= Solution
In this <two-pool calcium model>, $c$ is the cytosolic <calcium ion> <concentration>, and $c_s$ measures <calcium> in an intracellular store, such as the <endoplasmic reticulum>. The variables in these balances are expressed using compatible effective volumes, so internal transfers enter their two equations with equal and opposite signs. If actual compartment <concentrations> use different reference volumes, the corresponding volume ratio must first be included in their balances.
The <flux> $J_+$ pumps <calcium> from the <cytosol> into the store, $J_-$ releases it back, and $k_sc_s$ is passive store leakage back to the <cytosol>. The external input $r$ supplies cytosolic <calcium>, while $kc$ exports it from the <biological cell>. Thus $k,k_s$ have units of inverse time and all five <fluxes> have units of <concentration> per time. Their directions can be sketched as
$$
\text{exterior}\ \xrightarrow{\ r\ }\ \text{cytosol }c
\ \xrightarrow{\ J_+\ }\ \text{store }c_s,\qquad
\text{store }c_s\ \xrightarrow{\ J_-+k_sc_s\ }\ \text{cytosol }c
\ \xrightarrow{\ kc\ }\ \text{exterior}.
$$
Adding the two <ordinary differential equations> verifies the total <calcium> balance
$$
\boxed{\frac{d}{dt}(c+c_s)=r-kc.}
$$
Internal uptake, release and leakage redistribute <calcium>; only the exchanges across the <cell membrane> change this total. In particular any <equilibrium> must have $c=r/k$ when $k>0$.
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