title: Generation of time delays: simplified models of intracellular signalling in cerebellar Purkinje cells.
abstract: In many neuronal systems, information is encoded in temporal spike patterns. The recognition and storage of temporal patterns requires the generation and modulation of time delays between inputs and outputs. In cerebellar Purkinje cells, stimulation of metabotropic glutamate receptors (mGluRs) results in a delayed calcium and voltage response that has been implicated in classical conditioning and temporal pattern recognition. Here, we analyse and simplify a complex model of the intracellular signalling network that has been proposed as a substrate for this delayed response. We systematically simplify the original model, present a minimal model of time delay generation, and show that a delayed response can be produced by the combination of negative feedback and autocatalysis, without any intervening signalling steps that would contribute additive delays. The minimal model is analysed using phase plane methods, and classified as an excitable system. We discuss the implication of excitability for computations performed by intracellular signalling networks in general.
authors.affiliation: Department of Physiology, University College London, Gower Street, London, WC1E 6BT, UK. v.steuber@ucl.ac.uk
authors.forename: Volker
authors.initials: V
authors.lastname: Steuber
authors.forename: David
authors.initials: D
authors.lastname: Willshaw
authors.forename: Arjen
authors.initials: A
authors.lastname: Van Ooyen
mesh_terms: D000818:Animals; D001676:Biofeedback, Psychology; D002118:Calcium / Q000378:metabolism; D002531:Cerebellum / Q000166:cytology*; D008433:Mathematics; D008959:Models, Neurological; D011689:Purkinje Cells / Q000502:physiology*; D018094:Receptors, Metabotropic Glutamate / Q000502:physiology; D015398:Signal Transduction / Q000502:physiology*; D013997:Time Factors
chemical_list: D018094:Receptors, Metabotropic Glutamate; D002118:Calcium