Model Mathematics

\frac{d}{d time} (Vm) = 1.0

\frac{d}{d time} (cMgADP) = 0.0

\frac{d}{d time} (cNa_i) = 0.0

cPi = \frac{cPi_sum}{1.0 + \frac{cK_i}{eq_KPi} + \frac{cH}{eq_HPi} + \frac{cNa_i}{eq_NaPi}}

dG_Na = gas_const body_temp \ln (\frac{cNa_e}{cNa_i}) - (faraday_const 0.001 Vm)

dG_K = gas_const body_temp \ln (\frac{cK_i}{cK_e}) + faraday_const 0.001 Vm

dG_pump = 2.0 dG_K + 3.0 dG_Na

dG_ATP = -29600. - (gas_const body_temp \ln (\frac{cMgATP}{0.001 cMgADP cPi}))

net_free_energy = dG_ATP + dG_pump

dimless_Na_i = \frac{cNa_i}{eq_Na_base_i ⅇ^{\frac{partition_factor faraday_const 0.001 Vm}{3.0 gas_const body_temp}}}

dimless_Na_e = \frac{cNa_e}{eq_Na_base_e ⅇ^{\frac{(1. + partition_factor) faraday_const 0.001 Vm}{3.0 gas_const body_temp}}}

dimless_K_i = \frac{cK_i}{eq_K_i}

dimless_K_e = \frac{cK_e}{eq_K_e}

dimless_MgATP = \frac{cMgATP}{eq_MgATP}

alpha1 = \frac{k1 {dimless_Na_i}^{3}}{{(1.0 + dimless_Na_i)}^{3} + {(1.0 + dimless_K_i)}^{2} - 1.0}

alpha2 = k2

alpha3 = \frac{k3 {dimless_K_e}^{2}}{{(1.0 + dimless_Na_e)}^{3} + {(1.0 + dimless_K_e)}^{2} - 1.0}

alpha4 = \frac{k4 dimless_MgATP}{1.0 + dimless_MgATP}

minus_alpha1 = minus_k1 cMgADP

minus_alpha2 = \frac{minus_k2 {dimless_Na_e}^{3}}{{(1.0 + dimless_Na_e)}^{3} + {(1.0 + dimless_K_e)}^{2} - 1.0}

minus_alpha3 = \frac{minus_k3 cPi cH}{1.0 + dimless_MgATP}

minus_alpha4 = \frac{minus_k4 {dimless_K_i}^{2}}{{(1.0 + dimless_Na_i)}^{3} + {(1.0 + dimless_K_i)}^{2} - 1.0}

diagram_sum = minus_alpha3 minus_alpha2 minus_alpha1 + alpha4 minus_alpha2 minus_alpha1 + alpha4 alpha2 alpha3 + alpha4 minus_alpha1 alpha3 + minus_alpha3 minus_alpha2 alpha1 + alpha4 minus_alpha2 alpha1 + alpha4 alpha1 alpha3 + minus_alpha3 alpha1 alpha2 + alpha4 alpha1 alpha2 + alpha1 alpha2 alpha3 + minus_alpha4 minus_alpha3 minus_alpha1 + minus_alpha4 minus_alpha3 alpha2 + minus_alpha4 minus_alpha3 minus_alpha2 + minus_alpha4 minus_alpha1 minus_alpha2 + minus_alpha4 alpha2 alpha3 + minus_alpha4 minus_alpha1 alpha3

v_cyc = \frac{alpha1 alpha2 alpha3 alpha4 - (minus_alpha1 minus_alpha2 minus_alpha3 minus_alpha4)}{diagram_sum}