Model Mathematics

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Component: Environment

Component: Parameters

D_K = \frac{D_Ca 1.96}{0.79} D_Na = \frac{D_Ca 1.33}{0.79}

Component: Potassium_Conc_cyt

\frac{d}{d time} (conc_K_cyt) = \frac{(- (I_K_cyt_b + I_K_cyt_ir + I_K_cyt_ATP + I_K_cyt_v + I_K_cyt_Ca - (2 I_NaK_cyt_alpha1))) + F (J_cyt_KCl + J_cyt_NKCC + J_Kdiff)}{F vol_cyt}

Component: Potassium_Conc_md

\frac{d}{d time} (conc_K_md) = \frac{(- (I_K_md_b + I_K_md_ir + I_K_md_ATP + I_K_md_v + I_K_md_Ca - (2 I_NaK_md_alpha2))) + F (J_md_KCl + J_md_NKCC - J_Kdiff)}{F vol_md}

Component: Sodium_Conc_cyt

\frac{d}{d time} (conc_Na_cyt) = \frac{(- (I_Na_cyt_b + 3 I_NaK_cyt_alpha1 + I_VONa_cyt + I_Na_cyt_SOC)) + F (J_cyt_NaCl + J_cyt_NKCC + J_Nadiff)}{F vol_cyt}

Component: Sodium_Conc_md

\frac{d}{d time} (conc_Na_md) = \frac{(- (I_Na_md_b + 3 I_NaK_md_alpha2 + I_VONa_md + I_Na_md_SOC + 3 I_NaCa_md)) + F (J_md_NaCl + J_md_NKCC - J_Nadiff)}{F vol_md}

Component: Chloride_Conc_cyt

\frac{d}{d time} (conc_Cl_cyt) = \frac{I_Cl_cyt_b + I_Cl_cyt_Ca + F J_cyt_NaCl + F (J_cyt_KCl + 2 J_cyt_NKCC + J_Cldiff)}{F vol_cyt}

Component: Chloride_Conc_md

\frac{d}{d time} (conc_Cl_md) = \frac{I_Cl_md_b + I_Cl_md_Ca + F J_md_NaCl + F (J_md_KCl + 2 J_md_NKCC - J_Cldiff)}{F vol_md}

Component: Calcium_Conc_cyt

\frac{d}{d time} (conc_Ca_cyt) = \frac{(- (I_Ca_cyt_b + I_Ca_cyt_P + I_Ca_cyt_SOC + I_Ca_cyt_L + I_cyt_SERCa_IP3R + I_cyt_SERCa_RyR - I_cyt_RyR - I_cyt_IP3R)) + 2 F J_Cadiff}{2 F vol_cyt_Ca} - (2 (\frac{d}{d time} (conc_CaMN__) + \frac{d}{d time} (conc_CaM_C_) + \frac{d}{d time} (conc_CaM_CM))) - (\frac{d}{d time} (conc_BfCa_cyt))

Component: Bf_Kinetics

\frac{d}{d time} (conc_BfCa_cyt) = k_Bf_on conc_Ca_cyt (conc_Bf_tot - conc_BfCa_cyt) - (k_Bf_off conc_BfCa_cyt) \frac{d}{d time} (conc_BfCa_md) = k_Bf_on conc_Ca_md (conc_Bf_tot - conc_BfCa_md) - (k_Bf_off conc_BfCa_md)

Component: Calcium_Conc_md

\frac{d}{d time} (conc_Ca_md) = \frac{- ((I_Ca_md_b + I_Ca_md_P + I_Ca_md_SOC + I_Ca_md_L - (2 I_NaCa_md)) + I_md_SERCa_RyR + I_md_SERCa_IP3R - I_md_RyR - I_md_IP3R) - (2 F J_Cadiff)}{2 F vol_md} - (2 (\frac{d}{d time} (conc_CaMN__) + \frac{d}{d time} (conc_CaM_C_) + \frac{d}{d time} (conc_CaM_CM))) - (\frac{d}{d time} (conc_BfCa_md))

Component: Calcium_Conc_SR

\frac{d}{d time} (conc_Ca_IP3R) = \frac{(I_cyt_SERCa_IP3R - I_cyt_IP3R) + I_md_SERCa_IP3R - I_md_IP3R}{F vol_SR} - (\frac{d}{d time} (conc_CalseqCa_IP3R)) \frac{d}{d time} (conc_Ca_RyR) = \frac{(I_cyt_SERCa_RyR - I_cyt_RyR) + I_md_SERCa_RyR - I_md_RyR}{F vol_SR} - (\frac{d}{d time} (conc_CalseqCa_RyR))

Component: Background_Currents

I_K_cyt_b = G_K_b f_cyt (V_m_cyt - E_K_cyt) I_K_md_b = G_K_b f_md (V_m_md - E_K_md) I_Na_cyt_b = G_Na_b f_cyt (V_m_cyt - E_Na_cyt) I_Na_md_b = G_Na_b f_md (V_m_md - E_Na_md) I_Cl_cyt_b = G_Cl_b f_cyt (V_m_cyt - E_Cl_cyt) I_Cl_md_b = G_Cl_b f_md (V_m_md - E_Cl_md) I_Ca_cyt_b = G_Ca_b f_cyt (V_m_cyt - E_Ca_cyt) I_Ca_md_b = G_Ca_b f_md (V_m_md - E_Ca_md)

