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

Abstract

Auxin has critical roles in plant growth, dependent upon its heterogeneous distribution in tissues. Exactly how auxin signalling and 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 these effects and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues were derived. Models were analysed and solved numerically to examine the long-time behaviour and auxin distribution. Changes in auxin-related signalling processes were 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 auxin levels which have been observed experimentally. Cell growth was shown to have strong influence on PIN polarisation and determination of auxin distribution patterns. Numerical simulation results indicate that auxin-related signalling processes can explain the different auxin distributions observed in plant tissues, whereas interplay between auxin transport and growth can explain the 'reverse-fountain' pattern in auxin distribution observed at root tips.

All Roads Lead to Auxin: Post-translational Regulation of Auxin Transport by Multiple Hormonal Pathways

“…With an increasing number of confirmed molecular interactions and circuits that determine and fine-tune PAT, modeling and mathematical simulations might offer important tools to provide novel insights into the dynamics of PAT ( Prusinkiewicz et al., 2009 , Voß et al., 2014 , Allen and Ptashnyk, 2020 ). Several models have been developed to gain a better understanding of the hormonal regulation of PAT in the context of various developmental processes, such as root growth ( Di Mambro et al., 2017 ), apical hook development ( Žádníková et al., 2016 ), and vasculature differentiation ( De Rybel et al., 2014 , Mellor et al., 2019 ).…”

Smoothed particle hydrodynamics for root growth mechanics

“…A way to bring together these two aspects is to formulate a multi-scale approach, combining several levels of description and allowing them to interact. Several propositions exist and among them, gene-regulated network combined to growth [4,31,58,71,27], averaging approaches through analytical homogenisation [1,35,65,79,82], and the incorporation of a representation of individual cells in a continuous formulation of tissue deformation [5,13,42,48,53,99].…”

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“…( 2015 ), using advanced tools such as snaking from the field of bifurcation theory. Both periodic and stationary patterns are examined in Allen and Ptashnyk ( 2020 ), where the authors consider an extended with-the-gradient model. Haskovec and his coworkers derive local and global existence results together with an appropriate continuum limit for their graph-based diffusion model in Haskovec et al.…”