ssci sahil.science
← All Findings
arxiv 95% relevant

Mathematical Modelling of Auxin Transport in Plant Tissues: Flux meets Signalling and Growth

Henry R. Allen, Mariya Ptashnyk

plant-growthmorphogenesisauxinchemical-gradientsmathematical-modeling

Abstract

Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such as growth coordinate to achieve the precise patterns of auxin observed experimentally is not well understood. Here we use mathematical modelling to examine the interplay between auxin dynamics and growth and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing the auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues are derived. A key assumption of our models is the regulation of PIN proteins by the auxin-responsive ARF-Aux/IAA signalling pathway, with upregulation of PIN biosynthesis by ARFs. Models are analysed and solved numerically to examine the long-time behaviour and auxin distribution. Changes in auxin-related signalling processes are shown to be able to trigger transition between passage and spot type patterns in auxin distribution. The model was also shown to be able to generate isolated cells with oscillatory dynamics in levels of components of the auxin signalling pathway which could explain oscillations in levels of ARF targets that have been observed experimentally. Cell growth was shown to have influence on PIN polarisation and determination of auxin distribution patterns. Numerical simulation results indicate that auxin-related signalling processes can explain the different patterns in auxin distributions observed in plant tissues, whereas the interplay between auxin transport and growth can explain the 'reverse-fountain' pattern in auxin distribution observed at plant root tips.

Summary

This paper directly addresses the concept that plant tissues are controlled by chemical gradients. It presents comprehensive mathematical models showing how auxin (a key plant hormone) creates heterogeneous distributions across tissues, and how cells respond differently depending on their position in these gradients.

Key insights supporting the “tissues behaving differently in chemical gradients” concept:

  1. Gradient-dependent behavior: Cells do not act uniformly - their growth and differentiation depend on local auxin concentration and the direction of auxin flux through the tissue.

  2. Pattern formation: The models show how simple rules about cell responses to auxin gradients can generate complex patterns like “passage” (channel-like) and “spot” patterns in auxin distribution.

  3. Feedback loops: PIN transporter proteins create positive feedback - they help transport auxin, and their own distribution is influenced by auxin levels, creating self-reinforcing gradients.

  4. The “reverse-fountain” pattern: At root tips, auxin flows down through the center and back up through the outer layers, creating a gradient that instructs cells on how to differentiate.

This work provides mathematical proof that plant morphogenesis can emerge from cells responding to their local position in hormone gradients.

Read original