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Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition.
Jeff Wereszczynski, J. Andrew McCammon
Quarterly Reviews of Biophysics, in press (2012)
Molecular recognition plays a central role in biochemical processes. Although well studied, understanding the mechanisms of recognition is inherently difficult due to the range of potential interactions, the molecular rearrangement associated with binding, and the time and length scales involved. Computational methods have the potential for not only complementing experiments that have been performed, but also in guiding future ones through their predictive abilities. In this review, we discuss how molecular dynamics (MD) simulations may be used in advancing our understanding of the thermodynamics that drive biomolecular recognition. We begin with a brief review of the statistical mechanics that form a basis for these methods. This is followed by a description of some of the most commonly used methods: thermodynamic pathways employing alchemical transformations and potential of mean force calculations, along with end-point calculations for free energy differences, and harmonic and quasi-harmonic analysis for entropic calculations. Finally, a few of the fundamental findings that have resulted from these methods are discussed, such as the role of configurational entropy and solvent in intermolecular interactions, along with selected results of the model system T4 lysozyme to illustrate potential and current limitations of these methods.
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
M. Holst, J.A. McCammon, Z. Yu, Y.C. Zhou, Y. Zhu
Communications in Computational Physics, Vol. 11, pp. 179-214 (2012)
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L1 estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.
Introduction to Molecular Dynamics: Theory and Applications in Biomolecular Modeling
Y. Wang, J.A. McCammon
Independent-Trajectory Thermodynamic Integration: A Practical Guide to Protein-Drug Binding Free Energy Calculations Using Distributed Computing
Morgan Lawrenz, Riccardo Baron, Yi Wang, J. Andrew McCammon
The Independent-Trajectory Thermodynamic Integration (IT-TI) approach for free energy calculation with distributed computing is described. IT-TI utilizes diverse conformational sampling obtained from multiple, independent simulations to obtain more reliable free energy estimates compared to single TI predictions. The latter may significantly under- or over-estimate the binding free energy due to finite sampling. We exemplify the advantages of the IT-TI approach using two distinct cases of protein-ligand binding. In both cases, IT-TI yields distributions of absolute binding free energy estimates that are remarkably centered on the target experimental values. Alternative protocols for the practical and general application of IT-TI calculations are investigated. We highlight a protocol that maximizes predictive power and computational efficiency.
Guide to Virtual Screening: Application to the Akt Phosphatase PHLPP
William Sinko and Emma Sierecki and César A. F. de Oliveira and J. Andrew McCammon
We present an example-based description of virtual screening (VS) techniques used to identify new regulators of the Akt phosphatase PHLPP (PH domain Leucine repeat Protein Phosphatase). This enzyme opposes the effects of two kinases, Akt and PKC, which play a major role in cell growth and survival. Therefore, PHLPP is a potential therapeutic target in pathophysiologies where these pathways are either repressed, such as in diabetes and cardiovascular diseases, or over-activated as in cancer. To the best of our knowledge, no PHLPP inhibitors have been reported so far in the literature. In this study, we used a combination of chemical and virtual screening techniques that led to the identification of a number of inhibiting compounds with diverse scaffolds. These compounds bind PHLPP and inhibit cell death when tested in cellular assays. We employed GLIDE docking software to screen a library of more than 40,000 compounds selected from the NCI open depository (250,000 compounds) by similarity searches. We compare the efficiency at which we determined binding compounds from the chemical screen, and compare enrichment factors of the virtually discovered compounds over chemical screening.
A Molecular Dynamics Ensemble-Based Approach for the Mapping of Druggable Binding Sites
Anthony Ivetac, J. Andrew McCammon
An expanding repertoire of "allosteric" drugs is revealing that structure-based drug design (SBDD) is not restricted to the "active site" of the target protein. Such compounds have been shown to bind distant regions of the protein topography, potentially providing higher levels of target specificity, reduced toxicity and access to new regions of chemical space. Unfortunately, the location of such allosteric pockets is not obvious in the absence of a bound crystal structure and the ability to predict their presence would be useful in the discovery of novel therapies. Here, we describe a method for the prediction of "druggable" binding sites that takes protein flexibility into account through the use of molecular dynamics (MD) simulation. By using a dynamic representation of the target, we are able to sample multiple protein conformations that may expose new drug-binding surfaces. We perform a fragment-based mapping analysis of individual structures in the MD ensemble using the FTMAP algorithm and then rank the most prolific probe-binding protein residues to determine potential "hot-spots" for further examination. This approach has recently been applied to a pair of human G-protein-coupled receptors (GPCRs), resulting in the detection of five potential allosteric sites.
Accelerated Molecular Dynamics in Computational Drug Design
Jeff Wereszczynski, J. Andrew McCammon
The method of accelerated molecular dynamics (aMD) has been shown to increase the rate of phase-space sampling in biomolecular simulations. In this chapter, we discuss the theory behind aMD and describe the implementation of two versions: dual-boost and selective aMD. Each method has its practical advantages: dual-boost aMD is useful for increasing sampling of global conformational motions while selective aMD can improve the rate of convergence of free energy calculations. Special emphasis is placed on the use of these methods in computer-aided drug design, and the example of oseltamivir binding to neuraminidase is highlighted for both cases.
