Model Mathematics

F_b = A_iso (RUA_MADPPi + RUA_MADP)

Q_CaB = k_on RUNA Ca - (k_off RUTCa_off)

Q_TCaA = k_onI RUTCa_off - (k_offI RUTCa_on) k_offI = k_offi {(1 + k_OFF \frac{RUA}{RU_total})}^{2} {(1 + k_xboff \frac{RUA_MADPPi + RUA_MADP}{RU_total})}^{4.4}

Q_TMA = k_tmon RUTCa_on - (k_tmoff RUTM_on) k_tmon = k_tmonc \frac{RUTCa_on}{RU_total} {(1 + k_tmRU \frac{RUTM_on}{RU_total})}^{2} {(1 + k_tmxb \frac{RUA_MADPPi + RUA_MADP}{RU_total})}^{2}

Q_MB = k_12 KTitin MADPPi RUTM_on_eff - (k_minus12 RUAMADPPi)

f_titinNormal = k_Titin \frac{9.9663}{1 + ⅇ^{\frac{\frac{L}{L_0} + 1.0639}{0.0696}}} f_titinDamaged = k_Titin ((- 31) \frac{L}{L_0} + 40) KTitin = \{\begin{matrix} f_titinNormal if L ≦ 1.1 \\ f_titinDamaged otherwise \end{matrix}

Q_Fgen = k_3 RUAMADPPi - (k_minus3 RUA_MADPPi) k_3 = k_3c {(1 + \frac{k_3f (RUTCa_on_eff + RUTM_on_eff + RUAMADPPi)}{RU_total})}^{2} {(1 + \frac{k_3xb (RUA_MADPPi + RUA_MADP)}{RU_total})}^{2}

Q_PiR = k_4 RUA_MADPPi - (k_minus4 RUA_MADP)

Q_ADPR = k_5 RUA_MADP

\frac{d}{d time} (RUTCa_off) = Q_CaB - Q_TCaA \frac{d}{d time} (RUTCa_on) = Q_TCaA - Q_TMA \frac{d}{d time} (RUTM_on) = (Q_TMA - Q_MB) + Q_ADPR \frac{d}{d time} (RUAMADPPi) = Q_MB - Q_Fgen \frac{d}{d time} (RUA_MADPPi) = Q_Fgen - Q_PiR \frac{d}{d time} (RUA_MADP) = Q_PiR - Q_ADPR \frac{d}{d time} (Ca) = - Q_CaB RUNA = RU_total - (RUTCa_off + RUTCa_on + RUTM_on + RUAMADPPi + RUA_MADPPi + RUA_MADP) RUA = RUTCa_on + RUTM_on + RUAMADPPi + RUA_MADPPi + RUA_MADP RUTM_on_eff = alpha RUTM_on RUTCa_on_eff = alpha RUTCa_on

alpha = \{\begin{matrix} 1.5 \frac{L}{L_0} - 0.5 if L < 1 \\ 1 if 1 ≦ L \land L < 1.1 \\ (- 1.6) \frac{L}{L_0} + 2.76 otherwise \end{matrix}

L = L_0