title: A case study of linear versus non-linear modelling.
abstract: Theories for the facilitation of neurotransmitter release are discussed in a case study of the properties of linear and non-linear models for a phenomenon whose time course can be represented by a sum of decaying exponentials. Particular attention is paid to the effects of a "key factor" on the slopes and amplitudes of the exponentials that can be derived from semilog plots of the data. It is shown that the presence of such effects can give strong evidence for the inappropriateness of linear models. A non-linear model is demonstrated to be capable of describing the changes with extracellular Ca concentration of straight line segments that fit data in semilog plots of facilitation as a function of time. The conclusion is reached that even if data seems to be representable by several independently alterable exponentials one must be cautious in drawing inferences concerning the number, linearity, or independence of the underlying processes.
mesh_terms: D000200:Action Potentials; D002118:Calcium / Q000502:physiology; D008959:Models, Neurological; D018377:Neurotransmitter Agents / Q000502:physiology*; D013569:Synapses / Q000502:physiology; D009435:Synaptic Transmission
chemical_list: D018377:Neurotransmitter Agents; D002118:Calcium