Coarse molecular dynamics of a peptide fragment: Free energy, kinetics, and long-time dynamics computations

We present a “coarse molecular dynamics” approach and apply it to studying the kinetics and thermodynamics of a peptide fragment dissolved in water. Short bursts of appropriately initialized simulations are used to infer the deterministic and stochastic components of the peptide motion parametrized by an appropriate set of coarse variables. Techniques from traditional numerical analysis (Newton–Raphson, coarse projective integration) are thus enabled; these techniques help analyze important features of the free-energy landscape (coarse transition states, eigenvalues and eigenvectors, transition rates, etc.). Reverse integration of coarse variables backward in time can assist escape from free energy minima and trace low-dimensional free energy surfaces. To illustrate the coarse molecular dynamics approach, we combine multiple short (0.5 ps) replica simulations to map the free energy surface of the “alanine dipeptide” in water, and to determine the $\text{∼1/(1000\hspace{0.17em}}\mathrm{ps})$ rate of interconversion between the two stable configurational basins corresponding to the α-helical and extended minima.