Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

TL;DR

This paper demonstrates that adding dynamical noise to minimal square-wave burster neuron models reproduces complex interspike interval signatures observed in biological neurons, without requiring fine-tuning or chaos, highlighting the role of transient dynamics.

Contribution

It shows that stochastic noise in simple neuron models can generate realistic neural signatures, emphasizing the importance of transient dynamics over chaos for neural variability.

Findings

Noise induces complex signatures similar to biological neurons.

Transient dynamics in square-wave bursting models produce rich activity.

Minimal models with noise replicate biological interspike interval variability.

Abstract

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network revealsirregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine-tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained, and can approximate several possible sources of noise, e.g. random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node/homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).