Auxin transport model for leaf venation

Genome-wide identification and expression analysis of AUX/LAX family genes in Chinese hickory (Carya cathayensis Sarg.) Under various abiotic stresses and grafting

Auxin is essential for regulating plant growth and development as well as the response of plants to abiotic stresses. AUX/LAX proteins are auxin influx transporters belonging to the amino acid permease family of proton-driven transporters, and are involved in the transport of indole-3-acetic acid (IAA). However, how AUX/LAX genes respond to abiotic stresses in Chinese hickory is less studied. For the first time identification, structural characteristics as well as gene expression analysis of the AUX/LAX gene family in Chinese hickory were conducted by using techniques of gene cloning and real-time fluorescent quantitative PCR. Eight CcAUX/LAXs were identified in Chinese hickory, all of which had the conserved structural characteristics of AUX/LAXs. CcAUX/LAXs were most closely related to their homologous proteins in Populus trichocarpa , which was in consistence with their common taxonomic character of woody trees. CcAUX/LAXs exhibited different expression profiles in different tissues, indicating their varying roles during growth and development. A number of light-, hormone-, and abiotic stress responsive cis-acting regulatory elements were detected on the promoters of CcAUX/LAX genes. CcAUX/LAX genes responded differently to drought and salt stress treatments to varying degrees. Furthermore, CcAUX/LAX genes exhibited complex expression changes during Chinese hickory grafting. These findings not only provide a valuable resource for further functional validation of CcAUX/LAXs, but also contribute to a better understanding of their potential regulatory functions during grafting and abiotic stress treatments in Chinese hickory.

Scaling relations for auxin waves

We analyze an 'up-the-gradient' model for the formation of transport channels of the phytohormone auxin, through auxin-mediated polarization of the PIN1 auxin transporter. We show that this model admits a family of travelling wave solutions that is parameterized by the height of the auxin-pulse. We uncover scaling relations for the speed and width of these waves and verify these rigorous results with numerical computations. In addition, we provide explicit expressions for the leading-order wave profiles, which allows the influence of the biological parameters in the problem to be readily identified. Our proofs are based on a generalization of the scaling principle developed by Friesecke and Pego to construct pulse solutions to the classic Fermi-Pasta-Ulam-Tsingou model, which describes a one-dimensional chain of coupled nonlinear springs.