Role of slow temporal dynamics in reliableactivity of stochastically driven neurons

Neuronal networks maintain robust patterns of activity despite a backdrop of noise from various sources. Mutually inhibiting neurons is a standard network motif implicated in rhythm generation. In an elementary network motif of two neurons capable of swapping from an active state to a quiescent state, we ask how different sources of stochasticity alter firing patterns. In this system, the alternating activity occurs via combined action of a calcium-dependent potassium current, sAHP (slow afterhyperpolarization), and a fast GABAergic synapse. We show that simulating extrinsic noise arising from background activity extends the dynamical range of neuronal firing. Extrinsic noise also has the effect of increasing the switching frequency via a faster build-up of sAHP current. We show that switching frequency as a function of input current has a non-monotonic behavior. Interestingly the noise tolerance of this system varies with the input current. It shows maximum robustness to noise at an input current that corresponds to the minimum switching frequency between the neurons. The slow decay time scale of sAHP conductance allows neurons to act as a low-pass filter, attenuate noise, and integrate over ion channel fluctuations. Additionally, we show that the slow inactivation time of the sAHP channel allows the neuron to act as an action potential counter. We propose that this intrinsic property of the current allows the network to maintain rhythmic activity critical for various functions, despite the noise, and operate as a temporal integrator.