Component: Nernst_Potentials

E_K_cyt = \frac{RTF}{z_K} \ln (\frac{conc_K_out}{conc_K_cyt}) E_K_md = \frac{RTF}{z_K} \ln (\frac{conc_K_out}{conc_K_md}) E_Na_cyt = \frac{RTF}{z_Na} \ln (\frac{conc_Na_out}{conc_Na_cyt}) E_Na_md = \frac{RTF}{z_Na} \ln (\frac{conc_Na_out}{conc_Na_md}) E_Cl_cyt = \frac{RTF}{z_Cl} \ln (\frac{conc_Cl_out}{conc_Cl_cyt}) E_Cl_md = \frac{RTF}{z_Cl} \ln (\frac{conc_Cl_out}{conc_Cl_md}) E_Ca_cyt = \frac{RTF}{z_Ca} \ln (\frac{conc_Ca_out}{conc_Ca_cyt}) E_Ca_md = \frac{RTF}{z_Ca} \ln (\frac{conc_Ca_out}{conc_Ca_md}) RTF = \frac{R T}{F}

Component: SERCA_Currents_IP3R

I_cyt_SERCa_IP3R = I_SERCA_max f_cyt \frac{{(\frac{conc_Ca_cyt}{K_mf})}^{n_H} - ({(\frac{conc_Ca_IP3R}{K_mr})}^{n_H})}{1 + {(\frac{conc_Ca_cyt}{K_mf})}^{n_H} + {(\frac{conc_Ca_IP3R}{K_mr})}^{n_H}} I_md_SERCa_IP3R = I_SERCA_max f_md \frac{{(\frac{conc_Ca_md}{K_mf})}^{n_H} - ({(\frac{conc_Ca_IP3R}{K_mr})}^{n_H})}{1 + {(\frac{conc_Ca_md}{K_mf})}^{n_H} + {(\frac{conc_Ca_IP3R}{K_mr})}^{n_H}}

Component: SERCA_Currents_RyR

I_cyt_SERCa_RyR = I_SERCA_max f_cyt \frac{{(\frac{conc_Ca_cyt}{K_mf})}^{n_H} - ({(\frac{conc_Ca_RyR}{K_mr})}^{n_H})}{1 + {(\frac{conc_Ca_cyt}{K_mf})}^{n_H} + {(\frac{conc_Ca_RyR}{K_mr})}^{n_H}} I_md_SERCa_RyR = I_SERCA_max f_md \frac{{(\frac{conc_Ca_md}{K_mf})}^{n_H} - ({(\frac{conc_Ca_RyR}{K_mr})}^{n_H})}{1 + {(\frac{conc_Ca_md}{K_mf})}^{n_H} + {(\frac{conc_Ca_RyR}{K_mr})}^{n_H}}

Component: RyR_Currents

I_cyt_RyR = v_RyR P_cyt_RyR (conc_Ca_RyR - conc_Ca_cyt) 2 F vol_SR I_md_RyR = v_RyR P_md_RyR (conc_Ca_RyR - conc_Ca_md) 2 F vol_SR P_cyt_RyR = \frac{w_cyt (1 + {(\frac{conc_Ca_cyt}{K_b})}^{3})}{1 + {(\frac{K_a}{conc_Ca_cyt})}^{4} + {(\frac{conc_Ca_cyt}{K_b})}^{3}} P_md_RyR = \frac{w_md (1 + {(\frac{conc_Ca_md}{K_b})}^{3})}{1 + {(\frac{K_a}{conc_Ca_md})}^{4} + {(\frac{conc_Ca_md}{K_b})}^{3}} \frac{d}{d time} (w_cyt) = \frac{K_c_rate (w_inf_cyt - w_cyt)}{w_inf_cyt} \frac{d}{d time} (w_md) = \frac{K_c_rate (w_inf_md - w_md)}{w_inf_md} w_inf_cyt = \frac{1 + {(\frac{K_a}{conc_Ca_cyt})}^{4} + {(\frac{conc_Ca_cyt}{K_b})}^{3}}{1 + \frac{1}{K_c} + {(\frac{K_a}{conc_Ca_cyt})}^{4} + {(\frac{conc_Ca_cyt}{K_b})}^{3}} w_inf_md = \frac{1 + {(\frac{K_a}{conc_Ca_md})}^{4} + {(\frac{conc_Ca_md}{K_b})}^{3}}{1 + \frac{1}{K_c} + {(\frac{K_a}{conc_Ca_md})}^{4} + {(\frac{conc_Ca_md}{K_b})}^{3}}

Component: IP3R_Currents

\frac{d}{d time} (conc_IP3_cyt) = v_IP3 conc_IP3_ref \frac{conc_Ca_cyt + (1 - alpha_4) k4}{conc_Ca_cyt + k4} - (I_r conc_IP3_cyt) \frac{d}{d time} (conc_IP3_md) = v_IP3 conc_IP3_ref \frac{conc_Ca_md + (1 - alpha_4) k4}{conc_Ca_md + k4} - (I_r conc_IP3_md) I_cyt_IP3R = v_IP3R {x110_cyt}^{3} (conc_Ca_IP3R - conc_Ca_cyt) 2 F vol_SR I_md_IP3R = v_IP3R {x110_md}^{3} (conc_Ca_IP3R - conc_Ca_md) 2 F vol_SR

