Computational Approaches to the Chemical Equilibrium Constant in Protein‐ligand Binding

The physiological role played by protein‐ligand recognition has motivated the development of several computational approaches to the ligand binding affinity. Some of them, termed rigorous, have a strong theoretical foundation but involve too much computation to be generally useful. Some others alleviate the computational burden by introducing strong approximations and/or empirical calibrations, which also limit their general use. Most importantly, there is no straightforward correlation between the predictive power and the level of approximation introduced. Here, we present a general framework for the quantitative interpretation of protein‐ligand binding based on statistical mechanics. Within this framework, we re‐derive self‐consistently the fundamental equations of some popular approaches to the binding constant and pinpoint the inherent approximations. Our analysis represents a first step towards the development of variants with optimum accuracy/efficiency ratio for each stage of the drug discovery pipeline.

[1]  Amedeo Caflisch,et al.  Quantum mechanical methods for drug design. , 2010, Current topics in medicinal chemistry.

[2]  Youyong Li,et al.  Assessing the performance of MM/PBSA and MM/GBSA methods. 3. The impact of force fields and ligand charge models. , 2013, The journal of physical chemistry. B.

[3]  William L. Jorgensen,et al.  Efficient computation of absolute free energies of binding by computer simulations. Application to the methane dimer in water , 1988 .

[4]  E. Kandel,et al.  Proceedings of the National Academy of Sciences of the United States of America. Annual subject and author indexes. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[5]  D. Rognan,et al.  Predicting binding affinities of protein ligands from three-dimensional models: application to peptide binding to class I major histocompatibility proteins. , 1999, Journal of medicinal chemistry.

[6]  Amedeo Caflisch,et al.  Library screening by fragment‐based docking , 2009, Journal of molecular recognition : JMR.

[7]  Giulio Rastelli,et al.  Fast and accurate predictions of binding free energies using MM‐PBSA and MM‐GBSA , 2009, J. Comput. Chem..

[8]  Amedeo Caflisch,et al.  Efficient evaluation of binding free energy using continuum electrostatics solvation. , 2004, Journal of medicinal chemistry.

[9]  Stefan Boresch,et al.  Absolute Binding Free Energies: A Quantitative Approach for Their Calculation , 2003 .

[10]  Youyong Li,et al.  Assessing the performance of MM/PBSA and MM/GBSA methods. 4. Accuracies of MM/PBSA and MM/GBSA methodologies evaluated by various simulation protocols using PDBbind data set. , 2014, Physical chemistry chemical physics : PCCP.

[11]  Hugo Gutiérrez-de-Terán,et al.  Linear interaction energy: method and applications in drug design. , 2012, Methods in molecular biology.

[12]  David S. Goodsell,et al.  AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility , 2009, J. Comput. Chem..

[13]  U. Ryde,et al.  QM/MM-PBSA method to estimate free energies for reactions in proteins. , 2008, The journal of physical chemistry. B.

[14]  B. Roux,et al.  Computations of standard binding free energies with molecular dynamics simulations. , 2009, The journal of physical chemistry. B.

[15]  Holger Gohlke,et al.  Converging free energy estimates: MM‐PB(GB)SA studies on the protein–protein complex Ras–Raf , 2004, J. Comput. Chem..

[16]  T. L. Hill Cooperativity Theory in Biochemistry: Steady-State and Equilibrium Systems , 2011 .

[17]  A. Kidera,et al.  Protein structural change upon ligand binding: linear response theory. , 2005, Physical review letters.

[18]  Joel Lexchin,et al.  The cost of drug development: a systematic review. , 2011, Health policy.

[19]  Hans-Joachim Böhm,et al.  Prediction of binding constants of protein ligands: A fast method for the prioritization of hits obtained from de novo design or 3D database search programs , 1998, J. Comput. Aided Mol. Des..

[20]  J. Changeux,et al.  Allosteric Mechanisms of Signal Transduction , 2005, Science.

[21]  Lu Wang,et al.  Inclusion of Loss of Translational and Rotational Freedom in Theoretical Estimates of Free Energies of Binding. Application to a Complex of Benzene and Mutant T4 Lysozyme , 1997 .

[22]  A. Warshel,et al.  Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603. , 1992, Protein engineering.

[23]  William L. Jorgensen,et al.  Journal of Chemical Information and Modeling , 2005, J. Chem. Inf. Model..

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

[25]  J. Åqvist,et al.  The linear interaction energy method for predicting ligand binding free energies. , 2001, Combinatorial chemistry & high throughput screening.

[26]  Christophe Chipot,et al.  Good practices in free-energy calculations. , 2010, The journal of physical chemistry. B.

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

[28]  Srihari Keshavamurthy,et al.  Annual Review of Physical Chemistry , 2018 .

[29]  M. Cecchini,et al.  Accurate calculation of conformational free energy differences in explicit water: the confinement-solvation free energy approach. , 2015, The journal of physical chemistry. B.

[30]  M. Karplus,et al.  Evaluation of the configurational entropy for proteins: application to molecular dynamics simulations of an α-helix , 1984 .

