A simple mathematical model of second-messenger mediated slow excitatory postsynaptic potentials.
We have developed a novel and simple mathematical model of a slow excitatory postsynaptic potential (EPSP) based on an abstraction of the processes of activation, inactivation, and summation of a cAMP, protein kinase A (PKA)-dependent second-messenger cascade. The model describes the activation of receptors, G-proteins, and production of cAMP as the first stage and uses first-order, non-rate-limited kinetics. The second stage corresponds to the release of active, PKA catalytic subunit and can use first- or higher-order kinetics. The third stage represents simple phosphorylation of ion channels and is limited by the number of channels available. The decay of each stage is based on first-order, mass-action kinetics. These equations and some variations were solved numerically and values of the parameters were determined by fitting to a variety of experimental data from myenteric neurons of the guinea-pig ileum. The model produced a slow EPSP with a nonlinear stimulus-response relationship that resulted from the underlying kinetics of the signaling cascade. This system of equations is suitable for incorporation into a large-scale computer simulation, and the methodology should be generalizable to other pathways.
Bertrand
P P
PP
Department of Physiology, University of Melbourne, Parkville, Australia. p.bertrand@physiology.unimelb.edu.au
Thomas
E A
EA
Kunze
W A
WA
Bornstein
J C
JC
D000818:Animals; D002462:Cell Membrane / Q000378:metabolism / Q000648:ultrastructure; D000242:Cyclic AMP / Q000378:metabolism; D004558:Electric Stimulation / Q000379:methods; D004594:Electrophysiology / Q000379:methods; D017615:Enteric Nervous System / Q000166:cytology / Q000502:physiology; D019706:Excitatory Postsynaptic Potentials / Q000502:physiology*; D019204:GTP-Binding Proteins / Q000378:metabolism; D006168:Guinea Pigs; D008959:Models, Neurological; D009415:Nerve Net; D009474:Neurons / Q000166:cytology / Q000502:physiology; D011930:Reaction Time / Q000502:physiology; D015290:Second Messenger Systems / Q000502:physiology*; D013997:Time Factors
D000242:Cyclic AMP; D019204:GTP-Binding Proteins