Component: IP3R_Binding_Sites

\frac{d}{d time} (x000_cyt) = (- a4) (conc_Ca_cyt x000_cyt - (d4 x001_cyt)) - (a5 (conc_Ca_cyt x000_cyt - (d5 x010_cyt))) \frac{d}{d time} (x000_md) = (- a4) (conc_Ca_md x000_md - (d4 x001_md)) - (a5 (conc_Ca_md x000_md - (d5 x010_md))) \frac{d}{d time} (x001_cyt) = a4 (conc_Ca_cyt x000_cyt - (d4 x001_cyt)) - (a5 (conc_Ca_cyt x001_cyt - (d5 x011_cyt))) \frac{d}{d time} (x001_md) = a4 (conc_Ca_md x000_md - (d4 x001_md)) - (a5 (conc_Ca_md x001_md - (d5 x011_md))) \frac{d}{d time} (x010_cyt) = a5 (conc_Ca_cyt x000_cyt - (d5 x010_cyt)) - (a4 (conc_Ca_cyt x010_cyt - (d4 x011_cyt))) \frac{d}{d time} (x010_md) = a5 (conc_Ca_md x000_md - (d5 x010_md)) - (a4 (conc_Ca_md x010_md - (d4 x011_md))) x100_cyt = \frac{conc_IP3_cyt}{d1} x000_cyt x100_md = \frac{conc_IP3_md}{d1} x000_md x101_cyt = \frac{conc_IP3_cyt}{d3} x001_cyt x101_md = \frac{conc_IP3_md}{d3} x001_md x110_cyt = \frac{conc_IP3_cyt}{d1} x010_cyt x110_md = \frac{conc_IP3_md}{d1} x010_md x111_cyt = \frac{conc_IP3_cyt}{d3} x011_cyt x111_md = \frac{conc_IP3_md}{d3} x011_md x011_cyt = 1 - (x000_cyt + x001_cyt + x010_cyt + x100_cyt + x101_cyt + x110_cyt + x111_cyt) x011_md = 1 - (x000_md + x001_md + x010_md + x100_md + x101_md + x110_md + x111_md)

Component: SOC_Current_Ca

I_Ca_cyt_SOC = G_CaSOC_max \frac{K_SOC}{K_SOC + conc_Ca_SR} (V_m_cyt - E_Ca_cyt) I_Ca_md_SOC = G_CaSOC_max \frac{K_SOC}{K_SOC + conc_Ca_SR} (V_m_md - E_Ca_md) conc_Ca_SR = \frac{conc_Ca_IP3R + conc_Ca_RyR}{2}

Component: SOC_Current_Na

I_Na_cyt_SOC = I_Ca_cyt_SOC \frac{{z_Na}^{2}}{{z_Ca}^{2}} P_SOC_ratio \frac{conc_Na_cyt - (conc_Na_out ⅇ^{\frac{(- z_Na) F V_m_cyt}{R T}})}{conc_Ca_cyt - (conc_Ca_out ⅇ^{\frac{(- z_Ca) F V_m_cyt}{R T}})} \frac{1 - (ⅇ^{\frac{(- z_Ca) F V_m_cyt}{R T}})}{1 - (ⅇ^{\frac{(- z_Na) F V_m_cyt}{R T}})} I_Na_md_SOC = I_Ca_md_SOC \frac{{z_Na}^{2}}{{z_Ca}^{2}} P_SOC_ratio \frac{conc_Na_md - (conc_Na_out ⅇ^{\frac{(- z_Na) F V_m_md}{R T}})}{conc_Ca_md - (conc_Ca_out ⅇ^{\frac{(- z_Ca) F V_m_md}{R T}})} \frac{1 - (ⅇ^{\frac{(- z_Ca) F V_m_md}{R T}})}{1 - (ⅇ^{\frac{(- z_Na) F V_m_md}{R T}})}

Component: Cl_flux_NaCl

J_cyt_NaCl = J_NaCl_max f_cyt \frac{{(E_Na_cyt - E_Cl_cyt)}^{4}}{{(E_Na_cyt - E_Cl_cyt)}^{4} + {delta_CT}^{4}} J_md_NaCl = J_NaCl_max f_md \frac{{(E_Na_md - E_Cl_md)}^{4}}{{(E_Na_md - E_Cl_md)}^{4} + {delta_CT}^{4}}

Component: Cl_flux_KCl

J_cyt_KCl = J_KCl_max f_cyt \frac{E_K_cyt - E_Cl_cyt}{(E_K_cyt - E_Cl_cyt) + delta_CT} J_md_KCl = J_KCl_max f_md \frac{E_K_md - E_Cl_md}{(E_K_md - E_Cl_md) + delta_CT}

Component: Cl_flux_NKCC

J_cyt_NKCC = J_NKCC_max f_cyt \frac{(conc_Na_out conc_K_out {conc_Cl_out}^{2} - (conc_Na_cyt conc_K_cyt {conc_Cl_cyt}^{2})) K_NKCC_Na K_NKCC_K K_NKCC_Cl1 K_NKCC_Cl2}{(conc_Na_out + K_NKCC_Na) (conc_K_out + K_NKCC_K) (conc_Cl_out + K_NKCC_Cl1) (conc_Cl_out + K_NKCC_Cl2) (conc_Na_cyt + K_NKCC_Na) (conc_K_cyt + K_NKCC_K) (conc_Cl_cyt + K_NKCC_Cl1) (conc_Cl_cyt + K_NKCC_Cl2)} J_md_NKCC = J_NKCC_max f_md \frac{(conc_Na_out conc_K_out {conc_Cl_out}^{2} - (conc_Na_md conc_K_md {conc_Cl_md}^{2})) K_NKCC_Na K_NKCC_K K_NKCC_Cl1 K_NKCC_Cl2}{(conc_Na_out + K_NKCC_Na) (conc_K_out + K_NKCC_K) (conc_Cl_out + K_NKCC_Cl1) (conc_Cl_out + K_NKCC_Cl2) (conc_Na_md + K_NKCC_Na) (conc_K_md + K_NKCC_K) (conc_Cl_md + K_NKCC_Cl1) (conc_Cl_md + K_NKCC_Cl2)}

