# Mathematical Biology Seminar

### Alan Veliz-Cuba

Department of Mathematics, University of Houston

#### Continuous and discrete approaches to study gene and neural networks

#### Wednesday, February 4, 2015, at 3:05pm

LCB 219

In this talk, I will discuss two case studies of how seemingly
unrelated areas of mathematics can be used in tandem to understand
complementary aspects of biological systems.
First, I will cover how to identify the sources of variability in gene
networks: Understanding the effect of noise on gene networks is fundamental
in developing accurate models. Typically, comparing experimental data and
simulations only takes into account individual trajectories, but not the
lineage and the corresponding cell-cell variability and correlation. Here I
show that a model that includes intrinsic and extrinsic noise can capture
the variability and correlation seen in experimental data. The model is
based on an extension of the Gillespie algorithm that takes into account
cell growth, division, lineage dependence, and extrinsic noise. If time
allows, I will discuss the graph-theory approach to cell tracking that we
used to analyze the experimental data.
Second, I will cover how neural activity can reshape network structure,
resulting in neural coding: A central problem in neuroscience is how the
brain learns, stores, and decodes information. While bump attractor networks
have been proposed to explain memory storage, how such networks emerge is
still not well understood. Experiments have shown that the replay of neural
activity during sleep is a key factor in memory; so replay could be the
origin of bump attractor networks. Here I present a firing rate model with
synaptic plasticity that explains how this replay of neural activity can
reshape network structure, resulting in a bump attractor network. If time
allows, I will discuss the algebraic-geometry approach that we used to
recover place-field and network structure from neural activity.