03 force field (ff03 for proteins and gaff with AM1-BCC charges for ligands) performs the best, but the predictions given by the tested force fields are comparable, implying that the MM/GBSA predictions are not very sensitive to force fields.

Computational Insight Into the Structural Organization of Full-Length Toll-Like Receptor 4 Dimer in a Model Phospholipid Bilayer

Toll-like receptors (TLRs) are a unique category of pattern recognition receptors that recognize distinct pathogenic components, often utilizing the same set of downstream adaptors. Specific molecular features of extracellular, transmembrane (TM), and cytoplasmic domains of TLRs are crucial for coordinating the complex, innate immune signaling pathway. Here, we constructed a full-length structural model of TLR4-a widely studied member of the interleukin-1 receptor/TLR superfamily-using homology modeling, protein-protein docking, and molecular dynamics simulations to understand the differential domain organization of TLR4 in a membrane-aqueous environment. Results showed that each functional domain of the membrane-bound TLR4 displayed several structural transitions that are biophysically essential for plasma membrane integration. Specifically, the extracellular and cytoplasmic domains were partially immersed in the upper and lower leaflets of the membrane bilayer. Meanwhile, TM domains tilted considerably to overcome the hydrophobic mismatch with the bilayer core. Our analysis indicates an alternate dimerization or a potential oligomerization interface of TLR4-TM. Moreover, the helical properties of an isolated TM dimer partly agree with that of the full-length receptor. Furthermore, membrane-absorbed or solvent-exposed surfaces of the toll/interleukin-1 receptor domain are consistent with previous X-ray crystallography and biochemical studies. Collectively, we provided a complete structural model of membrane-bound TLR4 that strengthens our current understanding of the complex mechanism of receptor activation and adaptor recruitment in the innate immune signaling pathway.

Computational Exploration of Conformational Transitions in Protein Drug Targets

Protein drug targets vary from highly structured to completely disordered; either way dynamics governs function. Hence, understanding the dynamical aspects of how protein targets function can enable improved interventions with drug molecules. Computational approaches offer highly detailed structural models of protein dynamics which are becoming more predictive as model quality and sampling power improve. However, the most advanced and popular models still have errors owing to imperfect parameter sets and often cannot access longer timescales of many crucial biological processes. Experimental approaches offer more certainty but can struggle to detect and measure lightly populated conformations of target proteins and subtle allostery. An emerging solution is to integrate available experimental data into advanced molecular simulations. In the future, molecular simulation in combination with experimental data may be able to offer detailed models of important drug targets such that improved functional mechanisms or selectivity can be accessed.

Trypsin-Ligand binding affinities calculated using an effective interaction entropy method under polarized force field

Molecular dynamics (MD) simulation in the explicit water is performed to study the interaction mechanism of trypsin-ligand binding under the AMBER force field and polarized protein-specific charge (PPC) force field combined the new developed highly efficient interaction entropy (IE) method for calculation of entropy change. And the detailed analysis and comparison of the results of MD simulation for two trypsin-ligand systems show that the root-mean-square deviation (RMSD) of backbone atoms, B-factor, intra-protein and protein-ligand hydrogen bonds are more stable under PPC force field than AMBER force field. Our results demonstrate that the IE method is superior than the traditional normal mode (Nmode) method in the calculation of entropy change and the calculated binding free energy under the PPC force field combined with the IE method is more close to the experimental value than other three combinations (AMBER-Nmode, AMBER-IE and PPC-Nmode). And three critical hydrogen bonds between trypsin and ligand are broken under AMBER force field. However, they are well preserved under PPC force field. Detailed binding interactions of ligands with trypsin are further analyzed. The present work demonstrates that the polarized force field combined the highly efficient IE method is critical in MD simulation and free energy calculation.