Component: Cl_Channels_cyt

\frac{d}{d time} (y_C1_cyt) = ((- k_on) conc_Ca_cyt (y_C1_cyt - y_C0_cyt) + k_off (y_C2_cyt - y_C1_cyt) - (alpha1 y_C1_cyt)) + Beta_cyt y_O1_cyt \frac{d}{d time} (y_C2_cyt) = ((- k_on) conc_Ca_cyt (y_C2_cyt - y_C1_cyt) + k_off (y_C3_cyt - y_C2_cyt) - (alpha2 y_C2_cyt)) + Beta_cyt y_O2_cyt \frac{d}{d time} (y_C3_cyt) = (k_on conc_Ca_cyt y_C2_cyt - (k_off y_C3_cyt) - (alpha3 y_C3_cyt)) + Beta_cyt y_O3_cyt \frac{d}{d time} (y_O1_cyt) = alpha1 y_C1_cyt - (Beta_cyt y_O1_cyt) \frac{d}{d time} (y_O2_cyt) = alpha2 y_C2_cyt - (Beta_cyt y_O2_cyt) \frac{d}{d time} (y_O3_cyt) = alpha3 y_C3_cyt - (Beta_cyt y_O3_cyt) 1 = y_C0_cyt + y_C1_cyt + y_C2_cyt + y_C3_cyt + y_O1_cyt + y_O2_cyt + y_O3_cyt

Component: Cl_Channels_md

\frac{d}{d time} (y_C1_md) = ((- k_on) conc_Ca_md (y_C1_md - y_C0_md) + k_off (y_C2_md - y_C1_md) - (alpha1 y_C1_md)) + Beta_md y_O1_md \frac{d}{d time} (y_C2_md) = ((- k_on) conc_Ca_md (y_C2_md - y_C1_md) + k_off (y_C3_md - y_C2_md) - (alpha2 y_C2_md)) + Beta_md y_O2_md \frac{d}{d time} (y_C3_md) = (k_on conc_Ca_md y_C2_md - (k_off y_C3_md) - (alpha3 y_C3_md)) + Beta_md y_O3_md \frac{d}{d time} (y_O1_md) = alpha1 y_C1_md - (Beta_md y_O1_md) \frac{d}{d time} (y_O2_md) = alpha2 y_C2_md - (Beta_md y_O2_md) \frac{d}{d time} (y_O3_md) = alpha3 y_C3_md - (Beta_md y_O3_md) 1 = y_C0_md + y_C1_md + y_C2_md + y_C3_md + y_O1_md + y_O2_md + y_O3_md

Component: Cl_Channel_Rates

Beta_cyt = Lambda_Beta ⅇ^{V1 + V2 V_m_cyt} Beta_md = Lambda_Beta ⅇ^{V1 + V2 V_m_md}

Component: ClCa_Current

I_Cl_cyt_Ca = G_ClCa_max f_cyt (y_O1_cyt + y_O2_cyt + y_O3_cyt) (V_m_cyt - E_Cl_cyt) I_Cl_md_Ca = G_ClCa_max f_md (y_O1_md + y_O2_md + y_O3_md) (V_m_md - E_Cl_md)

Component: K_Inward_Rectifier_Current

I_K_cyt_ir = G_Kir_max f_cyt x_Kir_cyt \sqrt{\frac{conc_K_out}{conc_K_ref}} (V_m_cyt - E_K_cyt) I_K_md_ir = G_Kir_max f_md x_Kir_md \sqrt{\frac{conc_K_out}{conc_K_ref}} (V_m_md - E_K_md) x_Kir_cyt = \frac{alpha_Kir_cyt}{alpha_Kir_cyt + Beta_Kir_cyt} x_Kir_md = \frac{alpha_Kir_md}{alpha_Kir_md + Beta_Kir_md}

Component: K_ir_Rates

alpha_Kir_cyt = \frac{3.241}{1 + ⅇ^{\frac{V_m_cyt - E_K_cyt - 185.72}{1.596}}} alpha_Kir_md = \frac{3.241}{1 + ⅇ^{\frac{V_m_md - E_K_md - 185.72}{1.596}}} Beta_Kir_cyt = 1 \frac{0.013 ⅇ^{\frac{(V_m_cyt - E_K_cyt) + 5.7922}{0.294}} + ⅇ^{\frac{V_m_cyt - E_K_cyt - 653.73299999999995}{0.244}}}{1 + ⅇ^{\frac{- (V_m_cyt - E_K_cyt - 7.7775)}{0.0928}}} Beta_Kir_md = 1 \frac{0.013 ⅇ^{\frac{(V_m_md - E_K_md) + 5.7922}{0.294}} + ⅇ^{\frac{V_m_md - E_K_md - 653.73299999999995}{0.244}}}{1 + ⅇ^{- (\frac{V_m_md - E_K_md - 7.7775}{0.0928})}}

Component: K_Delayed_Rectifier_Current

I_K_cyt_v = G_Kv_max f_cyt {P_Kv_cyt}^{2} (V_m_cyt - E_K_cyt) I_K_md_v = G_Kv_max f_md {P_Kv_md}^{2} (V_m_md - E_K_md)

Component: Kv_Activations

P_Kv_cyt = 0.58 P1_cyt + 0.42 P2_cyt P_Kv_md = 0.58 P1_md + 0.42 P2_md \frac{d}{d time} (P1_cyt) = \frac{P_bar_Kv_cyt - P1_cyt}{Tau_P1_cyt} \frac{d}{d time} (P1_md) = \frac{P_bar_Kv_md - P1_md}{Tau_P1_md} \frac{d}{d time} (P2_cyt) = \frac{P_bar_Kv_cyt - P2_cyt}{Tau_P2_cyt} \frac{d}{d time} (P2_md) = \frac{P_bar_Kv_md - P2_md}{Tau_P2_md} P_bar_Kv_cyt = \frac{1}{1 + ⅇ^{\frac{- (V_m_cyt + 0.00177)}{0.01452}}} P_bar_Kv_md = \frac{1}{1 + ⅇ^{\frac{- (V_m_md + 0.00177)}{0.01452}}}

