Delineating Protein–Protein Curvilinear Dissociation Pathways and Energetics with Naïve Multiple‐Walker Umbrella Sampling Simulations

The protein–protein interaction energetics can be obtained by calculating the potential of mean force (PMF) from umbrella sampling (US) simulations, in which samplings are often enhanced along a predefined vector as the reaction coordinate. However, any slight change in the vector may significantly vary the calculated PMF, and therefore the energetics using a random choice of vector may mislead. A non‐predefined curve path‐based sampling enhancement approach is a natural alternative, but was relatively less explored for protein–protein systems. In this work, dissociation of the barnase–barstar complex is simulated by implementing non‐predefined curvilinear pathways in US simulations. A simple variational principle is applied to determine the lower bound PMF, which could be used to derive the standard free energy of binding. Two major dissociation pathways, which include interactions with the RNA‐binding loop and the Val 36 to Gly 40 loop, are observed. Further, the proposed approach was used to discriminate the decoys from protein–protein docking studies. © 2019 Wiley Periodicals, Inc.

[1]  B. Alder,et al.  THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD , 2010 .

[2]  Hao Wang,et al.  Assessing the Relative Stability of Dimer Interfaces in G Protein-Coupled Receptors , 2012, PLoS Comput. Biol..

[3]  David Perahia,et al.  Odorant Binding and Conformational Dynamics in the Odorant-binding Protein* , 2006, Journal of Biological Chemistry.

[4]  David L. Mobley,et al.  Chapter 4 Alchemical Free Energy Calculations: Ready for Prime Time? , 2007 .

[5]  W. Delano The PyMOL Molecular Graphics System , 2002 .

[6]  F Marty Ytreberg Absolute FKBP binding affinities obtained via nonequilibrium unbinding simulations. , 2009, The Journal of chemical physics.

[7]  Zhiping Weng,et al.  Accelerating Protein Docking in ZDOCK Using an Advanced 3D Convolution Library , 2011, PloS one.

[8]  Daniel R Roe,et al.  PTRAJ and CPPTRAJ: Software for Processing and Analysis of Molecular Dynamics Trajectory Data. , 2013, Journal of chemical theory and computation.

[9]  Benoît Roux,et al.  Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression , 2015, Journal of chemical theory and computation.

[10]  David L Mobley,et al.  Predicting Binding Free Energies: Frontiers and Benchmarks. , 2017, Annual review of biophysics.

[11]  J. Mccammon,et al.  Molecular recognition and ligand association. , 2013, Annual review of physical chemistry.

[12]  V. Helms,et al.  Energetics of Hydrophilic Protein-Protein Association and the Role of Water. , 2014, Journal of chemical theory and computation.

[13]  Haohao Fu,et al.  Extended Adaptive Biasing Force Algorithm. An On-the-Fly Implementation for Accurate Free-Energy Calculations. , 2016, Journal of chemical theory and computation.

[14]  Charles L. Brooks,et al.  Coupled folding and binding with 2D Window‐Exchange Umbrella Sampling , 2016, J. Comput. Chem..

[15]  J. Kästner Umbrella sampling , 2011 .

[16]  Noam Bernstein,et al.  Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression. , 2013, Journal of chemical theory and computation.

[17]  Christophe Chipot,et al.  Efficient determination of protein-protein standard binding free energies from first principles. , 2013, Journal of chemical theory and computation.

[18]  Mark A Olson,et al.  Calculation of absolute protein-ligand binding affinity using path and endpoint approaches. , 2006, Biophysical journal.

[19]  Eric Darve,et al.  Calculating Free Energies Using a Scaled-Force Molecular Dynamics Algorithm , 2002 .

[20]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

[21]  David L Mobley,et al.  Alchemical free energy methods for drug discovery: progress and challenges. , 2011, Current opinion in structural biology.

[22]  Michael K. Gilson,et al.  Theory of free energy and entropy in noncovalent binding. , 2009, Chemical reviews.

[23]  How Hydrophilic Proteins Form Nonspecific Complexes. , 2015, The journal of physical chemistry. B.

[24]  G Schreiber,et al.  Thermodynamics of the interaction of barnase and barstar: changes in free energy versus changes in enthalpy on mutation. , 1997, Journal of molecular biology.

