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Model Mathematics

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Component: ac

AC47_cyt = (1.0 - f_AC47_eca) (1.0 - f_AC56_AC47) AC_tot vr_cyt AC47_eca = f_AC47_eca (1.0 - f_AC56_AC47) AC_tot vr_eca AC56_cav = f_AC56_cav f_AC56_AC47 AC_tot vr_cav AC56_cyt = (1.0 - f_AC56_cav) f_AC56_AC47 AC_tot vr_cyt AC_tot = 3.0 beta_R_b1_tot ac_kAC47_cyt_gsa = {(beta_cyt_Gs_aGTP 1.0)}^{hGsAC47} ac_kAC47_eca_gsa = {(beta_eca_Gs_aGTP 1.0)}^{hGsAC47} ac_kAC56_cav_gsa = {(beta_cav_Gs_aGTP 1.0)}^{hGsAC56} ac_kAC56_cyt_gsa = {(beta_cyt_Gs_aGTP 1.0)}^{hGsAC56} dcAMP_AC47_cyt = kAC47_cyt AC47_cyt fATP dcAMP_AC47_eca = kAC47_eca AC47_eca fATP dcAMP_AC56_cav = kAC56_cav AC56_cav fATP dcAMP_AC56_cyt = kAC56_cyt AC56_cyt fATP fATP = \frac{ATP}{KmATP + ATP} f_AC56_AC47 = \frac{1.0}{1.0 + 0.35} gsi = {(beta_cav_Gs_aGTP 1.0)}^{hGsGiAC56} kAC47_cyt = afAC47 (basalAC47 + \frac{ac_kAC47_cyt_gsa}{KmGsAC47 + ac_kAC47_cyt_gsa}) kAC47_eca = afAC47 (basalAC47 + \frac{ac_kAC47_eca_gsa}{KmGsAC47 + ac_kAC47_eca_gsa}) kAC56_cav = afAC56 (basalAC56 + \frac{ac_kAC56_cav_gsa}{KmGsAC56 + ac_kAC56_cav_gsa}) (1.0 - (\frac{(1.0 - (\frac{vGsGiAC56 gsi}{KmGsGiAC56 + gsi})) beta_cav_Gi_bg}{KmGiAC56 + beta_cav_Gi_bg})) kAC56_cyt = afAC56 (basalAC56 + \frac{ac_kAC56_cyt_gsa}{KmGsAC56 + ac_kAC56_cyt_gsa})

Component: akap_sig

ICaL_akapf = \frac{(ICaL_akap - ICaL_tot) + ICaLf}{(\frac{PP1f_cav}{Ki} + 1.0) (\frac{PKAf}{Mi} + 1.0)} ICaL_arn = \frac{ICaLf ICaL_akapf PKAf}{Li Mi} ICaL_arp = \frac{ICaL_arn PP1f_cav}{Ki} ICaLf = \frac{Li}{2.0} (\sqrt{{akap_sig_ICaLf_sum}^{2.0} + \frac{4.0 ICaL_tot}{Li}} - akap_sig_ICaLf_sum) \frac{d}{d time} (ICaLp) = 0.001 (\frac{ka_ical pka_cav_C akap_sig_ICaLp_dif}{Ka_ical + akap_sig_ICaLp_dif} - (\frac{kp_ical PP1_cav ICaLp}{Kp_ical + ICaLp})) PKAf = akap_sig_PKAf_mag \cos akap_sig_PKAf_arg (1.0 - akap_sig_PKAf_x) - (\frac{akap_sig_PKAf_b}{3.0}) PP1f_cav = akap_sig_PP1f_cav_mag \cos akap_sig_PP1f_cav_arg (1.0 - akap_sig_PP1f_cav_x) - (\frac{akap_sig_PP1f_cav_b}{3.0}) RyR_akapf = \frac{(RyR_akap - RyR_tot) + RyRf}{(\frac{PP1f_cav}{Kr} + 1.0) (\frac{PKAf}{Mr} + 1.0)} RyR_arn = \frac{RyRf RyR_akapf PKAf}{Lr Mr} RyR_arp = \frac{RyR_arn PP1f_cav}{Kr} RyRf = \frac{Lr}{2.0} (\sqrt{{akap_sig_RyRf_sum}^{2.0} + \frac{4.0 RyR_tot}{Lr}} - akap_sig_RyRf_sum) \frac{d}{d time} (RyRp) = 0.001 (\frac{ka_ryr pka_cav_C akap_sig_RyRp_dif}{Ka_ryr + akap_sig_RyRp_dif} - (\frac{kp_ryr PP1_cav RyRp}{Kp_ryr + RyRp})) akap_sig_ICaLf_sum = 1.0 + \frac{ICaL_akap - ICaL_tot}{Li} akap_sig_ICaLp_dif = ICaL_arp - ICaLp akap_sig_PKAf_arg = \frac{\arctan (\frac{akap_sig_PKAf_yi}{akap_sig_PKAf_yr})}{3.0} akap_sig_PKAf_b = ICaL_akap + RyR_akap + Mi + Mr - PKA_cav akap_sig_PKAf_c = ICaL_akap Mr + RyR_akap Mi + Mi Mr - (PKA_cav (Mi + Mr)) akap_sig_PKAf_d = PKA_cav Mi Mr akap_sig_PKAf_mag = {(akap_sig_PKAf_yr akap_sig_PKAf_yr + akap_sig_PKAf_yi akap_sig_PKAf_yi)}^{\frac{1.0}{6.0}} akap_sig_PKAf_rr = (\frac{- akap_sig_PKAf_d}{27.0} {akap_sig_PKAf_b}^{3.0} - (\frac{akap_sig_PKAf_b akap_sig_PKAf_b akap_sig_PKAf_c akap_sig_PKAf_c}{108.0})) + \frac{akap_sig_PKAf_b akap_sig_PKAf_c akap_sig_PKAf_d}{6.0} + \frac{{akap_sig_PKAf_c}^{3.0}}{27.0} + \frac{akap_sig_PKAf_d akap_sig_PKAf_d}{4.0} akap_sig_PKAf_x = \frac{\frac{akap_sig_PKAf_c}{3.0} - (\frac{akap_sig_PKAf_b akap_sig_PKAf_b}{9.0})}{akap_sig_PKAf_mag akap_sig_PKAf_mag} akap_sig_PKAf_yi = \{\begin{matrix} \sqrt{- akap_sig_PKAf_rr} if akap_sig_PKAf_rr < 0.0 \\ 0.0 otherwise \end{matrix} akap_sig_PKAf_yr = \{\begin{matrix} \sqrt{akap_sig_PKAf_rr} if akap_sig_PKAf_rr > 0.0 \\ 0.0 otherwise \end{matrix} + \frac{akap_sig_PKAf_d}{2.0} + \frac{akap_sig_PKAf_b akap_sig_PKAf_c}{6.0} - (\frac{{akap_sig_PKAf_b}^{3.0}}{27.0}) akap_sig_PP1f_cav_arg = \frac{\arctan (\frac{akap_sig_PP1f_cav_yi}{akap_sig_PP1f_cav_yr})}{3.0} akap_sig_PP1f_cav_b = ICaL_akap + RyR_akap + Ki + Kr - PP1_cav akap_sig_PP1f_cav_c = ICaL_akap Kr + RyR_akap Ki + Ki Kr - (PP1_cav (Ki + Kr)) akap_sig_PP1f_cav_d = PP1_cav Ki Kr akap_sig_PP1f_cav_mag = {(akap_sig_PP1f_cav_yr akap_sig_PP1f_cav_yr + akap_sig_PP1f_cav_yi akap_sig_PP1f_cav_yi)}^{\frac{1.0}{6.0}} akap_sig_PP1f_cav_rr = (\frac{- akap_sig_PP1f_cav_d}{27.0} {akap_sig_PP1f_cav_b}^{3.0} - (\frac{akap_sig_PP1f_cav_b akap_sig_PP1f_cav_b akap_sig_PP1f_cav_c akap_sig_PP1f_cav_c}{108.0})) + \frac{akap_sig_PP1f_cav_b akap_sig_PP1f_cav_c akap_sig_PP1f_cav_d}{6.0} + \frac{{akap_sig_PP1f_cav_c}^{3.0}}{27.0} + \frac{akap_sig_PP1f_cav_d akap_sig_PP1f_cav_d}{4.0} akap_sig_PP1f_cav_x = \frac{\frac{akap_sig_PP1f_cav_c}{3.0} - (\frac{akap_sig_PP1f_cav_b akap_sig_PP1f_cav_b}{9.0})}{akap_sig_PP1f_cav_mag akap_sig_PP1f_cav_mag} akap_sig_PP1f_cav_yi = \{\begin{matrix} \sqrt{- akap_sig_PP1f_cav_rr} if akap_sig_PP1f_cav_rr < 0.0 \\ 0.0 otherwise \end{matrix} akap_sig_PP1f_cav_yr = \{\begin{matrix} \sqrt{akap_sig_PP1f_cav_rr} if akap_sig_PP1f_cav_rr > 0.0 \\ 0.0 otherwise \end{matrix} + \frac{akap_sig_PP1f_cav_d}{2.0} + \frac{akap_sig_PP1f_cav_b akap_sig_PP1f_cav_c}{6.0} - (\frac{{akap_sig_PP1f_cav_b}^{3.0}}{27.0}) akap_sig_RyRf_sum = 1.0 + \frac{RyR_akap - RyR_tot}{Lr} akap_sig_RyRp_dif = RyR_arp - RyRp fp_ICaL = \frac{ICaLp + ICaL_arn}{ICaL_tot} fp_RyR = \frac{RyRp + RyR_arn}{RyR_tot}

Component: beta

Gs_tot = 224.0 R_b1_tot R_b1_tot = 0.85 0.025 R_b2_tot = 0.15 0.025 f_Gi_eca = 1.0 - f_Gi_cav f_Gs_cyt = 1.0 - f_Gs_cav - f_Gs_eca f_Rb1_cyt = 1.0 - f_Rb1_cav - f_Rb1_eca f_Rb2_eca = 1.0 - f_Rb2_cav k_grk_dp = rate_bds 0.0009833 k_grk_p = rate_bds 0.00133 k_hydr_Gi = k_hydr_Gs k_pka_dp = 0.15629 k_pka_p k_pka_p = rate_bds 0.0065 k_reas_Gi = k_reas_Gs

