\section{DISCUSSION}

We can examine the \citet{Krumholz_2005} model for the star formation in these systems which predicts that the star formation efficiency $(\propto \tau_{\mathrm{H2}}^{-1})$ should scale like
\begin{equation}
\mathrm{SFE} = \epsilon_{\mathrm{SF}} \frac{(\mathcal{M}/100)^{-0.32}}{\tau_{\mathrm{ff}}} \left(\frac{\alpha_{\mathrm{vir}}}{1.3}\right)^{-0.68}
\end{equation}
where $\epsilon_{\mathrm{SF}}$ is the star formation efficiency per free-fall time in the system (=0.014) and $\tau_{\mathrm{ff}}$ is the free-fall time: 
\begin{equation}
\tau_{\mathrm{ff}} = \sqrt{\frac{3\pi}{32 G \bar{\rho}}}
\end{equation}
where $\bar{\rho}$ is the average mass density in the cloud.

In Fig.~\ref{SFE}, we examine the relationship between the ISM depletion times, the corresponding star formation efficiencies, $SFE$, and the changing cloud populations. Here $SFE$, defined by Eq.~\ref{sfeeqn}, is a quantity proportional to the Krumholz-Mckee SFE.

\begin{equation}
\mathrm{SFE} \propto \sigma ^{-0.32} \left( \frac{M_\mathrm{lum}}{R^3} \right) ^{0.5}.
\label{sfeeqn}
\end{equation}

There is some separation between the three populations, including differences between the arm and inter-arm populations as well as between the nucleus and the remainder. Thus, while there is not a clear correlation between depletion time and any one parameter in the study, the {\it combination} of parameters that is thought to shape star formation efficiency on the large scales does show good correlation. Therefore, the clouds here in M100 seem to be consistent with a turbulence-regulated star formation model.