Computational Models for the Study of Various Immunological and Electrophysiological Systems

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Many physiological processes in immunology and endocrinology are extremely complex and remain incompletely understood. These highly nonlinear biological systems continue to be investigated using experimental methods, but with the emergence of the field of computational biology, they can now be examined theoretically using mathematical methods and computational tools. Our goal in this research program is to use these alternative and powerful theoretical approaches to tackle fundamental questions arising in various immunological and electrophysiological systems that cannot be answered experimentally. More specifically, we aim to use methods from computational biology and nonlinear dynamics (steady states and stability analysis, bifurcation methods, and numerical computations) to construct deterministic and stochastic differential-equation models that describe the (spatio)temporal dynamics of these systems and provide predictions and insightful conclusions about their behavior. Particularly, we plan to: (1) examine the processes controlling immune-cell recruitment and interaction, using both gene-network and population models, and identify potential targets for manipulating the immune response; (2) analyze the molecular mechanisms (involving several receptors and ion channels) underlying the dynamic regulation of neuronal synchrony/rhythmicity and hormone secretion, that could eventually be used to determine the main causes of abnormalities. This work will be conducted in close collaboration with several, internationally renowned, experimental laboratories. Beside their valuable relevance to physiology, these models will also generate intriguing mathematical problems that are either solved numerically or theoretically using nonlinear stability analysis.