My main focus is the development of mathematical tools and numerical
methods for the analysis of dynamical systems which are both
stochastic and multiscale. The particular areas of applications I am
interested in include molecular dynamics, chemical and biological
networks, materials science, atmosphere-ocean science, and fluids
dynamics. My main objectives are to understand the pathways and rate
of occurrence of rare events in complex systems; to develop and
analyze multiscale algorithms for the simulation of random dynamical
systems; and, more generally, to quantify the effects of random
perturbations on the systems dynamics.
For more details and publications, see:
- Sampling techniques for rare events
- Random perturbations of dynamical systems
- Multiscale analysis: modeling and computations
- Stochastic PDEs and other models in turbulence theory and beyond
- The string method page
Together with international collaborators we used novel computational methods in combination with molecular dynamics simulations to identify the pathways of diffusion of a carbon monoxide molecule inside myoglobin, a protein involved in oxygen transport and storage in various animal species including humans. These results shed light on the important mechanism of ligand-protein binding and indicate how dynamical aspects of protein function are related to its structure. The full article was published in the Journal of the American Chemical Society and can be found here.
In collaboration with Cameron Abrams (Drexel University) we used a new molecular dynamics simulation method to investigate the conformational variability of large proteins, a problem of interest e.g. in drug design. The method was applied to two complex proteins, a subunit of GroEL, a protein that catalyzes folding of substrate proteins, and the HIV-1 envelope gp120, a protein responsible for the fusion of the virus with a target cell. In this second example, the method generates plausible all-atom models of the unliganded conformation of HIV-1 gp120, which was uncharacterized so far and may prove useful in the development of inhibitors and immunogens. The full article was published in the Proceeding of the National Academy of Science and can be found here.