(217c) A Modular Computational Framework for Multi-Scale Simulation of Chemotaxis in Complex Environments

Chemotaxis has long served as a model system for signal transduction in both bacteria and eukaryotes. Numerous mathematical models have been developed over the years to explore different aspect of these pathways. These models have tended to focus either on the intracellular mechanisms governing pathway dynamics or the coarse-grained, population-level behavior of swimming/migrating cells in chemical gradients. Only a few models have attempted to link the two. In this work, we developed a modular multi-scale computational framework for simulating cell behavior in complex chemical environments using a hybrid-continuum approach. This framework enables us to directly employ intracellular pathway models for individual cells to determine population-level, macroscale cell behavior. Our strategy is based on the particle-in-cell approach. Here, the aggregate effect of many cells in a Lagrangian frame of reference is interpolated onto Eulerian (stationary) mesh points, where the moments of the continuum distribution (e.g. concentration) are also computed and updated. The typical cycle involves the following: (i) integration of the pathway equations of motion for individual cells; (ii) interpolation of the cell effects (e.g. metabolism) onto the stationary mesh; (iii) computation of the new field values using this information; and (iv) interpolation of the fields from the mesh back to the particle locations. To validate this framework, we investigated bacterial chemotaxis in complex chemical and spatial environments. As we demonstrate, our simulation results are quantitatively in agreement with the corresponding experimental results. While this framework was developed to study chemotaxis, we will also illustrate how it can be used to simulate at multiple scales any biological system involving cell populations interacting via chemical signaling.