Project abstract for group stolarsm

Mathematical Modeling of Mechano-Chemical Aspects of Cell Substrate Interaction

In order for biological cells to move efficiently they must interact mechanically and chemically with their environment. Typically, this mechanical and chemical interaction is coupled, and, while there are still many open questions, experimental research continues to investigate the nature of this coupling. During the past year, this group was able to develop a mathematical/computational model of the mechanics of cell-substrate interaction in two-dimensions. In this model, the cell is treated as a hypoelastic continuum that is connected to a substrate, which is modeled as linearly elastic, by a collection of discrete linear springs that can be added and removed dynamically throughout a simulation of a cell spreading over the substrate.

In 2014, the researchers use MSI resources to expand on the existing model and mathematically/computationally investigate how the mechanics and biochemistry must be coupled in order to obtain experimentally observed cell-substrate traction patterns. Mathematically, this investigation will involve coupling various types of models of intracellular biochemistry to the existing model of mechanical interactions and computationally investigating the effects of these different couplings. The proposed models are programmed in Matlab and additional software, such as Tecplot, is used for visualization. The numerical implementation of these models results in large, nonlinear algebraic systems for which the speed and capacity of MSI resources is beneficial.