Component: Kv_Time_Constants

Tau_P1_cyt = 0.2109873 ⅇ^{- ({(\frac{V_m_cyt + 0.21434}{0.19535})}^{2})} - 0.02059 Tau_P1_md = 0.2109873 ⅇ^{- ({(\frac{V_m_md + 0.21434}{0.19535})}^{2})} - 0.02059 Tau_P2_cyt = 0.82139 ⅇ^{- ({(\frac{V_m_cyt + 0.03159}{0.02746})}^{2})} + 0.00019 Tau_P2_md = 0.82139 ⅇ^{- ({(\frac{V_m_md + 0.03159}{0.02746})}^{2})} + 0.00019

Component: K_ATP_Current

I_K_cyt_ATP = G_KATP_max f_cyt {(\frac{conc_K_out}{conc_K_ref})}^{n_ATP} (V_m_cyt - E_K_cyt) I_K_md_ATP = G_KATP_max f_md {(\frac{conc_K_out}{conc_K_ref})}^{n_ATP} (V_m_md - E_K_md)

Component: K_Ca_Current

I_K_cyt_Ca = G_KCa_max f_cyt P_KCa_cyt (V_m_cyt - E_K_cyt) I_K_md_Ca = G_KCa_max f_md P_KCa_md (V_m_md - E_K_md)

Component: KCa_Activations

P_KCa_cyt = 0.65 PF_cyt + 0.35 PS_cyt P_KCa_md = 0.65 PF_md + 0.35 PS_md \frac{d}{d time} (PF_cyt) = \frac{P_bar_KCa_cyt - PF_cyt}{Tau_PF} \frac{d}{d time} (PF_md) = \frac{P_bar_KCa_md - PF_md}{Tau_PF} \frac{d}{d time} (PS_cyt) = \frac{P_bar_KCa_cyt - PS_cyt}{Tau_PS} \frac{d}{d time} (PS_md) = \frac{P_bar_KCa_md - PS_md}{Tau_PS} P_bar_KCa_cyt = \frac{1}{1 + ⅇ^{\frac{- (V_m_cyt - V_KCa_cyt)}{0.0308}}} P_bar_KCa_md = \frac{1}{1 + ⅇ^{\frac{- (V_m_md - V_KCa_md)}{0.0308}}}

Component: NaK_alpha_Current

I_NaK_cyt_alpha1 = I_NaK_alpha1_max Psi_NaK_cyt \frac{conc_K_out}{conc_K_out + K_m_K} \frac{{conc_Na_cyt}^{1.5}}{{conc_Na_cyt}^{1.5} + {K_m_Na_alpha1}^{1.5}} I_NaK_md_alpha2 = I_NaK_alpha1_max Psi_NaK_md \frac{conc_K_out}{conc_K_out + K_m_K} \frac{{conc_Na_md}^{1.5}}{{conc_Na_md}^{1.5} + {K_m_Na_alpha2}^{1.5}} I_NaK_alpha2_max = I_NaK_alpha1_max

Component: NaK_alpha_Waveform

Psi_NaK_cyt = \frac{1}{1 + 0.1245 ⅇ^{\frac{(- 0.1) V_m_cyt F}{R T}} + 0.0365 Sigma ⅇ^{\frac{(- V_m_cyt) F}{R T}}} Psi_NaK_md = \frac{1}{1 + 0.1245 ⅇ^{\frac{(- 0.1) V_m_md F}{R T}} + 0.0365 Sigma ⅇ^{\frac{(- V_m_md) F}{R T}}} Sigma = \frac{1}{7} (ⅇ^{\frac{conc_Na_out}{67.299999999999997}} - 1)

Component: NCX_Current

I_NaCa_md = I_NaCa_max K_a_NaCa \frac{Psi_F {conc_Na_md}^{3} conc_Ca_out - (Psi_R {conc_Na_out}^{3} conc_Ca_md)}{G (1 + k_sat Psi_R)}

Component: NCX_Waveform

K_a_NaCa = \frac{1}{1 + {(\frac{K_mCa_act}{conc_Ca_md})}^{2}} Psi_F = ⅇ^{\frac{gamma V_m_md F}{R T}} Psi_R = ⅇ^{\frac{(gamma - 1) V_m_md F}{R T}} G = {conc_Na_out}^{3} conc_Ca_md + {conc_Na_md}^{3} conc_Ca_out + {K_m_Nao}^{3} conc_Ca_md + K_m_Cao {conc_Na_md}^{3} + {K_m_Nai}^{3} conc_Ca_out (1 + \frac{conc_Ca_md}{K_m_Cai}) + K_m_Cai {conc_Na_out}^{3} (1 + {(\frac{conc_Na_md}{K_m_Nai})}^{3})

Component: VONa_Current

I_VONa_cyt = G_VONa_max f_cyt m_VONa_cyt h_VONa_cyt (V_m_cyt - E_Na_cyt) I_VONa_md = G_VONa_max f_md m_VONa_md h_VONa_md (V_m_md - E_Na_md)

