Hybrid Computational Modeling and Advanced Numerical Methods for Biomolecular Interactions

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This project develops rigorous scientific theories and powerful computational tools to investigate the principal mechanisms by which drug and protein molecules associate and dissociate. Often, a drug molecule moves around in a crowded environment, and finds a spot of the surface of a protein to bind to, stays there, and can also leave, unbinding from the protein. During such binding and unbinding events, often repeated, both molecules constantly change their internal atomic positions. They also interact with other molecules, particularly the water molecules, in the surrounding environment. There are two key scientific questions on such complex processes that are characterized by multiple spatiotemporal scales and many-body effects. One is how stable the drug-protein bound unit is. Such thermodynamic stability serves as a criterion for searching drug molecules capable of binding to targeted proteins. The other is how fast or slow the binding and unbinding can occur. Such kinetics has been found recently in experiments and computer simulations to be critical to the drug effectiveness and efficacy. For decades, the scientific communities have made an enormous amount of effect, searching the quantitative answers to these questions to guide the computer-aided drug design and discovery. A recent assessment by the National Institutes of Health of the existing such computer programs, however, has concluded that advanced scientific theories are needed urgently to improve the practice. The success of this project can therefore provide a solid theoretical foundation as well as computational algorithms for drug design and discovery, potentially helping reduce the very high cost often needed for laboratory experiments and speed up the process of drug discovery. In addition, this highly interdisciplinary research project provides unique opportunities for students at different levels to receive training at the interface of mathematical, computational, and biological sciences, keeping our nation's strength in scientific research in a highly competitive international environment.To tackle the complex problem of molecular association and dissociation, the investigators will design, implement, and analyze a very fast binary level-set method for interface relaxation to capture the molecular interfacial structures in the framework of an advanced, variational molecular solvation theory. The new method combines the strength of the threshold dynamics and the binary level-set representation, and utilizes the locality of the underlying energy landscape, and new pixel-flipping techniques, to achieve very high efficiency. They also develop a new and hybrid computational approach to the kinetics of interface stochastic dynamics, coupling the interfacial energy minimization by the fast algorithm, the string method for transition pathways, and a novel, multi-state Brownian dynamics simulations. All these are applied specifically to investigating the molecular binding and unbinding kinetics for which some of the conventional methods, such as the standard Brownian dynamics simulations, may fail. It is expected that this project will advance significantly basic research in scientific computing and numerical analysis, particularly at the interface of dynamics and stochastic modeling. This research will help resolve some of the bottle-neck issues in solving very complex scientific problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.