- Mathematical modeling.
- Computational electrophysiology and endocrinology.
- Quantitative immunology.
- Nonlinear dynamics and synchronization.
- Stability analysis and differential equations.
- Chaos control.
- Impulsive control methods and delayed impulsive systems.
Statement of Research Interests
Delineating the mechanisms underlying the behaviour of physiological and biological systems is central for advancing our knowledge of human health.
These highly nonlinear systems are usually investigated using experimental tools, but with the advance of the field of computational
biology and nonlinear dynamics, they can now be analyzed theoretically. Understanding the various aspects of these physiological systems
by developing mathematical models and designing computational tools to investigate them represents the core focus of our research group.
These models provide important insights into the cellular and molecular processes occurring in these systems, as well as raise intriguing
mathematical questions that are either tackled numerically using computational tools or theoretically using methods of nonlinear stability
analysis. The three main goals of our research group can be summarized as follows:
The projects listed above are conducted in close collaboration with several experimental and theoretical laboratories belonging to different
institutes and universities, including the National Institutes of Health (S.S. Stojilkovic and A. Sherman), University of Calgary (P. Santamaria),
Baylor School of Medicine (M. Pietropaolo), Université de TOURS (A. Duittoz), the University of Michigan (S. Moenter and S. Schnell) and
McGill University (C. Brown and D. Bowie).
- Decipher the gating properties of P2X receptor channels by constructing Markov state models that describe their kinetics. These models
can help illustrate the interplay between receptor-sensitization, desensitization, pore-opening and dilation, and identify the main factors
responsible for the differences in their downstream signaling effect (including apoptosis and differentiation). We develop signal
processing and fitting algorithms to achieve these goals.
- Elucidate the role of beta-cell-specific autoreactive immune cells and autoantigens in the progression and onset of type 1 diabetes. By
developing competition-based population models of T and B cells, one can achieve this goal as well as understand the process of "avidity
maturation", correlate T-cell avidity with autoantibody binding affinity, identify the most effective treatment regimens associated with
nanoparticle therapy and decipher the biophysics of T-cell activation. Molecular based models are also developed to uncover the role of
autoantigens and negative selection in pathogenicity.
- Analyze the various hormonal and electrophysiological rhythms exhibited by several neuronal systems. This is done by building neural
network and Hodgkin-Huxley type models aimed at identifying the underlying mechanisms regulating both synchrony and bursting in these neuronal
- Investigate microscopically the dynamics of cell adhesions and protein-protein interactions involved in cell motility. We develop probabilistic
and molecularly explicit (stochastic) models that uncover the processes regulating these systems and determine how abnormalities can cause disease.