Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_K + i_K_Ca + i_K_ATP + i_Ca_f + i_Ca_s + i_CRAC)}{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{Vn - V}{Sn}}} tau_n = \frac{4.86}{1.0 + ⅇ^{\frac{V + 15.0}{6.0}}}

i_K_ATP = g_K_ATP (V - V_K)

i_Ca_f = g_Ca_f m_f_infinity (V - V_Ca)

m_f_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_f - V}{Sm_f}}}

i_Ca_s = g_Ca_s j m_s_infinity (V - V_Ca)

m_s_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{Vm_s - V}{Sm_s}}}

\frac{d}{d time} (j) = \frac{j_infinity - j}{tau_j} j_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{Vj - V}{Sj}}} tau_j = \frac{50000.0}{ⅇ^{\frac{V + 53.0}{4.0}} + ⅇ^{\frac{- (V + 53.0)}{4.0}} + 1500.0}

i_K_Ca = g_K_Ca \frac{{Ca_i}^{5.0}}{{Ca_i}^{5.0} + {0.55}^{5.0}} (V - V_K)

i_CRAC = g_CRAC r_infinity Ca_er (V - V_CRAC)

r_infinity = \frac{1.0}{1.0 + ⅇ^{Ca_er - 3.0}}

\frac{d}{d time} (Ca_i) = \frac{1.0}{lamda} ((\frac{P_leak}{P_ip3} + O_infinity) (Ca_er - Ca_i) - (\frac{J_er}{P_ip3})) + \frac{J_mem}{Vi_eff} \frac{d}{d time} (Ca_er) = (- (\frac{1.0}{lamda sigma})) ((\frac{P_leak}{P_ip3} + O_infinity) (Ca_er - Ca_i) - (\frac{J_er}{P_ip3})) Vi_eff = \frac{Vi}{fi} Ver_eff = \frac{Ver}{fer} lamda = \frac{Vi_eff}{P_ip3} sigma = \frac{Ver_eff}{Vi_eff} O_infinity = a_infinity b_infinity h_infinity a_infinity = \frac{Ca_i}{Ca_i + 0.1} b_infinity = \frac{IP3}{IP3 + 0.2} h_infinity = \frac{0.4}{Ca_i + 0.4} J_er_p = P_ip3 Ver_p \frac{{Ca_i}^{2.0}}{{Ca_i}^{2.0} + {0.09}^{2.0}}

J_mem = (- alpha) (i_Ca_s + i_Ca_f) - (K_Ca Ca_i)

J_er = (P_leak + P_ip3 O_infinity) (Ca_er - Ca_i) - J_er_p