# Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

### From Particle Diffusion to Neuronal Networks: A Multi-scale Study of the Role Astrocytes Have in the Brain

**Mathematical Biology**

Speaker: | Greg Handy, University of Utah |

Location: | 2112 MSB |

Start time: | Mon, Jan 14 2019, 3:10PM |

Astrocytes are glial cells that make up 50% of brain volume and exhibit calcium signals in the presence of neuronal activity. In collaboration with experimentalists, we have studied the underlying dynamics generating these calcium responses via short applications of ATP. Even in this controlled experimental setup, calcium transients exhibit a vast range of amplitudes and durations. We present an open-cell model that captures the diversity of responses and use it to propose a classification system for the types of transients observed.

We show that variability in the time course of the signaling molecule IP3 is enough to create the variability of the observed calcium responses. We investigate the source of this variability through a novel stochastic process in which n particles are diffusing and interacting with membrane bound receptors. We prove that by accounting for the finite recharge time that occurs between binding events, the expected number of captured particles has an upper-bound of order log(n). Thus, only a small number of molecules are binding to receptors, leading to a greater amount of variability than previously expected.

Lastly, we discuss preliminary work on incorporating these results into a new type of neuronal network that includes the effects of astrocytes.