Calculation of absolute free energy of binding for theophylline and its analogs to RNA aptamer using nonequilibrium work values

Abstract

The massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) has been developed [H. Fujitani, Y. Tanida, M. Ito, G. Jayachandran, C. D. Snow, M. R. Shirts, E. J. Sorin, and V. S. Pande, J. Chem. Phys. ${\bf 123}$, 084108 (2005)]. As an application, we perform the binding affinity calculations of six theophylline-related ligands with RNA aptamer. Basically, our method is applicable when using many compute nodes to accelerate simulations, thus a parallel computing system is also developed. To further reduce the computational cost, the adequate non-uniform intervals of coupling constant $\lambda$, connecting two equilibrium states, namely bound and unbound, are determined. The absolute binding energies $\Delta G$ thus obtained have effective linear relation between the computed and experimental values. If the results of two other different methods are compared, thermodynamic integration (TI) and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) by the paper of Gouda $et al$ [H. Gouda, I. D. Kuntz, D. A. Case, and P. A. Kollman, Biopolymers ${\bf 68}$, 16 (2003)], the predictive accuracy of the relative values $\Delta\Delta G$ is almost comparable to that of TI: the correlation coefficients (R) obtained are 0.99 (this work), 0.97 (TI), and 0.78 (MM-PBSA). On absolute binding energies meanwhile, a constant energy shift of $\sim$ -7 kcal/mol against the experimental values is evident. To solve this problem, several presumable reasons are investigated.