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Background  Rhizobium nitrogen fixation in legumes takes place in specialized organs called root nodules. The initiation of these symbiotic organs has two important components. First, symbiotic rhizobium bacteria are recognized at the epidermis through specific bacterially secreted lipo-chitooligosaccharides (LCOs). Second, signaling processes culminate in the formation of a local auxin maximum marking the site of cell divisions. Both processes are spatially separated. This separation is most pronounced in legumes forming indeterminate nodules, such as model organism  Medicago truncatula , in which the nodule primordium is formed from pericycle to most inner cortical cell layers.    Results  We used computer simulations of a simplified root of a legume that can form indeterminate nodules. A diffusive signal that inhibits auxin transport is produced in the epidermis, the site of rhizobium contact. In our model, all cells have the same response characteristics to the diffusive signal. Nevertheless, we observed the fastest and strongest auxin accumulation in the pericycle and inner cortex. The location of these auxin maxima correlates with the first dividing cells of future nodule primordia in  M. truncatula . The model also predicts a transient reduction of the vascular auxin concentration rootward of the induction site as is experimentally observed. We use our model to investigate how competition for the vascular auxin source could contribute to the regulation of nodule number and spacing.    Conclusion  Our simulations show that the diffusive signal may invoke the strongest auxin accumulation response in the inner root layers, although the signal itself is strongest close to its production site.    Electronic supplementary material  The online version of this article (doi:10.1186/s12870-016-0935-9) contains supplementary material, which is available to authorized users.

Quantitative modelling of legume root nodule primordium induction by a diffusive signal of epidermal origin that inhibits auxin efflux