GNEIMO-Fixman: An Accurate Torsional Molecular Dynamics Simulation Method for Studying Biomolecular Dynamics

Abstract

Torsion angle Molecular Dynamics simulations provide a powerful alternative to all-atom MD since they place constraints on the bond lengths and angles, and thereby efficiently simulate large scale conformational changes in torsional space. The previous uses of torsional MD have been severely limited by the lack of efficient algorithms to solve the mathematical complexities of torsional MD. Our development of an advanced Generalized Newton-Euler Inverse Mass Operator (GNEIMO) torsional MD method overcomes these limitations with several theoretical and algorithmic advancements. We will outline these advancements and the effectiveness of the GNEIMO method in critical applications such as protein homology model refinement and protein conformational dynamics.Due to the rigidity in the model the torsional MD simulations show a bias in the partition function, which results in inaccuracies in the calculated thermodynamic and kinetic properties. Fixman developed a compensating potential that rigorously annuls the bias in the partition function, but the calculation of the Fixman potential has remained mathematically intractable even for moderate size molecules. Recently, we have developed a low-cost algorithm, based on Spatial Operator Algebra for calculating Fixman potential and torque for any molecule. We will present results on the validation and the effect of the Fixman correction potential in recovering the correct population distribution function, transition rates, and free energy surface for large branched systems.We have designed a modular software platform for the GNEIMO-Fixman method that can be readily combined with any type of forcefield engine. We have combined GNEIMO algorithm with Rosetta forcefield and performed homology model refinement with torsional MD. Thus our GNEIMO-Fixman torsional MD method allows for the use of larger integration time steps than for all-atom MD simulations, and enables enhanced conformational sampling in the low frequency torsional degrees of freedom.