Introduction

This project seeks to develop new mathematical and computational methods for modeling large biological molecules. The motivation is to facilitate the study of the structure and function of proteins and other cellular components, and to assist in the design of medicinal drugs. Important applications have been enabled by molecular dynamics and statistical sampling techniques. However, there are limitations in what current methods can simulate effectively. In particular, simulations are in the scale of nanoseconds, whereas processes of interest, such as protein dynamics and folding, occur in microseconds to seconds. Also, most simulations model individual or just a few biological molecules, whereas many systems of interest are complex aggregates of many such molecules. The large size of these systems and the length of the simulations needed creates an urgent need for more efficient mathematical and computational methods such as those proposed here.

In molecular dynamics (MD) the major limitation of current methods is the stability of simulations, which forces the use of small time steps relative to the total length of the simulation. For example, a one nanosecond simulation of a solvated biomolecule takes weeks in parallel supercomputers. However, many of the processes that have to be resolved at such small time intervals because of stability restrictions, have no significant impact in the dynamics of interest, that typically happen in scales of six or more orders of magnitude.

In an attempt to accelerate MD, researchers have produced novel methods: (i) separation of time scales coupled to multiple time stepping (MTS) algorithms; (ii) constraint of fastest motions; (iii) use of implicit solvers with extended stability properties; and (iv) use of stochastic techniques to avoid instability, cf. Section 2.1.1. Each of these techniques has produced a speedup between two and four over conventional MD.

We propose to devise new multiscale algorithms for MD that will separate time scales cleanly and allow speedups of one or more orders of magnitude over any of the above technologies taken by themselves, depending on the degree of accuracy desired. Preliminary results along this direction are encouraging: we have recently shown an asymptotic twofold speedup over state-of-the-art MTS algorithms, and a fourfold speedup when using stochastic techniques. We have also shown the feasibility of using a semi-implicit, that is, mixed implicit-explicit solver that balances the stability gain of an implicit method and the efficiency of the explicit solver to get speedups of two orders of magnitude or more, cf. Section 3.1.

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 fail 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. A scalability analysis of the new method is presented in Section 3.3.

These algorithms will be incorporated into an open source software framework called PROTOMOL, that has been released and runs on a variety of platforms, including parallel computers. To enhance ease of use of the software, runtime optimizations will select appropriate algorithms and parameters automatically.

This project addresses not only the technical aspects, but also makes contributions towards facilitating truly interdisciplinary research and training, through educational and collaborative initiatives. It will produce learning material, and it will enable students from biological, mathematical, and computational disciplines to collaborate on the solution to some of the outstanding problems in computational molecular biology.

This research project will involve two graduate students, and several undergraduates, who will have a first hand opportunity to learn about the challenges in computational molecular biology. In particular, the modeling of the dynamics and function of potassium channels will be undertaken with a graduate student who has a background in biology, and in collaboration with Prof. J. Andrew McCammon and his postdoctoral research associate Dr. Jung-Hsing Lin at the University of California at San Diego. Also, a study of the computational effectiveness of anti breast cancer drugs will be conducted with Prof. Martin Tenniswood from the Department of Biological Sciences at the University of Notre Dame. They will provide expertise from the biology and current methodology side, that will be complemented by the PI's expertise in the development of new methods.