Analysis of Activity Dependent Development of Topographic Maps in Neural Field Theory with Short Time Scale Dependent Plasticity

Topographic maps are a brain structure connecting pre-synpatic andpost-synaptic brain regions. Topographic development is dependent onHebbian-based plasticity mechanisms working in conjunction with spontaneouspatterns of neural activity generated in the pre-synaptic regions. Studiesperformed in mouse have shown that these spontaneous patterns can exhibitcomplex spatial-temporal structures which existing models cannot incorporate.Neural field theories are appropriate modelling paradigms for topographicsystems due to the dense nature of the connections between regions and can beaugmented with a plasticity rule general enough to capture complex time-varyingstructures. We propose a theoretical framework for studying the development of topographyin the context of complex spatial-temporal activity fed-forward from thepre-synaptic to post-synaptic regions. Analysis of the model leads to ananalytic solution corroborating the conclusion that activity can drive therefinement of topographic projections. The analysis also suggests thatbiological noise is used in the development of topography to stabilise thedynamics. MCMC simulations are used to analyse and understand the differencesin topographic refinement between wild-type and the $\beta2$ knock-out mutantin mice. The time scale of the synaptic plasticity window is estimated as$0.56$ seconds in this context with a model fit of $R^2 = 0.81$.Comment: 15 pages, 5 figure