Efficient sampling of puckering states of monosaccharides through replica exchange with solute tempering and bond softening.

A molecular-level understanding of the structure, dynamics, and reactivity of carbohydrates is fundamental to the understanding of a range of key biological processes. The six-membered pyranose ring, a central component of biological monosaccharides and carbohydrates, has many different puckering conformations, and the conformational free energy landscape of these biologically important monosaccharides remains elusive. The puckering conformations of monosaccharides are separated by high energy barriers, which pose a great challenge for the complete sampling of these important conformations and accurate modeling of these systems. While metadynamics or umbrella sampling methods have been used to study the conformational space of monosaccharides, these methods might be difficult to generalize to other complex ring systems with more degrees of freedom. In this paper, we introduce a new enhanced sampling method for the rapid sampling over high energy barriers that combines our previously developed enhanced sampling method REST (replica exchange with solute tempering) with a bond softening (BOS) scheme that makes a chemical bond in the ring weaker as one ascends the replica ladder. We call this new method replica exchange with solute tempering and bond softening (REST/BOS). We demonstrate the superior sampling efficiency of REST/BOS over other commonly used enhanced sampling methods, including temperature replica exchange method and REST. The conformational free energy landscape of four biologically important monosaccharides, namely, α-glucose, ß-glucose, ß-mannose, and ß-xylose, is studied using REST/BOS, and results are compared with previous experimental and theoretical studies.

Predicting reaction coordinates in energy landscapes with diffusion anisotropy.

We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method "spectral gap optimization of order parameters (SGOOP)" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. We show how available information about dynamical observables in addition to static information can be incorporated into SGOOP, which can then be used to accurately determine the "best" reaction coordinate for arbitrary anisotropies. We compare our results with transmission coefficient calculations and published benchmarks wherever applicable or available, respectively.

Advancing Drug Discovery through Enhanced Free Energy Calculations.

A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates, is potentially transformative in enabling hard to drug targets to be attacked, and in facilitating the development of superior compounds, in various dimensions, for a wide range of targets. More effective integration of FEP+ calculations into the drug discovery process will ensure that the results are deployed in an optimal fashion for yielding the best possible compounds entering the clinic; this is where the greatest payoff is in the exploitation of computer driven design capabilities. A key conclusion from the work described is the surprisingly robust and accurate results that are attainable within the conventional classical simulation, fixed charge paradigm. No doubt there are individual cases that would benefit from a more sophisticated energy model or dynamical treatment, and properties other than protein-ligand binding energies may be more sensitive to these approximations. We conclude that an inflection point in the ability of MD simulations to impact drug discovery has now been attained, due to the confluence of hardware and software development along with the formulation of "good enough" theoretical methods and models.

How and when does an anticancer drug leave its binding site?

Obtaining atomistic resolution of drug unbinding from a protein is a much sought-after experimental and computational challenge. We report the unbinding dynamics of the anticancer drug dasatinib from c-Src kinase in full atomistic resolution using enhanced sampling molecular dynamics simulations. We obtain multiple unbinding trajectories and determine a residence time in agreement with experiments. We observe coupled protein-water movement through multiple metastable intermediates. The water molecules form a hydrogen bond bridge, elongating a specific, evolutionarily preserved salt bridge and enabling conformation changes essential to ligand unbinding. This water insertion in the salt bridge acts as a molecular switch that controls unbinding. Our findings provide a mechanistic rationale for why it might be difficult to engineer drugs targeting certain specific c-Src kinase conformations to have longer residence times.

Simulated Force Quench Dynamics Shows GB1 Protein Is Not a Two State Folder.

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a "two-state" model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

How wet should be the reaction coordinate for ligand unbinding?

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

Prediction of Protein-Ligand Binding Poses via a Combination of Induced Fit Docking and Metadynamics Simulations.