On the Use of Molecular Dynamics Receptor Conformations for Virtual Screening
Sara E. Nichols, Riccardo Baron, J. Andrew McCammon
Receptors are inherently dynamic and this flexibility is important to consider when constructing a model of molecular association. Conformations from molecular dynamics simulations, a well-established method for examining protein dynamics, can be used in virtual screening to account for flexibility in structure-based drug discovery. Different receptor configurations influence docking results. Molecular dynamics simulations can provide snapshots that improve virtual screening predictive power over known crystal structures, most likely as a result of sampling more relevant receptor conformations. Here we highlight some details and nuances of using such snapshots and evaluating them for predictive performance.
Hydrophobic Association and Volume-confined Water Molecules
R. Baron, P. Setny, J.A. McCammon
Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver
B. Zhang, B.Z. Lu, X. Cheng, X. Sun, N. Pitsianis, J. Huang, J.A. McCammon
Communications in Computational Physics, in press (2012)
This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the node-patch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. The potential of the solver is demonstrated with preliminary numerical results.
Protecting High Energy Barriers: A New Equation to Regulate Boost Energy in Accelerated Molecular Dynamics Simulations
William Sinko, César Augusto F. de Oliveira, Levi C.T. Pierce, J. Andrew McCammon
Journal of Chemical Theory and Computation, in press (2012)
Molecular dynamics (MD) is one of the most common tools in computational chemistry. Recently, our group has employed accelerated molecular dynamics (aMD) to improve the conformational sampling over conventional molecular dynamics techniques. In the original aMD implementation, sampling is greatly improved by raising energy wells below a predefined energy level. Recently, our group presented an alternative aMD implementation where simulations are accelerated by lowering energy barriers of the potential energy surface. When coupled with thermodynamic integration simulations, this implementation showed very promising results. However, when applied to large systems, such as proteins, the simulation tends to be biased to high energy regions of the potential landscape. The reason for this behavior lies in the boost equation used since the highest energy barriers are dramatically more affected than the lower ones. To address this issue, in this work, we present a new boost equation that prevents oversampling of unfavorable high energy conformational states. The new boost potential provides not only better recovery of statistics throughout the simulation but also enhanced sampling of statistically relevant regions in explicit solvent MD simulations.
Computer-aided Drug Discovery: Two Antiviral Drugs for HIV/AIDS
J.A. McCammon
Level-Set Variational Implicit-Solvent Modeling of Biomolecules with the Coulomb-Field Approximation
Zhongming Wang, Jianwei Che, Li-Tien Cheng, Joachim Dzubiella, Bo Li, J. Andrew McCammon
Journal of Chemical Theory and Computation, in press (2012)
AutoClickChem: Click Chemistry in Silico
Jacob D. Durrant, J. Andrew McCammon
PLoS Computational Biology, in press (2012)
Accelerated Molecular Dynamics: Theory, Implementation and Application.
Y. Wang, J.A. McCammon
Simulations of the p97 complex suggest novel conformational states of hydrolysis intermediates
Jeff Wereszczynski, J. Andrew McCammon
Protein Science, in press (2012)
The vitally important AAA protein p97 is involved in cellular functions ranging from replication to degradation of misfolded proteins and has recently been proposed as a novel chemotherapeutic target. p97 is a large molecular machine that has been shown to hexamerize in vitro, with each monomer consisting of an N-domain responsible for binding to effector proteins and two AAA repeats (D1 and D2). However, structural studies are inconclusive or in disagreement with one another on several important features such as the locations of the N domains, the relative orientations of the D1 and D2 rings, and the dimensions of the central pore. Here, we present atomic-scale simulations of the p97 hexamer in the pre-hydrolysis, transition, and post-hydrolysis states. To improve the agreement between low- and high-resolution experimental studies, we first use a biased simulation technique, molecular dynamics flexible fitting (MDFF), to improve the correlation between the structures described in these experiments. We follow this with extended, classical molecular dynamics simulations, which not only show that structures generated in the MDFF phase are stable, but reveal insights into the dynamics important to each state. Simulation results suggest a hybrid model for hydrolysis, in which the N and D2 domains are dynamic while the D1 domains are relatively static, salt bridges stabilize the position of the N-domains in the pre-hydrolysis state, and the rings formed by D1 and D2 rotate relative to one another.
Multiscale Continuum Modeling and Simulation of Biological Processes: From Molecular Electro-diffusion to Sub-Cellular Signaling Transduction.
Y. Cheng, P. Kekenes-Huskey, J. Hake, M.J. Holst, J.A. McCammon, A.P. Michailova
Computational Science & Discovery, in press (2012)
Thermodynamic integration to predict host-guest binding affinities
M. Lawrenz, J. Wereszczynski, J.M. Ortiz-Sánchez, S.E. Nichols, J.A. McCammon