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$\Gamma_c \equiv $ cytosolic invasion rate per attached bacteria, per host cell  $\quad \Gamma_x \equiv $ combined invasion rate per attached bacteria, per host cell $ = \Gamma_v + Gamma_c$ \Gamma_c $  %\noindent There is evidence that suggests a physical limit to the number of ruffles per cell $\tilde{r}_{\rm max}$, and the number of invaded bacteria per cell $\tilde{b}_{x, \rm max}$, so we define the following effective rates.  \noindent There is evidence that suggests a physical limit to the number of invaded bacteria per cell $\tilde{b}_{x, \rm max}$, so we define the following effective rate.