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From spiking neuron models to linear-nonlinear models.

dc.contributor.author Ostojic, S
dc.contributor.author Brunel, Nicolas
dc.coverage.spatial United States
dc.date.accessioned 2017-08-01T13:39:29Z
dc.date.available 2017-08-01T13:39:29Z
dc.date.issued 2011-01-20
dc.identifier https://www.ncbi.nlm.nih.gov/pubmed/21283777
dc.identifier.uri https://hdl.handle.net/10161/15128
dc.description.abstract Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
dc.language eng
dc.relation.ispartof PLoS Comput Biol
dc.relation.isversionof 10.1371/journal.pcbi.1001056
dc.subject Action Potentials
dc.subject Humans
dc.subject Linear Models
dc.subject Neurons
dc.subject Nonlinear Dynamics
dc.title From spiking neuron models to linear-nonlinear models.
dc.type Journal article
pubs.author-url https://www.ncbi.nlm.nih.gov/pubmed/21283777
pubs.begin-page e1001056
pubs.issue 1
pubs.organisational-group Basic Science Departments
pubs.organisational-group Duke
pubs.organisational-group Neurobiology
pubs.organisational-group Physics
pubs.organisational-group School of Medicine
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published online
pubs.volume 7
dc.identifier.eissn 1553-7358


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