Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2009 / B / 4 / d / i / Solution

At steady state the interior free-substrate balance gives $B_i=-J$. Substituting this into the interior free-carrier balance gives $0=J+k(c_e-c_i)$. ThereforeFor positive inward throughput there are more free carriers facing inward: release of transported substrate must be followed by outward return of empty carriers at net rate $k(c_i-c_e)=J$.