  We examine the physical parameters that affect the accumulation of gas in
molecular clouds to high column densities where the formation of stars takes
place. In particular, we analyze the dense gas mass fraction (DGMF) in a set of
self-gravitating, isothermal, magnetohydrodynamic turbulence simulations
including sink particles to model star formation. We find that the simulations
predict close to exponential DGMFs over the column density range N(H2) = 3-25 x
10^{21} cm^{-2} that can be easily probed via, e.g., dust extinction
measurements. The exponential slopes correlate with the type of turbulence
driving and also with the star formation efficiency. They are almost
uncorrelated with the sonic Mach number and magnetic-field strength. The slopes
at early stages of cloud evolution are steeper than at the later stages. A
comparison of these predictions with observations shows that only simulations
with relatively non-compressive driving (b ~< 0.4) agree with the DGMFs of
nearby molecular clouds. Massive infrared dark clouds can show DGMFs that are
in agreement with more compressive driving. The DGMFs of molecular clouds can
be significantly affected by how compressive the turbulence is on average.
Variations in the level of compression can cause scatter to the DGMF slopes,
and some variation is indeed necessary to explain the spread of the observed
DGMF slopes. The observed DGMF slopes can also be affected by the clouds' star
formation activities and statistical cloud-to-cloud variations.
