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Article: Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization.

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Masoli S; Solinas S; D'Angelo E
Front Cell Neurosci, 2015


Ionic mechanisms in the PC model: II.

Conductance state variables n α (s-1) β (s-1)
Nav1.6 Open
Blocked
Closed
Inactivated
Kv1.1 Activation 4 Alphan=0.12889 * exp-(v+45) -33.90877 Betan=0.12889 *exp-(v+45)12.42101
Ninf=0.12889 *exp-(v+45) -33.908770.12889∗exp-(v+45) -33.90877 + 0.12889 *exp-(v+45)12.42101 Taun=1(qt) *(0.12889) *exp-(v+45) -33.90877+ 0.12889 *exp-(v+45)12.42101
Kv1.5 Activation 3 Malp=q10 *0.65exp-(v + 10)8.5+exp-(v - 30)59 Mbet=q10 *0.652.5 +expv + 8217
Inactivation 1 Nalp=0.001 *q102.4 +10.9 *exp-v + 9078 Nbet=q10 *0.001 *expv - 16816
Nce=1 *0.25+11.35 +expv + 714
Inactivation 1 Mce=11+exp-v + 30.39.6 Uce=1 *0.1+11.1 +expv + 714
Mtau=1a + b3 *Tauact Ntau=1a + b3 *Tauinactf
Uau=6800 *Tauinacts 
Kv3.3 Activation 4 Alpha=0.22 *exp-(v+16)-26.5 Beta=0.22 *exp-(v+16)26.5
Taun=10.22 *exp-(v+16)-26.5+0.22 *exp-(v+16)26.5
Kv3.4 Activation 3 Minf=11+exp-v+2415.4 Hinf=0. 31 + 0.691+expv- (-5.802)11.2
Inactivation 1 Mtau=1000  * mtau_func(v)qt        If Vm<-35 Htau=1000  * htau_func(v)qt           If Vm>0
Mtau=(3.4225e-5+0.00498exp-v-28.29) *3                              elseMtau=0.00012851+1expv+ 100.712.9+expv+ -56.0-23.1 Htau=0.0012+0.0023 *exp-0.141∗Vm                    elseHtau=1.2202e-05+ 0.012 ∗ exp-(Vm-(-56.3))49.62
Kv4.3 Activation 2 Alp_a=Q10∗0.8147∗sigm(v-(-9.17203,-23.32708)) Bet_a=Q10∗ 0.1655expv-( -18.27914)19.47175
Inactivation 1 Alp_b=Q10∗0.0368∗sigm(v-(-111.33209,12.8433))Tau_a=1q10∗0.8147∗sigm(v- (-9.17203, -23.32708))+ Q10∗ 0.1655expv-(-18.27914)19.47175 Bet_b=Q10∗0.0345∗sigm(v-(-49.9537,-8.90123))Tau_b=1Q10∗ 0.0368 ∗sigm(v- (-111.33209, 12.8433))+ Q10∗ 0.0345∗sigm(v- (-49.9537, -8.90123)) 
Kir2.x Activation 1 Alp_d=Q10∗ 0.13289∗expv- (-83.94)-24.3902             Bet_d=Q10∗0.16994∗expv- (-83.94 )35.714Tau_d=1Q10∗ 0.13289∗expv- (-83.94)-24.3902+ Q10∗ 0.16994∗expv- (-83.94 )35.714
Kca1.1 Open/closed
Kca2.2 Open/closed
Kca3.1                            Cai<0.01Yconcdep=500(1ms)∗0.015-cai∗(1mM)exp0.015-cai∗1(1mM)0.0013 -1          Yconcdep=500(1ms)∗0.005exp0.0050.0013 -1                                   TauY=1Yalpha + Ybeta
Cav2.1 Activation 3                                  If x>=-40Taumfkt=0.2702+1.1622∗exp-(v+26.798)∗(v+26.798)164.19                                   Taumfkt=0.6923∗expv1089.372
Cav3.1 Activation 2 Minf= 1/(1+exp((v+52)/-5)) Hinf=1/(1+exp((v+72)/7))
Inactivation 1 τm=1+1exp(v+40)9+exp((v+102)/-18) τh=(15+1/exp((v+32)/7))
Cav3.2 Activation 2 M_inf=1.01 + exp-(v+shift+54.8)7.4 H_inf=1.01 + expv+shift+85.57.18
Inactivation 1 Tau_m=1.9 + 1.0expv+shift+37.011.9+ exp-(v+shift+131.6)2151210 Tau_h=13.7 + 1942 + expv+shift+1649.21 + expv+shift+89.33.731210
Cav3.3 Activation 2 N_inf=1(1+exp)-(v-vhalfn)kn If v>-60 
Inactivation 1 L_inf =11+exp-(v-vhalfl)kl Tau_n=7.2+0.02∗exp-v14.7qtTau_l=79.5+2.0∗exp-v9.3qtTau_n=0.875∗expv+12041qt                        Tau_l=260qt
HCN1 Activation 1 h = 1(0.0018)∗ ( expv-( -58,7) / -22)+ exp v-( -58,7)7.14 /qt

The table reports the equations used to calculate membrane conductances used in the model. In most cases, the rate constants ax, bx, ay, and by were used to calculate x8, y8, τx and τy according to a Hodgkin-Huxley scheme (Hodgkin and Huxley, 1952). For each ionic channel i, the conductance gi is gi=Gmaxi*xizi*yi where, Gmaxi is the maximum ionic conductance, xi and yi are state variables (probabilities ranging from 0 to 1) for a gating particle, and zi is the number of such gating particles. x and y (the suffix i omitted) were related to the first order rate constants a and ß by the equations x∞=αxalphax+βx,y∞=αyαy+βy;τx=1(αx+βx),τy=1(αx+βx) where a and b are functions of voltage.

The state variable kinetics were: dxdt= (x∞-x)τx,dydt=(y∞-y)τy

In some cases, the equations for x∞, y∞, τx or τy are reported directly. Exceptions to this general scheme were Markovian channel models for Nav1.6 and KCa1.1. Eventually, the probability of channel opening was transformed into ionic conductances and used to calculate the model currents. More details on the construction of this table were reported previously (D'Angelo et al., 2001; Solinas et al., 2007a; Subramaniyam et al., 2014).
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