Monte Carlo Simulations for Biomolecules User’s Manual (original) (raw)
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A semi-implicit solvent model for the simulation of peptides and proteins
Journal of Computational Chemistry, 2004
We present a new model of biomolecules hydration based on macroscopic electrostatic theory, that can both describe the microscopic details of solvent-solute interactions and allow for an efficient evaluation of the electrostatic hydration free energy. This semi-implicit model considers the solvent as an ensemble of polarizable pseudoparticles whose induced dipole describe both the electronic and orientational solvent polarization. In the presented version of the model, there is no mutual dipolar interaction between the particles, and they only interact through short-ranged Lennard-Jones interactions. The model has been integrated into a molecular dynamics code, and offers the possibility to simulate efficiently the conformational evolution of biomolecules. It is able to provide estimations of the electrostatic solvation free energy within short time windows during the simulation. It has been applied to the study of two small peptides, the octaalanine and the N-terminal helix of ribonuclease A, and two proteins, the bovine pancreatic trypsin inhibitor and the B1 immunoglobin-binding domain of streptococcal protein G. Molecular dynamics simulations of these biomolecules, using a slightly modified Amber force field, provide stable and meaningful trajectories in overall agreement with experiments and all-atom simulations. Correlations with respect to Poisson-Boltzmann electrostatic solvation free energies are also presented to discuss the parameterization of the model and its consequences.
Journal of chemical theory and computation, 2018
The generation of a complete ensemble of geometrical configurations is required to obtain reliable estimations of absolute binding free energies by alchemical free energy methods. Molecular dynamics (MD) is the most popular sampling method, but the representation of large biomolecular systems may be incomplete owing to energetic barriers that impede efficient sampling of the configurational space. Monte Carlo (MC) methods can possibly overcome this issue by adapting the attempted movement sizes to facilitate transitions between alternative local-energy minima. In this study, we present an MC statistical mechanics algorithm to explore the protein-ligand conformational space with emphasis on the motions of the protein backbone and side chains. The parameters for each MC move type were optimized to better reproduce conformational distributions of 18 dipeptides and the well-studied T4-lysozyme L99A protein. Next, the performance of the improved MC algorithms was evaluated by computing a...
An increasing number of studies have reported computations of the standard (absolute) binding free energy of small ligands to proteins using molecular dynamics (MD) simulations and explicit solvent molecules that are in good agreement with experiments. This encouraging progress suggests that physics-based approaches hold the promise of making important contributions to the process of drug discovery and optimization in the near future. Two types of approaches are principally used to compute binding free energies with MD simulations. The most widely known is the alchemical double decoupling method, in which the interaction of the ligand with its surroundings are progressively switched off. It is also possible to use a potential of mean force (PMF) method, in which the ligand is physically separated from the protein receptor. For both of these computational approaches, restraining potentials may be activated and released during the simulation for sampling efficiently the changes in translational, rotational, and conformational freedom of the ligand and protein upon binding. Because such restraining potentials add bias to the simulations, it is important that their effects be rigorously removed to yield a binding free energy that is properly unbiased with respect to the standard state. A review of recent results is presented, and differences in computational methods are discussed. Examples of computations with T4-lysozyme mutants, FKBP12, SH2 domain, and cytochrome P450 are discussed and compared. Remaining difficulties and challenges are highlighted. ) in 1994 and obtained a M.Sc. under the guidance of Zhida Chen in theoretical physical chemistry from Peking University (Beijing, China) in 1996. He then moved on to Brown University where he obtained his Ph.D. in 2002 on the mechanism of polyatomic vibrational relaxation in simple liquids under the direction of Richard Stratt. During his postdoctoral work with Benoît Roux, he developed computational methodologies for free energy calculations. He currently works as a molecular simulation scientist at Zymeworks Inc. (Vancouver, BC).
Accurate determination of absolute solvation free energy plays a critical role in numerous areas of biomolecular modeling and drug discovery. A quantitative representation of ligand and receptor desolvation, in particular, is an essential component of current docking and scoring methods. Furthermore, the partitioning of a drug between aqueous and nonpolar solvents is one of the important factors considered in pharmacokinetics. In this study, the absolute hydration free energy for a set of 239 neutral ligands spanning diverse chemical functional groups commonly found in drugs and drug-like candidates is calculated using the molecular dynamics free energy perturbation method (FEP/MD) with explicit water molecules, and compared to experimental data as well as its counterparts obtained using implicit solvent models. The hydration free energies are calculated from explicit solvent simulations using a staged FEP procedure permitting a separation of the total free energy into polar and nonpolar contributions. The nonpolar component is further decomposed into attractive (dispersive) and repulsive (cavity) components using the Weeks-Chandler-Anderson (WCA) separation scheme. To increase the computational efficiency, all of the FEP/MD simulations are generated using a mixed explicit/implicit solvent scheme with a relatively small number of explicit TIP3P water molecules, in which the influence of the remaining bulk is incorporated via the spherical solvent boundary potential (SSBP). The performances of two fixed-charge force fields designed for small organic molecules, the General Amber force field (GAFF), and the all-atom CHARMm-MSI, are compared. Because of the crucial role of electrostatics in solvation free energy, the results from various commonly used charge generation models based on the semiempirical (AM1-BCC) and QM calculations [charge fitting using ChelpG and RESP] are compared. In addition, the solvation free energies of the test set are also calculated using Poisson-Boltzmann (PB) and Generalized Born model of solvation (GB), which are two widely used continuum electrostatic implicit solvent models. The protocol for running the absolute solvation free energy calculations used throughout is automated as much as possible, with minimum user intervention, so that it can be used in large-scale analysis and force field optimization. Figure 2. Average unsigned error [AUE] in the absolute solvation free energies. The AUE is shown in the y-axis, and the chemical functionalities in the small molecules are plotted in the x-axis. The solid bars represent the solvation free energies calculated using explicit solvent/FEP method in CHARMM. The bars with dotted line and stripes represent the solvation free energy calculated using GB and PB model in Amber9.