Adaptive simulations, towards interactive protein-ligand modeling

Modeling the dynamic nature of protein-ligand binding with atomistic simulations is one of the main challenges in computational biophysics, with important implications in the drug design process. Although in the past few years hardware and software advances have significantly revamped the use of molecular simulations, we still lack a fast and accurate ab initio description of the binding mechanism in complex systems, available only for up-to-date techniques and requiring several hours or days of heavy computation. Such delay is one of the main limiting factors for a larger penetration of protein dynamics modeling in the pharmaceutical industry. Here we present a game-changing technology, opening up the way for fast reliable simulations of protein dynamics by combining an adaptive reinforcement learning procedure with Monte Carlo sampling in the frame of modern multi-core computational resources. We show remarkable performance in mapping the protein-ligand energy landscape, being able to reproduce the full binding mechanism in less than half an hour, or the active site induced fit in less than 5 minutes. We exemplify our method by studying diverse complex targets, including nuclear hormone receptors and GPCRs, demonstrating the potential of using the new adaptive technique in screening and lead optimization studies.

Differential flap dynamics in l,d-transpeptidase2 from mycobacterium tuberculosis revealed by molecular dynamics

Despite the advances in tuberculosis treatment, TB is still one the most deadly infectious diseases and remains a major global health quandary. Mycobacterium tuberculosis (Mtb) is the only known mycobacterium with a high content of 3→3 crosslinks in the biosynthesis of peptidoglycan, which is negligible in most bacterial species. An Mtb lacking Ldt_Mt2 leads to alteration of the colony morphology and loss of virulence which makes this enzyme an attractive target. Regardless of the vital role of Ldt_Mt2 for cell wall survival, the impact of ligand binding on the dynamics of the β-hairpin flap is still unknown. Understanding the structural and dynamical behaviour of the flap regions provides clear insight into the design of the effective inhibitors against Ldt_Mt2. Carbapenems, an specific class of β-lactam family, have been shown to inactivate this enzyme. Herein a comprehensive investigation of the flap dynamics of Ldt_Mt2 complex with substrate and three carbapenems namely, ertapenem, imipenem and meropenem is discussed and analyzed for the first account using 140 ns molecular dynamics simulations. The structural features (RMSD, RMSF and R_g) derived by MD trajectories were analyzed. Distance analysis, particularly tip-tip SER135-ASN167 index, identified conformational changes in terms of flap opening and closure within binding process. Principal component analysis (PCA) was employed to qualitatively understand the divergent effects of different inhibitors on the dominant motion of each residue. To probe different internal dynamics induced by ligand binding, dynamic cross-correlation marix (DCCM) analysis was used. The binding free energies of the selected complexes were assessed using MM-GBSA method and per residue free energy decomposition analysis were performed to characterize the contribution of the key residues to the total binding free energies.

Calculating free energies of organic molecules on insulating substrates

The challenges and limitations in calculating free energies and entropies of adsorption and interaction of organic molecules on an insulating substrate are discussed. The adhesion of 1,3,5-tri(4'-cyano-[1,1'-biphenyl]-4-yl)benzene (TCB) and 1,4-bis(4-cyanophenyl)-2,5-bis(decyloxy)benzene (CDB) molecules to step edges on the KCl(001) surface and the formation of molecular dimers were studied using classical molecular dynamics. Both molecules contain the same anchoring groups and benzene ring structures, yet differ in their flexibility. Therefore, the entropic contributions to their free energy differ, which affects surface processes. Using potential of mean force and thermodynamic integration techniques, free energy profiles and entropy changes were calculated for step adhesion and dimer formation of these molecules. However, converging these calculations is nontrivial and comes at large computational cost. We illustrate the difficulties as well as the possibilities of applying these methods towards understanding dynamic processes of organic molecules on insulating substrates.

Joint refinement of FRET measurements using spectroscopic and computational tools

The variability of the orientation factor is a long-standing challenge in converting FRET efficiency measurements into donor-acceptor distances. We propose the use of molecular dynamics (MD) simulations to characterize orientation distributions and thus improve the accuracy of distance measurements. Here, we test this approach by comparing experimental and simulated FRET efficiencies for a model donor-acceptor pair of enhanced cyan and enhanced yellow FPs connected by a flexible linker. Several spectroscopic techniques were used to characterize FRET in solution. In addition, a series of atomistic MD simulations of a total length of 1.5 μs were carried out to calculate the distances and the orientation factor in the FRET-pair. The resulting MD-based and experimentally measured FRET efficiency histograms coincided with each other, allowing for direct comparison of distance distributions. Despite the fact that the calculated average orientation factor was close to 2/3, the application of the average κ² to the entire histogram of FRET efficiencies resulted in a substantial artificial broadening of the calculated distribution of apparent donor-acceptor distances. By combining single pair-FRET measurements with computational tools, we demonstrate that accounting for the donor and acceptor orientation heterogeneity is critical for accurate representation of the donor-acceptor distance distribution from FRET measurements.

