TITLE Triple-exp model of NMDAR has (HH-type gating) (temp. sensitivity) (voltage-dependent time constants) (desensitization) COMMENT This is a Triple-exponential model of an NMDAR that has a slow voltage-dependent gating component in its conductance time constants are voltage-dependent and temperature sensitive Mg++ voltage dependency from Spruston95 -> Woodhull, 1973 Desensitization is introduced in this model. Actually, this model has 4 differential equations becasue desensitization is solved analitically. It can be reduced to 3 by solving its A state analitically. For more info read the original paper. Keivan Moradi 2012 ENDCOMMENT NEURON { POINT_PROCESS Exp5NMDA NONSPECIFIC_CURRENT i RANGE tau1, tau2_0, a2, b2, wtau2, tau3_0, a3, b3, tauV, e, i, gVI, gVDst, gVDv0, Mg, K0, delta, tp, wf, tau_D1, d1 GLOBAL inf, tau2, tau3 THREADSAFE } UNITS { (nA) = (nanoamp) (mV) = (millivolt) (uS) = (microsiemens) (mM) = (milli/liter) (S) = (siemens) (pS) = (picosiemens) (um) = (micron) (J) = (joules) } PARAMETER { : Parameters Control Neurotransmitter and Voltage-dependent gating of NMDAR tau1 = 1.69 (ms) <1e-9,1e9> : Spruston95 CA1 dend [Mg=0 v=-80 celcius=18] be careful: Mg can change these values : parameters control exponential rise to a maximum of tau2 tau2_0 = 3.97 (ms) a2 = 0.70 (ms) b2 = 0.0243 (1/mV) wtau2= 0.65 <1e-9,1> : Hestrin90 : parameters control exponential rise to a maximum of tau3 tau3_0 = 41.62 (ms) a3 = 34.69 (ms) b3 = 0.01 (1/mV) : Hestrin90 CA1 soma [Mg=1 v=-40 celcius=30-32] the decay of the NMDA component of the EPSC recorded at temperatures above 30 degC : the fast phase of decay, which accounted for 65%-+12% of the decay, had a time constant of 23.5-+3.8 ms, : whereas the slow component had a time constant of 123-+83 ms. : wtau2= 0.78 Spruston95 CA1 dend [Mg=0 v=-80 celcius=18] percentage of contribution of tau2 in deactivation of NMDAR Q10_tau1 = 2.2 : Hestrin90 Q10_tau2 = 3.68 : Hestrin90 -> 3.5-+0.9, Korinek10 -> NR1/2B -> 3.68 Q10_tau3 = 2.65 : Korinek10 T0_tau = 35 (degC) : reference temperature : Hestrin90 CA1 soma [Mg=1 v=-40 celcius=31.5->25] The average Q10 for the rising phase was 2.2-+0.5, : and that for the major fast decaying phase was 3.5-+0.9 tp = 30 (ms) : time of the peack -> when C + B - A reaches the maximum value or simply when NMDA has the peack current : tp should be recalculated when tau1 or tau2 or tau3 changes : Parameters control desensitization of the channel : these values are from Fig.3 in Varela et al. 1997 : the (1) is needed for the range limits to be effective d1 = 0.2 (1) < 0, 1 > : fast depression tau_D1 = 2500 (ms) < 1e-9, 1e9 > : Parameters Control voltage-dependent gating of NMDAR tauV = 7 (ms) <1e-9,1e9> : Kim11 : at 26 degC & [Mg]o = 1 mM, : [Mg]o = 0 reduces value of this parameter : Because TauV at room temperature (20) & [Mg]o = 1 mM is 9.12 Clarke08 & Kim11 : and because Q10 at 26 degC is 1.52 : then tauV at 26 degC should be 7 gVDst = 0.007 (1/mV) : steepness of the gVD-V graph from