EPSRC Advanced Research Fellowship 2002-2007

Synaptic Travelling Waves

An important goal of neuroscience is to establish a series of direct links between the abstract nature of biophysical model equations and their interpretation in terms of experimental findings in biological neural networks. I propose to address this issue by developing a novel mathematical analysis of the dynamics of synaptically interacting neural systems and by establishing a framework for comparison with experimental measures of neural activity. The focus of the study will be on travelling waves and spatially structured activity observed in cortex during epileptic seizures, the travelling spindle waves observed in thalamus at the onset of sleep or drowsiness and waves of activity in animal motor systems. The understanding of the mechanisms for such a wide range of both pathological and naturally occuring phenomena is directly relevant to both improved clinical treatments and the understanding of the role of dynamics in neurobiological function. Since neuronal rhythmic activity also manifests itself in various aspects of normal brain function, that include synchronisation and waves of excitation observed in cortex during sensory processing, the work will have broad application in the neurosciences.


To address the biological significance of the following on travellling waves in neural systems:

  1. Realistic patterns of axo-dendritic synapses
  2. Excitable membrane properties of dendritic spines
  3. Slow T-type Calcium currents
  4. Anode break excitation and reciprocal inhibition
  5. Anisotropy and inhomogeneity

To develop the mathematical analysis of

  1. Coupled bursting oscillators
  2. Strongly coupled relaxation oscillators
  3. Integral equations with space-dependent delays

To apply results to the following distinct neural phenomena

  1. Synchronised bursting and the travelling wave transition in epilepsy
  2. Lurching waves observed in thalamic slices
  3. Rhythm generation for swimming in the spinal cord of the Xenopus tadpole

A complete copy of the research proposal may be downloaded in pdf format, by clicking here.