The proposed research will develop novel geometric model reduction methods along with computational methods for the dynamical simulation and eventual control of stochastic mechanical systems involving multiple-scales. These new dynamical and simulation tools will be applied to specific molecular and biomolecular systems. An exciting development in geometric model reduction has been the development of the radii of gyration as coarse variables along with the discovery of specific fine variables that act as triggers that induce conformation changes. A further development of and deeper understanding of such triggers will be important in the eventual control of biomolecular conformation changes and reactions. Going along with these geometric model reduction techniques is the theoretical and computational development of stochastic asynchronous variational integration methods and their applications to the simulation and control of stochastic mechanical systems spanning many temporal-scales.
Structure-preserving integrators for stochastic multiscale Hamiltonian systems (possibly with constraints) characterized by multiple time scales and a large number of degrees of freedom are in great demand in computational chemistry, molecular dynamics and biophysics. The proposed work will have a direct and substantial impact on those fields by integrating a new class algorithms in the classical molecular dynamics open source code LAMMPS. Bio-molecules are in general robust to noise; at the same time, these molecules may be responsive to low energy structured actuation. By allowing for the computation of these organized mechanisms, the proposed research will facilitate the development of a new paradigm and novel experimental methods for the control and design of bio-molecules. The proposed research through the identification of resonant frequencies of molecules specific to the membrane of malignant cells and/or known pathogens has the potential to facilitate the discovery and development of a new class of non-invasive and nontoxic therapies. New cancer therapies based on the injection and electro-magnetic excitation of carbon or gold nanotubes/nanorods are already at the clinical trial stage.
