$(1)$ Charging substrates and recovery of high$-$energy phosphate bonds, pool derivation. $(10$ points$)$

Consider the system:

$($a$)$ Derive the differential equation for the following pool in terms of the boundary and reaction fluxes. All work must be shown to receive full credit.

Given $p=x_1+2x_2+2$ATP$+$ADP, what is $\frac{dp}{dt}?$

$($b$)$ What does this pool physiologically represent?