TITLE minimal model of GABAb receptors COMMENT ----------------------------------------------------------------------------- Kinetic model of GABA-B receptors ================================= MODEL OF SECOND-ORDER G-PROTEIN TRANSDUCTION AND FAST K+ OPENING WITH COOPERATIVITY OF G-PROTEIN BINDING TO K+ CHANNEL PULSE OF TRANSMITTER SIMPLE KINETICS WITH NO DESENSITIZATION Features: - peak at 100 ms; time course fit to Tom Otis' PSC - SUMMATION (psc is much stronger with bursts) Approximations: - single binding site on receptor - model of alpha G-protein activation (direct) of K+ channel - G-protein dynamics is second-order; simplified as follows: - saturating receptor - no desensitization - Michaelis-Menten of receptor for G-protein production - "resting" G-protein is in excess - Quasi-stat of intermediate enzymatic forms - binding on K+ channel is fast Kinetic Equations: dR/dt = K1 * T * (1-R-D) - K2 * R dG/dt = K3 * R - K4 * G R : activated receptor T : transmitter G : activated G-protein K1,K2,K3,K4 = kinetic rate cst n activated G-protein bind to a K+ channel: n G + C <-> O (Alpha,Beta) If the binding is fast, the fraction of open channels is given by: O = G^n / ( G^n + KD ) where KD = Beta / Alpha is the dissociation constant ----------------------------------------------------------------------------- Parameters estimated from patch clamp recordings of GABAB PSP's in rat hippocampal slices (Otis et al, J. Physiol. 463: 391-407, 1993). ----------------------------------------------------------------------------- PULSE MECHANISM Kinetic synapse with release mechanism as a pulse. Warning: for this mechanism to be equivalent to the model with diffusion of transmitter, small pulses must be used... For a detailed model of GABAB: Destexhe, A. and Sejnowski, T.J. G-protein activation kinetics and spill-over of GABA may account for differences between inhibitory responses in the hippocampus and thalamus. Proc. Natl. Acad. Sci. USA 92: 9515-9519, 1995. For a review of models of synaptic currents: 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, 1996. This simplified model was introduced in: Destexhe, A., Bal, T., McCormick, D.A. and Sejnowski, T.J. Ionic mechanisms underlying synchronized oscillations and propagating waves in a model of ferret thalamic slices. Journal of Neurophysiology 76: 2049-2070, 1996. See also http://cns.iaf.cnrs-gif.fr Alain Destexhe, Salk Institute and 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 GABAb POINTER pre RANGE C, R, G, g, gmax, lastrelease, TimeCount NONSPECIFIC_CURRENT i GLOBAL Cmax, Cdur, Prethresh, Deadtime GLOBAL K1, K2, K3, K4, KD, Erev } UNITS { (nA) = (nanoamp) (mV) = (millivolt) (umho) = (micromho) (mM) = (milli/liter) } PARAMETER { dt (ms) Cmax = 0.5 (mM) : max transmitter concentration Cdur = 0.3 (ms) : transmitter duration (rising phase) Prethresh = 0 : voltage level nec for release Deadtime = 1 (ms) : mimimum time between release events : : From Kfit with long pulse (5ms 0.5mM) : K1 = 0.52 (/ms mM) : forward binding rate to receptor K2 = 0.0013 (/ms) : backward (unbinding) rate of receptor K3 = 0.098 (/ms) : rate of G-protein production K4 = 0.033 (/ms) : rate of G-protein decay KD = 100 : dissociation constant of K+ channel n = 4 : nb of binding sites of G-protein on K+ Erev = -95 (mV) : reversal potential (E_K) gmax (umho) : maximum conductance } ASSIGNED { v (mV) : postsynaptic voltage i (nA) : current = g*(v - Erev) g (umho) : conductance C (mM) : transmitter concentration Gn pre : pointer to presynaptic variable lastrelease (ms) : time of last spike TimeCount (ms) : time counter } STATE { R : fraction of activated receptor G : fraction of activated G-protein } INITIAL { C = 0 lastrelease = -1000 R = 0 G = 0 TimeCount=-1 } BREAKPOINT { SOLVE bindkin METHOD derivimplicit Gn = G^n g = gmax * Gn / (Gn+KD) i = g*(v - Erev) } DERIVATIVE bindkin { release() : evaluate the variable C R' = K1 * C * (1-R) - K2 * R G' = K3 * R - K4 * G } 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 lastrelease = t TimeCount=Cdur } } else if (TimeCount > 0) { : still releasing? : do nothing } else if (C == Cmax) { : in dead time after release C = 0. } }