%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Modeling of Ca-dependent inactivation by changing Ca affinity of the pore % % % % Roman Shirokov, UMDNJ, Victor Matveev, NJIT % % January, 2006 % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % PARAMETERS % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %---- Charge1 - Charge2 parameters------------- V1 = -10; V2 = -110; K = 8 % mV a1 = 0.3; a2 =0.0033 % ms^-1, parameters "a" and "b" are used to define b = 0.1 % voltage-dependent rates of Charge1 and Charge2 movements tauIna = 2000 % ms, onset of inactivation without Ca extIna = 5 % extent of inactivation without Ca, extIna=1/K.A in the paper tauRec = 100 % ms, recovery from inactivation without Ca kIna = 1 / tauIna % ms^-1, rate of inactivation without Ca kRec = 1 / tauRec % ms^-1, rate of recovery without Ca extRec = extIna exp((V2 - V1)/K) % extent of recovery without Ca, extRec=1/K.R in the paper %-----Whole-cell parameters-------------------- Cm = 20 % pF, cell capacitance Rs = 5 % MOhm, series resistance CHD = 500 % pF^-1, density of channels Nch = Cm CHD %-----Ca parameters---------------------------- Ca.out = 10000 % microM, concentration of extracellular Ca Ca.in = 0.1 % microM, concentration of intracellular Ca ECa = 12.5 log( Ca.out/Ca.in ) % mV, equilibrium potential for Ca X = 0.08 % i.s.ch scaling factor for GHK to make i.s.ch=0.5pA at 0mV 10Ca.out Y = 0.008 % i.s.ch scaling factor for Ohmic to make i.s.ch=0.5pA at 0mV 10Ca.out %-----Ca binding to inactivation site-------- k.on = 0.1 % microM^-1 ms^-1, the ON rate for Ca delta = 0.5 % electrical position of the binding site Kd = 10000 % microM, dissociation constant of the site Gamma = 50 % extent of enhancement of inactivation by Ca % it is the same as extent of reduction of Kd in inactivated channels %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % RATE CONSTANTS % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% k.RP.AP := a1 exp( (V - V1) / (2 K) - b ( (V - V1) / (2 K) )^2 ) k.AP.RP := k.RP.AP exp( (V1 - V) / K ) k.RI.AI := a2 exp( (V - V2) / (2 K) - b ( (V - V2) / (2 K) )^2 ) k.AI.RI := k.RI.AI exp( (V2 - V) / K ) % To limit the rate increase, % the free energy difference between starting and transitional states % is assumed to be a second order function of voltage % (as done by Simon & Beam, 1985. J Gen Physiol, 85, 21-42.) k.AI.AP = kIna / (1 + extIna ) k.AP.AI = kIna - k.AI.AP k.RI.RP = kRec / (1 + extRec ) k.RP.RI = kRec - k.RI.RP Kd.eff := Kd exp(delta V/12.5) (1+exp(-V/25)) / (1+exp((V - 2 ECa)/25)) PoCa:= 1 / ( 1 + (Kd.eff/Ca.out) ) PiCa:= 1 / ( 1 + (Kd.eff/(Gamma Ca.out)) ) PinnCa = 1 / ( 1 + (Kd/(Gamma Ca.out)) ) PcCa = 1 / ( 1 + (Kd/Ca.out) ) k.RPCa.APCa := k.RP.AP k.APCa.RPCa := k.AP.RP k.APCa.AICa = k.AP.AI Gamma k.AICa.APCa = k.AI.AP k.RICa.AICa := k.RI.AI k.AICa.RICa := k.AI.RI k.RPCa.RICa = k.RP.RI Gamma k.RICa.RPCa = k.RI.RP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % KINETIC SCHEMA % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% AP := O ( 1 - PoCa ) APCa := O PoCa F.O :=(-k.AP.RP -k.AP.AI ) AP +k.RP.AP RP +k.AI.AP AI ... +(-k.APCa.RPCa -k.APCa.AICa ) APCa +k.RPCa.APCa RPCa +k.AICa.APCa AICa AI := In ( 1 - PiCa ) AICa := In PiCa F.In :=(-k.AI.AP -k.AI.RI ) AI +k.AP.AI AP +k.RI.AI RI ... +(-k.AICa.APCa -k.AICa.RICa ) AICa +k.APCa.AICa APCa +k.RICa.AICa RICa RI := Inn (1 - PinnCa) RICa := Inn PinnCa F.Inn :=(-k.RI.AI -k.RI.RP ) RI +k.RP.RI RP +k.AI.RI AI ... +(-k.RICa.AICa -k.RICa.RPCa ) RICa +k.AICa.RICa AICa +k.RPCa.RICa RPCa C := 1 - AP - APCa - AI - AICa - RI - RICa RP := C / (1 + PcCa) RPCa := C PcCa / (1 + PcCa) dO/dt = F.O dIn/dt = F.In dInn/dt = F.Inn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % EFFECT OF CURRENT ON VOLTAGE % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dV/dt = (Vf - V) / (0.001 * Cm * Rs) - I.total / Cm % t in ms, I in pA, V in mV, % Cm in pF, Rs in MOhm V(0) = -100 %pseudo-GHK: %i.ghk := X 12.5 (Ca.in - Ca.out) / (Ca.out + Kd) (V == 0) + ... % X (V/(1-exp(-V/12.5))) (Ca.in - Ca.out exp(-V/12.5)) / (Ca.out + Kd) % %I.ionic := Nch O i.ghk %%% %pseudo-Ohmic: %i.ohm := Y (V-ECa) (Ca.out-Ca.in) / (Ca.out + Kd) % %I.ionic := Nch O i.s.ch %%% %Single site a la Woodhull: i.s.ch.P := ... 2 1.6 0.0001 ( k.on Ca.in exp((1-delta) V/25) - k.on Ca.out exp(-delta V/25) ) (1-PoCa) i.s.ch.I := ... 2 1.6 0.0001 ( k.on Ca.in exp((1-delta) V/25) - k.on Ca.out exp(-delta V/25) ) (1-PiCa) i.P := Nch AP i.s.ch.P i.I := Nch AI i.s.ch.I I.ionic := i.P + i.I %%% I.gating := Nch 25 1.6 0.0001 (F.O + F.In) / K I.total := I.gating + I.ionic %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % SOLVING % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mode = ODE verbose=0 % removes console output for speed, comment it out to compile run T C(0) = 1 for Pulse = 0 to 20 step 1 Vp = -100 + 10 Pulse if Pulse == 0 then Vf = - 100 T = 5000 % equilibration time, ms Export T "save.dat" else Import "save.dat" Vf := (-100 - Vp) * (t > 300) + Vp T = 320 plot mute I.total "I" Vp % plot mute i.P "IP" Vp %this could work only for the Woodhul formulation % plot mute i.I "II" Vp %this could work only for the Woodhul formulation plot mute V "V" Vp endif %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % THE END % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%