Discovery of spatial pattern of prickles on stem of Rosa hybrida 'Red Queen' and mathematical model of the pattern.

The developmental patterns of many organisms are orchestrated by the diffusion of factors. Here, we report a novel pattern on plant stems that appears to be controlled by inhibitor diffusion. Prickles on rose stems appear to be randomly distributed, but we deciphered spatial patterns of prickles on Rosa hybrida cv. 'Red Queen' stem. The prickles primarily emerged at 90 to 135 degrees from the spiral phyllotaxis that connected leaf primordia. We proposed a simple mathematical model that explained the emergence of the spatial patterns and reproduced the prickle density distribution on rose stems. We confirmed the model can reproduce the observed prickle patterning on stems of other plant species using other model parameters. These results indicated that the spatial patterns of prickles on stems of different plant species are organized by similar systems. Rose cultivation by humans has a long history. However, prickle development is still unclear and this is the first report of prickle spatial pattern with a mathematical model. Comprehensive analysis of the spatial pattern, genome, and metabolomics of other plant species may lead to novel insights for prickle development.