Component: beta_cav

\frac{d}{d time} (Gi_aGDP) = 0.001 (k_hydr_Gi Gi_aGTP - (k_reas_Gi Gi_bg Gi_aGDP)) \frac{d}{d time} (Gi_aGTP) = 0.001 (k_act2_Gi Rb2Gi + k_act1_Gi LRb2Gi - (k_hydr_Gi Gi_aGTP)) Gi_abg = f_Gi_cav Gi_tot vr_cav - Gi_aGTP - Gi_aGDP \frac{d}{d time} (Gi_bg) = 0.001 (k_act2_Gi Rb2Gi + k_act1_Gi LRb2Gi - (k_reas_Gi Gi_bg Gi_aGDP)) Gi_f = \frac{Gi_abg}{1.0 + \frac{Rb2_pka_f}{k_b2_a} (1.0 + \frac{iso_L}{k_b2_f})} \frac{d}{d time} (Gs_aGDP) = 0.001 (k_hydr_Gs Gs_aGTP - (k_reas_Gs Gs_bg Gs_aGDP)) \frac{d}{d time} (Gs_aGTP) = 0.001 (k_act2_Gs RGs_tot + k_act1_Gs LRGs_tot - (k_hydr_Gs Gs_aGTP)) Gs_abg = f_Gs_cav Gs_tot vr_cav - Gs_aGTP - Gs_aGDP \frac{d}{d time} (Gs_bg) = 0.001 (k_act2_Gs RGs_tot + k_act1_Gs LRGs_tot - (k_reas_Gs Gs_bg Gs_aGDP)) Gs_f = \sqrt{beta_cav_Gs_f_r beta_cav_Gs_f_r + beta_cav_Gs_f_i beta_cav_Gs_f_i} LRGs_tot = LRb1Gs + k_GsAct_b2 LRb2Gs LRb1 = \frac{iso_L Rb1_f}{k_b1_l} LRb1Gs = \frac{iso_L Rb1_f Gs_f}{k_b1_c k_b1_h} LRb2 = \frac{iso_L Rb2_f}{k_b2_l} LRb2Gi = \frac{Rb2Gi iso_L}{k_b2_f} LRb2Gs = \frac{iso_L Rb2_f Gs_f}{k_b2_c k_b2_h} RGs_tot = Rb1Gs + k_GsAct_b2 Rb2Gs R_b1_tot = f_Rb1_cav beta_R_b1_tot vr_cav R_b2_tot = f_Rb2_cav beta_R_b2_tot vr_cav Rb1Gs = \frac{Rb1_f Gs_f}{k_b1_c} Rb1_f = \frac{Rb1_np_tot}{1.0 + \frac{iso_L}{k_b1_l} + \frac{Gs_f (k_b1_h + iso_L)}{k_b1_c k_b1_h}} \frac{d}{d time} (Rb1_grk_tot) = 0.001 (k_grk_p GRK (LRb1 + LRb1Gs) - (k_grk_dp Rb1_grk_tot)) Rb1_np_tot = R_b1_tot - Rb1_pka_tot - Rb1_grk_tot \frac{d}{d time} (Rb1_pka_tot) = 0.001 (k_pka_p pka_cav_C Rb1_np_tot - (k_pka_dp Rb1_pka_tot)) Rb2Gi = \frac{Rb2_pka_f Gi_f}{k_b2_a} Rb2Gs = \frac{Rb2_f Gs_f}{k_b2_c} Rb2_f = \frac{Rb2_np_tot}{1.0 + \frac{iso_L}{k_b2_l} + \frac{Gs_f (k_b2_h + iso_L)}{k_b2_c k_b2_h}} \frac{d}{d time} (Rb2_grk_tot) = 0.001 (k_grk_p GRK (LRb2 + LRb2Gs) - (k_grk_dp Rb2_grk_tot)) Rb2_np_tot = R_b2_tot - Rb2_pka_tot - Rb2_grk_tot Rb2_pka_f = \frac{(- beta_cav_Rb2_pka_f_b) + \sqrt{beta_cav_Rb2_pka_f_b beta_cav_Rb2_pka_f_b - (4.0 beta_cav_Rb2_pka_f_a beta_cav_Rb2_pka_f_c)}}{2.0 beta_cav_Rb2_pka_f_a} \frac{d}{d time} (Rb2_pka_tot) = 0.001 (k_pka_p pka_cav_C Rb2_np_tot - (k_pka_dp Rb2_pka_tot)) beta_cav_Gs_f_a = k_b1_l k_b2_l (k_b1_h + iso_L) (k_b2_h + iso_L) beta_cav_Gs_f_arg = \frac{\arctan (\frac{beta_cav_Gs_f_yi}{beta_cav_Gs_f_yr})}{3.0} beta_cav_Gs_f_b = \frac{beta_cav_Gs_f_c11 + beta_cav_Gs_f_c22}{beta_cav_Gs_f_a} + Rb1_np_tot + Rb2_np_tot - Gs_abg beta_cav_Gs_f_c = \frac{beta_cav_Gs_f_c22 (Rb1_np_tot - Gs_abg) + beta_cav_Gs_f_c11 (Rb2_np_tot - Gs_abg) + beta_cav_Gs_f_c33}{beta_cav_Gs_f_a} beta_cav_Gs_f_c11 = k_b1_c k_b1_h k_b2_l (k_b2_h + iso_L) (k_b1_l + iso_L) beta_cav_Gs_f_c22 = k_b2_c k_b2_h k_b1_l (k_b1_h + iso_L) (k_b2_l + iso_L) beta_cav_Gs_f_c33 = k_b1_c k_b2_c k_b1_h k_b2_h (k_b1_l + iso_L) (k_b2_l + iso_L) beta_cav_Gs_f_d = \frac{Gs_abg beta_cav_Gs_f_c33}{beta_cav_Gs_f_a} beta_cav_Gs_f_i = beta_cav_Gs_f_mag \sin beta_cav_Gs_f_arg (1.0 + beta_cav_Gs_f_x) beta_cav_Gs_f_mag = {(beta_cav_Gs_f_yr beta_cav_Gs_f_yr + beta_cav_Gs_f_yi beta_cav_Gs_f_yi)}^{\frac{1.0}{6.0}} beta_cav_Gs_f_r = beta_cav_Gs_f_mag \cos beta_cav_Gs_f_arg (1.0 - beta_cav_Gs_f_x) - (\frac{beta_cav_Gs_f_b}{3.0}) beta_cav_Gs_f_rr = (\frac{- beta_cav_Gs_f_d}{27.0} {beta_cav_Gs_f_b}^{3.0} - (\frac{beta_cav_Gs_f_b beta_cav_Gs_f_b beta_cav_Gs_f_c beta_cav_Gs_f_c}{108.0})) + \frac{beta_cav_Gs_f_b beta_cav_Gs_f_c beta_cav_Gs_f_d}{6.0} + \frac{{beta_cav_Gs_f_c}^{3.0}}{27.0} + \frac{beta_cav_Gs_f_d beta_cav_Gs_f_d}{4.0} beta_cav_Gs_f_x = \frac{\frac{beta_cav_Gs_f_c}{3.0} - (\frac{beta_cav_Gs_f_b beta_cav_Gs_f_b}{9.0})}{beta_cav_Gs_f_mag beta_cav_Gs_f_mag} beta_cav_Gs_f_yi = \{\begin{matrix} \sqrt{- beta_cav_Gs_f_rr} if beta_cav_Gs_f_rr < 0.0 \\ 0.0 otherwise \end{matrix} beta_cav_Gs_f_yr = \{\begin{matrix} \sqrt{beta_cav_Gs_f_rr} if beta_cav_Gs_f_rr > 0.0 \\ 0.0 otherwise \end{matrix} + \frac{beta_cav_Gs_f_d}{2.0} + \frac{beta_cav_Gs_f_b beta_cav_Gs_f_c}{6.0} - (\frac{{beta_cav_Gs_f_b}^{3.0}}{27.0}) beta_cav_Rb2_pka_f_a = \frac{(k_b2_f + iso_L) (k_b2_n + iso_L)}{k_b2_n} beta_cav_Rb2_pka_f_b = (Gi_abg (iso_L + k_b2_f) - (Rb2_pka_tot (k_b2_f + iso_L))) + k_b2_a k_b2_f (1.0 + \frac{iso_L}{k_b2_n}) beta_cav_Rb2_pka_f_c = (- Rb2_pka_tot) k_b2_a k_b2_f

Component: beta_cyt

\frac{d}{d time} (Gs_aGDP) = 0.001 (k_hydr_Gs Gs_aGTP - (k_reas_Gs Gs_bg Gs_aGDP)) \frac{d}{d time} (Gs_aGTP) = 0.001 (k_act2_Gs Rb1Gs_np + k_act1_Gs LRb1Gs_np - (k_hydr_Gs Gs_aGTP)) Gs_abg = f_Gs_cyt Gs_tot vr_cyt - Gs_aGTP - Gs_aGDP \frac{d}{d time} (Gs_bg) = 0.001 (k_act2_Gs Rb1Gs_np + k_act1_Gs LRb1Gs_np - (k_reas_Gs Gs_bg Gs_aGDP)) Gs_f = \frac{Gs_abg}{1.0 + \frac{Rb1_np_f}{k_b1_c} (1.0 + \frac{iso_L}{k_b1_h})} LRb1Gs_np = \frac{iso_L Rb1_np_f Gs_f}{k_b1_c k_b1_h} LRb1_np = \frac{iso_L Rb1_np_f}{k_b1_l} R_b1_tot = f_Rb1_cyt beta_R_b1_tot vr_cyt Rb1Gs_np = \frac{Gs_f Rb1_np_f}{k_b1_c} \frac{d}{d time} (Rb1_grk_tot) = 0.001 (k_grk_p GRK (LRb1_np + LRb1Gs_np) - (k_grk_dp Rb1_grk_tot)) Rb1_np_f = \frac{(- beta_cyt_Rb1_np_f_b) + \sqrt{beta_cyt_Rb1_np_f_b beta_cyt_Rb1_np_f_b - (4.0 beta_cyt_Rb1_np_f_a beta_cyt_Rb1_np_f_c)}}{2.0 beta_cyt_Rb1_np_f_a} Rb1_np_tot = R_b1_tot - Rb1_pka_tot - Rb1_grk_tot \frac{d}{d time} (Rb1_pka_tot) = 0.001 (k_pka_p pka_cyt_C Rb1_np_tot - (k_pka_dp Rb1_pka_tot)) beta_cyt_Rb1_np_f_a = \frac{(k_b1_h + iso_L) (k_b1_l + iso_L)}{k_b1_l} beta_cyt_Rb1_np_f_b = (Gs_abg (k_b1_h + iso_L) - (Rb1_np_tot (k_b1_h + iso_L))) + k_b1_c k_b1_h (1.0 + \frac{iso_L}{k_b1_l}) beta_cyt_Rb1_np_f_c = (- Rb1_np_tot) k_b1_h k_b1_c

