Collaborative Research: Multi-Scale Modeling and Numerical Methods for Charge Transport in Ion Channels

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Systems in biology are inherited, with all the information being in genes that are sequences of nucleotides in DNA. These genes produce proteins. Molecular and cell biologists have identified and analyzed these proteins in great detail: structural biologists now know the position of individual atoms of more than a hundred thousand proteins. Site-directed mutagenesis is done in thousands of laboratories every day to change biological function. A central challenge in biology is to understand how the atoms control biological function when biological structures are some 10 million times larger than atoms and move at a ten thousand billionth of their speed. Ion channels, the subject of this research, are good examples of such systems. They facilitate the transport of ions through cell membranes and control many biological processes, including cell-cell communication, signaling, muscle contraction etc. During ion transport, electrostatic interactions and ion correlation and size effects are all important factors to understand the channel selectivity, conductance, and other critical behaviors. Ion channels play critical roles in almost all biological systems including heart and nerves. About 13% of known drugs have their primary therapeutic actions targeted at ion channels. The methods developed in this project will advance the field of ion channel research, which will have an impact on research on enzyme catalysis, protein engineering, rational drug design, drug delivery, and new diagnostic and therapeutic strategies. In this proposal, the PIs will develop multiscale mathematical theories and numerical methods to study the multi-physics problems related to the ion channel dynamics involving a disparity of scales. The tasks to be focused on include a) developing a reaction field based hybrid solvation model for electrostatic interactions, and multi-step accelerated dynamics integration methods for all-atom MD simulations of ion channels, accounting for layered membrane and solvent environments; b) developing new improved PNP continuum models and new numerical methods to address crowded ions effects and relative drags between ion species in ion channels; c) pursuing mathematical analysis and physical understanding of the new PNP models; d) simulations based on the multi-scale electrostatic solvation MD and the PNP models. Educational efforts at high school, undergraduate, and graduate level will be an integrated part of this project, and research results from this project will be incorporated into the applied/computational mathematics curriculum at the two participating institutions.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.