Model Mathematics

nuclearNFAT = NFATN_n + NFATp_n

timeInStim_modTrainPeriod = t - (⌊ \frac{t}{trainPeriod} ⌋ trainPeriod) timeInStim_modPulsePeriod = t - (⌊ \frac{t}{0.1} ⌋ 0.1) Ca = \{\begin{matrix} 1000 (timeInStim_modTrainPeriod - 5) (- 9.884615385) + 290.6923077 if timeInStim_modTrainPeriod \geq 5 \land timeInStim_modTrainPeriod ≦ 5.02 \land t < stimEnd \\ 1000 timeInStim_modPulsePeriod 51.89423077 + 290.6923077 if timeInStim_modTrainPeriod < 5 \land timeInStim_modPulsePeriod ≦ 0.016 \land t < stimEnd \\ 1000 (timeInStim_modPulsePeriod - 0.016) (- 9.884615385) + 1121 if timeInStim_modTrainPeriod < 5 \land timeInStim_modPulsePeriod > 0.016 \land t < stimEnd \\ 93 otherwise \end{matrix}

act_N = \frac{{Ca}^{n}}{{Ca}^{n} + {K_mN}^{n} (1 + \frac{K_dN}{M})} act_Napp = \{\begin{matrix} act_N if t < tNinhib \\ act_N ⅇ^{\frac{- (t - tNinhib)}{tau_actN}} if t \geq tNinhib \end{matrix}

J1 = k_f1 NFATp_c Ntot act_N - (k_r1 NFATN_c (1 - act_N)) J2 = k_f2 NFATN_c J3 = k_f3 NFATN_n (1 - act_N) - (k_r3 NFATp_n Ntot act_N) J4 = k_f4 NFATp_n \frac{d}{d t} (NFATp_c) = \frac{J4}{Ccn} - J1 \frac{d}{d t} (NFATN_c) = J1 - J2 \frac{d}{d t} (NFATN_n) = J2 Ccn - J3 \frac{d}{d t} (NFATp_n) = J3 - J4