### Victor Matveev

Associate Professor

Applied Math, Biophysics & Computational Neuroscience

Department of Mathematical Sciences

New Jersey Institute of Technology

October 6, 2015

Modeling cell calcium dynamics on fine spatio-temporal scales: comparison of deterministic and stochastic approaches, and novel steady-state approximations

Calcium is known to control a vast array of crucial physiological processes, from gene transcription to programmed cell death. In the case of synaptic or endocrine secretory vesicle release and myocyte contraction, highly localized “nano-domains” of calcium produced by the opening of a few membrane calcium channels lead to physiologically measurable response. However, spatio-temporal resolution of optical calcium imaging techniques is insufficient to measure calcium concentration on the spatio-temporal scales needed for a full understanding of these processes. As a result, there has been sustained interest in mathematical and computational modeling of calcium dynamics underlying neurotransmitter and hormone release, myocyte contraction and other fast calcium-controlled cell mechanisms. Apart from important biological questions addressed by computational modeling of calcium diffusion and its interaction with buffers and other calcium-binding substances, there are several interesting mathematical challenges and questions relevant to such work. Here we will discuss two different mathematical problems arising in the modeling of localized calcium dynamics: (1) quantitative comparison between solutions of continuous deterministic reaction-diffusion equations describing buffered calcium diffusion and binding on the one hand, and trial-averaged stochastic Monte-Carlo simulations of these processes on the other hand, and (2) developing efficient equilibrium approximations for calcium concentration near a single calcium source, which have more uniform applicability with respect to the relevant diffusion and buffering parameters as compared to existing asymptotic approximations such as the Rapid Buffering or the Excess Buffer approximations.