= Solution
Choose positive reference <concentrations> $C,C_s$ and a reference <flux> $J_0$, and define
$$
u=\frac cC,\qquad v=\frac{c_s}{C_s},\qquad
\tau=kt,\qquad j_\pm=\frac{J_\pm}{J_0}.
$$
Overdots now mean <derivatives> with respect to the dimensionless time $\tau$. The store balance becomes
$$
\frac{kC_s}{J_0}\dot v=j_+-j_--\frac{k_sC_s}{J_0}v.
$$
The total balance becomes $\dot u+(C_s/C)\dot v=r/(kC)-u$. Therefore
$$
\boxed{\mu=\frac r{kC},\qquad
\gamma=\frac{C_s}{C},\qquad
\varepsilon=\frac{kC_s}{J_0},\qquad
\delta=\frac{k_sC_s}{J_0},}
$$
and
$$
\boxed{\dot u=\mu-u-\gamma\dot v,\qquad
\varepsilon\dot v=j_+-j_--\delta v.}
$$
The reference quantities are scale choices, not additional kinetic variables; typically the response functions supply natural saturation <concentrations> and a maximal uptake <flux>. The identity $\delta/\varepsilon=k_s/k$ checks the <nondimensionalization>. A small $\varepsilon$ means store exchange is fast compared with external cytosolic removal.
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