Rapid, Accurate, Precise, and Reliable Relative Free Energy Prediction Using Ensemble Based Thermodynamic Integration

The accurate prediction of the binding affinities of ligands to proteins is a major goal in drug discovery and personalized medicine. The time taken to make such predictions is of similar importance to their accuracy, precision, and reliability. In the past few years, an ensemble based molecular dynamics approach has been proposed that provides a route to reliable predictions of free energies based on the molecular mechanics Poisson-Boltzmann surface area method which meets the requirements of speed, accuracy, precision, and reliability. Here, we describe an equivalent methodology based on thermodynamic integration to substantially improve the speed, accuracy, precision, and reliability of calculated relative binding free energies. We report the performance of the method when applied to a diverse set of protein targets and ligands. The results are in very good agreement with experimental data (90% of calculations agree to within 1 kcal/mol), while the method is reproducible by construction. Statistical uncertainties of the order of 0.5 kcal/mol or less are achieved. We present a systematic account of how the uncertainty in the predictions may be estimated.

Can We Rely on Computational Predictions To Correctly Identify Ligand Binding Sites on Novel Protein Drug Targets? Assessment of Binding Site Prediction Methods and a Protocol for Validation of Predicted Binding Sites

In the field of medicinal chemistry there is increasing focus on identifying key proteins whose biochemical functions can firmly be linked to serious diseases. Such proteins become targets for drug or inhibitor molecules that could treat or halt the disease through therapeutic action or by blocking the protein function respectively. The protein must be targeted at the relevant biologically active site for drug or inhibitor binding to be effective. As insufficient experimental data is available to confirm the biologically active binding site for novel protein targets, researchers often rely on computational prediction methods to identify binding sites. Presented herein is a short review on structure-based computational methods that (i) predict putative binding sites and (ii) assess the druggability of predicted binding sites on protein targets. This review briefly covers the principles upon which these methods are based, where they can be accessed and their reliability in identifying the correct binding site on a protein target. Based on this review, we believe that these methods are useful in predicting putative binding sites, but as they do not account for the dynamic nature of protein-ligand binding interactions, they cannot definitively identify the correct site from a ranked list of putative sites. To overcome this shortcoming, we strongly recommend using molecular docking to predict the most likely protein-ligand binding site(s) and mode(s), followed by molecular dynamics simulations and binding thermodynamics calculations to validate the docking results. This protocol provides a valuable platform for experimental and computational efforts to design novel drugs and inhibitors that target disease-related proteins.

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.

MTS-MD of Biomolecules Steered with 3D-RISM-KH Mean Solvation Forces Accelerated with Generalized Solvation Force Extrapolation

We developed a generalized solvation force extrapolation (GSFE) approach to speed up multiple time step molecular dynamics (MTS-MD) of biomolecules steered with mean solvation forces obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model with the Kovalenko-Hirata closure). GSFE is based on a set of techniques including the non-Eckart-like transformation of coordinate space separately for each solute atom, extension of the force-coordinate pair basis set followed by selection of the best subset, balancing the normal equations by modified least-squares minimization of deviations, and incremental increase of outer time step in motion integration. Mean solvation forces acting on the biomolecule atoms in conformations at successive inner time steps are extrapolated using a relatively small number of best (closest) solute atomic coordinates and corresponding mean solvation forces obtained at previous outer time steps by converging the 3D-RISM-KH integral equations. The MTS-MD evolution steered with GSFE of 3D-RISM-KH mean solvation forces is efficiently stabilized with our optimized isokinetic Nosé-Hoover chain (OIN) thermostat. We validated the hybrid MTS-MD/OIN/GSFE/3D-RISM-KH integrator on solvated organic and biomolecules of different stiffness and complexity: asphaltene dimer in toluene solvent, hydrated alanine dipeptide, miniprotein 1L2Y, and protein G. The GSFE accuracy and the OIN efficiency allowed us to enlarge outer time steps up to huge values of 1-4 ps while accurately reproducing conformational properties. Quasidynamics steered with 3D-RISM-KH mean solvation forces achieves time scale compression of conformational changes coupled with solvent exchange, resulting in further significant acceleration of protein conformational sampling with respect to real time dynamics. Overall, this provided a 50- to 1000-fold effective speedup of conformational sampling for these systems, compared to conventional MD with explicit solvent. We have been able to fold the miniprotein from a fully denatured, extended state in about 60 ns of quasidynamics steered with 3D-RISM-KH mean solvation forces, compared to the average physical folding time of 4-9 μs observed in experiment.

