Quantitative inference of cellular parameters from microfluidic cell culture systems

Microfluidic cell culture systems offer a convenient way to measure cell biophysical parameters in conditions close to the physiological environment. We demonstrate the application of a mathematical model describing the spatial distribution of nutrient and growth factor concentrations in inferring cellular oxygen uptake rates from experimental measurements. We use experimental measurements of oxygen concentrations in a poly(dimethylsiloxane) (PDMS) microreactor culturing human hepatocellular liver carcinoma cells (HepG2) to infer quantitative information on cellular oxygen uptake rates. We use a novel microchannel design to avoid the parameter correlation problem associated with simultaneous cellular uptake and diffusion of oxygen through the PDMS surface. We find that the cellular uptake of oxygen is dependent on the cell density and can be modeled using a logistic term in the Michaelis–Menten equation. Our results are significant not only for the development of novel assays to quantitatively infer cell response to stimuli, but also for the development, design, and optimization of novel in vitro systems for drug discovery and tissue engineering. Biotechnol. Bioeng. 2009;103: 966–974. © 2009 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63052/1/22334_ftp.pd

Phase-Locked Signals Elucidate Circuit Architecture of an Oscillatory Pathway

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways

Computational Reaction-Diffusion Analysis of Cellular Systems for Tissue Engineering and Quantitative Microscopy.

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 (Kd) 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 Kd, 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.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/63653/1/khamir_1.pd

Dynamics of Molecular Weight Distributions for Polymer Scission

The dynamics of molecular weight distributions (MWDs) for polymer degradation is of interest to various applications. The time evolutions of MWDs can be determined by solving the governing population balance equations, which are generally solved by moment techniques wherein the initial distribution is represented by a gamma distribution. The evolution of MWD is determined by the time dependence of the gamma distribution parameters. The population balance equations (PBEs) can also be solved numerically by converting them to partial differential equations (PDEs). The degradation rate coefficient in the PBE depends on the molecular weight x as $(x - x_o)^{\lambda}$ or as a quadratic polynomial in x. The solutions obtained with the moment technique, which are inaccurate for certain cases, are compared with the solutions determined by solving the PDEs. The utility of the numerical scheme is also discussed for cases where the initial distribution cannot be represented satisfactorily by a gamma distribution