# Mathematical Biology Seminar

### Roman Borisyuk

School of Computing, Electronics and Mathematics, Plymouth University

#### Mathematical and computational modelling of the *Xenopus* tadpole spinal cord: Biologically realistic models of connectivity and functionality

#### Wednesday, November 9, 2016, at 3:05pm

LCB 225

In close collaboration with neurobiologists from the University of Bristol (Alan
Roberts and Steve Soffe) we have developed a new computational method to define
synaptic connectivity (in the form of a “connectome”) between neurons in the
tadpole spinal cord. The connectome is generated by a “developmental” process
where the growing axons intersect dendrites and create connections. The resulting
network has around 1,500 neurons with around 100,000 connections, and its
statistical properties are similar to experimental measurements. We study the
properties of the connectome using graph theory methods and find some similarities
with the *C. Elegans* network, in terms of how close to a small world network it is.
We have developed a functional network of spiking (Hodgkin-Huxley) neurons and
used the generated connectome to produce a pattern of neural activity. Remarkably,
the generated activity is very stable and corresponds with the typical pattern
seen in vivo during fictive swimming (anti-phase oscillations between left and
right sides of the body). Mathematical study of a simplified functional model
shows that there is another limit cycle corresponding to synchrony (in-phase
oscillations of two body sides), which can be stable under some conditions but has
a small basin of attraction in comparison with that of swimming. These results are
in a good agreement with experimental study of swimming and synchrony patterns in
the tadpole spinal cord. (with Robert Merrison-Hort, Andrea Ferrario)