Component: VONa_Channels

\frac{d}{d time} (m_VONa_cyt) = \frac{m_bar_cyt - m_VONa_cyt}{Tau_m} \frac{d}{d time} (m_VONa_md) = \frac{m_bar_md - m_VONa_md}{Tau_m} \frac{d}{d time} (h_VONa_cyt) = \frac{h_bar_cyt - h_VONa_cyt}{Tau_h} \frac{d}{d time} (h_VONa_md) = \frac{h_bar_md - h_VONa_md}{Tau_h} m_bar_cyt = \frac{1}{1 + ⅇ^{\frac{- (V_m_cyt + 0.0239)}{0.0048}}} m_bar_md = \frac{1}{1 + ⅇ^{\frac{- (V_m_md + 0.0239)}{0.0048}}} h_bar_cyt = \frac{1}{1 + ⅇ^{\frac{V_m_cyt + 0.0661}{0.0065}}} h_bar_md = \frac{1}{1 + ⅇ^{\frac{V_m_md + 0.0661}{0.0065}}}

Component: Ca_Pump_Current

I_Ca_cyt_P = I_CaP_max f_cyt \frac{conc_Ca_cyt}{K_m_CaP + conc_Ca_cyt} I_Ca_md_P = I_CaP_max f_md \frac{conc_Ca_md}{K_m_CaP + conc_Ca_md}

Component: CaL_Current

I_Ca_cyt_L = G_CaL_max f_cyt d_L_cyt f_L_cyt (V_m_cyt - E_Ca_cyt) I_Ca_md_L = G_CaL_max f_md d_L_md f_L_md (V_m_md - E_Ca_md)

Component: CaL_Activations

f_L_cyt = 0.74 f_F_cyt + 0.26 f_L_md = 0.74 f_F_md + 0.26 \frac{d}{d time} (d_L_cyt) = \frac{d_bar_L_cyt - d_L_cyt}{Tau_d_cyt} \frac{d}{d time} (d_L_md) = \frac{d_bar_L_md - d_L_md}{Tau_d_md} \frac{d}{d time} (f_F_cyt) = \frac{f_bar_F_cyt - f_F_cyt}{Tau_f_cyt} \frac{d}{d time} (f_F_md) = \frac{f_bar_F_md - f_F_md}{Tau_f_md} d_bar_L_cyt = \frac{1}{1 + ⅇ^{\frac{- (V_m_cyt + 0.00188)}{0.00757}}} d_bar_L_md = \frac{1}{1 + ⅇ^{\frac{- (V_m_md + 0.00188)}{0.00757}}} f_bar_F_md = \frac{1}{1 + ⅇ^{\frac{V_m_md + 0.02932}{0.00154}}} f_bar_F_cyt = \frac{1}{1 + ⅇ^{\frac{V_m_cyt + 0.02932}{0.00154}}}

Component: CaL_Time_Constants

Tau_d_cyt = 0.00289 ⅇ^{- ({(\frac{V_m_cyt + 0.00863}{0.01239})}^{2})} + 0.00243 Tau_d_md = 0.0289 ⅇ^{- ({(\frac{V_m_md + 0.00863}{0.01239})}^{2})} + 0.00243 Tau_f_cyt = 0.29559 ⅇ^{- ({(\frac{V_m_cyt - 0.00472}{0.11255})}^{2})} + 0.02319 Tau_f_md = 0.29559 ⅇ^{- ({(\frac{V_m_md - 0.00472}{0.11255})}^{2})} + 0.02319

Component: Calseq_Kinetics

\frac{d}{d time} (conc_CalseqCa_IP3R) = k_Calseq_on conc_Ca_IP3R (conc_Calseq_SR_tot - conc_CalseqCa_IP3R) - (k_Calseq_off conc_CalseqCa_IP3R) \frac{d}{d time} (conc_CalseqCa_RyR) = k_Calseq_on conc_Ca_RyR (conc_Calseq_SR_tot - conc_CalseqCa_RyR) - (k_Calseq_off conc_CalseqCa_RyR)

Component: Md_Cyt_Flux_K

J_Kdiff = \{\begin{matrix} Volsec (conc_K_md - conc_K_cyt) if V_m_md - V_m_cyt = 0 \\ Volsec Xi_K \frac{conc_K_md - (conc_K_cyt ⅇ^{- Xi_K})}{1 - (ⅇ^{- Xi_K})} otherwise \end{matrix} Xi_K = \frac{z_K F}{R T} (V_m_md - V_m_cyt) P_K_diff = \frac{hcon D_K}{L} Volsec = DiffArea P_K_diff

Component: Md_Cyt_Flux_Na

J_Nadiff = \{\begin{matrix} Volsec (conc_Na_md - conc_Na_cyt) if V_m_md - V_m_cyt = 0 \\ Volsec Xi_Na \frac{conc_Na_md - (conc_Na_cyt ⅇ^{- Xi_Na})}{1 - (ⅇ^{- Xi_Na})} otherwise \end{matrix} Xi_Na = \frac{z_Na F}{R T} (V_m_md - V_m_cyt) P_Na_diff = \frac{hcon D_Na}{L} Volsec = DiffArea P_Na_diff

Component: Md_Cyt_Flux_Ca

J_Cadiff = \{\begin{matrix} Volsec (conc_Ca_md - conc_Ca_cyt) if V_m_md - V_m_cyt = 0 \\ Volsec Xi_Ca \frac{conc_Ca_md - (conc_Ca_cyt ⅇ^{- Xi_Ca})}{1 - (ⅇ^{- Xi_Ca})} otherwise \end{matrix} Xi_Ca = \frac{z_Ca F}{R T} (V_m_md - V_m_cyt) P_Ca_diff = \frac{hcon D_Ca}{L} Volsec = DiffArea P_Ca_diff

Component: Md_Cyt_Flux_Cl

J_Cldiff = \{\begin{matrix} Volsec (conc_Cl_md - conc_Cl_cyt) if V_m_md - V_m_cyt = 0 \\ Volsec Xi_Cl \frac{conc_Cl_md - (conc_Cl_cyt ⅇ^{- Xi_Cl})}{1 - (ⅇ^{- Xi_Cl})} otherwise \end{matrix} Xi_Cl = \frac{z_Cl F}{R T} (V_m_md - V_m_cyt) P_Cl_diff = \frac{hcon D_Cl}{L} Volsec = DiffArea P_Cl_diff

