CAREER: Scalable Mathematical and Computational Models for Biomolecular Modeling

University Of Notre Dame, Notre Dame IN

Investigators

Abstract

The proposed activities aim to create mathematical and computational methods for modeling large biological molecules. Computational simulation of dynamics and sampling of proteins, DNA, and nucleic acids promise to be a tool for understanding the relationship between structure and function, and for computer assisted drug design. Processes of interest include protein dynamics and folding and the study of other cellular components. Despite significant progress in the field, there is still a gap between the simulations that can be routinely performed with current technology and the complexity of processes and systems of biological interest. The proposed mathematical and computational methods will overcome the size and time scale limitations inherent in atomistic dynamics and sampling, while preserving the atomistic resolution of the biological systems. The new methods will be disseminated for research and educational purposes through an open source and scalable software framework called ProtoMol, and tested in a range of systems, from small proteins to potassium channels that reside in lipid bilayers. These new algorithms will translate into speedups of one or more orders of magnitude over current methodologies. This technology will enable simulations that are sorely needed in the expanding field of proteomics and the processing of data from the human genome project. To study dynamical processes, trajectories of large biomolecules are generated using molecular dynamics (MD). In an attempt to overcome the time scale limitations, multiple time stepping (MTS) integrators have been introduced. Nevertheless, even these methods have been limited by stability, and thus the time steps used in MD have not been dramatically increased. The PI proposes to devise multiscale algorithms for MD that are not limited by stability. To accomplish this goal, research will proceed in two phases: the _rst will extend the PI's work on stabler MTS numerical integrators by overcoming instabilities present in these methods. This will allow an estimated two- to eight-fold speedup over current methods for MD. The second phase involves the use of a symplectic semi-implicit method for MD using a splitting that separates cleanly many time scales, and incorporates the faster and less interesting ones in a more approximate manner. Speedups of two orders of magnitude or more are possible, depending on the degree of accuracy desired. This proposal will also tackle the related problem of statistical sampling. The large conformational space of biomolecular systems causes many difficulties to traditional sampling methodologies such as MD and Monte Carlo methods, or hybrids of both, all of which super performance degradation as the system size increases. We will use a biased hybrid Monte Carlo method that scales nearly linearly with system size. This will produce speedups of one or two orders of magnitude over MD, MC, or conventional hybrid MC methods. Synergy between this research project and teaching will occur at several levels. There will be an enhancement of materials of undergraduate and graduate courses taught by the PI, on data structures and applied algorithms, numerical methods, and computational methods for biomolecular modeling. Learning modules for engineering and science students will be developed in ProtoMol to facilitate an understanding of the behavior of large biological molecules.