Accurate Calculations of Relative Melting Temperatures of Mutant Proteins by Molecular Dynamics/Free Energy Perturbation Methods

Abstract

Melting-temperature shifts of mutant proteins were successfully calculated to high accuracy by improving the methods of molecular dynamics (MD) simulation and free energy perturbation calculations. First, MD simulations were performed by explicitly calculating long-range Coulomb interactions by the Particle—Particle and Particle—Cell (PPPC) method without truncating the interactions as in the conventional cutoff method. Second, free energy differences between the wild-type proteins and mutant proteins were estimated by the Acceptance Ratio Method (ARM) instead of the ordinary free energy perturbation method (FEPM). Melting-temperature shifts calculated for 14 mutant proteins of RNaseHl, human lysozyme, and the Myb R2 domain agreed well with their experimental values, although the calculation methodology does not include any adjustable parameters or experimental data for the mutants.

The conventional MD simulation/free energy calculation methodology is based on a cutoff and FEPM cannot successfully calculate the melting-temperature shifts for the following reasons: First, the truncation of the long-range Coulomb interactions by the cutoff method causes the protein structures for sampling conformations to be artificially deformed during the MD simulations. Second, the free energy calculations based on FEPM cannot give reliable values of changes in bond free energy due to the mutations because it utilizes conformations sampled from either state. Therefore, the conventional methodology has a large hysteresis error (mutation-path dependence) and statistical error.

In contrast, MD simulations explicitly including the long-range Coulomb interactions by the PPPC method maintained the protein structures near their X-ray structures and, furthermore, the thermal fluctuations around the equilibrium structures correlated well with both the experimental fluctuations deduced from X-ray temperature factors and with the order parameters of NMR spectroscopy. In addition, the free energy calculations based on ARM successfully gave reliable values for changes in bond free energy because it utilizes conformations sampled from both states. Therefore, the present MD/free energy calculation methodology based on PPPC and ARM suppressed the hysteresis error and statistical error.