Multi-scale continuum modeling of biological processes: from molecular electro-diffusion to sub-cellular signaling transduction

This paper presents a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales ( http://mccammon.ucsd.edu/smol/ , http://FETK.org ) by numerical solution of the time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times, with increasing ionic strength, and demonstrate the role of an enzyme's electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a nonlinear, reaction-diffusion system describing Ca 2+ ligand buffering and diffusion in experimentally derived rodent ventricular myocyte geometries. Results reveal the important role of mobile and stationary Ca 2+ buffers, including Ca 2+ indicator dye. We found that alterations in Ca 2+ -binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate sub-cellular Ca 2+ signals. The model predicts that reduced off-rate in the whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca 2+ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for the integration of molecular-scale information into simulations of cellular-scale systems.