title: Relating neural dynamics to neural coding.
abstract: We demonstrate that two key theoretical objects used widely in computational neuroscience, the phase-resetting curve (PRC) from dynamics and the spike triggered average (STA) from statistical analysis, are closely related when neurons fire in a nearly regular manner and the stimulus is sufficiently small. We prove that the STA due to injected noisy current is proportional to the derivative of the PRC. We compare these analytic results with numerical calculations for the Hodgkin-Huxley neuron and we apply the method to neurons in the olfactory bulb of mice. This observation allows us to relate the stimulus-response properties of a neuron to its dynamics, bridging the gap between dynamical and information theoretic approaches to understanding brain computations and facilitating the interpretation of changes in channels and other cellular properties as influencing the representation of stimuli.
authors.affiliation: University of Pittsburgh, Department of Mathematics, Thackeray Hall, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: G Bard
authors.initials: GB
authors.lastname: Ermentrout
authors.forename: Roberto F
authors.initials: RF
authors.lastname: Galán
authors.forename: Nathaniel N
authors.initials: NN
authors.lastname: Urban
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*