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)