Component: Membrane_Potential_Cyt

I_cyt_tot = (((I_K_cyt_b + I_K_cyt_ir + I_K_cyt_ATP + I_K_cyt_v + I_K_cyt_Ca - (F J_Kdiff)) + I_NaK_cyt_alpha1 + I_Na_cyt_b + I_VONa_cyt + I_Na_cyt_SOC - (F J_Nadiff)) + I_Cl_cyt_b + I_Cl_cyt_Ca + F J_Cldiff + I_Ca_cyt_b + I_Ca_cyt_P + I_Ca_cyt_L + I_Ca_cyt_SOC - (2 F J_Cadiff)) + I_cyt_up - I_cyt_RyR - I_cyt_IP3R I_cyt_up = I_cyt_SERCa_IP3R + I_cyt_SERCa_RyR

Component: Membrane_Voltage

\frac{d}{d time} (V_m_cyt) = \frac{- I_cyt_tot}{f_cyt C_m} \frac{d}{d time} (V_m_md) = \frac{- I_md_tot}{f_md C_m}

Component: Membrane_Potential_md

I_md_tot = (I_K_md_b + I_K_md_ir + I_K_md_ATP + I_K_md_v + I_K_md_Ca + F J_Kdiff + I_NaK_md_alpha2 + I_Na_md_b + I_VONa_md + I_Na_md_SOC + I_NaCa_md + F J_Nadiff + I_Cl_md_b + I_Cl_md_Ca - (F J_Cldiff)) + I_Ca_md_b + I_Ca_md_P + I_Ca_md_L + I_Ca_md_SOC + 2 F J_Cadiff + I_md_up - I_md_RyR - I_md_IP3R I_md_up = I_md_SERCa_IP3R + I_md_SERCa_RyR

Component: Parameters_VR

Component: MLCK_Activation_CaM

\frac{d}{d time} (conc_CaM___) = ((- k1_CAM_on) {conc_Ca_cyt}^{2} conc_CaM___+ k1_CAM_off conc_CaM_C_- (k2_CAM_on {conc_Ca_cyt}^{2} conc_CaM___)) + k2_CAM_off conc_CaMN__\frac{d}{d time} (conc_CaMN__) = (k2_CAM_on {conc_Ca_cyt}^{2} conc_CaM___- (k2_CAM_off conc_CaMN__) - (k3_CAM_on {conc_Ca_cyt}^{2} conc_CaMN__)) + k3_CAM_off conc_CaMNC_\frac{d}{d time} (conc_CaM_C_) = ((k1_CAM_on {conc_Ca_cyt}^{2} conc_CaM___- (k1_CAM_off conc_CaM_C_) - (k4_CAM_on {conc_Ca_cyt}^{2} conc_CaM_C_)) + k4_CAM_off conc_CaMNC_- (k5_CAM_on conc_MLCK_free conc_CaM_C_)) + k5_CAM_off conc_CaM_CM \frac{d}{d time} (conc_CaM_CM) = (k5_CAM_on conc_MLCK_free conc_CaM_C_- (k5_CAM_off conc_CaM_CM) - (k6_CAM_on {conc_Ca_cyt}^{2} conc_CaM_CM)) + k6_CAM_off conc_CaMNCM \frac{d}{d time} (conc_CaMNCM) = (k6_CAM_on {conc_Ca_cyt}^{2} conc_CaM_CM - (k6_CAM_off conc_CaMNCM)) + k7_CAM_on conc_MLCK_free conc_CaMNC_- (k7_CAM_off conc_CaMNCM) conc_CaMNC_= conc_CaM_tot - (conc_CaM___+ conc_CaMN__+ conc_CaM_C_+ conc_CaM_CM + conc_CaMNCM) conc_MLCK_free = conc_MLCK_tot - (conc_CaM_CM + conc_CaMNCM)

Component: MLCK_Phospho_Myosin

\frac{d}{d time} (conc_Myo) = (- k1_6_Myo) conc_Myo + k2_Myo conc_MyoP + k7_Myo conc_AMyo \frac{d}{d time} (conc_MyoP) = (k1_6_Myo conc_Myo - (k2_Myo conc_MyoP) - (k3_Myo conc_MyoP)) + k4_Myo conc_AMyoP \frac{d}{d time} (conc_AMyo) = (- k7_Myo) conc_AMyo + k5_Myo conc_AMyoP - (k1_6_Myo conc_AMyo) conc_AMyoP = conc_Myo_tot - (conc_Myo + conc_MyoP + conc_AMyo)

Component: MLCP_Rate_Constants

k1_6_Myo = k_Myo_MLCK conc_CaMNCM k2_Myo = \frac{k_Myo_MLCP (1 + 3.65 \frac{{conc_cGMP}^{2}}{{K_M_cGMP}^{2} + {conc_cGMP}^{2}})}{R_MLCP} k5_Myo = k2_Myo R_MLCP = 1 + alpha_MLCP \frac{{conc_H2O2_cyt}^{2}}{{K_MLCP_H2O2}^{2} + {conc_H2O2_cyt}^{2}}

Component: NO_Kinetics

\frac{d}{d time} (conc_NO_cyt) = \frac{Area}{2 vol_cyt} (J_NO - (P_NO conc_NO_cyt)) - (k_NO_O2 conc_NO_cyt conc_O2_cyt) - (k_NO_cons conc_NO_cyt)

