Model Mathematics

nuclearNFAT = NFATN_n + NFATp_n

Ca = \{\begin{matrix} \frac{(459 - 576) t}{180} + 576 if t \geq 0 \land t ≦ 180 \\ \frac{(406 - 459) (t - 180)}{180} + 459 if t > 180 \land t ≦ 360 \\ \frac{(377 - 406) (t - 360)}{180} + 406 if t > 360 \land t ≦ 540 \\ \frac{(348 - 377) (t - 540)}{180} + 377 if t > 540 \land t ≦ 720 \\ \frac{(336 - 348) (t - 720)}{180} + 348 if t > 720 \land t ≦ 900 \\ \frac{(334 - 336) (t - 900)}{180} + 336 if t > 900 \land t ≦ 1080 \\ 334 if t > 1080 \land t ≦ stimEnd \\ 60 otherwise \end{matrix}

act_N = \frac{{Ca}^{n}}{{Ca}^{n} + {K_mN}^{n} (1 + \frac{K_dN}{M})}

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