Simon Donnelly MRes

Simon Donnelly

Research Interests

My research relates to alterations of Purkinje cell dendritic morphology and electrical activity in a mouse model of spinocerebellar ataxia type 5 (SCA5). In order to develop treatments for SCA5 and other late-onset degenerative diseases, it is important to determine whether these changes are connected, and especially whether any of the differences during development underlie the later onset of symptoms.

Currently I am investigating differences in development of Purkinje cell planar morphology between wild-type and SCA5 model mice (beta-III spectrin knockouts). To this end I will be using confocal microscopy of Purkinje cells and parallel fibres (which are aligned at right-angles to Purkinje cells), followed by morphological analysis of reconstructed dendritic trees. This will aid in understanding the role of beta-III spectrin in the development of the cerebellar cortex, as well as how the loss of beta-III spectrin might lead to disease symptoms.

I am also interested in combinatorics, graph theory, graph algorithms, procedural content generation for games, and multi-agent systems. I am currently tutoring Fundamentals of Pure Mathematics in the School of Mathematics, which involves elementary group theory and real analysis.

  Computational convergence of the path integral for real dendritic morphologies
Caudron, Q, Donnelly, SR, Brand, S & Timofeeva, Y 2012, 'Computational convergence of the path integral for real dendritic morphologies' Journal of Mathematical Neuroscience, vol 2, pp. 32.
Neurons are characterised by a morphological structure unique among biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of subthreshold dendritic currents. The Green's function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites, and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient Matrix method which can be applied to arbitrary branching structures.
General Information
Organisations: Neuroinformatics DTC.
Authors: Caudron, Quentin, Donnelly, Simon R., Brand, Samuel & Timofeeva, Yulia.
Number of pages: 1
Pages: 32
Publication Date: 2012
Publication Information
Category: Article
Journal: Journal of Mathematical Neuroscience
Volume: 2
Original Language: English