The relationships between modeled I_HCN/I_CO, f(n > 10^4.5 cm⁻³), f_grav, and t_dep. Left: Modeled I_HCN/I_CO as a function of the gravitationally bound fraction of gas (f_grav) predicted by the LN+PL analytical models of star formation. Center: Fraction of dense gas above n > 10^4.5 cm⁻³ as a function of the gravitationally bound fraction of gas (f_grav) predicted by the LN+PL analytical models of star formation. The formatting is the same as in Fig. 3. The Spearman rank coefficients are shown in the lower right corner of the left and center panels. Right: Total gas depletion time (t_dep) as a function of I_HCN/I_CO ratio. The models are shown as colored points. The measurements of t_dep and I_HCN/I_CO from our sample of galaxies and the EMPIRE sample are shown as the solid black and dashed black contours, respectively. Our models find that the I_HCN/I_CO ratio is negatively correlated with f_grav as predicted by gravoturbulent models of star formation. Additionally, the fraction of dense gas above n > 10^4.5 cm⁻³ has an even steeper negative correlation with f_grav, as predicted by gravoturbulent models of star formation (e.g., Burkhart 2018; Burkhart & Mocz 2019). Thus, although I_HCN/I_CO is sensitive to gas above moderate densities, we conclude that a single molecular line ratio, such as HCN/CO, does not necessarily scale with the fraction of directly star-forming gas in clouds. We also find that models with the lowest estimates of f_grav and highest f(n > 10^4.5 cm⁻³) have the shortest depletion times, and the corresponding modeled I_HCN/I_CO and predicted depletion times are consistent with our data.