Component: beta_eca

\frac{d}{d time} (Gi_aGDP) = 0.001 (k_hydr_Gi Gi_aGTP - (k_reas_Gi Gi_bg Gi_aGDP)) \frac{d}{d time} (Gi_aGTP) = 0.001 (k_act2_Gi Rb2Gi + k_act1_Gi LRb2Gi - (k_hydr_Gi Gi_aGTP)) Gi_abg = f_Gi_eca Gi_tot vr_eca - Gi_aGTP - Gi_aGDP \frac{d}{d time} (Gi_bg) = 0.001 (k_act2_Gi Rb2Gi + k_act1_Gi LRb2Gi - (k_reas_Gi Gi_bg Gi_aGDP)) Gi_f = \frac{Gi_abg}{1.0 + \frac{Rb2_pka_f}{k_b2_a} (1.0 + \frac{iso_L}{k_b2_f})} \frac{d}{d time} (Gs_aGDP) = 0.001 (k_hydr_Gs Gs_aGTP - (k_reas_Gs Gs_bg Gs_aGDP)) \frac{d}{d time} (Gs_aGTP) = 0.001 (k_act2_Gs RGs_tot + k_act1_Gs LRGs_tot - (k_hydr_Gs Gs_aGTP)) Gs_abg = f_Gs_eca Gs_tot vr_eca - Gs_aGTP - Gs_aGDP \frac{d}{d time} (Gs_bg) = 0.001 (k_act2_Gs RGs_tot + k_act1_Gs LRGs_tot - (k_reas_Gs Gs_bg Gs_aGDP)) Gs_f = \sqrt{beta_eca_Gs_f_r beta_eca_Gs_f_r + beta_eca_Gs_f_i beta_eca_Gs_f_i} LRGs_tot = LRb1Gs + k_GsAct_b2 LRb2Gs LRb1 = \frac{iso_L Rb1_f}{k_b1_l} LRb1Gs = \frac{iso_L Rb1_f Gs_f}{k_b1_c k_b1_h} LRb2 = \frac{iso_L Rb2_f}{k_b2_l} LRb2Gi = \frac{iso_L}{k_b2_f} Rb2Gi LRb2Gs = \frac{iso_L Rb2_f Gs_f}{k_b2_c k_b2_h} RGs_tot = Rb1Gs + k_GsAct_b2 Rb2Gs R_b1_tot = f_Rb1_eca beta_R_b1_tot vr_eca R_b2_tot = f_Rb2_eca beta_R_b2_tot vr_eca Rb1Gs = \frac{Rb1_f Gs_f}{k_b1_c} Rb1_f = \frac{Rb1_np_tot}{1.0 + \frac{iso_L}{k_b1_l} + \frac{Gs_f (k_b1_h + iso_L)}{k_b1_c k_b1_h}} \frac{d}{d time} (Rb1_grk_tot) = 0.001 (k_grk_p GRK (LRb1 + LRb1Gs) - (k_grk_dp Rb1_grk_tot)) Rb1_np_tot = R_b1_tot - Rb1_pka_tot - Rb1_grk_tot \frac{d}{d time} (Rb1_pka_tot) = 0.001 (k_pka_p pka_eca_C Rb1_np_tot - (k_pka_dp Rb1_pka_tot)) Rb2Gi = \frac{Rb2_pka_f Gi_f}{k_b2_a} Rb2Gs = \frac{Rb2_f Gs_f}{k_b2_c} Rb2_f = \frac{Rb2_np_tot}{1.0 + \frac{iso_L}{k_b2_l} + \frac{Gs_f (k_b2_h + iso_L)}{k_b2_c k_b2_h}} \frac{d}{d time} (Rb2_grk_tot) = 0.001 (k_grk_p GRK (LRb2 + LRb2Gs) - (k_grk_dp Rb2_grk_tot)) Rb2_np_tot = R_b2_tot - Rb2_pka_tot - Rb2_grk_tot Rb2_pka_f = \frac{(- beta_eca_Rb2_pka_f_b) + \sqrt{beta_eca_Rb2_pka_f_b beta_eca_Rb2_pka_f_b - (4.0 beta_eca_Rb2_pka_f_a beta_eca_Rb2_pka_f_c)}}{2.0 beta_eca_Rb2_pka_f_a} \frac{d}{d time} (Rb2_pka_tot) = 0.001 (k_pka_p pka_eca_C Rb2_np_tot - (k_pka_dp Rb2_pka_tot)) beta_eca_Gs_f_a = k_b1_l k_b2_l (k_b1_h + iso_L) (k_b2_h + iso_L) beta_eca_Gs_f_arg = \frac{\arctan (\frac{beta_eca_Gs_f_yi}{beta_eca_Gs_f_yr})}{3.0} beta_eca_Gs_f_b = \frac{beta_eca_Gs_f_c11 + beta_eca_Gs_f_c22}{beta_eca_Gs_f_a} + Rb1_np_tot + Rb2_np_tot - Gs_abg beta_eca_Gs_f_c = \frac{beta_eca_Gs_f_c22 (Rb1_np_tot - Gs_abg) + beta_eca_Gs_f_c11 (Rb2_np_tot - Gs_abg) + beta_eca_Gs_f_c33}{beta_eca_Gs_f_a} beta_eca_Gs_f_c11 = k_b1_c k_b1_h k_b2_l (k_b2_h + iso_L) (k_b1_l + iso_L) beta_eca_Gs_f_c22 = k_b2_c k_b2_h k_b1_l (k_b1_h + iso_L) (k_b2_l + iso_L) beta_eca_Gs_f_c33 = k_b1_c k_b2_c k_b1_h k_b2_h (k_b1_l + iso_L) (k_b2_l + iso_L) beta_eca_Gs_f_d = \frac{Gs_abg beta_eca_Gs_f_c33}{beta_eca_Gs_f_a} beta_eca_Gs_f_i = beta_eca_Gs_f_mag \sin beta_eca_Gs_f_arg (1.0 + beta_eca_Gs_f_x) beta_eca_Gs_f_mag = {(beta_eca_Gs_f_yr beta_eca_Gs_f_yr + beta_eca_Gs_f_yi beta_eca_Gs_f_yi)}^{\frac{1.0}{6.0}} beta_eca_Gs_f_r = beta_eca_Gs_f_mag \cos beta_eca_Gs_f_arg (1.0 - beta_eca_Gs_f_x) - (\frac{beta_eca_Gs_f_b}{3.0}) beta_eca_Gs_f_rr = (\frac{- beta_eca_Gs_f_d}{27.0} {beta_eca_Gs_f_b}^{3.0} - (\frac{beta_eca_Gs_f_b beta_eca_Gs_f_b beta_eca_Gs_f_c beta_eca_Gs_f_c}{108.0})) + \frac{beta_eca_Gs_f_b beta_eca_Gs_f_c beta_eca_Gs_f_d}{6.0} + \frac{{beta_eca_Gs_f_c}^{3.0}}{27.0} + \frac{beta_eca_Gs_f_d beta_eca_Gs_f_d}{4.0} beta_eca_Gs_f_x = \frac{\frac{beta_eca_Gs_f_c}{3.0} - (\frac{beta_eca_Gs_f_b beta_eca_Gs_f_b}{9.0})}{beta_eca_Gs_f_mag beta_eca_Gs_f_mag} beta_eca_Gs_f_yi = \{\begin{matrix} \sqrt{- beta_eca_Gs_f_rr} if beta_eca_Gs_f_rr < 0.0 \\ 0.0 otherwise \end{matrix} beta_eca_Gs_f_yr = \{\begin{matrix} \sqrt{beta_eca_Gs_f_rr} if beta_eca_Gs_f_rr > 0.0 \\ 0.0 otherwise \end{matrix} + \frac{beta_eca_Gs_f_d}{2.0} + \frac{beta_eca_Gs_f_b beta_eca_Gs_f_c}{6.0} - (\frac{{beta_eca_Gs_f_b}^{3.0}}{27.0}) beta_eca_Rb2_pka_f_a = \frac{(k_b2_f + iso_L) (k_b2_n + iso_L)}{k_b2_n} beta_eca_Rb2_pka_f_b = (Gi_abg (iso_L + k_b2_f) - (Rb2_pka_tot (k_b2_f + iso_L))) + k_b2_a k_b2_f (1.0 + \frac{iso_L}{k_b2_n}) beta_eca_Rb2_pka_f_c = (- Rb2_pka_tot) k_b2_a k_b2_f

Component: calcium

Ca = \frac{- calcium_Ca_b}{3.0} + \frac{2.0}{3.0} \sqrt{calcium_Ca_b calcium_Ca_b - (3.0 calcium_Ca_c)} \cos (\frac{\arccos (\frac{9.0 calcium_Ca_b calcium_Ca_c - (2.0 calcium_Ca_b calcium_Ca_b calcium_Ca_b) - (27.0 calcium_Ca_d)}{2.0 {(calcium_Ca_b calcium_Ca_b - (3.0 calcium_Ca_c))}^{1.5}})}{3.0}) Ca_CaL = \frac{- calcium_Ca_CaL_b}{3.0} + \frac{2.0}{3.0} \sqrt{calcium_Ca_CaL_b calcium_Ca_CaL_b - (3.0 calcium_Ca_CaL_c)} \cos (\frac{\arccos (\frac{9.0 calcium_Ca_CaL_b calcium_Ca_CaL_c - (2.0 calcium_Ca_CaL_b calcium_Ca_CaL_b calcium_Ca_CaL_b) - (27.0 calcium_Ca_CaL_d)}{2.0 {(calcium_Ca_CaL_b calcium_Ca_CaL_b - (3.0 calcium_Ca_CaL_c))}^{1.5}})}{3.0}) Ca_jsr = \frac{\sqrt{calcium_Ca_jsr_b calcium_Ca_jsr_b + 4.0 calcium_Ca_jsr_c} - calcium_Ca_jsr_b}{2.0} \frac{d}{d time} (Ca_nsr) = Iup - (calcium_Ca_nsr_r1 Itr) Ca_sr = \frac{- calcium_Ca_sr_b}{3.0} + \frac{2.0}{3.0} \sqrt{calcium_Ca_sr_b calcium_Ca_sr_b - (3.0 calcium_Ca_sr_c)} \cos (\frac{\arccos (\frac{9.0 calcium_Ca_sr_b calcium_Ca_sr_c - (2.0 calcium_Ca_sr_b calcium_Ca_sr_b calcium_Ca_sr_b) - (27.0 calcium_Ca_sr_d)}{2.0 {(calcium_Ca_sr_b calcium_Ca_sr_b - (3.0 calcium_Ca_sr_c))}^{1.5}})}{3.0}) ICa_tot = ical_ICaL + ICab + IpCa - (INaCa 2.0) - (INaCaSR 2.0) bar_sum = bsr_bar + bsl_bar calcium_Ca_CaL_b = ss_sum - uCa_CaL calcium_Ca_CaL_c = ss_pro - (uCa_CaL km_sum) calcium_Ca_CaL_d = (- km_pro) uCa_CaL calcium_Ca_b = (ksum - uCa) + cbar + tbar calcium_Ca_c = (kpro - (uCa ksum)) + tbar kc + cbar kt calcium_Ca_d = (- kpro) uCa calcium_Ca_jsr_b = csqn_bar + csqn_km - uCa_jsr calcium_Ca_jsr_c = uCa_jsr csqn_km calcium_Ca_nsr_r1 = \frac{v_jsr}{v_nsr} calcium_Ca_sr_b = ss_sum - uCa_sr calcium_Ca_sr_c = ss_pro - (uCa_sr km_sum) calcium_Ca_sr_d = (- km_pro) uCa_sr calcium_fhat_val = \frac{f_tni - 0.6735188}{0.9991797 - 0.6735188} calcium_uCa_CaL_r1 = \frac{AF}{2.0 v_CaL} calcium_uCa_CaL_r2 = \frac{v_sr}{v_CaL} calcium_uCa_r1 = \frac{AF}{2.0 v_cyt} calcium_uCa_r2 = \frac{v_nsr}{v_cyt} calcium_uCa_sr_r1 = \frac{- AF}{v_sr} calcium_uCa_sr_r2 = \frac{- v_jsr}{v_sr} \frac{d}{d time} (f_tni) = 0.001 (\frac{ka_tni pka_cyt_C (1.0 - f_tni)}{Ka_tni + (1.0 - f_tni) 1.0} - (\frac{kp_tni PP2A f_tni}{Kp_tni + f_tni 1.0})) fhat = \{\begin{matrix} 0.0 if calcium_fhat_val < 0.0 \\ calcium_fhat_val otherwise \end{matrix} km_pro = bsr_km bsl_km km_sum = bsr_km + bsl_km kpro = kt kc ksum = kt + kc kt = (1.0 - fhat) ktn + fhat ktp ktp = 1.5 ktn r3 = \frac{v_sr}{v_cyt} ss_pro = bsr_bar bsl_km + bsl_bar bsr_km + km_pro ss_sum = bar_sum + km_sum \frac{d}{d time} (uCa) = ((- calcium_uCa_r1) (ICab + IpCa - (2.0 INaCa)) - (calcium_uCa_r2 Iup)) + r3 Idiff_Ca \frac{d}{d time} (uCa_CaL) = (- calcium_uCa_CaL_r1) ical_ICaL + calcium_uCa_CaL_r2 Idiff_sr \frac{d}{d time} (uCa_jsr) = Itr - Irel \frac{d}{d time} (uCa_sr) = - (calcium_uCa_sr_r1 INaCaSR + calcium_uCa_sr_r2 Irel + Idiff_Ca + Idiff_sr)

