A sophisticated simulation method is developed to investigate the interactions between whole cell intracellular calcium dynamics and the building blocks of calcium handling, spatially localized subcellular calcium elevations known as "calcium puffs" and "sparks." Using techniques originally developed in theoretical physical chemistry and statistical physics, equations are derived and analyzed for the moments of the local calcium concentration associated with the large number of calcium release sites in living cells. This extends the classical "gating variable" approach to modeling the opening and closing of ion channels - introduced by Nobel prize winners Hodgkin and Huxley - to account for the short range of action of intracellular calcium and local coupling of intracellular calcium channels. Traditional models of coupled local and global calcium responses involve stochastic simulation methods that are computationally intensive and often prohibit both mathematical analysis and large-scale parameters studies. Conversely, moment-based whole cell models of intracellular calcium responses are systems of ordinary differential equations that can be studied using geometric and graphical approaches. Gregory Smith (William & Mary) and students develop, validate, and benchmark this mathematical modeling framework and, subsequently, deploy it in the laboratories of Eric Sobie (Mount Sinai) and Sandor Gyorke (Ohio State) to interpret live cell calcium imaging experiments that probe how beat-to-beat calcium cycling in heart muscle cells changes in response to drugs, mutations, and disease.
User-friendly software is produced to assist other laboratories in their development of more realistic and predictive models of calcium responses in cardiac, smooth, and striated muscle, neurons, and non-excitable cells. Graduate students involved in this project experience high-quality interdisciplinary scientific training at the interface of applied mathematics and cell physiology. The project also expands and supports Smith's activities as Director of the William & Mary Biomathematics Initiative, e.g., curriculum development in biological modeling, coordination of an interdisciplinary faculty-student journal club, mentoring of undergraduate research students, and authorship of an undergraduate text introducing neuroscience majors to nonlinear dynamics in the context of electrophysiology (with Christopher Del Negro).