Bumps, breathers, and waves in a neural network with spike frequency adaptation

In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon the non-local network connectivity, synaptic response, and firing rate of a single neuron. A phenomenological model of SFA is examined whereby the firing rate is taken to be a simple state-dependent threshold function. As in the case without SFA classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps). Importantly an analysis of bump stability using recent Evans function techniques shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Direct numerical simulations both confirm our theoretical predictions and illustrate the rich dynamic behavior of this model, including the appearance of self-replicating bumps.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

Effect of maternal cold exposure and nutrient restriction on insulin-like growth factor sensitivity in adipose tissue of newborn sheep

Adipose tissue mass in the newborn is determined in part by insulin-like growth factor (IGF)s, which are dependent on the maternal nutritional and metabolic environment during late gestation. The present study was designed to determine whether maternal cold exposure (CE) commencing in mid gestation could modulate some of the adaptive effects of nutrient restriction in late gestation on adipose tissue endocrine sensitivity in the resulting offspring. Twenty eight pregnant sheep were entered into the study and were either shorn, i.e. cold exposed, from 70 days gestation (term = 147 days), or remained unshorn, and were fed either their total calculated metabolisable energy (ME) requirements for body weight and pregnancy from 110 days gestation or 50% of this amount (n=7 per group). Adipose tissue was sampled from the offspring at one day of age and the mRNA abundance for IGF-I, II their receptors (R) and GH secretagogue receptor-1a (GHSR-1a) were determined. CE mothers produced larger offspring with more perirenal adipose tissue, an adaptation prevented by maternal nutrient restriction. Nutrient restriction in unshorn mothers increased IGF-I and IIR mRNA abundance. The mRNA abundances for IGF-I, II and IIR in adipose tissue were reduced by CE, adaptations independent of maternal food intake, whereas CE plus nutrient restriction increased GHSR-1a mRNA. In conclusion, maternal nutrient restriction with or without CE has very different effects on IGF sensitivity of adipose tissue and may act to ensure adequate fat stores are present in the newborn in the face of very different maternal endocrine and metabolic environments.