Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons
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Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f–I curve. We introduce a novel classification of neurons into Types A, B−, and B+ according to how f–I curves are modulated by input fluctuations. In Type A neurons, the f–I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B− neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple “energy barrier” model.
KeywordsNoise Gain f–I curve Stimulus fluctuations Single neuron Time scales Dynamical systems Phase portrait Hodgkin-Huxley Slow adaptation Slow AHP
We thank Bard Ermentrout for helpful conversations during initial stages of the project at the Marine Biological Laboratory’s Methods in Computational Neuroscience 2007 course, Matthew Higgs and Michele Giugliano for helpful discussions and providing data for a figure, and Randy Powers and Sungho Hong for comments on a draft of this manuscript.
This work was supported by a Burroughs-Wellcome Careers at the Scientific Interface grant and a McKnight Scholar Award; BNL was supported by grant number F30NS055650 from the National Institute of Neurological Disorders and Stroke, the Medical Scientist Training Program at UW supported by the National Institute of General Medical Sciences, and an ARCS fellowship; WJS was supported by a VA Merit Review.
Conceived of, designed, and performed the simulations: BL. Analyzed the data: BL MF LS AF. Wrote the paper: BL MF WS AF. Developed the conceptual framework: BL MF LS WS AF.
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