  We investigate the structure of galaxies formed in a suite of high-resolution
cosmological simulations. Consistent with observations of high-redshift
galaxies, our simulated galaxies show irregular, prolate shapes, which are
dominated by turbulent motions instead of rotation. Yet molecular gas and young
stars are restricted to a relatively thin plane. We examine the accuracy of
applying the Toomre linear stability analysis to predict the location and
amount of gas available for star formation. We find that the Toomre criterion
still works for these irregular galaxies, after correcting for multiple gas and
stellar components: the $Q$ parameter in $\rm{H_2}$ rich regions is in the
range $0.5-1$, remarkably close to unity. Due to the violent stellar feedback
from supernovae and strong turbulent motions, young stars and molecular gas are
not always spatially associated. Neither the $Q$ map nor the $\rm{H_2}$ surface
density map coincide with recent star formation exactly. We argue that the
Toomre criterion is a better indicator of future star formation than a single
$\rm{H_2}$ surface density threshold because of the smaller dynamic range of
$Q$. The depletion time of molecular gas is below 1~Gyr on kpc scale, but with
large scatter. Centering the aperture on density peaks of gas/young stars
systematically biases the depletion time to larger/smaller values and increases
the scatter.
