The "ballistic shape" of the epsp can also be modeled by a simple, nonlinear, chemical kinetic model. In this case, consider a nicotinic acetylcholine (ACh) synapse in which two molecules of ACh must bind to a subsynaptic receptor site in order for the ion channel to open, depolarizing the SSM. Stated in terms of a chemical reaction, a bolus of ACh is released by the presynaptic action potential, and it diffuses across the cleft to the receptors. There, at every receptor, two transmitter molecules must bind to open the ion channels. In the reactions below, T is an (active) transmitter molecule; R is an unbound receptor site; RT2 is two transmitters bound to a receptor, opening the ion channel; T is an enzymatically inactivated transmitter molecule; the k are reaction rate constants. Thus,
By mass-action kinetics (Northrop, 1999), one can write y = a(t) - k4y + k22x-k1yn (N-x) 4.1-8A
where x is the fraction of the total receptors each bound to two ACh molecules that are conducting ions that depolarize the SSM. Thus it is assumed that the depolarization voltage is proportional to x; y is the concentration of free transmitter in the cleft and the exponent n = 2. To simulate this synaptic epsp, the Simnon program, nicochan.t, is used:
Continuous System nicochan " 3/11/99 System to emulate nicotinic ACh STATE x y " channel dynamics. EPSP V proportional to x. DER dx dy " Note 2 ACh molecules required/channel to TIME t " t in ms. open it and cause epsp. " y = ACh conc in synaptic cleft.
dx = k1*(y^2)*(N -x) - (k2 + k3)*x " x = Density of open channels on SSM. " vm epsp is proportional to x.
alpha = IF t < to THEN ao ELSE 0 " Pulse input rate of ACh. alphad = DELAY(alpha/to, D)
N:1" Max fraction of ion channels. (N - x)=fraction of unbound channels. to:.1
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