deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 20933a3..7691bbf 100644  --- a/untitled.tex  +++ b/untitled.tex 
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H_{\rm tot} = \left\vert{ \left\{H(t) \right\} \cup \left\{H_a (t) \right\} \cup \left\{H_v (t) \right\} \cup \left\{H_c (t) \right\} }\right\vert   \end{equation}  We also define infected host cells $H_x$ as any with internalized bacteria (vacuolar or cytosolic):  \begin{equation}  H_{x} = \left\vert{ \left\{H_v (t) \right\} \cup \left\{H_c (t) \right\} }\right\vert   \end{equation}  A well-studied feature of invasion by \textit{Salmonella} is the formation of epithelial cell membrane ruffles, triggered by effectors secreted via the bacterium's type III secretion system 1 (TTSS-1). We call the total number of ruffles $R (t)$, and the number of host cells with at least one ruffle $H_r (t)$.  An important and controllable quantity when performing invasion assays is the ratio of bacteria to host cells at inoculation. This is called the multiplicity of infection (MOI) and in terms of previously defined parameters, $m = B_{\rm tot} / H_{\rm tot}$. Another is the confluency, which is an estimate of the proportion of area covered by a monolayer of cells in a culture dish. In terms of average host cell area $A$ and side length of the square well $L$, we calculate confluency as $c = H_{\rm tot} A / L^2$. A similar, although time-dependent quantity, is the bacterial density per unit area $\rho_B (t) = B(t) / L^2$. More specifically, this is the density of bacteria have yet to attach to a host. 
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$h_a (t) \equiv $ fraction of host cells with attached bacteria $ = \frac{H_a}{H_{\rm tot}}$  $h_x (t) \equiv$ fraction of host cells with invaded bacteria $ = \frac{H_x}{H_{\rm tot}}$  $h_v (t) \equiv $ fraction of host cells with invaded vacuolar bacteria $ = \frac{H_v}{H_{\rm tot}}$  $h_c (t) \equiv $ fraction of host cells with invaded cytosolic bacteria $ = \frac{H_c}{H_{\rm tot}}$ 
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$\Gamma_b \equiv $ ruffle recruitment rate per bacterial density, per ruffle  \noindent Once attached, a bacterium can cause ruffling, invade the host cell and stay vacuolar, or invade the host cell and escape early  into the cytosol. $\Gamma_r \equiv $ ruffle formation rate per attached bacteria, per host cell