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Summer Research Fellowship Programme of India's Science Academies

Role of Entropy in Binding Free Energy Calculations of Protein-Ligand Complex

Mandar Deshpande

Indian Institute of Science Education and Research, Bhopal 462066

Dr. Sabyashachi Mishra

Associate Professor, Department of Chemistry, Indian Institute of Technology, Kharagpur 721302

Abstract

Computer simulations are extensively used to estimate the binding free energy of ligand after binding to a pharmacologically important target which helps in screening potential drug candidates. Simulations provide the information about the energy microstates occupied by a molecule. Statistical Thermodynamics provides the link between microscopic and observable macroscopic properties. MMPB/GBSA (Molecular Mechanics Poisson Boltzmann/Generalized Born Surface Area ) is one of the most popular post-processing free energy calculation methods, where the binding free energy (∆Gbin.) is calculated as the sum of changes in force field energy (∆EMM), solvation energy (∆GPB for polar contribution and ∆GSA for non-polar contribution) and free energy change associated with entropy change (-T∆S) of system after binding. Configurational entropy change during complex formation consists of vibrational entropy change and conformational entropy change (translational and rotational). MMPBSA calculations neglect changes in conformational entropy (∆Sconfo.) of solute. In MMPBSA calculations, change in entropy during enzyme-ligand complex is estimated using Rigid Rotor-Harmonic Oscillator (RRHO) approximation. Statistical mechanical calculations are done separately for each of Translational, Rotational and Vibrational contributions to entropy change which are computationally intensive. This method assumes ligand and enzyme as rigid bodies neglecting the flexibility of biomolecules. A new, computationally more efficient method BEERT (Binding Energy Estimation of Rotation and Translation) is proposed by Ben-Shalom et al. which treats binding process using flexible molecule (FM) approach. FM approach is based \on classical statistical thermodynamics. At temperatures attained by biological systems, quantum mechanical descriptions of ligand composed of rigid rotors reduce to classical mechanical results. Motion of ligand with respect to internal coordinates of protein after binding is considered to contribute towards ∆Sconfo in FM approach. ∆Sconfo is approximated as reduction in effective translational and rotational volume of ligand after binding to protein. BEERT provide simple expressions to calculate configurational entropy (∆Sconfig). In this project, BEERT calculations are done for complex formed by enzyme lipoxygenase (PDB code 4QWT) and ligand ACD (Arachidonic acid) from trajectory snapshots obtained from MD simulations of complex. BEERT calculations are also performed for docking poses obtained for protease inhibitor, KB62 in complex with wild type HIV-1 protease and enzyme lipoxygenase. VMD, AutoDock 4.2 software package and python code are used to perform calculations.

Keywords: Statistical Thermodynamics, MMPBSA, RRHO, Flexible Molecule Approach, BEERT, Molecular Dynamics (MD) Simulations, Docking , AutoDock

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