Model Mathematics

Rate_Ca_influx_across_the_SR = k1 (Ca_e - Ca_f)

dCa2_S1_dt = k_on1 Ca_f S1 - (\frac{{k_off1}^{2}}{k_on1 Ca_f} Ca_2_S1) dCa_S2_dt = k_on2 Ca_f S2 - (k_off2 Ca_S2) r_o = cas1 (1 - cas2) \frac{d}{d time} (cas1) = dcas1_dt dcas1_dt = k_on1 Ca_f (1 - cas1) - (\frac{{k_off1}^{2}}{k_on1 Ca_f} cas1) \frac{d}{d time} (cas2) = dcas2_dt dcas2_dt = k_on2 Ca_f (1 - cas2) - (k_off2 cas2) Rate_Ca_movement_through_the_SRRC = k_s r_o (Ca_s - Ca_f)

Rate_Ca_efflux_across_the_SR_by_NaCa_exchange = \frac{Vmax_NaCaX Ca_f}{Km_NaCaX + Ca_f}

Rate_Ca_movement_between_the_fuzzy_space_and_cytosol = kf (Ca_f - Ca_c)

Rate_Ca_uptake_by_SR_Ca_ATPase = \frac{Vmax_s ({Ca_c}^{2} - (\frac{{Ca_s}^{2}}{7000^{2}}))}{{Km_s}^{2} + {Ca_c}^{2} + \frac{{Ca_s}^{2}}{7000^{2}}}

Rate_Ca_buffering_in_the_SR = K_ons Ca_s (Bmax_s - Ca_CSQ) - (K_offs Ca_CSQ)

\frac{d}{d time} (Ca_f) = \frac{(Rate_Ca_movement_through_the_SRRC - (Rt (dcas1_dt + dcas2_dt) + Rate_Ca_movement_between_the_fuzzy_space_and_cytosol + Rate_Ca_efflux_across_the_SR_by_NaCa_exchange)) + Rate_Ca_influx_across_the_SR}{\frac{Bmax_f1 Kb_f1}{{(Ca_f + Kb_f1)}^{2}} + \frac{Bmax_f2 Kb_f2}{{(Ca_f + Kb_f2)}^{2}} + V_f}

\frac{d}{d time} (Ca_c) = \frac{Rate_Ca_movement_between_the_fuzzy_space_and_cytosol - Rate_Ca_uptake_by_SR_Ca_ATPase}{\frac{Bmax_c Kb_c}{{(Ca_c + Kb_c)}^{2}} + \frac{dye_c Kb_dye}{{(Ca_c + Kb_dye)}^{2}} + V_c}

\frac{d}{d time} (Ca_s) = \frac{Rate_Ca_uptake_by_SR_Ca_ATPase - Rate_Ca_movement_through_the_SRRC}{V_s} - Rate_Ca_buffering_in_the_SR

\frac{d}{d time} (Ca_CSQ) = Rate_Ca_buffering_in_the_SR

\frac{d}{d time} (S1) = - dCa2_S1_dt

\frac{d}{d time} (S2) = - dCa_S2_dt

\frac{d}{d time} (Ca_2_S1) = dCa2_S1_dt

\frac{d}{d time} (Ca_S2) = dCa_S2_dt