Component: camk

PP1_tot = \frac{PP1_cav}{vr_cav} + \frac{PP1_eca}{vr_eca} + \frac{PP1f_cyt}{vr_cyt} active = bound + trap bound = \frac{CaMK0 (1.0 - trap)}{1.0 + \frac{Km}{Ca_sr}} c = \frac{active}{active + K} camk_f_ryr_d = \frac{1.0}{1.0 + {(\frac{K}{active})}^{2.0}} \frac{d}{d time} (f_ical) = \frac{c - f_ical}{tau_cal} \frac{d}{d time} (f_ik1) = \frac{c - f_ik1}{tau_ik1} \frac{d}{d time} (f_ina) = \frac{c - f_ina}{tau_ina} \frac{d}{d time} (f_ito) = \frac{c - f_ito}{tau_ito} \frac{d}{d time} (f_plb) = \frac{c - f_plb}{tau_plb} \frac{d}{d time} (f_ryr) = \frac{camk_f_ryr_d - f_ryr}{tau_ryr} tau_cal = tau_ryr tau_ik1 = tau_plb tau_ina = tau_plb tau_ito = tau_plb \frac{d}{d time} (trap) = camk_trap_alpha bound active - (camk_trap_beta trap (0.1 + \frac{0.9 PP1_tot}{0.1371}))

Component: camp

\frac{d}{d time} (cAMP_cav) = 0.001 (pka_cav_dcAMP + dcAMP_AC56_cav - camp_cAMP_cav_pde - camp_cAMP_cav_j1 - camp_cAMP_cav_j2) \frac{d}{d time} (cAMP_cyt) = 0.001 ((pka_cyt_dcAMP + dcAMP_AC47_cyt + dcAMP_AC56_cyt - camp_cAMP_cyt_pde) + camp_cAMP_cyt_j1 + camp_cAMP_cyt_j2) \frac{d}{d time} (cAMP_eca) = 0.001 ((pka_eca_dcAMP + dcAMP_AC47_eca - camp_cAMP_eca_pde) + camp_cAMP_eca_j1 - camp_cAMP_eca_j2) camp_cAMP_cav_j1 = \frac{j_cav_eca (cAMP_cav - cAMP_eca)}{v_cav} camp_cAMP_cav_j2 = \frac{j_cav_cyt (cAMP_cav - cAMP_cyt)}{v_cav} camp_cAMP_cav_pde = dcAMP_PDE2_cav + dcAMP_PDE3_cav + dcAMP_PDE4_cav camp_cAMP_cyt_j1 = \frac{j_cav_cyt (cAMP_cav - cAMP_cyt)}{v_cyt} camp_cAMP_cyt_j2 = \frac{j_eca_cyt (cAMP_eca - cAMP_cyt)}{v_cyt} camp_cAMP_cyt_pde = dcAMP_PDE2_cyt + dcAMP_PDE3_cyt + dcAMP_PDE4_cyt camp_cAMP_eca_j1 = \frac{j_cav_eca (cAMP_cav - cAMP_eca)}{v_eca} camp_cAMP_eca_j2 = \frac{j_eca_cyt (cAMP_eca - cAMP_cyt)}{v_eca} camp_cAMP_eca_pde = dcAMP_PDE2_eca + dcAMP_PDE4_eca j_cav_cyt = (7.5e-14) 1000000.0 j_cav_eca = (5e-15) 1000000.0 j_eca_cyt = (9e-15) 1000000.0

Component: cell

AF = \frac{capArea}{F} capArea = 2.0 geoArea geoArea = 2.0 pi radius (radius + length) v_CaL = volume 0.002 v_cav = 0.02 volume v_cyt = volume 0.678 v_eca = 0.04 volume v_jsr = volume 0.0048 v_nsr = volume 0.0552 v_sr = volume 0.02 volume = 1000.0 pi radius radius length vr_cav = \frac{volume}{v_cav} vr_cyt = \frac{volume}{v_cyt} vr_eca = \frac{volume}{v_eca}

Component: chloride

\frac{d}{d time} (Cl) = chloride_Cl_r1 IClb + CTNaCl + CTKCl + chloride_Cl_r2 Idiff_Cl \frac{d}{d time} (Cl_sr) = chloride_Cl_sr_r1 IClCa - Idiff_Cl ICl_tot = IClb + IClCa chloride_Cl_r1 = \frac{AF}{v_cyt} chloride_Cl_r2 = \frac{v_sr}{v_cyt} chloride_Cl_sr_r1 = \frac{AF}{v_sr}

Component: ctkcl

CTKCl = \frac{KClBar ctkcl_CTKCl_z1}{ctkcl_CTKCl_z1 + ctkcl_CTKCl_z2} ctkcl_CTKCl_z1 = EK - ECl

Component: ctnacl

CTNaCl = \frac{NaClBar ctnacl_CTNaCl_z1}{ctnacl_CTNaCl_z1 + ctnacl_CTNaCl_z2} ctnacl_CTNaCl_z1 = {(ENa - ECl)}^{4.0} ctnacl_CTNaCl_z2 = {87.8251}^{4.0}

Component: diff

Idiff_Ca = \frac{Ca_sr - Ca}{tau} Idiff_Cl = \frac{Cl_sr - Cl}{tau} Idiff_Na = \frac{Na_sr - Na}{tau} Idiff_sr = \frac{Ca_sr - Ca_CaL}{tau_sr} Itr = \frac{Ca_nsr - Ca_jsr}{tau_tr}

Component: engine

Component: extra

Component: icab

ICab = \frac{pCab 2.0 F vfrt (Ca efrt - (0.341 Cao))}{efrt - 1.0} efrt = ⅇ^{vfrt} vfrt = 2.0 V FRT

Component: ical

ICaL = (1.0 - f_hat) ical_np_ICaL + f_hat ical_camk_ICaL f_hat = \{\begin{matrix} 0.0 if ical_f_hat_val < 0.0 \\ ical_f_hat_val otherwise \end{matrix} ical_f_hat_ratio = 0.0269 + \frac{ICaL_arn}{ICaL_tot} ical_f_hat_val = \frac{fp_ICaL - ical_f_hat_ratio}{0.9273 - ical_f_hat_ratio}

Component: ical_camk

\frac{d}{d time} (C) = (- (alpha + delta + y)) C + beta O + theta Cs + x CI \frac{d}{d time} (CI) = (- (alpha + delta1 + x)) CI + y C + theta1 CIs + beta OI \frac{d}{d time} (CIs) = (- (alpha + theta1 + xs)) CIs + ys Cs + delta1 CI + beta OIs \frac{d}{d time} (Cs) = (- (alpha + theta + ys)) Cs + delta C + beta Os + xs CIs IBar = \frac{PCa 4.0 V FFRT (Ca_sr ical_camk_IBar_vv - (0.341 Cao))}{ical_camk_IBar_vv - 1.0} ICaL = IBar (O + Os) \frac{d}{d time} (O) = (- (beta + delta + y)) O + alpha C + theta Os + x OI \frac{d}{d time} (OI) = (- (beta + delta1 + x)) OI + y O + theta1 OIs + alpha CI \frac{d}{d time} (OIs) = (- (beta + theta1 + xs)) OIs + ys Os + delta1 OI + alpha CIs \frac{d}{d time} (Os) = (- (beta + theta + ys)) Os + delta O + alpha Cs + xs OIs PCa = 0.0002579 (1.0 + 0.1 f_ical) ac_inf = \frac{1.0}{(1.0 + ⅇ^{\frac{4.798 + V}{- 7.5699}}) (1.0 + ⅇ^{\frac{25.0 + V}{- 5.0}})} alpha = \frac{ac_inf}{ac_tau} beta = \frac{1.0 - ac_inf}{ac_tau} delta = \frac{6.0}{ss_cal_4} delta1 = \frac{theta1 x ys delta}{ical_camk_delta1_y_cor ical_camk_delta1_xs_cor theta} delta_tau = 0.1 f_ical ical_camk_IBar_vv = ⅇ^{2.0 V FRT} ical_camk_delta1_xs_cor = \{\begin{matrix} 1e-12 if | xs | < 1e-12 \\ xs otherwise \end{matrix} ical_camk_delta1_y_cor = \{\begin{matrix} 1e-12 if | y | < 1e-12 \\ y otherwise \end{matrix} in_hi_inf = \frac{0.0001 + in_inf}{1.0001} in_hi_tau = \frac{1.0}{in_a + \frac{in_b}{inca}} in_inf = \frac{1.0}{1.0 + ⅇ^{\frac{29.979 + V}{3.1775}}} in_lo_inf = \frac{0.1 + in_inf}{1.1} in_lo_tau = \frac{1.0}{in_a + \frac{in_b}{38.494}} inca = 32.5 - (\frac{18.0 - delta_tau}{ss_cal_4}) - (\frac{10.0}{ss_cal_10}) ss_cal_10 = 1.0 + {(\frac{0.01}{Ca_sr})}^{10.0} ss_cal_4 = 1.0 + {(\frac{0.002}{Ca_sr})}^{4.0} x = \frac{in_lo_inf}{in_lo_tau} xs = \frac{in_hi_inf}{in_hi_tau} y = \frac{1.0 - in_lo_inf}{in_lo_tau} ys = \frac{1.0 - in_hi_inf}{in_hi_tau}

