Mathematical and experimental studies in cellular decision making

Abstract

The biological sciences are undergoing an epistemological revolution. Mathematical modeling, quantitative experiments and data analysis, machine learning and other methods of "big-data" modeling are slowly but surely changing the way the biological and biomedical sciences and engineering are being carried out. This thesis presents work that seeks to advance understanding of biological processes using mathematical modeling as well as experiments coupled with sophisticated quantitative analysis. The central theme of the research presented is cellular decision-making. A cellular decision is defined here as a transition from one cell state, or phenotype, to another, based upon information received from an external or internal signal. This work explores the mechanisms behind cellular decisions with three specific systems and a variety of mathematical and modeling techniques. This dissertation begins with a brief survey of the use of mathematical modeling in cellular biology, utilizing specific example of various approaches. This reviews the diversity of techniques available from detailed mechanistic models to simplified phenomenological representations, and notes some applications demonstrating the utility of such models. The first exploration of cellular decisions is concerned with the question of how cells can make decisions in the face of cross-talk from multiple signals. The real cellular environment is noisy, with stochastically varying levels of external signals and cellular decisions required in spite of this noise. In Chapter 3 the ubiquitous bacterial two-component signaling system and the similarly structured mammalian TGF-β pathway are modeled with stochastic simulations of the chemical master equation. Information theory is utilized to quantify the amount of information transmitted by these signaling systems in the presence of competing signals from cross-talk, revealing that the mammalian TGF- pathway was able to transmit information accurately despite high levels of cross-talk, while the bacterial two-component system, due to a smaller system size and the structure of phospho-transfer rather than phospho-relay, was poor at discriminating from competing cross-talk. This work presents a novel thesis: many signal transduction systems suffer less from cross-talk than was commonly imagined, and may actually make use of cross-talk for cross-regulation. The second system of cellular decisions studied in this work is a bistable synthetic toggle switch network motif composed of mutually repressible promoters in Chapter 4. This motif has been widely studied in isolation for its dynamical and static properties. However, the behavior of these switches has never previously been analyzed when coupled with a downstream binding partner, termed a "load". Real toggle switches, whether synthetic or natural, always have loads connected with them. The toggle-switch system was modeled mathematically with ordinary differential equations as well as using stochastic simulations of the chemical master equation to determine the effect of a load. The quasi-potential energy landscape of the bistable switch was calculated utilizing a novel method which revealed that, in some parameter spaces, a downstream component can significantly alter the stability of the switch; addition of a positive feedback loop could provide for a tunable switch. Chapter 5 is concerned with developing methods for identifying a complex cellular transition from less metastatic to more metastatic cancer cells. The importance of metastatic disease in the pathology of cancer cannot be understated as it is the cause of 90% of deaths from cancer. The process by which cancerous cells become metastatic is complex, but requires specific cellular mechanical conditions in order to occur. The use of cancer cell shape to predict metastatic behavior in pathology samples is a key component of prognostication, however in vitro cancer cell shape is less commonly studied. This work developed a mathematical algorithm to extract shape parameters from images of cancer cells and applied multiple statistical techniques to elucidate differences between metastatic and non-metastatic cancer cells. While both simple and complex statistical techniques including t-tests, principle component analysis (PCA) and non-metric multidimensional scaling (NMDS) revealed distinct changes, the population of cells from highly metastatic and less metastatic paired osteosarcoma cells showed significant overlap. Machine learning algorithms were, however, able to successfully classify samples of cells to high or low metastatic lines with high accuracy. The concluding chapter presents a brief analysis of the new questions that this research has elucidated, and delineates some future tasks to address them.