Component: O2_Kinetics

\frac{d}{d time} (conc_O2_cyt) = G_O2 - (\frac{Area}{2 vol_cyt} P_O2 conc_O2_cyt \frac{zeta}{1 - (ⅇ^{- zeta})}) - (k_NO_O2 conc_NO_cyt conc_O2_cyt) - (k_SOD_O2 conc_SOD conc_O2_cyt)

Component: Zeta

zeta = \frac{(- F) V_m_cyt}{R T}

Component: H2O2_Kinetics

\frac{d}{d time} (conc_H2O2_cyt) = \frac{Area}{2 vol_cyt} (J_H2O2 - (P_H2O2 conc_H2O2_cyt)) + k_SOD_O2 conc_SOD conc_O2_cyt - (k_cat conc_H2O2_cyt conc_CAT)

Component: sGC_Activation

\frac{d}{d time} (conc_Eb) = (- k_sGC_for) conc_Eb conc_NO_cyt + k_sGC_back conc_E6c + k4_sGC_for conc_E5c \frac{d}{d time} (conc_E5c) = k3_sGC_for conc_E6c conc_NO_cyt + k2_sGC_for conc_E6c - (k4_sGC_for conc_E5c) conc_E6c = 1 - (conc_Eb + conc_E5c) k4_sGC_for = K4_sGC conc_cGMP

Component: cGMP_Kinetics

\frac{d}{d time} (conc_cGMP) = V_sGC_max conc_E5c - (\frac{k_PDE {conc_cGMP}^{2}}{K_M_PDE + conc_cGMP})

Component: cGMP_Ca_Interaction

V_KCa_cyt = (V_Ca \log_{10} (\frac{conc_Ca_cyt}{1}) - V_B - (V_KCa_NO \frac{conc_NO_cyt}{K_KCa_NO + conc_NO_cyt}) - (V_KCa_cGMP \frac{{conc_cGMP}^{2}}{{K_KCa_cGMP}^{2} + {conc_cGMP}^{2}})) convert V_KCa_md = (V_Ca \log_{10} (\frac{conc_Ca_md}{1}) - V_B - (V_KCa_NO \frac{conc_NO_cyt}{K_KCa_NO + conc_NO_cyt}) - (V_KCa_cGMP \frac{{conc_cGMP}^{2}}{{K_KCa_cGMP}^{2} + {conc_cGMP}^{2}})) convert

Component: SERCA_Activation

K_mf = \frac{K_mf_rest}{K_mod} (1 - (\frac{conc_cGMP}{2 (K_SERCA + conc_cGMP)}))

Component: CaP_Current_Max

I_CaP_max = I_PMCA_rest_max (1 + \frac{3.6 conc_cGMP}{K_PMCA + conc_cGMP})

Component: ROS_SERCA_Interaction

theta_SERCA_O2 = \frac{\sqrt{conc_O2_cyt}}{\sqrt{K_SERCA_O2} + \sqrt{conc_O2_cyt}} theta_SERCA_H2O2 = \frac{conc_H2O2_cyt}{K_SERCA_H2O2 + conc_H2O2_cyt} I_SERCA_max = I_SERCA_rest_max (1 - theta_SERCA_O2) (1 - theta_SERCA_H2O2)

Component: ROS_NaK_Interaction

I_NaK_alpha1_max = I_NaK_alpha1_rest_max (1 - (\frac{conc_O2_cyt}{K_NaK_O2 + conc_O2_cyt})) (1 - (\frac{conc_H2O2_cyt}{K_NaK_H2O2 + conc_H2O2_cyt}))

Component: MLCK_Activation_CaM_md

\frac{d}{d time} (conc_CaM___) = ((- k1_CAM_on) {conc_Ca_md}^{2} conc_CaM___+ k1_CAM_off conc_CaM_C_- (k2_CAM_on {conc_Ca_md}^{2} conc_CaM___)) + k2_CAM_off conc_CaMN__\frac{d}{d time} (conc_CaMN__) = (k2_CAM_on {conc_Ca_md}^{2} conc_CaM___- (k2_CAM_off conc_CaMN__) - (k3_CAM_on {conc_Ca_md}^{2} conc_CaMN__)) + k3_CAM_off conc_CaMNC_\frac{d}{d time} (conc_CaM_C_) = ((k1_CAM_on {conc_Ca_md}^{2} conc_CaM___- (k1_CAM_off conc_CaM_C_) - (k4_CAM_on {conc_Ca_md}^{2} conc_CaM_C_)) + k4_CAM_off conc_CaMNC_- (k5_CAM_on conc_MLCK_free conc_CaM_C_)) + k5_CAM_off conc_CaM_CM \frac{d}{d time} (conc_CaM_CM) = (k5_CAM_on conc_MLCK_free conc_CaM_C_- (k5_CAM_off conc_CaM_CM) - (k6_CAM_on {conc_Ca_md}^{2} conc_CaM_CM)) + k6_CAM_off conc_CaMNCM \frac{d}{d time} (conc_CaMNCM) = (k6_CAM_on {conc_Ca_md}^{2} conc_CaM_CM - (k6_CAM_off conc_CaMNCM)) + k7_CAM_on conc_MLCK_free conc_CaMNC_- (k7_CAM_off conc_CaMNCM) conc_CaMNC_= conc_CaM_tot - (conc_CaM___+ conc_CaMN__+ conc_CaM_C_+ conc_CaM_CM + conc_CaMNCM) conc_MLCK_free = conc_MLCK_tot - (conc_CaM_CM + conc_CaMNCM)

Component: Contractile_Force

f_p = \frac{conc_MyoP + conc_AMyoP}{conc_Myo_tot} F_contract = (a - (b f_p)) + c {f_p}^{2} - (d {f_p}^{3})