Component: ical_np

\frac{d}{d time} (C) = (- (alpha + delta + y)) C + beta O + theta Cs + x CI \frac{d}{d time} (CI) = (- (alpha + delta1 + x)) CI + y C + theta1 CIs + beta OI \frac{d}{d time} (CIs) = (- (alpha + theta1 + xs)) CIs + ys Cs + delta1 CI + beta OIs \frac{d}{d time} (Cs) = (- (alpha + theta + ys)) Cs + delta C + beta Os + xs CIs IBar = \frac{PCa 4.0 V FFRT (Ca_sr ical_np_IBar_vv - (0.341 Cao))}{ical_np_IBar_vv - 1.0} ICaL = IBar (O + Os) \frac{d}{d time} (O) = (- (beta + delta + y)) O + alpha C + theta Os + x OI \frac{d}{d time} (OI) = (- (beta + delta1 + x)) OI + y O + theta1 OIs + alpha CI \frac{d}{d time} (OIs) = (- (beta + theta1 + xs)) OIs + ys Os + delta1 OI + alpha CIs \frac{d}{d time} (Os) = (- (beta + theta + ys)) Os + delta O + alpha Cs + xs OIs PCa = 0.0001552 (1.0 + 0.4 f_ical) ac_inf = \frac{1.0}{(1.0 + ⅇ^{\frac{13.56 - V}{9.45}}) (1.0 + ⅇ^{\frac{25.0 + V}{- 5.0}})} ac_tau = 0.59 + \frac{0.8 ⅇ^{0.052 (V + 13.0)}}{1.0 + ⅇ^{0.132 (V + 13.0)}} alpha = \frac{ac_inf}{ac_tau} beta = \frac{1.0 - ac_inf}{ac_tau} delta = \frac{14.9186}{ss_cal_4} delta1 = \frac{theta1 x ys delta}{ical_np_delta1_y_cor ical_np_delta1_xs_cor theta} delta_tau = 5.0 f_ical ical_np_IBar_vv = ⅇ^{2.0 V FRT} ical_np_delta1_xs_cor = \{\begin{matrix} 1e-12 if | xs | < 1e-12 \\ xs otherwise \end{matrix} ical_np_delta1_y_cor = \{\begin{matrix} 1e-12 if | y | < 1e-12 \\ y otherwise \end{matrix} in_a = \frac{1.0}{70.0 (1.0 - (0.5 f_ical)) (1.0 + ⅇ^{\frac{V + 49.1}{10.349}})} in_b = \frac{1.0}{1.0 + ⅇ^{\frac{V + 0.213}{- 10.807}}} in_hi_inf = \frac{0.001 + in_inf}{1.001} in_hi_tau = \frac{1.0}{in_a + \frac{in_b}{inca}} in_inf = \frac{1.0}{1.0 + ⅇ^{\frac{17.5 + V}{3.0}}} in_lo_inf = \frac{0.2474 + in_inf}{1.2474} in_lo_tau = \frac{1.0}{in_a + \frac{in_b}{26.553}} inca = 13.825 - (\frac{6.3836 - delta_tau}{ss_cal_4}) - (\frac{3.3696}{ss_cal_10}) ss_cal_10 = 1.0 + {(\frac{0.012}{Ca_sr})}^{10.0} ss_cal_4 = 1.0 + {(\frac{0.0011}{Ca_sr})}^{4.0} x = \frac{in_lo_inf}{in_lo_tau} xs = \frac{in_hi_inf}{in_hi_tau} y = \frac{1.0 - in_lo_inf}{in_lo_tau} ys = \frac{1.0 - in_hi_inf}{in_hi_tau}

Component: iclb

IClb = Gbar (V - ECl)

Component: iclca

IClCa = IClCa_bar KClCa i2 IClCa_bar = \frac{PCl V FFRT (Cl - (Clo vexp))}{1.0 - vexp} KClCa = 1.0 - (\frac{1.0}{1.0 + {(\frac{Irel_pure}{kCaCl})}^{2.0}}) \frac{d}{d time} (i2) = \frac{\frac{iclca_i2_alpha}{iclca_i2_alpha + iclca_i2_beta} - i2}{tau} iclca_i2_alpha = \frac{0.025}{1.0 + ⅇ^{\frac{V + 58.0}{5.0}}} iclca_i2_beta = \frac{0.2}{1.0 + ⅇ^{\frac{V + 19.0}{- 9.0}}} vexp = ⅇ^{V FRT}

Component: ik1

Gbar = 0.5 \sqrt{\frac{Ko}{5.4}} IK1 = (1.0 - f_ik1) IK1_np + f_ik1 IK1_camk IK1_camk = IK1_np 1.2 IK1_np = Gbar \frac{ik1_IK1_np_alpha}{ik1_IK1_np_alpha + ik1_IK1_np_beta} ik1_IK1_np_vv ik1_IK1_np_alpha = \frac{1.02}{1.0 + ⅇ^{0.2385 (ik1_IK1_np_vv - 59.215)}} ik1_IK1_np_beta = \frac{0.49124 ⅇ^{0.08032 (ik1_IK1_np_vv + 5.476)} + ⅇ^{0.06175 (ik1_IK1_np_vv - 594.31)}}{1.0 + ⅇ^{(- 0.5143) (ik1_IK1_np_vv + 4.753)}} ik1_IK1_np_vv = V - EK

Component: ikr

GKr = 0.0138542 \sqrt{\frac{Ko}{5.4}} IKr = GKr ac inx (V - EK) \frac{d}{d time} (ac) = \frac{\inf - ac}{ikr_ac_tau} ikr_ac_tau = \frac{1.0}{\frac{0.0006 (V - 1.7384)}{1.0 - (ⅇ^{(- 0.136) (V - 1.7384)})} - (\frac{0.0003 (V + 38.3608)}{1.0 - (ⅇ^{0.1522 (V + 38.3608)})})} \inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 10.085}{- 4.25}}} inx = \frac{1.0}{1.0 + ⅇ^{\frac{V + 10.0}{15.4}}}

Component: iks

G = 0.19561 (1.0 + \frac{0.6}{1.0 + {(\frac{3.8e-05}{Ca})}^{1.4}}) IKs = f_hat IKs_pka + (1.0 - f_hat) IKs_np IKs_np = G (iks_np_O1 + iks_np_O2) (V - EKs) IKs_pka = G (iks_pka_O1 + iks_pka_O2) (V - EKs) f_hat = \{\begin{matrix} 0.0 if iks_f_hat_val < 0.0 \\ iks_f_hat_val otherwise \end{matrix} iks_f_hat_ratio = 0.0306 + \frac{IKs_arn}{IKs_tot} iks_f_hat_val = \frac{fp_iks - iks_f_hat_ratio}{0.785 - iks_f_hat_ratio}

Component: iks_np

\frac{d}{d time} (C1) = b C2 - (C1 4.0 a) \frac{d}{d time} (C10) = b C11 + g C7 - (C10 (2.0 a + 2.0 d)) \frac{d}{d time} (C11) = 2.0 a C10 + 2.0 b C12 + 2.0 g C8 + 3.0 d C13 - (C11 (a + b + g + 2.0 d)) \frac{d}{d time} (C12) = a C11 + 3.0 g C9 + 3.0 d C14 - (C12 (2.0 b + 2.0 g + 2.0 d)) \frac{d}{d time} (C13) = b C14 + g C11 - (C13 (a + 3.0 d)) \frac{d}{d time} (C14) = a C13 + 2.0 g C12 + 4.0 d C15 - (C14 (b + g + 3.0 d)) \frac{d}{d time} (C15) = (g C14 - (C15 (4.0 d + t))) + e O1 \frac{d}{d time} (C2) = 4.0 a C1 + 2.0 b C3 + d C6 - (C2 (3.0 a + b + g)) \frac{d}{d time} (C3) = 3.0 a C2 + 3.0 b C4 + d C7 - (C3 (2.0 a + 2.0 b + 2.0 g)) \frac{d}{d time} (C4) = 2.0 a C3 + 4.0 b C5 + d C8 - (C4 (a + 3.0 b + 3.0 g)) \frac{d}{d time} (C5) = a C4 + d C9 - (C5 (4.0 b + 4.0 g)) \frac{d}{d time} (C6) = b C7 + g C2 - (C6 (3.0 a + d)) \frac{d}{d time} (C7) = 3.0 a C6 + 2.0 b C8 + 2.0 g C3 + 2.0 d C10 - (C7 (2.0 a + b + g + d)) \frac{d}{d time} (C8) = 2.0 a C7 + 3.0 b C9 + 3.0 g C4 + 2.0 d C11 - (C8 (a + 2.0 b + 2.0 g + d)) \frac{d}{d time} (C9) = a C8 + 4.0 g C5 + 2.0 d C12 - (C9 (3.0 b + 3.0 g + d)) \frac{d}{d time} (O1) = (- (e + p)) O1 + o O2 + t C15 \frac{d}{d time} (O2) = p O1 - (o O2) a = \frac{0.007399}{1.0 + ⅇ^{\frac{FRT (V - 0.031196)}{- 0.80019}}} b = \frac{0.0056992}{1.0 + ⅇ^{\frac{FRT (V - 0.04152)}{1.3489}}} d = 0.090654 ⅇ^{(- 0.11157) V FRT} e = 0.0031124 + \frac{0.02833 - 0.0031124}{1.0 + ⅇ^{\frac{FRT (V + 0.05166)}{1.5522}}} g = \frac{0.38839}{1.0 + ⅇ^{\frac{FRT (V + 0.15019)}{- 0.60693}}} o = (4.41980000000000020e-04) ⅇ^{(- 1.2022) V FRT} p = (4.01729999999999991e-04) ⅇ^{(2.08729999999999989e-04) V FRT}

