Refinement of mathematical models to understand and control the dynamics of living systems
In this group, we study life systems and develop mathematical and computational models to elucidate the mechanisms that drive their kinetics. While theoretical biology is vast, for this project our work will focus primarily on two applications:
1. Describing the cyclic activity levels of genes involved in controlling circadian rhythms
The biological clock, which has remained a mystery for more than 60 years, led to the Nobel Prize in 2017 and remains a subject of ongoing genetic research. Temperature compensation is a phenomenon in which the cycle remains unchanged even if the temperature rises and the reaction speeds up. We plan to combine a simulator, integrable model analysis, and data analysis to predict a mathematical model for temperature compensation. A study by members of this group (BioPhys 2019) suggests the distortion of the time-series waveform (amplitude of the harmonics) is important in setting the period. We will elucidate the determinants of the period by constructing an amplitude reduction model using an operator-theoretic method.
2. Characterizing the impact of rare infection events on the course and outcome of virus infections in cell cultures
Just as the severity of influenza virus infections can vary season to season, virus replication efficacy within a cell culture also varies greatly for different strains. Mathematical study of a strain's replication kinetics within a cell culture allows us to uncover the mechanisms responsible for experimentally observed behaviours, and exploit them to develop therapies. Continuous and deterministic mathematical models are typically used to represent these systems, and have provided important insights. Unfortunately, such models incorrectly predict infection occurs 100% of the time if any virus is present, even for vanishingly small effective virus concentrations, like in the presence of antivirals. We will construct a discrete and stochastic predictive model of virus infection in cell cultures, informed by extensive experimental data and Bayesian parameter estimation, to characterize the role of stochasticity in modulating infection kinetics.
Living systems are the result of several complex, interconnected mechanisms, operating over several spatial and temporal scales. As such, they are an ideal domain of application and validation for the methodologies to be developed by the other research groups. This group provides important, topical problems in health sciences that will benefit greatly from the application of the advanced techniques developed by the methodological groups.