Clarke08 -> 2 units / 285 mv gVDv0 = -100 (mV) : Membrane potential at which there is no voltage dependent current, from Clarke08 -> -90 or -100 gVI = 1 (uS) : Maximum Conductance of Voltage Independent component, This value is used to calculate gVD Q10 = 1.52 : Kim11 T0 = 26 (degC) : reference temperature celsius (degC) : actual temperature for simulation, defined in Neuron : Parameters Control Mg block of NMDAR Mg = 1 (mM) : external magnesium concentration from Spruston95 K0 = 4.1 (mM) : IC50 at 0 mV from Spruston95 delta = 0.8 (1) : the electrical distance of the Mg2+ binding site from the outside of the membrane from Spruston95 : The Parameter Controls Ohm haw in NMDAR e = -0.7 (mV) : in CA1-CA3 region = -0.7 from Spruston95 } CONSTANT { T = 273.16 (degC) F = 9.648e4 (coul) : Faraday's constant (coulombs/mol) R = 8.315 (J/degC): universal gas constant (joules/mol/K) z = 2 (1) : valency of Mg2+ } ASSIGNED { v (mV) dt (ms) i (nA) g (uS) factor wf q10_tau2 q10_tau3 inf (uS) tau (ms) tau2 (ms) tau3 (ms) wtau3 } STATE { A : Gating in response to release of Glutamate B : Gating in response to release of Glutamate C : Gating in response to release of Glutamate gVD (uS): Voltage dependent gating } INITIAL { Mgblock(v) : temperature-sensitivity of the of NMDARs tau1 = tau1 * Q10_tau1^((T0_tau - celsius)/10(degC)) q10_tau2 = Q10_tau2^((T0_tau - celsius)/10(degC)) q10_tau3 = Q10_tau3^((T0_tau - celsius)/10(degC)) : temperature-sensitivity of the slow unblock of NMDARs tau = tauV * Q10^((T0 - celsius)/10(degC)) rates(v) wtau3 = 1 - wtau2 : if tau3 >> tau2 and wtau3 << wtau2 -> Maximum conductance is determined by tau1 and tau2 : tp = tau1*tau2*log(tau2/(wtau2*tau1))/(tau2 - tau1) factor = -exp(-tp/tau1) + wtau2*exp(-tp/tau2) + wtau3*exp(-tp/tau3) factor = 1/factor A = 0 B = 0 C = 0 gVD = 0 wf = 1 } BREAKPOINT { SOLVE state METHOD runge : derivimplicit : : we found acceptable results with "runge" integration method : However, M. Hines encouraged us to use "derivimplicit" method instead - which is slightly slower than runge - : to avoid probable unstability problems i = (wtau3*C + wtau2*B - A)*(gVI + gVD)*Mgblock(v)*(v - e) } DERIVATIVE state { rates(v) A' = -A/tau1 B' = -B/tau2 C' = -C/tau3 : Voltage Dapaendent Gating of NMDA needs prior binding to Glutamate Kim11 gVD' = ((wtau3*C + wtau2*B)/wf)*(inf-gVD)/tau : gVD' = (inf-gVD)/tau } NET_RECEIVE(weight, D1, tsyn (ms)) { INITIAL { : these are in NET_RECEIVE to be per-stream : this header will appear once per stream D1 = 1 tsyn = t } D1 = 1 - (1-D1)*exp(-(t - tsyn)/tau_D1) tsyn = t wf = weight*factor*D1 A = A + wf B = B + wf C = C + wf D1 = D1 * d1 } FUNCTION Mgblock(v(mV)) { : from Spruston95 Mgblock = 1 / (1 + (Mg/K0)*exp((0.001)*(-z)*delta*F*v/R/(T+celsius))) } PROCEDURE rates(v (mV)) { inf = (v - gVDv0) * gVDst * gVI tau2 = (tau2_0 + a2*(1-exp(-b2*v)))*q10_tau2 tau3 = (tau3_0 + a3*(1-exp(-b3*v)))*q10_tau3 if (tau1/tau2 > .9999) { tau1 = .9999*tau2 } if (tau2/tau3 > .9999) { tau2 = .9999*tau3 } }