A statistical mechanics handbook for proteinligand binding simulation
Walter Rocchia^{1}, Sara Bonella^{2
}
^{} 1Drug Discovery and Development, Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy, ^{2}Department of Physics, University of Rome "La Sapienza" and CNISM Unit 1, Ple A. Moro 2, 00185 Rome, Italy
TABLE OF CONTENTS
 1. Abstract
 2. 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 FokkerPlank 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
1. ABSTRACT
In this work, the fundamental elements of statistical mechanics underlying the simulation of the proteinligand binding process, such as statistical ensembles and the concept of microscopic estimators of macroscopic observables and free energy, are summarized in a self consistent fashion. Particular attention is then devoted to the introduction of some mathematical tools that are used in atomistic simulations aimed at estimating binding affinities and free energy profiles, and to the illustration of the origins of the difficulties encountered in this endeavor.
