Reaction-diffusion mechanisms underlie communication of cells within and among themselves and also with their environment. In this thesis, I have developed computational approaches to better understand these mechanisms in the context of tissue engineering and quantitative microscopy.

In the first part of my thesis I use an agent-based formalism to describe the interactions of the hematopoietic stem cells in the bone marrow niche and their role in hematopoiesis. Using a mathematical representation of the interactions, I create a framework that can be used to question the role and relative importance of cellular interactions inside the niche in the context of hematopoiesis. In the second part, I apply deterministic models to identify general principles for design and operation of microfluidics-based perfusion bioreactors for cell cultures. I use model-based analysis to arrive at optimal strategies for designing bioreactor geometry, media perfusion and recirculation, initial cell seeding composition for co-cultures, and retaining cell-secreted autocrine factors. I further demonstrate the utility of these models to infer the cellular properties from data on experimental measurements by inferring oxygen uptake parameters of HepG2 (human hepatocellular carcinoma) cells. In the final part of my thesis, I turn my attention to the reaction systems inside the cell and present computational algorithms to infer the local protein binding dissociation constant (K_d) from 3-dimensional Fluorescence Resonance Energy Transfer (FRET) microscopy data on live cells. I analyze the performance of the algorithm using synthetic test data, both in the absence and presence of endogenous (unlabeled) proteins, and show that deconvolution is essential for quantitative inference of local K_d, I test the algorithm to quantify the interaction between YFP (yellow fluorescent protein)-Rac and CFP (cyan fluorescent protein)-PBD in mammalian cells.

Taken together, the results offer novel insights into model-based design of in vitro biological systems for target applications in tissue engineering, microfluidic bioanalytical devices and quantitative microscopy and also present new approaches for quantitative inference from the associated experimental data.