Mode locking in a periodically forced "ghostbursting" neuron model

We study a minimal integrate-and-fire based model of a "ghostbursting" neuron under periodic stimulation. These neurons are involved in sensory processing in weakly electric fish. There exist regions in parameter space in which the model neuron is mode-locked to the stimulation. We analyse this locked behavior and examine the bifurcations that define the boundaries of these regions. Due to the discontinuous nature of the flow, some of these bifurcations are nonsmooth. This exact analysis is in excellent agreement with numerical simulations, and can be used to understand the response of such a model neuron to biologically realistic input.

Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.

Delays in activity based neural networks

In this paper we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First we focus on the use of linear stability theory to show how to destabilise a fixed point, leading to the onset of oscillatory behaviour. Next we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally we comment on the role of delays in the generation of bursting oscillations, and discuss natural extensions of the work in this paper.