TITLE minimal model of NMDA receptors COMMENT ----------------------------------------------------------------------------- Minimal kinetic model for glutamate NMDA receptors ================================================== Model of Destexhe, Mainen & Sejnowski, 1994: (closed) + T <-> (open) The simplest kinetics are considered for the binding of transmitter (T) to open postsynaptic receptors. The corresponding equations are in similar form as the Hodgkin-Huxley model: dr/dt = alpha * [T] * (1-r) - beta * r I = gmax * [open] * B(V) * (V-Erev) where [T] is the transmitter concentration and r is the fraction of receptors in the open form. B(V) represents the voltage-dependent Mg++ block (see Jahr & Stevens J Neurosci 10: 1830, 1990; Jahr & Stevens J Neurosci 10: 3178, 1990). If the time course of transmitter occurs as a pulse of fixed duration, then this first-order model can be solved analytically, leading to a very fast mechanism for simulating synaptic currents, since no differential equation must be solved (see Destexhe, Mainen & Sejnowski, 1994). ----------------------------------------------------------------------------- Based on voltage-clamp recordings of NMDA receptor-mediated currents in rat hippocampal slices (Hessler et al., Nature 366: 569-572, 1993), this model was fit directly to experimental recordings in order to obtain the optimal values for the parameters (see Destexhe, Mainen and Sejnowski, 1996). ----------------------------------------------------------------------------- This mod file includes a mechanism to describe the time course of transmitter on the receptors. The time course is approximated here as a brief pulse triggered when the presynaptic compartment produces an action potential. The pointer "pre" represents the voltage of the presynaptic compartment and must be connected to the appropriate variable in oc. ----------------------------------------------------------------------------- See details in: Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. An efficient method for computing synaptic conductances based on a kinetic model of receptor binding Neural Computation 6: 10-14, 1994. Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Kinetic models of synaptic transmission. In: Methods in Neuronal Modeling (2nd edition; edited by Koch, C. and Segev, I.), MIT press, Cambridge, 1998, pp. 1-28. (electronic copy available at http://cns.iaf.cnrs-gif.fr) Written by Alain Destexhe, Laval University, 1995 27-11-2002: the pulse is implemented using a counter, which is more stable numerically (thanks to Yann LeFranc) ----------------------------------------------------------------------------- ENDCOMMENT INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)} NEURON { POINT_PROCESS NMDA POINTER pre RANGE C, R, R0, R1, g, gmax, B, lastrelease, TimeCount NONSPECIFIC_CURRENT i GLOBAL Cmax, Cdur, Alpha, Beta, Erev, mg GLOBAL Prethresh, Deadtime, Rinf, Rtau } UNITS { (nA) = (nanoamp) (mV) = (millivolt) (umho) = (micromho) (mM) = (milli/liter) } PARAMETER { dt (ms) Cmax = 1 (mM) : max transmitter concentration Cdur = 1 (ms) : transmitter duration (rising phase) Alpha = 0.072 (/ms mM) : forward (binding) rate Beta = 0.0066 (/ms) : backward (unbinding) rate Erev = 0 (mV) : reversal potential Prethresh = 0 : voltage level nec for release Deadtime = 1 (ms) : mimimum time between release events gmax (umho) : max conductance (100 pS single syn) mg = 1 (mM) : external magnesium concentration } ASSIGNED { v (mV) : postsynaptic voltage i (nA) : current = g*(v - Erev) g (umho) : conductance C (mM) : transmitter concentration R : fraction of open channels R0 : open channels at start of release R1 : open channels at end of release Rinf : steady state channels open Rtau (ms) : time constant of channel binding pre : pointer to presynaptic variable lastrelease (ms) : time of last spike B : magnesium block TimeCount (ms) : time counter } INITIAL { R = 0 C = 0 Rinf = Cmax*Alpha / (Cmax*Alpha + Beta) Rtau = 1 / ((Alpha * Cmax) + Beta) lastrelease = -1000 R1=0 TimeCount=-1 } BREAKPOINT { SOLVE release B = mgblock(v) : B is the block by magnesium at this voltage g = gmax * R * B i = g*(v - Erev) } PROCEDURE release() { :will crash if user hasn't set pre with the connect statement TimeCount=TimeCount-dt : time since last release ended : ready for another release? if (TimeCount < -Deadtime) { if (pre > Prethresh) { : spike occured? C = Cmax : start new release R0 = R lastrelease = t TimeCount=Cdur } } else if (TimeCount > 0) { : still releasing? : do nothing } else if (C == Cmax) { : in dead time after release R1 = R C = 0. } if (C > 0) { : transmitter being released? R = Rinf + (R0 - Rinf) * exptable (- (t - lastrelease) / Rtau) } else { : no release occuring R = R1 * exptable (- Beta * (t - (lastrelease + Cdur))) } VERBATIM return 0; ENDVERBATIM } FUNCTION exptable(x) { TABLE FROM -10 TO 10 WITH 2000 if ((x > -10) && (x < 10)) { exptable = exp(x) } else { exptable = 0. } } FUNCTION mgblock(v(mV)) { TABLE DEPEND mg FROM -140 TO 80 WITH 1000 : from Jahr & Stevens mgblock = 1 / (1 + exp(0.062 (/mV) * -v) * (mg / 3.57 (mM))) }