Model Mathematics

\frac{d}{d time} (Ca_SS) = J_release + J_DHPR + J_efflux + J_buf J_DHPR = - (\frac{I_DHPR}{2.0 F V_SS}) J_release = \sum (RyR_open J_RyR) J_RyR = D_RyR (Ca_lumen - Ca_SS) RyR_open = \{\begin{matrix} 0.0 if i = 0.0 \\ 1.0 otherwise \end{matrix} \frac{d}{d time} (Ca_B_SR) = k_on_SR Ca_SS Ca_B_SR - (k_off_SR (Ca_B_SR_tot - Ca_B_SR)) \frac{d}{d time} (Ca_B_trpnC) = k_on_trpnC Ca_SS Ca_B_trpnC - (k_off_trpnC (Ca_B_trpnC_tot - Ca_B_trpnC)) \frac{d}{d time} (Ca_B_CaM) = k_on_CaM Ca_SS Ca_B_CaM - (k_off_CaM (Ca_B_CaM_tot - Ca_B_CaM)) \frac{d}{d time} (Ca_B_SL) = k_on_SL Ca_SS Ca_B_SL - (k_off_SL (Ca_B_SL_tot - Ca_B_SL)) J_buf = (k_on_CaM Ca_SS Ca_B_CaM - (k_off_CaM (Ca_B_CaM_tot - Ca_B_CaM))) + (k_on_trpnC Ca_SS Ca_B_trpnC - (k_off_trpnC (Ca_B_trpnC_tot - Ca_B_trpnC))) + (k_on_SR Ca_SS Ca_B_SR - (k_off_SR (Ca_B_SR_tot - Ca_B_SR))) + (k_on_SL Ca_SS Ca_B_SL - (k_off_SL (Ca_B_SL_tot - Ca_B_SL))) J_efflux = \frac{Ca_myo + Ca_SS}{tau_efflux}

\frac{d}{d time} (Ca_lumen) = beta_JSR ((- J_RyR) \frac{V_SS}{V_JSR} + J_refill) J_refill = \frac{Ca_NSR - Ca_lumen}{tau_refill} beta_JSR = {(1.0 + \frac{CSQ_tot K_CSQ}{{(CSQ + K_CSQ)}^{2.0}})}^{-1.0}

k_close = CF_close 480.0 k_open = CF_open 30000.0 \frac{{Ca_SS}^{4.0}}{{Ca_SS}^{4.0} + {K_m}^{4.0}} K_m = 6.0 - (0.0024 Ca_lumen) CF_open = 1.0 + \frac{N_open + 1.0}{N_open + N_closed} CF_close = k_coop (1.0 + \frac{N_closed + 1.0}{N_open + N_closed})

\frac{d}{d time} (Ca) = DC Ca + J_dye + J_buf + J_pump + J_leak + J_RyR \frac{d}{d time} (Ca_F) = DF Ca_F - J_dye J_dye = (- k_F_plus) Ca (F_T - Ca_F) + k_F_minus Ca_F J_pump = \frac{Vmax_pump {Ca}^{m}}{Km_pump + {Ca}^{m}} J_leak = - (\frac{Vmax_pump {C_infinity}^{m}}{Km_pump + {C_infinity}^{m}})