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IK1:

IK1=GK1⋅koko+210μM(Vm−6.1373−EK)0.1653+exp⁡(0.0319(Vm−6.1373−EK))EK=VTln⁡koki\begin{align} \mathrm{I_{K1}} &= \mathrm{G_{K1}} \cdot \frac{k_o}{k_o + 210 \mathrm{\mu M}} \frac{ ( V_m - 6.1373 - E_K )}{0.1653 + \exp(0.0319 (V_m - 6.1373 - E_K))} \\ E_K &= V_T \ln\frac{k_o}{k_i} \\ \end{align}
(1)

Ito:

Ito=Gt⋅ir((1−fis)is,slow+fisis)(Vm−EK)ddtir=r∞−irτrddtis=s∞−isτsddtis,slow=slow∞−is,slowτs,slows∞=(1+exp⁡((Vm+31.97156)/4.64291))−1r∞=(1+exp⁡(−(Vm−3.55716)/14.61299))−1slow∞=s∞τr=1000ms45.16exp⁡(0.03577(Vm+50))+98.9exp⁡(−0.1(Vm+38))τs=8.1ms+350ms⋅exp⁡(−1225(Vm+70)2)τs,slow=72.4ms+3700ms⋅exp⁡(−1900(Vm+70)2)\begin{align} \mathrm{I_{to}} &= G_t \cdot i_r ((1 - f_{is} ) i_{s,slow} + f_{is} i_s )(V_m - E_K) \\ \frac{d}{dt} i_r &= \frac{r_∞ - i_r }{τ_r} \\ \frac{d}{dt} i_s &= \frac{s_∞ - i_s }{τ_s} \\ \frac{d}{dt} i_{s,slow} &= \frac{slow_∞ - i_{s,slow} }{τ_{s,slow}} \\ s_∞ &= (1 + \exp((V_m + 31.97156) / 4.64291))^{-1} \\ r_∞ &= (1 + \exp(-(V_m - 3.55716) / 14.61299))^{-1 } \\ slow_∞ &= s_∞ \\ τ_r &= \frac{1000 \text{ms}}{45.16 \exp(0.03577( V_m + 50)) + 98.9 \exp( -0.1 ( V_m + 38))} \\ τ_s &= 8.1\text{ms} + 350\text{ms} \cdot \exp( - \frac{1}{225}(V_m + 70)^{2}) \\ τ_{s,slow} &= 72.4\text{ms} + 3700\text{ms} \cdot \exp( - \frac{1}{900}( V_m + 70 )^{2}) \\ \end{align}
(2)

IKs:

IKs=2GKs⋅inKs2(0.68804+0.71283IKURPKAp)(Vm−EK)ddtinKs=nks∞−inKsτnKsnks∞=αnksαnks+βnksαnks=0.00000481333/0.128⋅exprel(−0.128(Vm+26.5))βnks=0.0000953333⋅exp⁡(−0.038(Vm+26.5))\begin{align} \mathrm{I_{Ks}} &= 2 G_{Ks} \cdot i_{nKs}^{2}(0.68804 + 0.71283 \mathrm{IKUR_{PKAp}}) (V_m - E_K) \\ \frac{d}{dt} i_{nKs} &= \frac{nks_∞ - i_{nKs}}{τ_{nKs}} \\ nks_∞ &= \frac{\alpha_{nks}}{\alpha_{nks} + \beta_{nks}} \\ \alpha_{nks} &= 0.00000481333 / 0.128 \cdot exprel(-0.128 (V_m + 26.5)) \\ \beta_{nks} &= 0.0000953333 \cdot \exp(-0.038 (V_m + 26.5)) \\ \end{align}
(3)

IKr:

IKr=GKr⋅iOK(Vm−EKr)EKr=VTln⁡(0.98ko+0.02nao0.98ki+0.02ai)diCK1dt=kb,IKriCK2−kf,IKriCK1+k01iCK0−k10iCK1diCK2dt=−kb,IKriCK2+kf,IKriCK1−k2oiCK2+ko2iOKdiOKdt=kioiIK+k2oiCK2−ko2iOK−koiiOKdiIKdt=−kioiIK+koiiOKk01=0.022348ms−1exp⁡(0.01176Vm)k10=0.047002ms−1exp⁡(−0.0631Vm)k2o=0.013733ms−1exp⁡(0.038198Vm)ko2=6.89⋅10−5ms−1exp⁡(−0.04178Vm)koi=0.090821ms−1exp⁡(0.023391Vm)kio=0.006497ms−1exp⁡(−0.03268Vm)1=iCK0+iCK1+iCK2+iOK+iIK\begin{align} \mathrm{I_{Kr}} &= G_{Kr} \cdot i_{OK} (V_m - E_{Kr}) \\ E_{Kr} &= V_T \ln\left( \frac{0.98 k_o + 0.02na_o}{0.98 k_i + 0.02a_i} \right) \\ \frac{d i_{CK1} }{dt} &= k_{b, IKr} i_{CK2} - k_{f, IKr} i_{CK1} + k_{01} i_{CK0} - k_{10} i_{CK1} \\ \frac{d i_{CK2} }{dt} &= - k_{b, IKr} i_{CK2} + k_{f, IKr} i_{CK1} - k_{2o} i_{CK2} + k_{o2} i_{OK} \\ \frac{d i_{OK} }{dt} &= k_{io} i_{IK} + k_{2o} i_{CK2} - k_{o2} i_{OK} - k_{oi} i_{OK} \\ \frac{d i_{IK} }{dt} &= -k_{io} i_{IK} + k_{oi} i_{OK} \\ k_{01} &= 0.022348\mathrm{ms}^{-1} \exp(0.01176 V_m ) \\ k_{10} &= 0.047002\mathrm{ms}^{-1} \exp(-0.0631 V_m ) \\ k_{2o} &= 0.013733\mathrm{ms}^{-1} \exp(0.038198 V_m) \\ k_{o2} &= 6.89 \cdot 10^{-5}\mathrm{ms}^{-1} \exp(-0.04178 V_m) \\ k_{oi} &= 0.090821\mathrm{ms}^{-1} \exp(0.023391 V_m) \\ k_{io} &= 0.006497\mathrm{ms}^{-1} \exp(-0.03268 V_m) \\ 1 &= i_{CK0} + i_{CK1} + i_{CK2} + i_{OK} + i_{IK} \\ \end{align}
(4)

If:

IfNa=fNa⋅Gf⋅iy⋅(Vm−ENa)IfK=(1−fNa)⋅Gf⋅iy⋅(Vm−EK)If=IfK+IfNaddtiy=y∞−iyτyy∞=expit(−0.15798(Vm+78.65))τy=1000ms0.56236exp⁡(−0.070472(Vm+75))+0.11885exp⁡(0.035249(Vm+75))\begin{align} \mathrm{I_{fNa}} &= f_{Na} \cdot G_f \cdot i_y \cdot ( V_m - E_{Na}) \\ \mathrm{I_{fK}} &= (1 - f_{Na}) \cdot G_f \cdot i_y \cdot ( V_m - E_K ) \\ \mathrm{I_{f}} &= \mathrm{I_{fK}} + \mathrm{I_{fNa}} \\ \frac{d}{dt} i_y &= \frac{y_∞ - i_y}{τ_y} \\ y_∞ &= expit(-0.15798 (V_m + 78.65)) \\ τ_y &= \frac{1000 \text{ms}}{0.56236 \exp(-0.070472 (V_m + 75)) + 0.11885 \exp(0.035249 ( V_m + 75))} \\ \end{align}
(5)
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