Ligand docking is a widely used tool for lead discovery and binding mode prediction based drug discovery. The greatest challenges in docking occur when the receptor significantly reorganizes upon small molecule binding, thereby requiring an induced fit docking (IFD) approach in which the receptor is allowed to move in order to bind to the ligand optimally. IFD methods have had some success but suffer from a lack of reliability. Complementing IFD with all-atom molecular dynamics (MD) is a straightforward solution in principle but not in practice due to the severe time scale limitations of MD. Here we introduce a metadynamics plus IFD strategy for accurate and reliable prediction of the structures of protein-ligand complexes at a practically useful computational cost. Our strategy allows treating this problem in full atomistic detail and in a computationally efficient manner and enhances the predictive power of IFD methods. We significantly increase the accuracy of the underlying IFD protocol across a large data set comprising 42 different ligand-receptor systems. We expect this approach to be of significant value in computationally driven drug design.

Kramers turnover: From energy diffusion to spatial diffusion using metadynamics.

We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength using the recently proposed infrequent metadynamics approach [P. Tiwary and M. Parrinello, Phys. Rev. Lett. 111, 230602 (2013)]. We are interested in understanding how this approach for obtaining rate constants performs as the dynamics regime changes from energy diffusion to spatial diffusion. Reassuringly, we find that the approach works remarkably well for various coupling strengths in the strong coupling regime, and to some extent even in the weak coupling regime.

Spectral gap optimization of order parameters for sampling complex molecular systems.

In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.

How a Kinase Inhibitor Withstands Gatekeeper Residue Mutations.

Mutations in the gatekeeper residue of kinases have emerged as a key way through which cancer cells develop resistance to treatment. As such, the design of gatekeeper mutation resistant kinase inhibitors is a crucial way forward in increasing the efficacy of a broad range of anticancer drugs. In this work we use atomistic simulations to provide detailed thermodynamic and structural insight into how two inhibitors of cSrc kinase, namely, a commercial drug and type I kinase inhibitor Dasatinib and the type II inhibitor RL45, respectively fail and succeed in being effective against the T338M gatekeeper residue mutation in the kinase binding site. Given the well-known limitations of atomistic simulations in sampling biomolecular systems, we use an enhanced sampling technique called free energy perturbation with replica exchange solute tempering (FEP/REST). Our calculations find that the type I inhibitor Dasatinib binds favorably to the wild type but unfavorably to T338M mutated kinase, while RL45 binds favorably to both. The predicted relative binding free energies are well within 1 kcal/mol accuracy compared to experiments. We find that Dasatinib's impotency against gatekeeper residue mutations arises from a loss of ligand-kinase hydrogen bonding due to T338M mutation and from steric hindrance due to the presence of an inflexible phenyl ring close to the ligand. On the other hand, in the type II binding RL45, the central phenyl ring has very pronounced flexibility. This leads to the inhibitor overcoming effects of steric clashes on mutation and maintaining an electrostatically favorable "edge-to-face" orientation with a neighboring phenylalanine residue. Our work provides useful insight into the mechanisms of mutation resistant kinase inhibitors and demonstrates the usefulness of enhanced sampling techniques in computational drug design.

Role of water and steric constraints in the kinetics of cavity-ligand unbinding.

A key factor influencing a drug's efficacy is its residence time in the binding pocket of the host protein. Using atomistic computer simulation to predict this residence time and the associated dissociation process is a desirable but extremely difficult task due to the long timescales involved. This gets further complicated by the presence of biophysical factors such as steric and solvation effects. In this work, we perform molecular dynamics (MD) simulations of the unbinding of a popular prototypical hydrophobic cavity-ligand system using a metadynamics-based approach that allows direct assessment of kinetic pathways and parameters. When constrained to move in an axial manner, the unbinding time is found to be on the order of 4,000 s. In accordance with previous studies, we find that the cavity must pass through a region of sharp wetting transition manifested by sudden and high fluctuations in solvent density. When we remove the steric constraints on ligand, the unbinding happens predominantly by an alternate pathway, where the unbinding becomes 20 times faster, and the sharp wetting transition instead becomes continuous. We validate the unbinding timescales from metadynamics through a Poisson analysis, and by comparison through detailed balance to binding timescale estimates from unbiased MD. This work demonstrates that enhanced sampling can be used to perform explicit solvent MD studies at timescales previously unattainable, to our knowledge, obtaining direct and reliable pictures of the underlying physiochemical factors including free energies and rate constants.

Role of Desolvation in Thermodynamics and Kinetics of Ligand Binding to a Kinase.

