White-noise susceptibility and critical slowing in neurons near spiking threshold

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dc.contributor.authorSteyn-Ross, D. Alistair
dc.contributor.authorSteyn-Ross, Moira L.
dc.contributor.authorWilson, Marcus T.
dc.contributor.authorSleigh, James W.
dc.coverage.spatialUnited Statesen_NZ
dc.date.accessioned2008-11-20T23:19:26Z
dc.date.available2008-11-20T23:19:26Z
dc.date.issued2006
dc.description.abstractWe present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon (“resonator”) and a human cortical neuron (“integrator”). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate voltage fluctuations that exhibit critical slowing down—that is, the voltage responsiveness to noisy input currents grows in amplitude while slowing in frequency—as the membrane approaches spiking threshold from below. We define threshold unambiguously as that dc current that renders a zero real eigenvalue for the Jacobian matrix for the integrator neuron, and, for the resonator neuron, as the dc current that gives a complex eigenvalue pair whose real part is zero. Using a linear Ornstein-Uhlenbeck analysis, we give exact small-noise expressions for the variance, power spectrum, and correlation function of the voltage fluctuations, and we derive the scaling laws for the divergence of susceptibility and correlation times for approach to threshold. We compare these predictions with numerical simulations of the nonlinear stochastic equations, and demonstrate that, provided the white-noise perturbations are kept sufficiently small, the linearized theory works well. These predictions should be testable in the laboratory using a current-clamped cell configuration. If confirmed, then the proximity of a neuron to its spike-transition point can be judged by measuring its subthreshold susceptibility to white-noise stimulation. We postulate that such temporally correlated fluctuations could provide a means of subthreshold signaling via gap-junction connections with neighboring neurons.en_US
dc.identifier.citationSteyn-Ross, D. A., Steyn-Ross, M. L., Wilson, M. T. & Sleigh, J. W. (2006). White-noise susceptibility and critical slowing in neurons near spiking threshold. Physical Review E, 74, 051920.en_US
dc.identifier.doi10.1103/PhysRevE.74.051920en_US
dc.identifier.urihttps://hdl.handle.net/10289/1435
dc.language.isoen
dc.publisherAmerican Physical Societyen_NZ
dc.relation.isPartOfPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics)en_NZ
dc.subjectneuronen_US
dc.subjectresonatoren_US
dc.subjectintegratoren_US
dc.titleWhite-noise susceptibility and critical slowing in neurons near spiking thresholden_US
dc.typeJournal Articleen_US
pubs.begin-page1en_NZ
pubs.elements-id32106
pubs.end-page15en_NZ
pubs.issue5en_NZ
pubs.volume74en_NZ
uow.identifier.article-noARTN 051920en_NZ
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