Model Mathematics

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

i_K = g_K n (V - V_K)

\frac{d}{d time} (n) = \frac{lambda_n (n_infinity - n)}{tau_n} n_infinity = \frac{1}{1 + ⅇ^{\frac{Vn - V}{Sn}}} tau_n = \frac{9.09}{1 + ⅇ^{\frac{V - Vn}{Sn}}}

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}{1 + ⅇ^{\frac{Vm_f - V}{Sm_f}}}

i_Ca_s = g_Ca_s m_s_infinity (1 - jm) (V - V_Ca)

m_s_infinity = \frac{1}{1 + ⅇ^{\frac{Vm_s - V}{Sm_s}}}

jm_infinity = 1 - (\frac{1}{1 + ⅇ^{\frac{V - Vj}{Sj}}}) tau_j = \frac{50000}{ⅇ^{\frac{V - Vj}{4}} + ⅇ^{\frac{Vj - V}{4}}} + 1500 \frac{d}{d time} (jm) = \frac{jm_infinity - jm}{tau_j}

i_Ca = i_Ca_f + i_Ca_s

i_K_Ca = \frac{g_K_Ca {Ca_i}^{5}}{{Ca_i}^{5} + {kdkca}^{5}} (V - V_K)

i_CRAC = g_CRAC r_infinity (V - V_CRAC)

r_infinity = \frac{1}{1 + ⅇ^{\frac{Ca_er - Ca_er_bar}{sloper}}}

i_leak = g_leak (V - V_CRAC)

J_er_p = \frac{verp {Ca_i}^{2}}{{Ca_i}^{2} + {kerp}^{2}} a_infinity = \frac{1}{1 + \frac{dact}{Ca_i}} b_infinity = \frac{IP3}{IP3 + dip3} h_infinity = \frac{1}{1 + \frac{Ca_i}{dinh}} O = {a_infinity}^{3} {b_infinity}^{3} {h_infinity}^{3} 1

J_er_tot = J_er_leak + J_er_IP3 - J_er_p J_er_leak = perl (Ca_er - Ca_i) J_er_IP3 = O (Ca_er - Ca_i) \frac{d}{d time} (Ca_er) = \frac{- J_er_tot}{lambda_er sigma_er} \frac{d}{d time} (Ca_i) = \frac{J_er_tot}{lambda_er} + J_mem_tot

Jmp = \frac{vmp {Ca_i}^{2}}{{Ca_i}^{2} + {kmp}^{2}} J_mem_tot = (- f) (gamma i_Ca + Jmp)