Computer simulations are used to determine the free energy landscape for the binding of the anticancer drug Dasatinib to its src kinase receptor and show that before settling into a free energy basin the ligand must surmount a free energy barrier. An analysis based on using both the ligand-pocket separation and the pocket-water occupancy as reaction coordinates shows that the free energy barrier is a result of the free energy cost for almost complete desolvation of the binding pocket. The simulations further show that the barrier is not a result of the reorganization free energy of the binding pocket. Although a continuum solvent model gives the location of free energy minima, it is not able to reproduce the intermediate free energy barrier. Finally, it is shown that a kinetic model for the on rate constant in which the ligand diffuses up to a doorway state and then surmounts the desolvation free energy barrier is consistent with published microsecond time-scale simulations of the ligand binding kinetics for this system [Shaw, D. E. et al. J. Am. Chem. Soc.2011, 133, 9181-9183].

Interface-limited growth of heterogeneously nucleated ice in supercooled water.

Heterogeneous ice growth exhibits a maximum in freezing rate arising from the competition between kinetics and the thermodynamic driving force between the solid and liquid states. Here, we use molecular dynamics simulations to elucidate the atomistic details of this competition, focusing on water properties in the interfacial region along the secondary prismatic direction. The crystal growth velocity is maximized when the efficiency of converting interfacial water molecules to ice, collectively known as the attachment kinetics, is greatest. We find water molecules that contact the intermediate ice layer in concave regions along the atomistically roughened surface are more likely to freeze directly. An increased roughening of the solid surface at large undercoolings consequently plays an important limiting role in the rate of ice growth, as water molecules are unable to integrate into increasingly deeper surface pockets. These results provide insight into the molecular mechanisms for self-assembly of solid phases that are important in many biological and atmospheric processes.

How hydrophobic drying forces impact the kinetics of molecular recognition.

A model of protein-ligand binding kinetics, in which slow solvent dynamics results from hydrophobic drying transitions, is investigated. Molecular dynamics simulations show that solvent in the receptor pocket can fluctuate between wet and dry states with lifetimes in each state that are long enough for the extraction of a separable potential of mean force and wet-to-dry transitions. We present a diffusive surface hopping model that is represented by a 2D Markovian master equation. One dimension is the standard reaction coordinate, the ligand-pocket separation, and the other is the solvent state in the region between ligand and binding pocket which specifies whether it is wet or dry. In our model, the ligand diffuses on a dynamic free-energy surface which undergoes kinetic transitions between the wet and dry states. The model yields good agreement with results from explicit solvent molecular dynamics simulation and an improved description of the kinetics of hydrophobic assembly. Furthermore, it is consistent with a "non-Markovian Brownian theory" for the ligand-pocket separation coordinate alone.

When does trimethylamine N-oxide fold a polymer chain and urea unfold it?

Longstanding mechanistic questions about the role of protecting osmolyte trimethylamine N-oxide (TMAO) that favors protein folding and the denaturing osmolyte urea are addressed by studying their effects on the folding of uncharged polymer chains. Using atomistic molecular dynamics simulations, we show that 1 M TMAO and 7 M urea solutions act dramatically differently on these model polymer chains. Their behaviors are sensitive to the strength of the attractive dispersion interactions of the chain with its environment: when these dispersion interactions are sufficiently strong, TMAO suppresses the formation of extended conformations of the hydrophobic polymer as compared to water while urea promotes the formation of extended conformations. Similar trends are observed experimentally for real protein systems. Quite surprisingly, we find that both protecting and denaturing osmolytes strongly interact with the polymer, seemingly in contrast with existing explanations of the osmolyte effect on proteins. We show that what really matters for a protective osmolyte is its effective depletion as the polymer conformation changes, which leads to a negative change in the preferential binding coefficient. For TMAO, there is a much more favorable free energy of insertion of a single osmolyte near collapsed conformations of the polymer than near extended conformations. By contrast, urea is preferentially stabilized next to the extended conformation and thus has a denaturing effect.

Elasticity, structure, and relaxation of extended proteins under force.

