Computation of dynamics of biomolecules significantly enhances our understanding of their function and enables a better design of new biological materials. Nevertheless, a significant drawback of Molecular Dynamics (MD) simulations is of time scales. At the present, routing simulations are not longer than a few nanoseconds of real time. This time is far too short to investigate many biochemical processes, such as conformational transitions, protein activation, or protein folding, which may last from microseconds to minutes. It is proposed to further develop a new methodology to compute bio-molecular dynamics on extended time scales. The new methodology is based on the optimization of an action. It enables the computations of trajectories using an almost arbitrary time step. It is rigorously shown that the algorithm automatically filters high frequency motions that occur on time scales shorter than the time step. The filtering ensures the stability and the soundness of the new approach over a broad range of times and motions. The methodology was tested for a conformational transition of a small peptide, the folding of a protein fragment embedded in a box of solvating water molecules, and for the R-greater than T transition in hemoglobin. It is shown that for the folding of a protein fragment the new algorithm is more efficient than MD by a factor of 50. For the R-greater than T transition in hemoglobin, the new algorithm is more efficient by a factor of 20,000. The new approach will extend the scope of molecular simulations making it possible to investigate dynamics and function at the atomic level at times longer by many orders of magnitude than was possible before.
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