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L-type calcium channels, T-type calcium channels, and background calcium currents.

LCC

JCaSL=(2INaCa−ICaL−ICaT−ICab)ACAPCm2FVsubSLICaL=ICascale⋅GCaL,k⋅id⋅if⋅ifca⋅GHK(GCaL,2,Vm,casl,0.341cao)⋅GCaL,k=GCaL(1+0.1CaMKAct)diddt=d∞−idτddifdt=f∞−ifτfdifcadt=(fca∞−ifca)(1−(fca∞>ifca)(Vm>−60mV))τfcaICascale=ICascale,0(1+0.561−fracLCCbpISOfracLCCbp0)d∞=(1+exp⁡(−(V+11.1)/7.2))−1τd=(αdβd+γd)αd=1.4(1+exp⁡(−(Vm+35)/13))−1+0.25βd=1.4(1+exp⁡((Vm+5)/5))−1γd=(1+exp⁡(−(Vm−50)/20))−1f∞=(1+exp⁡((Vm+23.3)/5.4))−1τf=120+1651+exp⁡(−(Vm−25)/10)+1125exp⁡(−(Vm+27)2/240)fca∞=(αfca+βfca+γfca+0.23)/1.46αfca=0.487580.48758+casl8βfca=0.11+exp⁡((casl−0.5)/0.1)−1γfca=0.21+exp⁡((casl−0.75)/0.8)−1\begin{align} J_{CaSL} &= (2 I_{NaCa} - I_{CaL} - I_{CaT} - I_{Cab}) \frac{A_{CAP} C_m}{2 F V_{subSL}} \\ \mathrm{I_{CaL}} &= \mathrm{ICa_{scale}} \cdot G_{CaL,k} \cdot i_d \cdot i_f \cdot i_fca \cdot GHK(G_{CaL}, 2, V_m, \mathrm{ca_{sl}}, 0.341 \mathrm{ca_o}) \\ \cdot G_{CaL,k} &= G_{CaL} (1 + 0.1CaMK_{Act}) \\ \frac{d i_d }{dt} &= \frac{d_∞ - i_d}{τ_d} \\ \frac{d i_f }{dt} &= \frac{f_∞ - i_f}{τ_f} \\ \frac{d i_{fca} }{dt} &= \frac{(fca_∞ - i_{fca}) \left( 1 - \left( fca_∞ > i_{fca} \right) \left( V_m > -60 \text{mV} \right) \right)}{τ_{fca}} \\ \mathrm{ICa_{scale}} &= \mathrm{ICa_{scale, 0}} \left( 1 + \frac{0.56}{1 - \frac{\mathrm{fracLCCbpISO}}{\mathrm{fracLCCbp0}}} \right) \\ d_∞ &= (1 + \exp(-(V + 11.1) / 7.2))^{-1} \\ τ_d &= (\alpha_d \beta_d + \gamma_d) \\ \alpha_d &= 1.4 (1 + \exp(-(V_m + 35) / 13))^{-1} + 0.25 \\ \beta_d &= 1.4 (1 + \exp((V_m + 5) / 5))^{-1} \\ \gamma_d &= (1 + \exp(-(V_m - 50) / 20))^{-1} \\ f_∞ &= (1 + \exp((V_m + 23.3) / 5.4))^{-1} \\ τ_f &= 120 + \frac{165}{1 + \exp(-(V_m - 25) / 10)} + 1125 \exp( -(V_m + 27)^{2} / 240) \\ fca_∞ &= (\alpha_{fca} + \beta_{fca} + \gamma_{fca} + 0.23) / 1.46 \\ \alpha_{fca} &= \frac{0.4875^8}{0.4875 ^8 + \mathrm{ca_{sl}}^8} \\ \beta_{fca} &= 0.1 {1 + \exp((\mathrm{ca_{sl}} - 0.5) / 0.1)}^{-1} \\ \gamma_{fca} &= 0.2 {1 + \exp((\mathrm{ca_{sl}} - 0.75) / 0.8)}^{-1} \\ \end{align}
(1)

TCC

ICaT=gCaT⋅ib⋅ig(Vm+106.5−ECa)ECa=0.5VTln⁡caocaslddtib=b∞−ibτbddtig=g∞−igτgb∞=(1+exp⁡(−(Vm+37.49098)/5.40634))−1τb=0.6+5.4(1+exp⁡(0.03(Vm+100)))−1g∞=(1+exp⁡((Vm+66)/6))−1τg=1+40(1+exp⁡(0.08(Vm+65)))−1\begin{align} \mathrm{I_{CaT}} &= \mathrm{gCaT} \cdot i_b \cdot i_g ( V_m + 106.5 - \mathrm{E_Ca}) \\ E_{Ca} &= 0.5V_T \ln \frac{ca_o}{ca_{sl}} \\ \frac{d}{dt} i_b &= \frac{b_∞ - i_b}{τ_b} \\ \frac{d}{dt} i_g &= \frac{g_∞ - i_g}{τ_g} \\ b_∞ &= (1 + \exp(-(V_m + 37.49098) / 5.40634))^{-1} \\ τ_b &= 0.6 + 5.4 (1 + \exp(0.03 (V_m + 100)))^{-1} \\ g_∞ &= (1 + \exp((V_m + 66) / 6))^{-1} \\ τ_g &= 1 + 40 (1 + \exp(0.08 (V_m + 65)))^{-1} \\ \end{align}
(2)

Background

ICab=gCab(Vm−ECa)\begin{align} \mathrm{I_{Cab}} &= \mathrm{gCab} (V_m - \mathrm{E_Ca}) \\ \end{align}
(3)

NCX $$

INaCa=kNaCa⋅ICascalenai3caoexp⁡(gNaCaVm/VT)−nao3caslfNaCaexp⁡((gNaCa−1)VmF/RT)1+(nai3cao+nao3caslfNaCa)dNaCa\begin{align} \mathrm{I_{NaCa}} &= \mathrm{kNaCa} \cdot \mathrm{ICa_{scale}} \frac{\mathrm{na_i}^{3} \mathrm{ca_o} \exp( \mathrm{gNaCa} V_m /V_T ) - \mathrm{na_o}^{3} \mathrm{ca_{sl}} \mathrm{fNaCa} \exp (( \mathrm{gNaCa} - 1 ) V_m F /RT )} {1 + \left(\mathrm{na_i}^3 \mathrm{ca_o} + \mathrm{na_o}^{3} \mathrm{ca_{sl}} \mathrm{fNaCa} \right) \mathrm{dNaCa}} \\ \end{align}
(4)

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NRVM CaMKII model
Sarcolemmal Potassium channels
NRVM CaMKII model
Sarcolemmal Na-K pump