Force spectroscopies have emerged as a powerful and unprecedented tool to study and manipulate biomolecules directly at a molecular level. Usually, protein and DNA behavior under force is described within the framework of the worm-like chain (WLC) model for polymer elasticity. Although it has been surprisingly successful for the interpretation of experimental data, especially at high forces, the WLC model lacks structural and dynamical molecular details associated with protein relaxation under force that are key to the understanding of how force affects protein flexibility and reactivity. We use molecular dynamics simulations of ubiquitin to provide a deeper understanding of protein relaxation under force. We find that the WLC model successfully describes the simulations of ubiquitin, especially at higher forces, and we show how protein flexibility and persistence length, probed in the force regime of the experiments, are related to how specific classes of backbone dihedral angles respond to applied force. Although the WLC model is an average, backbone model, we show how the protein side chains affect the persistence length. Finally, we find that the diffusion coefficient of the protein's end-to-end distance is on the order of 10(8) nm(2)/s, is position and side-chain dependent, but is independent of the length and independent of the applied force, in contrast with other descriptions.

Are hydrodynamic interactions important in the kinetics of hydrophobic collapse?

We study the kinetics of assembly of two plates of varying hydrophobicity, including cases where drying occurs and water strongly solvates the plate surfaces. The potential of mean force and molecular-scale hydrodynamics are computed from molecular dynamics simulations in explicit solvent as a function of particle separation. In agreement with our recent work on nanospheres [J. Phys. Chem. B 2012,116, 378-389], regions of high friction are found to be engendered by large and slow solvent fluctuations. These slow fluctuations can be due to either drying or confinement. The mean first passage times for assembly are computed by means of molecular dynamics simulations in explicit solvent and by Brownian dynamics simulations along the reaction path. Brownian dynamics makes use of the potential of mean force and hydrodynamic profile that we determined. Surprisingly, we find reasonable agreement between full-scale molecular dynamics and Brownian dynamics, despite the role of slow solvent relaxation in the assembly process. We found that molecular-scale hydrodynamic interactions are essential in describing the kinetics of assembly.

Unraveling quantum mechanical effects in water using isotopic fractionation.

When two phases of water are at equilibrium, the ratio of hydrogen isotopes in each is slightly altered because of their different phase affinities. This isotopic fractionation process can be utilized to analyze water's movement in the world's climate. Here we show that equilibrium fractionation ratios, an entirely quantum mechanical property, also provide a sensitive probe to assess the magnitude of nuclear quantum fluctuations in water. By comparing the predictions of a series of water models, we show that those describing the OH chemical bond as rigid or harmonic greatly overpredict the magnitude of isotope fractionation. Models that account for anharmonicity in this coordinate are shown to provide much more accurate results because of their ability to give partial cancellation between inter- and intramolecular quantum effects. These results give evidence of the existence of competing quantum effects in water and allow us to identify how this cancellation varies across a wide-range of temperatures. In addition, this work demonstrates that simulation can provide accurate predictions and insights into hydrogen fractionation.

On achieving high accuracy and reliability in the calculation of relative protein-ligand binding affinities.

We apply a free energy perturbation simulation method, free energy perturbation/replica exchange with solute tempering, to two modifications of protein-ligand complexes that lead to significant conformational changes, the first in the protein and the second in the ligand. The approach is shown to facilitate sampling in these challenging cases where high free energy barriers separate the initial and final conformations and leads to superior convergence of the free energy as demonstrated both by consistency of the results (independence from the starting conformation) and agreement with experimental binding affinity data. The second case, consisting of two neutral thrombin ligands that are taken from a recent medicinal chemistry program for this interesting pharmaceutical target, is of particular significance in that it demonstrates that good results can be obtained for large, complex ligands, as opposed to relatively simple model systems. To achieve quantitative agreement with experiment in the thrombin case, a next generation force field, Optimized Potentials for Liquid Simulations 2.0, is required, which provides superior charges and torsional parameters as compared to earlier alternatives.

Theory and simulations of quantum glass forming liquids.

A comprehensive microscopic dynamical theory is presented for the description of quantum fluids as they transform into glasses. The theory is based on a quantum extension of mode-coupling theory. Novel effects are predicted, such as reentrant behavior of dynamical relaxation times. These predictions are supported by path integral ring polymer molecular dynamics simulations. The simulations provide detailed insight into the factors that govern slow dynamics in glassy quantum fluids. Connection to other recent work on both quantum glasses as well as quantum optimization problems is presented.