Component: iks_pka

\frac{d}{d time} (C1) = b C2 - (C1 4.0 a) \frac{d}{d time} (C10) = b C11 + g C7 - (C10 (2.0 a + 2.0 d)) \frac{d}{d time} (C11) = 2.0 a C10 + 2.0 b C12 + 2.0 g C8 + 3.0 d C13 - (C11 (a + b + g + 2.0 d)) \frac{d}{d time} (C12) = a C11 + 3.0 g C9 + 3.0 d C14 - (C12 (2.0 b + 2.0 g + 2.0 d)) \frac{d}{d time} (C13) = b C14 + g C11 - (C13 (a + 3.0 d)) \frac{d}{d time} (C14) = a C13 + 2.0 g C12 + 4.0 d C15 - (C14 (b + g + 3.0 d)) \frac{d}{d time} (C15) = (g C14 - (C15 (4.0 d + t))) + e O1 \frac{d}{d time} (C2) = 4.0 a C1 + 2.0 b C3 + d C6 - (C2 (3.0 a + b + g)) \frac{d}{d time} (C3) = 3.0 a C2 + 3.0 b C4 + d C7 - (C3 (2.0 a + 2.0 b + 2.0 g)) \frac{d}{d time} (C4) = 2.0 a C3 + 4.0 b C5 + d C8 - (C4 (a + 3.0 b + 3.0 g)) \frac{d}{d time} (C5) = a C4 + d C9 - (C5 (4.0 b + 4.0 g)) \frac{d}{d time} (C6) = b C7 + g C2 - (C6 (3.0 a + d)) \frac{d}{d time} (C7) = 3.0 a C6 + 2.0 b C8 + 2.0 g C3 + 2.0 d C10 - (C7 (2.0 a + b + g + d)) \frac{d}{d time} (C8) = 2.0 a C7 + 3.0 b C9 + 3.0 g C4 + 2.0 d C11 - (C8 (a + 2.0 b + 2.0 g + d)) \frac{d}{d time} (C9) = a C8 + 4.0 g C5 + 2.0 d C12 - (C9 (3.0 b + 3.0 g + d)) \frac{d}{d time} (O1) = (- (e + p)) O1 + o O2 + t C15 \frac{d}{d time} (O2) = p O1 - (o O2) a = \frac{0.0099415}{1.0 + ⅇ^{\frac{FRT (V - 0.044809)}{- 0.58172}}} b = \frac{0.0033201}{1.0 + ⅇ^{\frac{FRT (V - 0.094217)}{0.95364}}} d = 0.0657 ⅇ^{(- 0.11899) V FRT} e = (3.85250000000000013e-04) + \frac{0.012406 - (3.85250000000000013e-04)}{1.0 + ⅇ^{\frac{FRT (V + 0.064118)}{0.77992}}} g = \frac{0.56356}{1.0 + ⅇ^{\frac{FRT (V + 0.17986)}{- 0.58381}}} o = 0.0002373 ⅇ^{(- 1.9742) V FRT} p = (2.26519999999999993e-04) ⅇ^{(2.46889999999999989e-04) V FRT}

Component: iks_sig

IKs_arn = \frac{IKsf Yotiaof PKAf}{L M} IKs_arp = \frac{IKs_arn PP1f_eca}{K} IKsf = \frac{L}{2.0} (\sqrt{{iks_sig_IKsf_sum}^{2.0} + \frac{4.0 IKs_tot}{L}} - iks_sig_IKsf_sum) \frac{d}{d time} (IKsp) = 0.001 (\frac{ka_iks pka_eca_C iks_sig_IKsp_dif}{Ka_iks + iks_sig_IKsp_dif} - (\frac{kp_iks PP1_eca IKsp}{Kp_iks + IKsp})) PKAf = \frac{M}{2.0} (\sqrt{{iks_sig_PKAf_sum}^{2.0} + \frac{4.0 PKA_eca}{M}} - iks_sig_PKAf_sum) PP1f_eca = \frac{K}{2.0} (\sqrt{{iks_sig_PP1f_eca_sum}^{2.0} + \frac{4.0 PP1_eca}{K}} - iks_sig_PP1f_eca_sum) Yotiaof = \frac{(Yotiao - IKs_tot) + IKsf}{(1.0 + \frac{PP1f_eca}{K}) (1.0 + \frac{PKAf}{M})} fp_iks = \frac{IKsp + IKs_arn}{IKs_tot} iks_sig_IKsf_sum = 1.0 + \frac{Yotiao - IKs_tot}{L} iks_sig_IKsp_dif = IKs_arp - IKsp iks_sig_PKAf_sum = 1.0 + \frac{Yotiao - PKA_eca}{M} iks_sig_PP1f_eca_sum = 1.0 + \frac{Yotiao - PP1_eca}{K}

Component: ikur

IKur = (1.0 - fhat) IKur_np + fhat IKur_p IKur_np = \frac{gbar_np (V - EK)}{1.0 + ⅇ^{\frac{15.0 - V}{17.0}}} IKur_p = \frac{gbar_np (V - EK)}{1.0 + ⅇ^{\frac{36.0 - V}{17.0}}} 3.62 \frac{d}{d time} (f_ikur) = 0.001 (\frac{ka_ikur pka_eca_C (1.0 - f_ikur)}{Ka_ikur + (1.0 - f_ikur) 1.0} - (\frac{kp_ikur PP1_eca f_ikur}{Kp_ikur + f_ikur 1.0})) fhat = \{\begin{matrix} 0.0 if ikur_fhat_val < 0.0 \\ ikur_fhat_val otherwise \end{matrix} ikur_fhat_val = \frac{f_ikur - (5.89379800000000009e-02)}{0.393747 - (5.89379800000000009e-02)}

Component: ina

INa = f_np INa_np + f_pka_only INa_pka + f_camk_only INa_camk + f_both INa_both INa_both = gNaBar {ina_pka_m}^{3.0} ina_camk_h ina_camk_j (V - ENa) INa_camk = gNaBar {ina_camk_m}^{3.0} ina_camk_h ina_camk_j (V - ENa) INa_np = gNaBar {ina_np_m}^{3.0} ina_np_h ina_np_j (V - ENa) INa_pka = gNaBar {ina_pka_m}^{3.0} ina_pka_h ina_pka_j (V - ENa) 1.25 f_both = f_pka camk_f_ina f_camk_only = camk_f_ina - f_both \frac{d}{d time} (f_ina) = 0.001 (\frac{ka_ina pka_cav_C (1.0 - f_ina)}{Ka_ina + (1.0 - f_ina) 1.0} - (\frac{kp_ina PP1_cav f_ina}{Kp_ina + f_ina 1.0})) f_np = 1.0 - f_pka_only - f_camk_only - f_both f_pka = \{\begin{matrix} 0.0 if ina_f_pka_val < 0.0 \\ ina_f_pka_val otherwise \end{matrix} f_pka_only = f_pka - f_both gNaBar = 2.15 8.25 1.1 ina_f_pka_val = \frac{f_ina - 0.2394795}{0.9501431 - 0.2394795}

Component: ina_camk

\frac{d}{d time} (h) = ina_camk_h_alpha (1.0 - h) - (ina_camk_h_beta h) ina_camk_h_alpha = \{\begin{matrix} 0.0 if V + dVIn \geq - 40.0 \\ 0.135 ⅇ^{\frac{87.0 + V + dVIn}{- 6.8}} otherwise \end{matrix} ina_camk_h_beta = \{\begin{matrix} \frac{1.0}{0.13 (1.0 + ⅇ^{\frac{V + dVIn + 27.4034}{- 11.1}})} if V + dVIn \geq - 40.0 \\ 3.56 ⅇ^{0.079 (V + dVIn + 7.0)} + 310000.0 ⅇ^{0.35 (V + dVIn + 7.0)} otherwise \end{matrix} ina_camk_j_alpha = \{\begin{matrix} 0.0 if V + dVIn \geq - 40.0 \\ \frac{((- 127140.0) ⅇ^{0.2444 (V + dVIn)} + (- (6.948e-05)) ⅇ^{(- 0.04391) (V + dVIn)}) (V + dVIn + 37.78)}{1.0 + ⅇ^{0.311 (V + dVIn + 79.23)}} otherwise \end{matrix} ina_camk_j_beta = \{\begin{matrix} \frac{0.3 ⅇ^{(- (2.535e-07)) (V + dVIn)}}{1.0 + ⅇ^{(- 0.1) (V + dVIn + 32.0)}} if V + dVIn \geq - 40.0 \\ \frac{0.1212 ⅇ^{(- 0.01052) (V + dVIn)}}{1.0 + ⅇ^{(- 0.1378) (V + dVIn + 40.14)}} otherwise \end{matrix} ina_camk_m_alpha = \frac{0.32 (V + 58.4729)}{1.0 - (ⅇ^{(- 0.1) (V + 58.4729)})} ina_camk_m_beta = 0.08 ⅇ^{\frac{13.7299 - V}{11.0}} \frac{d}{d time} (j) = ina_camk_j_alpha (1.0 - j) - (ina_camk_j_beta j) \frac{d}{d time} (m) = ina_camk_m_alpha (1.0 - m) - (ina_camk_m_beta m)

Component: ina_np

\frac{d}{d time} (h) = ina_np_h_alpha (1.0 - h) - (ina_np_h_beta h) ina_np_h_alpha = \{\begin{matrix} 0.0 if V \geq - 40.0 \\ 0.135 ⅇ^{\frac{87.0 + V}{- 6.8}} otherwise \end{matrix} ina_np_h_beta = \{\begin{matrix} \frac{1.0}{0.13 (1.0 + ⅇ^{\frac{V + 27.4034}{- 11.1}})} if V \geq - 40.0 \\ 3.56 ⅇ^{0.079 (V + 7.0)} + 310000.0 ⅇ^{0.35 (V + 7.0)} otherwise \end{matrix} ina_np_j_alpha = \{\begin{matrix} 0.0 if V \geq - 40.0 \\ \frac{((- 127140.0) ⅇ^{0.2444 V} - ((6.948e-05) ⅇ^{(- 0.04391) V})) (V + 37.78)}{1.0 + ⅇ^{0.311 (V + 79.23)}} otherwise \end{matrix} ina_np_j_beta = \{\begin{matrix} \frac{0.3 ⅇ^{(- (2.535e-07)) V}}{1.0 + ⅇ^{(- 0.1) (V + 32.0)}} if V \geq - 40.0 \\ \frac{0.1212 ⅇ^{(- 0.01052) V}}{1.0 + ⅇ^{(- 0.1378) (V + 40.14)}} otherwise \end{matrix} ina_np_m_alpha = \frac{0.32 (V + 58.4729)}{1.0 - (ⅇ^{(- 0.1) (V + 58.4729)})} ina_np_m_beta = 0.08 ⅇ^{\frac{13.7299 - V}{11.0}} \frac{d}{d time} (j) = ina_np_j_alpha (1.0 - j) - (ina_np_j_beta j) \frac{d}{d time} (m) = ina_np_m_alpha (1.0 - m) - (ina_np_m_beta m)

