Multi-Scale Spatio-Temporal Modeling: Lifelines of Microorganisms in Bioreactors and Tracking Molecules in Cells

Abstract

Agent-based models are rigorous tools for simulating the interactions of individual entities, such as organisms or molecules within cells and assessing their effects on the dynamic behavior of the system as a whole. In context with bioprocess and biosystems engineering there are several interesting and important applications. This contribution aims at introducing this strategy with the aid of two examples characterized by striking distinctions in the scale of the individual entities and the mode of their interactions. In the first example a structured-segregated model is applied to travel along the lifelines of single cells in the environment of a three-dimensional turbulent field of a stirred bioreactor. The modeling approach is based on an Euler-Lagrange formulation of the system. The strategy permits one to account for the heterogeneity present in real reactors in both the fluid and cellular phases, respectively. The individual response of the cells to local variations in the extracellular concentrations is pictured by a dynamically structured model of the key reactions of the central metabolism. The approach permits analysis of the lifelines of individual cells in space and time.

The second application of the individual modeling approach deals with dynamic modeling of signal transduction pathways in individual cells. Usually signal transduction networks are portrayed as being wired together in a spatially defined manner. Living circuitry, however, is placed in highly malleable internal architecture. Creating a homogenous bag of molecules, a well-mixed system, the dynamic behavior of which is modeled with a set of ordinary differential equations is normally not valid. The dynamics of the MAP kinase and a steroid hormone pathway serve as examples to illustrate how single molecule tracking can be linked with the stochasticity of biochemical reactions, where diffusion and reaction occur in a probabilistic manner. The problem of hindered diffusion caused by macromolecular crowding is also taken into account.