Towards more accurate and efficient free energy simulations

The free energy difference is the principal determinant whether a (bio)chemical reaction, such as binding of a ligand, can take place. Techniques to compute free energy differences based on Monte Carlo or molecular dynamics (MD) simulations (often referred to as free energy simulations (FES)) have become an important method in the toolbox of the computational chemist and molecular biologist. Successful applications of FES include, e.g., the study of solvation free energies, the thermodynamics of ligand binding, the effects of point mutations in proteins, and conformational equilibria. During the last years many methodological problems were resolved and a number of groups reported FES with unprecedented precision. However, if the MD (or Monte Carlo) simulations underlying the FES fail to sample all relevant parts of the conformational space, either imprecise or even inaccurate results are obtained. In this project we propose to systematically investigate the combination of methods that improve sampling in FES. On the one hand, we plan to test the suitability of existing techniques, in particular the novel non-equilibrium work methods based on Jarzynski`s identity, replica-exchange (in temperature and/or coupling parameter space) and methods using the coupling parameter as an additional dynamic degree of freedom. On the other hand, we want to try methods that have hitherto never been used in connection with FES, such as self-guided Langevin dynamics, the accelerated MD method by Hamelberg et al. and variants of replica-exchange which enhance sampling locally. All work will be carried out on the basis of the widely used program package CHARMM. First, methods which at present are not available will be implemented. All methods will then be compared by means of a series of benchmark problems, ranging in complexity from from four- and fiveatomic toy compounds to binding free energy calculations of peptidic ligands to SH2 domains. As project results we want to provide robust and efficient implementations of methods that combine techniques leading to enhanced (or accelerated) conformational sampling in FES. In addition, we want to be able to give concrete recommendations which method to use (based on convergence properties and computational efficiency).

The free energy difference is the principal determinant whether a (bio)chemical reaction, such as binding of a ligand, can take place. Techniques to compute free energy differences based on Monte Carlo or molecular dynamics (MD) simulations (often referred to as free energy simulations (FES)) have become a standard method in the toolbox of the computational chemist and molecular biologist. Successful applications of FES include, e.g., the study of solvation free energies or of the thermodynamics of ligand binding. During the last years many methodological problems were resolved and a number of groups reported FES with unprecedented precision. Yet, FES remain one of the computationally most expensive simulation techniques. One project focus, therefore, was to increase the efficiency of such calculations. On the one hand, we investigated how to optimize three standard techniques used in FES and presented a careful comparison of their performance. On the other hand, we explored ways to utilize simulation programs running on the graphics processing unit of modern desktop computers (GPU) instead of the CPU, profiting from the tremendous computational power of these devices. By enabling FES on the GPU free energy differences can be determined in hours instead of days on vanilla hardware. Another set of results concerns Bennett`s acceptance ratio method (BAR) to compute free energy differences. It turns out that this is not only one of the most efficient methods, but that it also can be used to compute "atypical" free energy differences, such as the free energy difference associated with changes of the force field parameters. We also worked out how to combine BAR with biasing potentials, a technique we refer to as NBB ("Non- Boltzmann-Bennett"). NBB can have rather diverse uses, ranging from overcoming conformational barriers to additional applications in force field optimization. Finally, one of the model calculations used in this project, the determination of solvation free energies of amino acids turned out to be of quite some biophysical relevance. It is often assumed that the solvent affinity of proteins can be estimated in terms of individual amino acid contributions, which in turn are estimated from side chain analog data. We demonstrated that this approximation does not hold and analyzed the physical origin of the differences in solvation free energies of amino acids and their corresponding side chain analogs.