| Biological phenomena that drive carcinogenesis are inherently multi-scale. Processes such as alteration of the genome, cellular communication, stem cell niche bifurcation, tissue homeostasis abrogation, and population interaction contribute to the development and increase the risks of cancer. Mathematical modeling, especially stochastic and multi-scale, is a tool for generating testable hypotheses and can be used to integrate the results of experiments. I introduce a methodology for estimating cell kinetics parameters, such as the net cell proliferation rate, the extinction coefficient and the initial viable population, in clonally expanding populations by exploring the connection of cellular fluctuations at different scales. To better understand colorectal carcinogenesis, I present a stochastic model framework for the homeostasis, or the maintenance of a constant internal environment, of colonic stem cells that integrates the dynamics at the level of a single stem cell, at the stem cell niche level and at the tissue level. This framework suggests stochastic constraints that effectively capture the underlying homeostatic feedback mechanisms. Finally, a model for the growth of biological organisms, including tumors, characterized by three distinct phases is presented, which explicitly incorporates size-dependent and age-specific signals for phase transitions. These models, informed by appropriate data, may help answer important questions pertaining to neoplastic progression and may be helpful for addressing practical issues in cancer prevention and early detection. |
