Consistent Multi-Scale Treatments of Ion Transport in Biological Environments

Trinity College, Hartford CT

Investigators

Abstract

Modeling and numerical simulations of practical biology processes have always been limited, either because the model itself lacks the accordance to important real world physics law or the prohibitively high computational cost to simulate the process at molecular level. Extensive research in molecular biology shows that molecules control macroscopic biological function. The communication between significantly different temporal and physical scales becomes vital in representing an accurate biological process. This project is designed to bridge the critical gaps between different physical scales. It emphasizes on adopting consistent physical laws throughout various scales. It aims to develop multi-scale models, and further conduct numerical simulations to investigate biological process. The result of the project will deliver a substantial advance in both scientific computing and biological modeling. A more complete model advances the understanding of living organisms, and will have broader impacts in bioengineering and human health. This project will investigate the ionic transport with applications to processes occurring near or across cell membranes. To study diffusion, ion transport, and heat flow in one consistent framework, we propose the following approach. (a) In order to ensure the consistency with important physical principles and the robustness of the model, we pose the mathematical problem within an energetic variational framework. Highly accurate numerical method will be chosen to simulate the model. (b) Based on the full molecular dynamics model, we will choose appropriate local ion density and current, the local energy and energy flux, while making sure that the conservation laws are exactly satisfied at every scale. This coarse-graining procedure reduces the full molecular description to a system of equations at a much larger spatial, and more importantly, much longer temporal scales. (c)The longer time regime and the finer time scale will communicate with each other and update the corresponding coefficients. With this new integrated mathematical framework, this project will address the fundamental modeling difficulty, and develop efficient numerical schemes to improve the realization of the role of ionic solutions in determining biological functions. 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.