A statistical mechanics handbook for protein-ligand binding simulation
Frontiers in Bioscience, 2013
Introduction 3. Basics 3.1. Fixed energy systems 3.2. Microscopic versus thermodynamic description 3.3. Fixed temperature systems 3.3.1. Consequences of the Boltzmann distribution 3.3.2. Time evolution in the canonical ensemble 3.4. From microscopic quantities to macroscopic observables 3.5. Complementary material to section 3 3.5.1. Derivation of Boltzmann distribution for the canonical ensemble 3.5.2. The Fokker-Plank equation 4. Tools and concepts for the description of the binding process 4.1. Role of the free energy and of the internal constraint 4.1.1. Obstacles to absolute free energy calculation 4.1.2. Free energy differences calculation 4.2. Free energy profiles and reaction paths 4.3. The definition of bound and unbound states and the reaction coordinate 4.4. Potential versus free energy surface 4.5. A didactic example 4.6. Volumetric effect on the unbound state 4.7. Complementary material to section 4 4.7.1. The zero temperature limit for free energy 5. Conclusions 6. Acknowledgements 7. References
Calculation of absolute protein–ligand binding free energy from computer simulations
A general methodology for calculating the equilibrium binding constant of a flexible ligand to a protein receptor is formulated on the basis of potentials of mean force. The overall process is decomposed into several stages that can be computed separately: the free ligand in the bulk is first restrained into the conformation it adopts in the bound state, position, and orientation by applying biasing potentials, then it is translated into the binding site, where it is released completely. The conformational restraining potential is based on the root-mean-square deviation of the peptide coordinates relative to its average conformation in the bound complex. Free energy contributions from each stage are calculated by means of free energy perturbation potential of mean force techniques by using appropriate order parameters. The present approach avoids the need to decouple the ligand from its surrounding (bulk solvent and receptor protein) as is traditionally performed in the doubledecoupling scheme. It is believed that the present formulation will be particularly useful when the solvation free energy of the ligand is very large. As an application, the equilibrium binding constant of the phosphotyrosine peptide pYEEI to the Src homology 2 domain of human Lck has been calculated. The results are in good agreement with experimental values. free energy perturbation ͉ molecular dynamics ͉ Src Homology 2 domain This paper was submitted directly (Track II) to the PNAS office.
Free energy simulations for protein ligand binding and stability
Molecular Simulation, 2018
We summarize several computational techniques to determine relative free energies for condensedphase systems. The focus is on practical considerations which are capable of making direct contact with experiments. Particular applications include the thermodynamic stability of apo-and holo-myoglobin, insulin dimerization free energy, ligand binding in lysozyme, and ligand diffusion in globular proteins. In addition to provide differential free energies between neighboring states, converged umbrella sampling simulations provide insight into migration barriers and ligand dissociation barriers and analysis of the trajectories yield additional insight into the structural dynamics of fundamental processes. Also, such simulations are useful tools to quantify relative stability changes for situations where experiments are difficult. This is illustrated for NO-bound myoglobin. For the dissociation of benzonitrile from lysozyme it is found that long umbrella sampling simulations are required to approximately converge the free energy profile. Then, however, the resulting differential free energy between the bound and unbound state is in good agreement with estimates from molecular mechanics with generalized Born surface area simulations. Furthermore, comparing the barrier height for ligand escape suggests that ligand dissociation contains a non-equilibrium component.
Treating Entropy and Conformational Changes in Implicit Solvent Simulations of Small Molecules
The Journal of Physical Chemistry B, 2008
Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TΔS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R 2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid. *Corresponding author. dmobley@gmail.com. Supporting Information Available: Coordinate files (mol2) with AM1-BCC partial charges for the small molecules in the test set used here; list of computed values for each compound with each of the implicit solvent models, and for the model of Onufriev, Bashford, and Case, using different conformations and different analysis methods; experimental solvation free energies (1M vacuum to 1M water) and references for the molecules in the test set; histograms of molecular weight and number of rotatable bonds for the test set; an alternative version of ; and a table of the 17 small molecules with TΔS larger than 0.5 kcal/mol. This information is available free of charge via the Internet at
The Journal of Physical Chemistry B, 1997
Monte Carlo computer simulations have been performed in conjunction with free-energy perturbation calculations to determine the relative binding constants of four benzamidine inhibitors with trypsin. The protein backbone was constrained in the simulations, but sampling of the side chains was allowed. The calculated free energies are very precise and are shown to yield closed thermodynamic cycles. The calculations correctly predict p-aminobenzamidine to be the strongest inhibitor and give relative free energies of binding for p-methyl-and p-chlorobenzamidine in excellent agreement with experiment. The predicted overly weak binding of the parent benzamidine is most likely due to a deficiency in the partial charges. The relative binding affinities are justified in terms of bulk-solvation arguments whereby the more polar inhibitors are preferentially stabilized in water. The calculations demonstrate that Monte Carlo computer simulations can be used to determine accurate and precise relative binding constants for protein systems.