Component: ina_pka

\frac{d}{d time} (h) = ina_pka_h_alpha (1.0 - h) - (ina_pka_h_beta h) ina_pka_h_alpha = \{\begin{matrix} 0.0 if V \geq - 40.0 \\ 0.135 ⅇ^{\frac{87.0 + V + dVIn}{- 6.8}} otherwise \end{matrix} ina_pka_h_beta = \{\begin{matrix} \frac{\frac{1.0}{0.13}}{1.0 + ⅇ^{\frac{V + dVIn + 27.4034}{- 11.1}}} if V \geq - 40.0 \\ 3.56 ⅇ^{0.079 (V + dVIn + 7.0)} + 310000.0 ⅇ^{0.35 (V + dVIn + 7.0)} otherwise \end{matrix} ina_pka_j_alpha = \{\begin{matrix} 0.0 if V \geq - 40.0 \\ \frac{((- 127140.0) ⅇ^{0.2444 (V + dVIn)} - ((6.948e-05) ⅇ^{(- 0.04391) (V + dVIn)})) (V + dVIn + 37.78)}{1.0 + ⅇ^{0.311 (V + dVIn + 79.23)}} otherwise \end{matrix} ina_pka_j_beta = \{\begin{matrix} \frac{0.3 ⅇ^{(- (2.535e-07)) (V + dVIn)}}{1.0 + ⅇ^{(- 0.1) (V + dVIn + 32.0)}} if V \geq - 40.0 \\ \frac{0.1212 ⅇ^{(- 0.01052) (V + dVIn)}}{1.0 + ⅇ^{(- 0.1378) (V + dVIn + 40.14)}} otherwise \end{matrix} ina_pka_m_alpha = \frac{0.32 (V + dVAc + 58.4729)}{1.0 - (ⅇ^{(- 0.1) (V + dVAc + 58.4729)})} ina_pka_m_beta = 0.08 ⅇ^{\frac{V + dVAc - 13.7299}{- 11.0}} \frac{d}{d time} (j) = ina_pka_j_alpha (1.0 - j) - (ina_pka_j_beta j) \frac{d}{d time} (m) = ina_pka_m_alpha (1.0 - m) - (ina_pka_m_beta m)

Component: inab

INab = \frac{P F inab_INab_phi (Na ePhi - Nao)}{ePhi - 1.0} ePhi = ⅇ^{inab_INab_phi} inab_INab_phi = V FRT

Component: inaca

INaCa = \frac{inaca_INaCa_num}{inaca_INaCa_denom1 inaca_INaCa_denom2 (inaca_INaCa_denom3 + inaca_INaCa_denom4)} INaCaSR = \frac{inaca_INaCaSR_num}{inaca_INaCaSR_denom1 inaca_INaCaSR_denom2 (inaca_INaCaSR_denom3 + inaca_INaCaSR_denom4)} KmNai3 = {Km_Nai}^{3.0} KmNao3 = {Km_Nao}^{3.0} Na_i3 = {Na}^{3.0} Na_o3 = {Nao}^{3.0} Na_ss3 = {Na_sr}^{3.0} exp1 = ⅇ^{eta V FRT} exp2 = ⅇ^{(eta - 1.0) V FRT} inaca_INaCaSR_denom1 = 1.0 + {(\frac{Km_Ca}{Ca_sr})}^{2.0} inaca_INaCaSR_denom2 = 1.0 + kSat exp2 inaca_INaCaSR_denom3 = Km_Cao Na_ss3 + KmNao3 Ca_sr + KmNai3 Cao (1.0 + \frac{Ca_sr}{Km_Cai}) inaca_INaCaSR_denom4 = Km_Cai Na_o3 (1.0 + \frac{Na_ss3}{KmNai3}) + Na_ss3 Cao + Na_o3 Ca_sr inaca_INaCaSR_num = 0.2 vMax (Na_ss3 Cao exp1 - (Na_o3 Ca_sr exp2)) inaca_INaCa_denom1 = 1.0 + {(\frac{Km_Ca}{Ca})}^{2.0} inaca_INaCa_denom2 = 1.0 + kSat exp2 inaca_INaCa_denom3 = Km_Cao Na_i3 + KmNao3 Ca + KmNai3 Cao (1.0 + \frac{Ca}{Km_Cai}) inaca_INaCa_denom4 = Km_Cai Na_o3 (1.0 + \frac{Na_i3}{KmNai3}) + Na_i3 Cao + Na_o3 Ca inaca_INaCa_num = 0.8 vMax (Na_i3 Cao exp1 - (Na_o3 Ca exp2))

Component: inak

INaK = (1.0 - fhat) INaK_np + fhat INaK_p INaK_np = phi {(\frac{Na}{Na + km_np})}^{3.0} INaK_p = phi {(\frac{Na}{Na + km_p})}^{3.0} \frac{d}{d time} (f_inak) = 0.001 (\frac{ka_inak pka_cav_C (1.0 - f_inak)}{Ka_inak + (1.0 - f_inak) 1.0} - (\frac{kp_inak PP1_cav f_inak}{Kp_inak + f_inak 1.0})) fhat = \{\begin{matrix} 0.0 if inak_fhat_val < 0.0 \\ inak_fhat_val otherwise \end{matrix} inak_fhat_val = \frac{f_inak - 0.1263453}{0.9980137 - 0.1263453} phi = \frac{ibar pk}{1.0 + ⅇ^{(- (V + 92.0)) FRT}} pk = \frac{Ko}{Ko + km_ko}

Component: inal

INaL = (1.0 - camk_f_ina) INaL_np + camk_f_ina INaL_camk INaL_camk = 0.016 conductance INaL_np = 0.0065 conductance conductance = m^{3.0} h (V - ENa) \frac{d}{d time} (h) = \frac{h_inf - h}{tau_h} h_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 91.0}{6.1}}} inal_m_alpha = \frac{0.32 (V + 47.13)}{1.0 - (ⅇ^{(- 0.1) (V + 47.13)})} inal_m_beta = 0.08 ⅇ^{\frac{V}{- 11.0}} \frac{d}{d time} (m) = inal_m_alpha (1.0 - m) - (inal_m_beta m)

Component: ipca

IpCa = \frac{IpCa_bar Ca}{Km_pCa + Ca}

Component: irel

Ileak_ryr = (1.0 - fhat) Ileak_ryr_np + fhat Ileak_ryr_p Ileak_ryr_np = k_ryr_leak_np ⅇ^{\frac{Ca_jsr}{Km_ryr_leak_np}} (Ca_jsr - Ca_sr) Ileak_ryr_p = k_ryr_leak_p ⅇ^{\frac{Ca_jsr}{Km_ryr_leak_p}} (Ca_jsr - Ca_sr) Irel = Ileak_ryr + Irel_pure \frac{d}{d time} (Irel_np) = \frac{- (irel_inf_np + Irel_np)}{irel_tau_np} \frac{d}{d time} (Irel_p) = \frac{- (irel_inf_p + Irel_p)}{irel_tau_p} Irel_pure = (1.0 - fhat) Irel_np + fhat Irel_p alpha_np = 0.1125 beta_np alpha_p = 0.1125 beta_p beta_0 = 0.6667 4.75 beta_np = beta_0 (1.0 + 2.0 f_ryr) beta_p = beta_0 (1.0 + 0.0 f_ryr) fhat = \{\begin{matrix} 0.0 if irel_fhat_val < 0.0 \\ irel_fhat_val otherwise \end{matrix} irel_fhat_ratio = 0.0329 + \frac{RyR_arn}{RyR_tot} irel_fhat_val = \frac{fp_RyR - irel_fhat_ratio}{0.9586 - irel_fhat_ratio} irel_inf_np = alpha_np y irel_inf_p = 1.9925 alpha_p y irel_tau_np = \frac{beta_np}{x} irel_tau_p = \frac{0.5357 beta_p}{x} x = 1.0 + \frac{0.0123}{Ca_jsr} y = \frac{ical_ICaL 1.0}{1.0 + {(\frac{1.0}{Ca_jsr})}^{8.0}}

Component: iso

Component: ito

ITo = (1.0 - f_ito) ITo_np + f_ito ITo_camk ITo_camk = x (0.7356 if_camk + 0.2644 is_camk) ITo_np = x (0.7356 if_np + 0.2644 is_np) R = ⅇ^{\frac{V}{550.0}} a_inf = \frac{1.0}{1.0 + ⅇ^{\frac{V + 9.437}{- 7.133}}} \frac{d}{d time} (a_np) = \frac{a_inf - a_np}{a_tau} a_tau = \frac{1.0}{\frac{ito_a_np_alpha}{1.2089} + 3.5 ito_a_np_beta} alph_if = \frac{1.0}{1.0 + ⅇ^{\frac{V + 58.0}{5.0}}} alph_is = \frac{\frac{1.0}{1.0 + ⅇ^{\frac{V + 60.0}{5.0}}}}{250.0} beta_i = \frac{\frac{\frac{1.0}{1.0 + ⅇ^{\frac{V + 19.0}{- 9.0}}}}{0.5}}{9.7953} \frac{d}{d time} (if_camk) = ito_if_camk_alpha (1.0 - if_camk) - (beta_i if_camk) \frac{d}{d time} (if_np) = ito_if_np_alpha (1.0 - if_np) - (beta_i if_np) \frac{d}{d time} (is_camk) = ito_is_camk_alpha (1.0 - is_camk) - (beta_i is_camk) \frac{d}{d time} (is_np) = ito_is_np_alpha (1.0 - is_np) - (beta_i is_np) ito_a_np_alpha = \frac{1.0}{1.0 + ⅇ^{\frac{V - 18.4099}{- 29.3814}}} ito_a_np_beta = \frac{1.0}{1.0 + ⅇ^{\frac{V + 100.0}{29.3814}}} ito_if_camk_alpha = 0.04796 alph_if ito_if_np_alpha = 0.02144 alph_if ito_is_camk_alpha = 2.46 alph_is ito_is_np_alpha = 0.56034 alph_is x = Gbar {a_np}^{3.0} R (V - EK)

Component: iup

Imax = (1.0 - f_SERCA2a) iupmax + f_SERCA2a iupmaxCAMK Iup = uptake - leak Km_both = Km_pka Km_camk = Km_np - 0.00017 Km_pka = Km_np (1.0 - 0.46) Km_up = f_np Km_np + f_pka_only Km_pka + f_camk_only Km_camk + f_both Km_both f_SERCA2a = \frac{1.0}{1.0 + {(\frac{0.03}{active})}^{2.0}} f_both = f_pka camk_f_plb f_camk_only = camk_f_plb - f_both f_np = 1.0 - f_pka_only - f_camk_only - f_both f_pka = \{\begin{matrix} 0.0 if iup_f_pka_val < 0.0 \\ iup_f_pka_val otherwise \end{matrix} f_pka_only = f_pka - f_both \frac{d}{d time} (f_plb) = 0.001 (\frac{ka_plb pka_cyt_C (1.0 - f_plb)}{Ka_plb + (1.0 - f_plb) 1.0} - (\frac{kp_plb PP1f_cyt f_plb}{Kp_plb + f_plb 1.0})) iup_f_pka_val = \frac{f_plb - 0.6591}{0.9945 - 0.6591} iupmaxCAMK = 3.25 iupmax leak = \frac{Imax Ca_nsr}{nsrmax} uptake = \frac{Imax Ca}{Ca + Km_up}

Component: membrane

\frac{d}{d time} (V) = \frac{- (i_ion + i_stim)}{1.0} i_ion = INa_tot + IK_tot + ICa_tot + ICl_tot

Component: nernst

ECl = (- RTF) \ln (\frac{Clo}{Cl}) EK = RTF \ln (\frac{Ko}{potassium_K}) EKs = RTF \ln (\frac{Ko + PNaK Nao}{potassium_K + PNaK Na}) ENa = RTF \ln (\frac{Nao}{Na})

