Figure 3. Filling fraction $F^{\ast }$ in the short-term approximation of constant receptor number as a function of the ratio of transition rates $\rho =\beta /\alpha$ for different combinations of $R$ and $S$.

(A) $F^{\ast }$ for a fixed number of $S=10000$ slots and three different receptor numbers as a function of $\rho$. (B) For fixed number of $R=10000$ receptors and three different numbers of slots. Note that $F^{\ast }$ reacts particularly sensitively to changes in $\rho$ when $\rho$ is small and when $R=S$ (black curves). In this regime, small changes to, say, the rate of detaching from slots $\beta$ have a great influence on the filling fraction. In all cases, the shown solution $F^{\ast }$ is only transient. Eventually the filling fraction will assume its steady state value $F$ given by Equation 7.