Recent advances in maximum entropy biasing techniques for molecular dynamics

ABSTRACT

This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in molecular simulation by minimally modifying the thermodynamic ensemble. This is especially important where force fields are approximate, such as when employing coarse-grain models, or where high accuracy is required, such as when attempting to mimic a multiscale self-assembly process. The authors review here the experiment directed simulation (EDS) and experiment directed metadynamics (EDM) methods that allow matching averages and distributions in simulations, respectively. Important system-specific considerations are discussed such as using enhanced sampling simultaneously, the role of pressure, treating uncertainty, and implementations of these methods. Recent examples of EDS and EDM are reviewed including applications to ab initio molecular dynamics of water, incorporating environmental fluctuations inside of a macromolecular protein complex, improving RNA force fields, and the combination of enhanced sampling with minimal biasing to model peptides     

Biased Brownian dynamics for rate constant calculation

An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampling of trajectories is then biased, but the sampling is unbiased when the trajectory outcomes are multiplied by their weights. With a suitable choice of the biasing force, more reacted trajectories are sampled. As a consequence, the variance of the estimate is reduced. In our test case, biased Brownian dynamics gives a sevenfold improvement in central processing unit (CPU) time with the choice of a simple centripetal biasing force.     

Nonlinear machine learning in simulations of soft and biological materials

Abstract

Interpretable parameterisations of free energy landscapes for soft and biological materials calculated from molecular simulation require the availability of ‘good’ collective variables (CVs) capable of discriminating the metastable states of the system and the barriers between them. If these CVs are coincident with the slow collective modes governing the long-time dynamical evolution, then they also furnish good coordinates in which to perform enhanced sampling to surmount high free energy barriers and efficiently explore and recover the landscape. Non-linear manifold learning techniques provide a means to systematically extract such CVs from molecular simulation trajectories by identifying and extracting low-dimensional manifolds lying latent within the high-dimensional coordinate space. We survey recent advances in data-driven CV discovery and enhanced sampling using non-linear manifold learning, describe the mathematical and theoretical underpinnings of these techniques, and present illustrative examples to molecular folding and colloidal self-assembly. We close with our outlook and perspective on future advances in this rapidly evolving field.     

High performance computing in biology: multimillion atom simulations of nanoscale systems

Computational methods have been used in biology for sequence analysis (bioinformatics), all-atom simulation (molecular dynamics and quantum calculations), and more recently for modeling biological networks (systems biology). Of these three techniques, all-atom simulation is currently the most computationally demanding, in terms of compute load, communication speed, and memory load. Breakthroughs in electrostatic force calculation and dynamic load balancing have enabled molecular dynamics simulations of large biomolecular complexes. Here, we report simulation results for the ribosome, using approximately 2.64 million atoms, the largest all-atom biomolecular simulation published to date. Several other nano-scale systems with different numbers of atoms were studied to measure the performance of the NAMD molecular dynamics simulation program on the Los Alamos National Laboratory Q Machine. We demonstrate that multimillion atom systems represent a 'sweet spot' for the NAMD code on large supercomputers. NAMD displays an unprecedented 85% parallel scaling efficiency for the ribosome system on 1024 CPUs. We also review recent targeted molecular dynamics simulations of the ribosome that prove useful for studying conformational changes of this large biomolecular complex in atomic detail.     

Conformational sampling for the impatient

Several new methods for sampling conformations of biomolecules have appeared recently. A brief review thereof is presented, with particular emphasis on applications that have been published, and suitability for different kinds of systems. Four methods (namely: RESPA, replica-exchange molecular dynamics, CONCOORD and Gaussian network method) are readily applicable for biomolecular systems.     

General trends of dihedral conformational transitions in a globular protein

Dihedral conformational transitions are analyzed systematically in a model globular protein, cytochrome P450cam, to examine their structural and chemical dependences through combined conventional molecular dynamics (cMD), accelerated molecular dynamics (aMD) and adaptive biasing force (ABF) simulations. The aMD simulations are performed at two acceleration levels, using dihedral and dual boost, respectively. In comparison with cMD, aMD samples protein dihedral transitions approximately two times faster on average using dihedral boost, and ～3.5 times faster using dual boost. In the protein backbone, significantly higher dihedral transition rates are observed in the bend, coil, and turn flexible regions, followed by the β bridge and β sheet, and then the helices. Moreover, protein side chains of greater length exhibit higher transition rates on average in the aMD‐enhanced sampling. Side chains of the same length (particularly N_χ = 2) exhibit decreasing transition rates with residues when going from hydrophobic to polar, then charged and aromatic chemical types. The reduction of dihedral transition rates is found to be correlated with increasing energy barriers as identified through ABF free energy calculations. These general trends of dihedral conformational transitions provide important insights into the hierarchical dynamics and complex free energy landscapes of functional proteins. Proteins 2016; 84:501–514. © 2016 Wiley Periodicals, Inc.     

Simulating the free energy of passive membrane permeation for small molecules

Abstract

Computer simulations of passive membrane permeation provide important microscopic insights into the molecular mechanism of this important biological process that are complementary to experimental data. Our review focuses on the main approaches for calculating the free energy, or potential of mean force, for permeation of small molecules through lipid bilayers. The theoretical background for most currently used methods for potential of mean force calculation is described, including particle insertion, thermodynamic integration, umbrella sampling, metadynamics, adaptive biasing force and milestoning. A brief comparison of strengths and weaknesses of the competing approaches is presented. This is followed by a survey of results obtained by the different methods, with special attention to describing the mechanistic insights generated by modelling and illustrating capabilities of the different techniques. We conclude with a discussion of recent advances and future directions in modelling membrane permeation, including latest methodological enhancements, consideration of multiple slow variables and memory effects.     