Component: pde

PDE2_cav = ibmx2 f_pde2_cav vr_cav PDE2_cyt = ibmx2 f_pde2_cyt vr_cyt PDE2_eca = ibmx2 f_pde2_eca vr_eca \frac{d}{d time} (PDE3_P_cav) = 0.001 (kfPDEp pka_cav_C (PDE3_cav - PDE3_P_cav) - (kbPDEp PDE3_P_cav)) \frac{d}{d time} (PDE3_P_cyt) = 0.001 (kfPDEp pka_cyt_C (PDE3_cyt - PDE3_P_cyt) - (kbPDEp PDE3_P_cyt)) PDE3_cav = ibmx3 f_pde3_cav vr_cav PDE3_cyt = ibmx3 f_pde3_cyt vr_cyt PDE3_tot = \frac{pde_PDE3_tot_alpha}{pde_PDE3_tot_beta} PDE2_tot \frac{d}{d time} (PDE4_P_cav) = 0.001 (kfPDEp pka_cav_C (PDE4_cav - PDE4_P_cav) - (kbPDEp PDE4_P_cav)) \frac{d}{d time} (PDE4_P_cyt) = 0.001 (kfPDEp pka_cyt_C (PDE4_cyt - PDE4_P_cyt) - (kbPDEp PDE4_P_cyt)) \frac{d}{d time} (PDE4_P_eca) = 0.001 (kfPDEp pka_eca_C (PDE4_eca - PDE4_P_eca) - (kbPDEp PDE4_P_eca)) PDE4_cav = ibmx4 f_pde4_cav vr_cav PDE4_cyt = ibmx4 f_pde4_cyt vr_cyt PDE4_eca = ibmx4 f_pde4_eca vr_eca PDE4_tot = \frac{(f_pde_part - f_pde2_part) PDE2_tot + f_pde_part PDE3_tot}{(1.0 + r_pde34_frac) f_pde4_part - f_pde_part} dcAMP_PDE2_cav = \frac{PDE2_cav kPDE2}{1.0 + \frac{KmPDE2}{cAMP_cav}} dcAMP_PDE2_cyt = \frac{PDE2_cyt kPDE2}{1.0 + \frac{KmPDE2}{cAMP_cyt}} dcAMP_PDE2_eca = \frac{PDE2_eca kPDE2}{1.0 + \frac{KmPDE2}{cAMP_eca}} dcAMP_PDE3_cav = \frac{(PDE3_cav + (delta_k_pde34 - 1.0) PDE3_P_cav) kPDE3}{1.0 + \frac{KmPDE3}{cAMP_cav}} dcAMP_PDE3_cyt = \frac{(PDE3_cyt + (delta_k_pde34 - 1.0) PDE3_P_cyt) kPDE3}{1.0 + \frac{KmPDE3}{cAMP_cyt}} dcAMP_PDE4_cav = \frac{(PDE4_cav + (delta_k_pde34 - 1.0) PDE4_P_cav) kPDE4}{1.0 + \frac{KmPDE4}{cAMP_cav}} dcAMP_PDE4_cyt = \frac{(PDE4_cyt + (delta_k_pde34 - 1.0) PDE4_P_cyt) kPDE4}{1.0 + \frac{KmPDE4}{cAMP_cyt}} dcAMP_PDE4_eca = \frac{(PDE4_eca + (delta_k_pde34 - 1.0) PDE4_P_eca) kPDE4}{1.0 + \frac{KmPDE4}{cAMP_eca}} f_pde2_cyt = 1.0 - f_pde2_cav - f_pde2_eca f_pde2_part = f_pde2_cav + f_pde2_eca f_pde3_cav = \frac{r_pde34_frac f_pde4_part PDE4_tot}{PDE3_tot} f_pde3_cyt = 1.0 - f_pde3_cav f_pde4_cyt = 1.0 - f_pde4_part f_pde4_eca = f_pde4_part - f_pde4_cav ibmx2 = (1.0 - (\frac{ibmx_h2}{KmIbmxPde2 + ibmx_h2})) PDE2_tot ibmx3 = (1.0 - (\frac{ibmx_h3}{KmIbmxPde3 + ibmx_h3})) PDE3_tot ibmx4 = (1.0 - (\frac{ibmx_h4}{KmIbmxPde4 + ibmx_h4})) PDE4_tot ibmx_h2 = {(ibmx 1.0)}^{h_ibmx_pde2} ibmx_h3 = {(ibmx 1.0)}^{h_ibmx_pde3} ibmx_h4 = {(ibmx 1.0)}^{h_ibmx_pde4} kbPDEp = KPDEp kfPDEp pde_PDE3_tot_alpha = r_pde3_cyt (f_pde4_part (1.0 + r_pde34_frac - (r_pde34_frac f_pde2_part) - f_pde_part) + f_pde2_part (f_pde_part - 1.0)) + r_pde34_frac f_pde4_part (f_pde_part - f_pde2_part) pde_PDE3_tot_beta = f_pde4_part (1.0 + r_pde34_frac + f_pde_part (r_pde3_cyt - r_pde34_frac)) - (f_pde_part (1.0 + r_pde3_cyt)) r_pde3_cyt = \frac{ff_pde3_cyt}{1.0 - ff_pde3_cyt}

Component: phys

FFRT = F FRT FRT = \frac{1.0}{RTF} RTF = \frac{R T}{F}

Component: pka

K_pki = \frac{0.01}{50.0} PKA_cav = f_cav PKA_tot vr_cav PKA_cyt = f_cyt PKA_tot vr_cyt PKA_eca = f_eca PKA_tot vr_eca PKI_cav = f_pki_cav PKI_tot vr_cav PKI_cyt = f_pki_cyt PKI_tot vr_cyt PKI_eca = f_pki_eca PKI_tot vr_eca PKI_tot = 0.2 PKA_tot b_pki = f_pki K_pki f_cyt = 1.0 - f_cav - f_eca f_pki_cav = f_cav f_pki_cyt = 1.0 - f_pki_cav - f_pki_eca f_pki_eca = f_eca

Component: pka_cav

\frac{d}{d time} (A2R) = 0.001 (f3 A2RC - (b3 A2R C)) \frac{d}{d time} (A2RC) = 0.001 ((f2 ARC cAMP_cav - ((b2 + f3) A2RC)) + b3 A2R C) \frac{d}{d time} (ARC) = 0.001 ((f1 RCf cAMP_cav - (b1 ARC) - (f2 ARC cAMP_cav)) + b2 A2RC) \frac{d}{d time} (C) = 0.001 ((f3 A2RC - (b3 A2R C)) + b_pki PKIC - (f_pki (PKI_cav - PKIC) C)) \frac{d}{d time} (PKIC) = 0.001 (f_pki (PKI_cav - PKIC) C - (b_pki PKIC)) RCf = PKA_cav - ARC - A2RC - A2R b1 = f1 K1 b2 = f2 K2 b3 = f3 K3 dcAMP = ((- f1) RCf cAMP_cav + b1 ARC - (f2 ARC cAMP_cav)) + b2 A2RC

Component: pka_cyt

\frac{d}{d time} (A2R) = 0.001 (f3 A2RC - (b3 A2R C)) \frac{d}{d time} (A2RC) = 0.001 ((f2 ARC cAMP_cyt - ((b2 + f3) A2RC)) + b3 A2R C) \frac{d}{d time} (ARC) = 0.001 ((f1 RCf cAMP_cyt - (b1 ARC) - (f2 ARC cAMP_cyt)) + b2 A2RC) \frac{d}{d time} (C) = 0.001 ((f3 A2RC - (b3 A2R C)) + b_pki PKIC - (f_pki (PKI_cyt - PKIC) C)) \frac{d}{d time} (PKIC) = 0.001 (f_pki (PKI_cyt - PKIC) C - (b_pki PKIC)) RCf = PKA_cyt - ARC - A2RC - A2R b1 = f1 K1 b2 = f2 K2 b3 = f3 K3 dcAMP = ((- f1) RCf cAMP_cyt + b1 ARC - (f2 ARC cAMP_cyt)) + b2 A2RC f1 = pka_cav_f1 f2 = pka_cav_f2 f3 = pka_cav_f3

Component: pka_eca

\frac{d}{d time} (A2R) = 0.001 (f3 A2RC - (b3 A2R C)) \frac{d}{d time} (A2RC) = 0.001 ((f2 ARC cAMP_eca - ((b2 + f3) A2RC)) + b3 A2R C) \frac{d}{d time} (ARC) = 0.001 ((f1 RCf cAMP_eca - (b1 ARC) - (f2 ARC cAMP_eca)) + b2 A2RC) \frac{d}{d time} (C) = 0.001 ((f3 A2RC - (b3 A2R C)) + b_pki PKIC - (f_pki (PKI_eca - PKIC) C)) K1 = pka_cav_K1 K2 = pka_cav_K2 K3 = pka_cav_K3 \frac{d}{d time} (PKIC) = 0.001 (f_pki (PKI_eca - PKIC) C - (b_pki PKIC)) RCf = PKA_eca - ARC - A2RC - A2R b1 = f1 K1 b2 = f2 K2 b3 = f3 K3 dcAMP = ((- f1) RCf cAMP_eca + b1 ARC - (f2 ARC cAMP_eca)) + b2 A2RC f1 = pka_cav_f1 f2 = pka_cav_f2 f3 = pka_cav_f3

Component: potassium

IK_tot = IK1 + IKr + IKs + IKur + ITo - (2.0 INaK) \frac{d}{d time} (K) = potassium_K_r1 (IK_tot + i_stim) + CTKCl potassium_K_r1 = \frac{- AF}{v_cyt}

Component: pp1

PP1f_cyt = 0.5 (\sqrt{{pp1_PP1f_cyt_sum}^{2.0} + 4.0 K PP1_cyt} - pp1_PP1f_cyt_sum) di = inhib1_tot - inhib1_p \frac{d}{d time} (inhib1_p) = 0.001 (\frac{kp pka_cyt_C di}{Kp + di} - (\frac{kdp PP2A inhib1_p}{Kdp + inhib1_p})) inhib1_tot = \frac{f}{1.0 - f} K + f PP1_cyt pp1_PP1f_cyt_sum = (K - PP1_cyt) + inhib1_p

Component: sodium

INa_cyt = INa + INab + INaL + INaK 3.0 + INaCa 3.0 INa_tot = INa_cyt + INaCaSR 3.0 \frac{d}{d time} (Na) = sodium_Na_r1 INa_cyt + sodium_Na_r2 Idiff_Na + CTNaCl \frac{d}{d time} (Na_sr) = - (sodium_Na_sr_r1 INaCaSR + Idiff_Na) sodium_Na_r1 = \frac{- AF}{v_cyt} sodium_Na_r2 = \frac{v_sr}{v_cyt} sodium_Na_sr_r1 = \frac{3.0 AF}{v_sr}

Component: stimulus

amplitude = - 80.0 i_stim = \{\begin{matrix} 1.0 if time - offset - (period ⌊ \frac{time - offset}{period} ⌋) < duration \\ 0.0 otherwise \end{matrix} amplitude

Source: Derived from workspace Heijman et al. 2011 at changeset c240497a46fb.

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