Several hypotheses have been formed to explain vein pattern formation. Sachs proposed that veins develop as a result of the gradual canalisation of auxin: the auxin transport capacity of some cell files increases, draining auxin from neighbouring cell files. Mitchison implemented models of auxin canalisation by postulating that the transport of auxin between cells is controlled by a feedback mechanism, in which the parameters of the transport process vary as a function of auxin flux. He considered two mechanisms: facilitated diffusion, in which transport is diffusive; and polar transport, in which transport has a non-diffusive character. Many experimental studies fit well within the canalisation hypothesis: auxin has been shown to be necessary for vein formation; it is transported in a polar way; and the PIN1 protein, involved in auxin efflux, localises progressively to one end of the cell. The growing amount of molecular data on auxin transport mechanisms and leaf venation patterns in Arabidopsis suggests that enough information may now be available to model these patterns in a realistic way. In that context, we examine Mitchison's models and show that models employing either facilitated diffusion or polar transport mechanisms can reproduce elements of Arabidopsis leaf vein pattern formation, such as the acropetal development of the primary vein, and the formation of the first two secondary veins. In the latter case, generating realistic loop patterns may depend on incorporating growth into the model. Finally, we use Mitchison's models to qualitatively reproduce some patterns observed in Arabidopsis mutants, such as the patterns that occur when the auxin transport is inhibited, and venation patterns with discontinuities.
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