Effect of intrinsic and extrinsic noise on a network motif of mutually inhibiting neurons

Abstract

Mutually inhibiting neurons is a common motif across many systems like Hip- pocampus, CPGs(Central Pattern Generators) and Olfaction. Their synaptic interac- tion ensures that they show alternating activity. The frequency of switching from an active to a quiescent period is a function of the biophysical properties of ion channels present in the neurons, synaptic interaction timescales, network properties, the stim- ulus and possibly channel uctuations from a small number of channels. Switching allows neurons to associate with different networks and coordinate patterns of activity that may be relevant for function. The frequency of switching dictates the sequential order of activity of neurons required for locomotion, for example in Lamprey. In this context, reliable switching might be a critical functional requirement. How do net- works of mutually inhibiting neurons, a simple most functional module of switching, achieve this reliability despite a noisy framework and environment? We have devel- oped a conductance-based model of two mutually inhibiting neurons wherein inherent switching takes place via a potassium current, sAHP that is triggered by calcium ions. We systematically study the effect of various sources of noise including channel con- ductance noise, and input noise on switching and robust generation of sequences. Our results show that switching frequency can be tuned with noise amplitude of the ex- trinsic noise. It has been previously shown that calcium channel uctuations are the largest contributors of stochasticity at the synapse. As a control simulation experi- ment, we isolate contributions of calcium channel uctuations. In this framework, only the calcium dynamics is modeled with a Markovian scheme, and other components are deterministic. Our results suggest that an optimal number of calcium channels help achieve precise switching. This study sheds light on how channel uctuations affect the network activity and cannot be ignored a priori when slow decay time scales are involved in the neuronal dynamics. Our understanding of the effects of various sources of noise in this illustrative network motif is likely to be applicable to a wide variety of systems.