Multiple Scales in the Simulation of Ion Channels and Proteins

Computation of biological processes creates great promise for everyday life and great challenges for physical scientists. Simulations of molecular dynamics appeal to biologists as a natural extension of structural biology. Once biologists see a structure, they want to see it move. Molecular biology shows that a few atoms, often messenger ions like Ca$^{2+}$, control biological function on the scale of cells, sometimes organisms. Enormously concentrated ions (~20 M) in protein channels and enzymes can control important characteristics of living systems, just as highly concentrated ions near electrodes control important characteristics of electrochemical systems. The scale differences needed to simulate all the atoms of biological cells are $10^7$ in linear dimension, $10^{21}$ in three dimensions, $10^{9}$ in resolution, $10^{11}$ in time, and $10^{13}$ in particle number (to deal with concentrations of Ca$^{2+}$). $\mathbf{These}$ $\mathbf{scales}$ $\mathbf{must}$ $\mathbf{be}$ $\mathbf{dealt}$ $\mathbf{with}$ $\mathbf{simultaneously}$ if the simulation is to deal with most biological functions. We suggest a computational approach using explicit multiscale analysis instead of implicit simulation of all scales. Successful computation of ions concentrated in special places may be a significant step to understanding the defining characteristics of biological and electrochemical systems.