Figure 6.

The $K_M$ ( = $k_8$) of the transport of DA into vesicles has a major influence on the controller accuracy for DOPA homeostasis toward step-wise increased perturbations by oxidative stress ($k_{14}$). (a) $k_8$ = $2.9\times {10}^{-3} \mathsf{\mu }$M; (b) $k_8$ = $2.9\times {10}^{-2} \mathsf{\mu }$M; (c) $k_8$ = $2.9\times {10}^{-1} \mathsf{\mu }$M; (d) 2.9 $\mathsf{\mu }$M. Other rate constants (a–d): $k_1$ = 10 $\mathsf{\mu }$M/min, $k_2$ = $1\times {10}^4$ $\mathsf{\mu }$M/min, $k_3$ = 74.4 $\mathsf{\mu }$M, $k_4$ = 6 $\mathsf{\mu }$M, $k_5$ = 10.0 $\mathsf{\mu }$M/min, $k_6$ = 346 $\mathsf{\mu }$M, $k_7$ = 6.0 $\mathsf{\mu }$M/min, $k_9$ = 2.3 $\mathsf{\mu }$M/min, $k_{10}$ = 0.025 min${}^{-1}$, $k_{11}$ = 1 $\mathsf{\mu }$M/min, $k_{12}$ = 50 $\mathsf{\mu }$M, $k_{13}$ = 437 $\mathsf{\mu }$M, $k_{14}$ phase 1: 0.0 min${}^{-1}$, $k_{14}$ phase 2: 0.01 min${}^{-1}$, $k_{14}$ phase 3: 0.1 min${}^{-1}$, $k_{15}$ = 2.3 $\mathsf{\mu }$M/min, $k_{16}$ = 56 $\mathsf{\mu }$M, $k_{17}$ = 0.01 min${}^{-1}$, $k_{18}$ = 90 $\mathsf{\mu }$M/min, $k_{19}$ = 111 $\mathsf{\mu }$M, $k_{20}$ = 0.1 $\mathsf{\mu }$M, $k_{21}$ = $1\times {10}^{-4} \mathsf{\mu }$M, $k_{22}$ = 0.0 min${}^{-1}$, $k_{23}$ = 0.0158 min${}^{-1}$. Initial concentrations, (a–d): $Tyr$ = 323.2 $\mathsf{\mu }$M, $DOPA$ = 52.9 $\mathsf{\mu }$M, $DA$ = 512.5 $\mathsf{\mu }$M, $D{A}_{ves}$ = 232.6 $\mathsf{\mu }$M, $D{A}_{ex}$ = 1.7 $\mathsf{\mu }$M. Framed panel c shows the calculations with the experimentally determined value [81] of $k_8$.