Effective in silico prediction of new oxazolidinone antibiotics: force field simulations of the antibiotic-ribosome complex supervised by experiment and electronic structure methods

We propose several new and promising antibacterial agents for the treatment of serious Gram-positive infections. Our predictions rely on force field simulations, supervised by first principle calculations and available experimental data. Different force fields were tested in order to reproduce linezolid's conformational space in terms of a) the isolated and b) the ribosomal bound state. In a first step, an all-atom model of the bacterial ribosome consisting of nearly 1600 atoms was constructed and evaluated. The conformational space of 30 different ribosomal/oxazolidinone complexes was scanned by stochastic methods, followed by an evaluation of their enthalpic penalties or rewards and the mechanical strengths of the relevant hydrogen bonds (relaxed force constants; compliance constants). The protocol was able to reproduce the experimentally known enantioselectivity favoring the S-enantiomer. In a second step, the experimentally known MIC values of eight linezolid analogues were used in order to crosscheck the robustness of our model. In a final step, this benchmarking led to the prediction of several new and promising lead compounds. Synthesis and biological evaluation of the new compounds are on the way.

Bending-Twisting Motions and Main Interactions in Nucleoplasmin Nuclear Import

Alpha solenoid proteins play a key role in regulating the classical nuclear import pathway, recognizing a target protein and transporting it into the nucleus. Importin-α (Impα) is the solenoid responsible for cargo protein recognition, and it has been extensively studied by X-ray crystallography to understand the binding specificity. To comprehend the main motions of Impα and to extend the information about the critical interactions during carrier-cargo recognition, we surveyed different conformational states based on molecular dynamics (MD) and normal mode (NM) analyses. Our model of study was a crystallographic structure of Impα complexed with the classical nuclear localization sequence (cNLS) from nucleoplasmin (Npl), which was submitted to multiple 100 ns of MD simulations. Representative conformations were selected for calculating the 87 lowest frequencies NMs of vibration, and a displacement approach was applied along each NM. Based on geometric criteria, using the radius of curvature and inter-repeat angles as the reference metrics, the main motions of Impα were described. Moreover, we determined the salt bridges, hydrogen bonds and hydrophobic interactions in the Impα-NplNLS interface. Our results show the bending and twisting motions participating in the recognition of nuclear proteins, allowing the accommodation and adjustment of a classical bipartite NLS sequence. The essential contacts for the nuclear import were also described and were mostly in agreement with previous studies, suggesting that the residues in the cNLS linker region establish important contacts with Impα adjusting the cNLS backbone. The MD simulations combined with NM analysis can be applied to the Impα-NLS system to help understand interactions between Impα and cNLSs and the analysis of non-classic NLSs.

Macromolecular Entropy Can Be Accurately Computed from Force

A method is presented to evaluate a molecule's entropy from the atomic forces calculated in a molecular dynamics simulation. Specifically, diagonalization of the mass-weighted force covariance matrix produces eigenvalues which in the harmonic approximation can be related to vibrational frequencies. The harmonic oscillator entropies of each vibrational mode may be summed to give the total entropy. The results for a series of hydrocarbons, dialanine and a β hairpin are found to agree much better with values derived from thermodynamic integration than results calculated using quasiharmonic analysis. Forces are found to follow a harmonic distribution more closely than coordinate displacements and better capture the underlying potential energy surface. The method's accuracy, simplicity, and computational similarity to quasiharmonic analysis, requiring as input force trajectories instead of coordinate trajectories, makes it readily applicable to a wide range of problems.