[31]  M. Cecchini Quantum Corrections to the Free Energy Difference between Peptides and Proteins Conformers. , 2015, Journal of chemical theory and computation.

[32]  Samuel Genheden,et al.  Comparison of end‐point continuum‐solvation methods for the calculation of protein–ligand binding free energies , 2012, Proteins.

[33]  J. Mccammon,et al.  Exploring the role of receptor flexibility in structure-based drug discovery. , 2014, Biophysical chemistry.

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

[35]  W. L. Jorgensen Free energy calculations: a breakthrough for modeling organic chemistry in solution , 1989 .

[36]  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.

[37]  Tingjun Hou,et al.  Assessing the performance of the molecular mechanics/Poisson Boltzmann surface area and molecular mechanics/generalized Born surface area methods. II. The accuracy of ranking poses generated from docking , 2011, J. Comput. Chem..

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

[39]  Charles C. Persinger,et al.  How to improve R&D productivity: the pharmaceutical industry's grand challenge , 2010, Nature Reviews Drug Discovery.

[40]  P. Kollman,et al.  Continuum Solvent Studies of the Stability of DNA, RNA, and Phosphoramidate−DNA Helices , 1998 .

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

[42]  Jens Carlsson,et al.  Improving the Accuracy of the Linear Interaction Energy Method for Solvation Free Energies. , 2007, Journal of chemical theory and computation.

[43]  Pedro J Ballester,et al.  Machine‐learning scoring functions to improve structure‐based binding affinity prediction and virtual screening , 2015, Wiley interdisciplinary reviews. Computational molecular science.

[44]  I. Kuntz,et al.  Automated docking with grid‐based energy evaluation , 1992 .

[45]  Rudolph A. Marcus,et al.  Chemical and Electrochemical Electron-Transfer Theory , 1964 .

[46]  G. Klebe,et al.  Knowledge-based scoring function to predict protein-ligand interactions. , 2000, Journal of molecular biology.

[47]  Cen Gao,et al.  Accounting for ligand conformational restriction in calculations of protein-ligand binding affinities. , 2010, Biophysical journal.

[48]  I. Kuntz,et al.  Pairwise GB/SA Scoring Function for Structure-based Drug Design , 2004 .

[49]  Peter A. Kollman,et al.  FREE ENERGY CALCULATIONS : APPLICATIONS TO CHEMICAL AND BIOCHEMICAL PHENOMENA , 1993 .

[50]  Andriy Kovalenko,et al.  An MM/3D-RISM approach for ligand binding affinities. , 2010, The journal of physical chemistry. B.

[51]  Matthieu Hamel,et al.  Journal of Medicinal Chemistry , 2010 .

[52]  B. Roux,et al.  The Hidden Energetics of Ligand-Binding and Activation in a Glutamate Receptor , 2010, Nature Structural &Molecular Biology.

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

[54]  Tingjun Hou,et al.  Assessing the Performance of the MM/PBSA and MM/GBSA Methods. 1. The Accuracy of Binding Free Energy Calculations Based on Molecular Dynamics Simulations , 2011, J. Chem. Inf. Model..

[55]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[56]  Xiaoqin Zou,et al.  Scoring functions and their evaluation methods for protein-ligand docking: recent advances and future directions. , 2010, Physical chemistry chemical physics : PCCP.

[57]  T. Hansson,et al.  On the Validity of Electrostatic Linear Response in Polar Solvents , 1996 .

[58]  Journal of Computer-Aided Molecular Design incorporating Perspectives in Drug Discovery and Design , 2005 .

[59]  Daniel Hoffmann,et al.  The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant , 2012, J. Chem. Inf. Model..

[60]  J. Aqvist,et al.  A new method for predicting binding affinity in computer-aided drug design. , 1994, Protein engineering.

[61]  Holger Gohlke,et al.  Binding Free Energy Calculations for Lead Optimization: Assessment of Their Accuracy in an Industrial Drug Design Context. , 2014, Journal of chemical theory and computation.

[62]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[63]  A. Caflisch,et al.  Is quantum mechanics necessary for predicting binding free energy? , 2008, Journal of medicinal chemistry.

[64]  L. A. Basso,et al.  Virtual Screening of Drugs: Score Functions, Docking, and Drug Design , 2008 .

[65]  J. Bajorath,et al.  Docking and scoring in virtual screening for drug discovery: methods and applications , 2004, Nature Reviews Drug Discovery.

[66]  M. Karplus,et al.  Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[67]  Arieh Ben-Naim,et al.  Solvation thermodynamics of nonionic solutes , 1984 .

[68]  Jennifer L. Knight,et al.  Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. , 2015, Journal of the American Chemical Society.

[69]  J. C. Bevington,et al.  Chemical Reviews , 1970, Nature.

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

[71]  M. Nadeau,et al.  Proteins : Structure , Function , and Bioinformatics , 2022 .

[72]  Thomas Simonson,et al.  Free energy simulations come of age: protein-ligand recognition. , 2002, Accounts of chemical research.

[73]  Kendall N Houk,et al.  Accounts of Chemical Research. , 2008, Accounts of chemical research.