Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_Ca + i_K + i_K_Ca + i_K_ATP)}{Cm}

i_K = g_K n (V - V_K)

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{- (16.0 + V)}{5.0}}}

i_Ca = g_Ca m_infinity (V - V_Ca)

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{- (20.0 + V)}{12.0}}}

i_K_Ca = g_K_Ca (V - V_K) g_K_Ca = g_K_Ca_\frac{{Ca}^{5.0}}{{kD}^{5.0} + {Ca}^{5.0}}

i_K_ATP = g_K_ATP (V - V_K) g_K_ATP = g_K_ATP_O_infinity_ADP_ATP MgADP = 0.165 ADP ADP3 = 0.135 ADP ATP4 = 0.05 ATP O_infinity_ADP_ATP = \frac{0.08 (1.0 + \frac{2.0 MgADP}{17.0}) + 0.89 {(\frac{MgADP}{17.0})}^{2.0}}{{(1.0 + \frac{MgADP}{17.0})}^{2.0} (1.0 + \frac{ADP3}{26.0} + \frac{ATP4}{1.0})}

\frac{d}{d time} (Ca) = fcyt (Jmem + Jer)

Jmem = - (alpha i_Ca + kPMCA Ca)

Jer = Jleak - J_SERCA

Jleak = pleak (Ca_er - Ca)

J_SERCA = kSERCA Ca

\frac{d}{d time} (Ca_er) = (- fer) Vcyt_Ver Jer

\frac{d}{d time} (G6P) = lamda (R_GK - R_PFK) \frac{d}{d time} (FBP) = lamda (R_PFK - (0.5 R_GPDH)) F6P = 0.3 G6P R_GPDH = 0.2 {(\frac{FBP}{1.0})}^{0.5} R_PFK = Vmax \frac{W11100 + lamda1 (sum_state fraction_state - W11100)}{sum_state fraction_state} fraction_state = \frac{1.0}{{f13}^{alpha gamma} {f23}^{beta gamma} {f41}^{delta alpha} {f42}^{delta beta} {f43}^{delta gamma} {f53}^{epsilon gamma}} \frac{{AMP}^{alpha}}{{K1}^{alpha}} \frac{{FBP}^{beta}}{{K2}^{beta}} \frac{{F6P}^{2.0 gamma}}{{K3}^{gamma}} \frac{{ATP}^{delta}}{{K4}^{delta}} \frac{{ATP}^{epsilon}}{{K5}^{epsilon}} W00000

\frac{d}{d time} (ADP) = \frac{ATP - (ADP ⅇ^{(r + gamma) (1.0 - (\frac{Ca}{r1}))})}{tau_a} AMP = \frac{{ADP}^{2.0}}{ATP} ATP = A_tot - (ADP + AMP) gamma = \frac{v_gamma R_GPDH}{k_gamma + R_GPDH}