Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons.
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 reveals irregular, 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 and 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).
Instituto de Física, Universidade de São Paulo, Brazil.
Bóris
B
Marin
Instituto de Física de São Carlos, Universidade de São Paulo, Brazil.
Reynaldo Daniel
RD
Pinto
Institute for Nonlinear Science, University of California, San Diego, California 92093-0402, USA.
Robert C
RC
Elson
Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil.
Eduardo
E
Colli
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D017952:Ganglia, Invertebrate / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D033521:Palinuridae; D013269:Stochastic Processes; D009435:Synaptic Transmission