Mathematical Modeling of Migration in Cancer and Bacteria
Abstract
Migration is a ubiquitous phenomenon in biology and is relevant to all scales ranging from bacteria to human beings. It is relevant to fundamental biological processes like bacterial chemotaxis, development, disease progression, etc. So, understanding migration is pivotal to addressing fundamental questions in biology. We address three broad questions relevant to cell migration using models from physics: (i) What are the critical features of cancer cell migration? (ii) Is it possible to explain complex cell migration data using minimal biochemical networks? And (iii) how does cell-to-cell communication affect its migration at the population level? To address these questions we performed (i) mathematical analysis using the Cellular Potts model, simulations using the Biased Persistent random walk model, and steady-state analysis of cell response to graded signals to explain cancer cell migration in response to single and multiple chemical and mechanical signals, (ii) rigorous network analysis of ∼ 500,000 minimal networks having features of fundamental biochemical processes like regulation, conversion or molecular binding to understand the origin of antagonism in multiple cue cancer cell migration experiments and (iii) the steady-state analysis of KellerSegel equations mimicking collective cell migration to understand the role of cell to cell communication on chemotaxis of a bacterial population. From our analysis, we found that (i) persistence and bias in cancer cell migration are decoupled from each other owing to a lack of memory about past movements and for any general cell migration they are inherently constrained to take only a fixed set of values. (ii) Bias in cancer cell migration in response to a combination of chemoattractant gradients can be less than the response to individual gradients (antagonism in bias) while the speed remains unaltered. This antagonism in bias and lack thereof in speed can be explained by several minimal networks having molecular regulation, conversion, or binding as its central feature and all these distinct mechanisms show convergence and saturation of an internal molecule common to both the chemoattractants. (iii) By analyzing the role of cell-cell communication in bacterial chemotaxis using the Keller-Segel model we find that communication enhances chemotaxis only when it is adaptive to its external surroundings and cell-to-cell variability helps in increasing the chemotactic drift in the bacterial population.
Degree
Ph.D.
Advisors
Mugler, Purdue University.
Subject Area
Communication|Cellular biology|Electrical engineering|Mathematics|Oncology
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