Molecular features of interaction between VEGFA and anti-angiogenic drugs used in retinal diseases: a computational approach

Anti-angiogenic agents are biological drugs used for treatment of retinal neovascular degenerative diseases. In this study, we aimed at in silico analysis of interaction of vascular endothelial growth factor A (VEGFA), the main mediator of angiogenesis, with binding domains of anti-angiogenic agents used for treatment of retinal diseases, such as ranibizumab, bevacizumab and aflibercept. The analysis of anti-VEGF/VEGFA complexes was carried out by means of protein-protein docking and molecular dynamics (MD) coupled to molecular mechanics-Poisson Boltzmann Surface Area (MM-PBSA) calculation. Molecular dynamics simulation was further analyzed by protein contact networks. Rough energetic evaluation with protein-protein docking scores revealed that aflibercept/VEGFA complex was characterized by electrostatic stabilization, whereas ranibizumab and bevacizumab complexes were stabilized by Van der Waals (VdW) energy term; these results were confirmed by MM-PBSA. Comparison of MM-PBSA predicted energy terms with experimental binding parameters reported in literature indicated that the high association rate (Kon) of aflibercept to VEGFA was consistent with high stabilizing electrostatic energy. On the other hand, the relatively low experimental dissociation rate (Koff) of ranibizumab may be attributed to lower conformational fluctuations of the ranibizumab/VEGFA complex, higher number of contacts and hydrogen bonds in comparison to bevacizumab and aflibercept. Thus, the anti-angiogenic agents have been found to be considerably different both in terms of molecular interactions and stabilizing energy. Characterization of such features can improve the design of novel biological drugs potentially useful in clinical practice.

ENCORE: Software for Quantitative Ensemble Comparison

There is increasing evidence that protein dynamics and conformational changes can play an important role in modulating biological function. As a result, experimental and computational methods are being developed, often synergistically, to study the dynamical heterogeneity of a protein or other macromolecules in solution. Thus, methods such as molecular dynamics simulations or ensemble refinement approaches have provided conformational ensembles that can be used to understand protein function and biophysics. These developments have in turn created a need for algorithms and software that can be used to compare structural ensembles in the same way as the root-mean-square-deviation is often used to compare static structures. Although a few such approaches have been proposed, these can be difficult to implement efficiently, hindering a broader applications and further developments. Here, we present an easily accessible software toolkit, called ENCORE, which can be used to compare conformational ensembles generated either from simulations alone or synergistically with experiments. ENCORE implements three previously described methods for ensemble comparison, that each can be used to quantify the similarity between conformational ensembles by estimating the overlap between the probability distributions that underlie them. We demonstrate the kinds of insights that can be obtained by providing examples of three typical use-cases: comparing ensembles generated with different molecular force fields, assessing convergence in molecular simulations, and calculating differences and similarities in structural ensembles refined with various sources of experimental data. We also demonstrate efficient computational scaling for typical analyses, and robustness against both the size and sampling of the ensembles. ENCORE is freely available and extendable, integrates with the established MDAnalysis software package, reads ensemble data in many common formats, and can work with large trajectory files.

Stability of Osaka Mutant and Wild-Type Fibril Models

Single amino acid mutations in amyloid-beta (Aβ) peptides can lead to early onset and increased severity of Alzheimer's disease. An example is the Osaka mutation (Aβ1-40E22D), which is more toxic than wild-type Aβ1-40. This mutant quickly forms early stage fibrils, one of the hallmarks of the disease, and these fibrils can even seed fibrilization of wild-type monomers. Using molecular dynamic simulations, we show that because of formation of various intra- and intermolecular salt bridges the Osaka mutant fibrils are more stable than wild-type fibrils. The mutant fibril also has a wider water channel with increased water flow than the wild type. These two observations can explain the higher toxicity and aggregation rate of the Osaka mutant over the wild type.