Hydration of proteins and nucleic acids: Advances in experiment and theory. A review

BackgroundMost biological processes involve water, and the interactions of biomolecules with water affect their structure, function and dynamics.Scope of reviewThis review summarizes the current knowledge of protein and nucleic acid interactions with water, with a special focus on the biomolecular hydration layer. Recent developments in both experimental and computational methods that can be applied to the study of hydration structure and dynamics are reviewed, including software tools for the prediction and characterization of hydration layer properties.Major conclusionsIn the last decade, important advances have been made in our understanding of the factors that determine how biomolecules and their aqueous environment influence each other. Both experimental and computational methods contributed to the gradually emerging consensus picture of biomolecular hydration.General significanceAn improved knowledge of the structural and thermodynamic properties of the hydration layer will enable a detailed understanding of the various biological processes in which it is involved, with implications for a wide range of applications, including protein-structure prediction and structure-based drug design.     

Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER

To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.     

Computational techniques for efficient conformational sampling of proteins

In this review, we summarize the computational methods for sampling the conformational space of biomacromolecules. We discuss the methods applicable to find only lowest energy conformations (global minimization of the potential-energy function) and to generate canonical ensembles (canonical Monte Carlo method and canonical molecular dynamics method and their extensions). Special attention is devoted to the use of coarse-grained models that enable simulations to be enhanced by several orders of magnitude.     

Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

BackgroundAtomic Force Microscopy (AFM) is an experimental technique to study structure-function relationship of biomolecules. AFM provides images of biomolecules at nanometer resolution. High-speed AFM experiments produce a series of images following dynamics of biomolecules. To further understand biomolecular functions, information on three-dimensional (3D) structures is beneficial.MethodWe aim to recover 3D information from an AFM image by computational modeling. The AFM image includes only low-resolution representation of a molecule; therefore we represent the structures by a coarse grained model (Gaussian mixture model). Using Monte-Carlo sampling, candidate models are generated to increase similarity between AFM images simulated from the models and target AFM image.ResultsThe algorithm was tested on two proteins to model their conformational transitions. Using a simulated AFM image as reference, the algorithm can produce a low-resolution 3D model of the target molecule. Effect of molecular orientations captured in AFM images on the 3D modeling performance was also examined and it is shown that similar accuracy can be obtained for many orientations.ConclusionsThe proposed algorithm can generate 3D low-resolution protein models, from which conformational transitions observed in AFM images can be interpreted in more detail.General significanceHigh-speed AFM experiments allow us to directly observe biomolecules in action, which provides insights on biomolecular function through dynamics. However, as only partial structural information can be obtained from AFM data, this new AFM based hybrid modeling method would be useful to retrieve 3D information of the entire biomolecule.     

A Free Energy Based Computational Pathway from Chemical Templates to Lead Compounds: A Case Study of COX-2 Inhibitors

Abstract

Automation of lead compound design in silico given the structure of the protein target and a definition of its active site vies for the top of the wish list in any drug discovery programme. We present here an enumeration of steps starting from chemical templates and propose a solution at the state of the art, in the form of a system independent comprehensive computational pathway. This methodology is illustrated with cyclooxygenase-2 (COX-2) as a target. We built candidate molecules including a few Non Steroidal Anti-inflammatory Drugs (NSAIDs) from chemical templates, passed them through empirical filters to assess drug-like properties, optimized their geometries, derived partial atomic charges via quantum calculations, performed Monte Carlo docking, carried out molecular mechanics and developed free energy estimates with Molecular Mechanics Generalized Born Solvent Accessibility (MMGBSA) methodology for each of the candidate molecules. For the case of aspirin, we also conducted molecular dynamics on the enzyme, the drug and the complex with explicit solvent followed by binding free energy analysis. Collectively, the results obtained from the above studies viz. sorting of drugs from non-drugs, semi-quantitative estimates of binding free energies, amply demonstrate the viability of the strategy proposed for lead selection/design for biomolecular targets.     

Biophysical studies of phase separation integrating experimental and computational methods

Biomolecular phase separation that contributes to the formation of membraneless organelles and biomolecular condensates has recently gained tremendous attention because of the importance of these assemblies in physiology, disease, and engineering applications. Understanding and directing biomolecular phase separation requires a multiscale view of the biophysical properties of these phases. Yet, many classic tools to characterize biomolecular properties do not apply in these condensed phases. Here, we discuss insights obtained from spectroscopic methods, in particular nuclear magnetic resonance and optical spectroscopy, in understanding the molecular and atomic interactions that underlie the formation of protein-rich condensates. We also review approaches closely coupling nuclear magnetic resonance data with computational methods especially coarse-grained and all-atom molecular simulations, which provide insight into molecular features of phase separation. Finally, we point to future methodolical developments, particularly visualizing biophysical properties of condensates in cells.     

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyse two different approaches: the QM/MM–MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analysed here, both approaches seem productive although care needs to be exercised when analysing the perturbative corrections.     

Enhanced sampling of chemical and biochemical reactions with metadynamics

Metadynamics (MetaD) is a method that augments molecular dynamics (MD) calculations of all types (classical and quantum) to help systems overcome energy barriers and explore regions of phase space that would otherwise not be seen during a simulation. The method has seen wide ranging uses, and it has proven especially useful for the study of reactions in which bonds break and form. In such cases, the timescale challenges of MD are profoundly limiting, and the advent of this new paradigm for biasing simulations has proven to be incredibly useful. In this review, we set out to summarise the large body of work that uses MetaD for studying reactions so that others can more easily implement this method in their own work. After a brief introduction of the method, we provide detailed summaries of the method applied in various contexts including condensed phase and biological reactions.     

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein–partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein–partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.