Long time dynamics of complex systems.

Molecular dynamics trajectories of large biological molecules are restricted to nanoseconds. We describe a computational method, based on optimization of a functional, to extend the time of molecular simulations by orders of magnitude. Variants of our technique have already produced microsecond and millisecond trajectories. The large steps enable feasible computations of atomically detailed approximate trajectories. Numerical examples are provided: (i) a conformational change in blocked glycine peptide and (ii) helix formation of an alanine-rich peptide.