[25]  C. Simmerling,et al.  ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB. , 2015, Journal of chemical theory and computation.

[26]  D. Ceperley Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions , 1978 .

[27]  M J Harvey,et al.  An Implementation of the Smooth Particle Mesh Ewald Method on GPU Hardware. , 2009, Journal of chemical theory and computation.

[28]  B. Roux,et al.  Calculation of absolute protein-ligand binding free energy from computer simulations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[30]  Wilfred F van Gunsteren,et al.  Practical Aspects of Free-Energy Calculations: A Review. , 2014, Journal of chemical theory and computation.

[31]  Daisuke Kihara,et al.  Ranking protein–protein docking results using steered molecular dynamics and potential of mean force calculations , 2016, J. Comput. Chem..

[32]  M. Gilson,et al.  The statistical-thermodynamic basis for computation of binding affinities: a critical review. , 1997, Biophysical journal.

[33]  Eric F Darve,et al.  Calculating free energies using average force , 2001 .

[34]  Duncan Poole,et al.  Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 2. Explicit Solvent Particle Mesh Ewald. , 2013, Journal of chemical theory and computation.

[35]  Wei Yang,et al.  Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems , 2008, Proceedings of the National Academy of Sciences.

[36]  Benoît Roux,et al.  Calculation of Standard Binding Free Energies:  Aromatic Molecules in the T4 Lysozyme L99A Mutant. , 2006, Journal of chemical theory and computation.

[37]  James Andrew McCammon,et al.  Ligand-receptor interactions , 1984, Comput. Chem..

[38]  J. Kirkwood Statistical Mechanics of Fluid Mixtures , 1935 .

[39]  J. Berg,et al.  Molecular dynamics simulations of biomolecules , 2002, Nature Structural Biology.

[40]  S. Genheden,et al.  The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities , 2015, Expert opinion on drug discovery.

[41]  P. Kollman,et al.  Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. , 2000, Accounts of chemical research.

[42]  Gregory A Voth,et al.  A Combined Metadynamics and Umbrella Sampling Method for the Calculation of Ion Permeation Free Energy Profiles. , 2011, Journal of chemical theory and computation.

[43]  Holger Gohlke,et al.  The Amber biomolecular simulation programs , 2005, J. Comput. Chem..

[44]  Wei Yang,et al.  Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method. , 2016, Journal of chemical theory and computation.

[45]  F. Noé,et al.  Complete protein–protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling , 2017, Nature Chemistry.

[46]  Christophe Chipot,et al.  Frontiers in free‐energy calculations of biological systems , 2014 .

[47]  C. Jarzynski Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[48]  Richard H. Henchman,et al.  Standard Free Energy of Binding from a One-Dimensional Potential of Mean Force. , 2009, Journal of chemical theory and computation.

[49]  Tai-Sung Lee,et al.  A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations. , 2013, Journal of chemical theory and computation.

[50]  R. Lazarus,et al.  Mining ancient proteins for next-generation drugs , 2017, Nature Biotechnology.

[51]  Christophe Chipot,et al.  Standard binding free energies from computer simulations: What is the best strategy? , 2013, Journal of chemical theory and computation.

[52]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

[53]  E. Vanden-Eijnden,et al.  Single-sweep methods for free energy calculations. , 2007, The Journal of chemical physics.

[54]  Nathan A. Baker,et al.  Electrostatics of nanosystems: Application to microtubules and the ribosome , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[55]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[56]  J A McCammon,et al.  Enzyme-inhibitor association thermodynamics: explicit and continuum solvent studies. , 1997, Biophysical journal.

[57]  Replica Exchange Gaussian Accelerated Molecular Dynamics: Improved Enhanced Sampling and Free Energy Calculation. , 2018, Journal of chemical theory and computation.

[58]  Ross C. Walker,et al.  An overview of the Amber biomolecular simulation package , 2013 .

[59]  M. Parrinello,et al.  Funnel metadynamics as accurate binding free-energy method , 2013, Proceedings of the National Academy of Sciences.

[60]  Walter Thiel,et al.  Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration". , 2005, The Journal of chemical physics.

[61]  B. Roux,et al.  Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials. , 2006, Biophysical journal.