1) v1 = Vmax1 a [t]/(a[t] + km1);

v2 = Vmax2 b [t]/(b[t] + km2);

v3 = Vmax3 c [t]/(b[t] + km3);

v4 = Vmax4 d [t]/(d[t] + km4); v4N = (Vmax4f*d[t]/(km4f) − Vmax4r*e[t]/(km4r))/(1 + d[t]/(km4f) + e[t]/(km4r));

v5 = Vmax5 e[t]/(e[t] + km5);

v6 = Vmax6 f[t]/(f[t] + km6);

v7 = Vmax7 q[t]/(q[t] + km7);

v8 = Vmax8 h[t]/(h@t) + km8);

2) Vmax1 = 1; km1 = 1; Vmax2 = 1; km2 = 1; Vmax3 = 1; km3 = 1; Vmax4 = 1; km4 = 1; Vmax4f = 1; km4f = 1;

Vmax4r = 1; km4r = 1; Vmax5 = 1; km5 = 1; Vmax6 = 1; km6 = 1; Vmax7 = 1; km7 = 1; Vmax8 = 1; km8 = 1;

3) NDSolve[{a'[t] == v8 − v1, b' [t] == v1 − v2, c' [t] == v2 − v3,

d'[t] == v3 − v4, e'[t] == v4 − v5, f'[t] == v5 − v6, q'[t] == v6 − v7,

h'[t] == v7 − v8, a[0] == 1, b[0] == 0, c[0] == 0, d[0] == 0, e[0] ==0,

f[0] == 0, q[0] == 0, h[0] == 0}, {a, b, c, d, e, f, q, h}, {t, 0, 15}];

4) Plot[{Evaluate[a[t] /. %], Evaluate[b[t] /. %],

Evaluate[c[t]/. %], Evaluate[d[t]/. %], Evaluate[e[t]/. %],

Evaluate[f[t]/. %], Evaluate[q[t]/. %], Evaluate[h[t]/. %]},

{t, 0, 15}, PlotRange ⇒ {0, 1}, PlotStyle ⇒ {Gray, Thickness[0.01], Dashed, Thickness[0.01], Dashed, Thickness[0.01], Dashed, Gray}]