  We have coupled a chemical model with two dynamical models of collapsing low
mass star-forming cores to predict abundances across the core of the commonly
used infall tracers, CS and HCO$^+$, at various stages of the collapse. The
models investigated are a new ambipolar diffusion model and the `inside-out'
collapse model. We have then used these results as an input to a radiative
transfer model to predict the line profiles of several transitions of these
molecules. For the inside-out collapse model, we predict significant molecular
depletion due to freeze-out in the core centre, which prevents the formation of
the blue asymmetry (believed to be the `signature' of infall) in the line
profiles. Molecular depletion also occurs in the ambipolar diffusion model
during the late stages of collapse, but the line profiles still exhibit a
strong blue asymmetry due to extended infall. For the inside-out collapse model
to exhibit the blue asymmetry it is necessary to impose a negative kinetic
temperature gradient on the core and suppress freeze-out. Since freeze-out is
observed in several class 0 protostars which are thought to be collapsing, this
presents a major inconsistency in the inside-out collapse model of star
formation.
