Simulation of biological molecules like proteins and RNA, as in the problem of protein folding, is a grand challenge that requires the development of new theory, numerical methods, and analysis tools. Most problems in trying to understand proteins can be described as trying to describe the thermodynamics of the main states of the molecule (mostly a sampling problem), as well as the kinetics that mark the interconversion among these states (mostly a problem of computing time correlations). This level of understanding can shed light on mechanisms underlying the function of these molecular machines, and has great value for designing new drugs, understanding disease and gaining valuable biophysical insight.
The main challenge is the presence of extremely long time scales in the solutions of the dynamical equations (timesteps in femtoseconds, time scales of interest in microseconds and longer), the lack of clear "slow" variables that can be subjected to classical multiscale analysis, and the strong coupling between different scales. My research tackles these challenges and has produced important solutions.