Model Mathematics

vol_cyt = fr_cyt vol_pmu V_tau = \frac{R T}{F}

VD = \frac{V}{V_tau} A_pmu = \frac{SVR_pmu vol_pmu 1 e -3 1 e -3 1 e -3}{1} V_Ca = 0.5 \ln (\frac{Ca_o}{Ca_i}) V_Na = \ln (\frac{Na_o}{Na_i}) V_K = \ln (\frac{K_o}{K_i}) \frac{d}{d t} (V) = \frac{F vol_cyt}{C_sp A_pmu} (J_Na + J_K + 2 J_Ca)

\frac{d}{d t} (Ca_i) = J_Ca \frac{d}{d t} (Na_i) = J_Na \frac{d}{d t} (K_i) = J_K

J_Ca = J_ca - (J_calb + 4 J_cam) J_ca = \frac{- 1}{2 F vol_cyt} (I_CaL + 2 I_pmca - (2 I_xm))

J_Na = \frac{- 1}{F vol_cyt} (3 I_nk + 3 I_xm + I_Na + I_Nalk + I_NaHCN)

I_K = I_Ksk + I_Kdr + I_Kir J_K = \frac{- 1}{F vol_cyt} (I_K - (2 I_nk))

J_calb = kcal_1 Calb Ca_i - (kcal_2 CaCalb) J_cam = alpha_cam Cam - (beta_cam CaCam) kcam_cb = 12000 {Ca_i}^{2} kcam_nb = 3.7 e 6 {Ca_i}^{2} alpha_cam = kcam_cb kcam_nb (\frac{1}{kcam_cb + kcam_nd} + \frac{1}{kcam_cd + kcam_nd}) beta_cam = kcam_cd kcam_nd (\frac{1}{kcam_cb + kcam_nd} + \frac{1}{kcam_cd + kcam_nd}) CaCalb = Calbtot - Calb CaCam = Camtot - Cam \frac{d}{d t} (Calb) = - J_calb \frac{d}{d t} (Cam) = - J_cam

I_CaL = \frac{g_cal m_cal h_cal \sqrt{Ca_i Ca_o} \sinh (VD - V_Ca)}{\frac{\sinh VD}{VD}} \frac{d}{d t} (m_cal) = \frac{\frac{1}{1 + ⅇ^{\frac{- (V + 15)}{7}}} - m_cal}{7.68 ⅇ^{- ({(\frac{V + 65}{17.33})}^{2})} + 0.7231} h_cal = \frac{0.00045}{0.00045 + Ca_i}

O_na = {m_na}^{3} h_na \frac{d}{d t} (m_na) = A_mna ⅇ^{za_mna VD} (1 - m_na) - (B_mna ⅇ^{(- zb_mna) VD} m_na) \frac{d}{d t} (h_na) = A_hna ⅇ^{za_hna VD} (1 - h_na) - (B_hna ⅇ^{(- zb_hna) VD} h_na) I_Na = \frac{g_na O_na \sqrt{Na_i Na_o} \sinh (0.5 (VD - V_Na))}{\frac{\sinh (0.5 VD)}{0.5 VD}}

I_Nalk = \frac{g_nalk \sqrt{Na_i Na_o} \sinh (0.5 (VD - V_Na))}{\frac{\sinh (0.5 VD)}{0.5 VD}}

\frac{d}{d t} (O_hcn) = kf_hcn (1 - O_hcn) - (kr_hcn O_hcn) kf_hcn = kf_free P_c + kf_bnd (1 - P_c) kr_hcn = kr_free P_o + kr_bnd (1 - P_o) kf_free = \frac{0.006}{1 + ⅇ^{\frac{V + 87.7}{6.45}}} kr_free = \frac{0.08}{1 + ⅇ^{\frac{- (V + 51.7)}{7}}} kf_bnd = \frac{0.0268}{1 + ⅇ^{\frac{V + 94.2}{13.3}}} kr_bnd = \frac{0.08}{1 + ⅇ^{\frac{- (V + 35.5)}{7}}} P_c = \frac{1}{1 + \frac{cAMP}{1.163 e -3}} P_o = \frac{1}{1 + \frac{cAMP}{1.45 e -5}} I_NaHCN = \frac{g_nahcn O_hcn \sqrt{Na_i Na_o} \sinh (0.5 (VD - V_Na))}{\frac{\sinh (0.5 VD)}{0.5 VD}}

O_sk = \frac{{Ca_i}^{4.2}}{{0.35 e -3}^{4.2} + {Ca_i}^{4.2}} I_Ksk = \frac{g_ksk O_sk \sqrt{K_i K_o} \sinh (0.5 (VD - V_K))}{\frac{\sinh (0.5 VD)}{0.5 VD}}

I_Kdr = g_kdr O_kdr (V - (V_K V_tau)) O_kdr = {m_kdr}^{3} \frac{d}{d t} (m_kdr) = \frac{\frac{1}{1 + ⅇ^{\frac{- (V + 25)}{12}}} - m_kdr}{\frac{18}{1 + ⅇ^{\frac{V + 39}{8}}} + 1}

I_Kir = g_kir O_kir (V - (V_K V_tau)) O_kir = \frac{1}{1 + ⅇ^{\frac{V + 85}{12.1}}}

I_pmca = K_pmca (k_1pc P_E1Spc y_pc - (k_2pc P_E2Spc (1 - y_pc))) 1 K_pmca = k_pmca (\frac{10.56 CaCam}{CaCam + 0.00005} + 1.2) \frac{d}{d t} (y_pc) = beta_pc (1 - y_pc) - (alpha_pc y_pc) k_1pc = \frac{1}{1 + \frac{0.1}{atp}} P_E1Spc = \frac{1}{1 + \frac{K_pci}{Ca_i}} P_E1pc = 1 - P_E1Spc P_E2Spc = \frac{1}{1 + \frac{K_pco}{Ca_o}} P_E2pc = 1 - P_E2Spc beta_pc = k_2pc P_E2Spc + k_4pc P_E2pc alpha_pc = k_1pc P_E1Spc + k_3pc P_E1pc K_pci = (\frac{173.6}{1 + \frac{CaCam}{0.00005}} + 6.4) 1 e -5

I_xm = \frac{k_xm ({Na_i}^{3} Ca_o ⅇ^{del VD} - ({Na_o}^{3} Ca_i ⅇ^{(del - 1) VD}))}{Dr} Dr = (1 + 0.001 ({Na_i}^{3} Ca_o + {Na_o}^{3} Ca_i)) (1 + \frac{Ca_i}{0.0069})

I_nk = k_nk (k_1nk P_E1Snk y_nk - (k_2nk P_E2Snk (1 - y_nk))) 1 k_1nk = \frac{0.37}{1 + \frac{0.094}{atp}} Na_eff = Na_o ⅇ^{(- 0.82) VD} \frac{d}{d t} (y_nk) = beta_nk (1 - y_nk) - (alpha_nk y_nk) beta_nk = k_2nk P_E2Snk + k_4nk P_E2Dnk alpha_nk = k_1nk P_E1Snk + k_3nk P_E1Dnk P_E1Snk = \frac{1}{1 + \frac{K_nknai}{Na_i} (1 + \frac{K_i}{K_nkki})} P_E1Dnk = \frac{1}{1 + \frac{K_nkki}{K_i} (1 + \frac{Na_i}{K_nknai})} P_E2Snk = \frac{1}{1 + \frac{K_nknao}{Na_eff} (1 + \frac{K_o}{K_nkko})} P_E2Dnk = \frac{1}{1 + \frac{K_nkko}{K_o} (1 + \frac{Na_eff}{K_nknao})}