Primary root growth: a biophysical model of auxin-related control

Abstract

Plant hormones control many aspects of plant development and play an important role in root growth. Many plant reactions, such as gravitropism and hydrotropism, rely on growth as a driving motor and hormones as signals. Thus, modelling the effects of hormones on expanding root tips is an essential step in understanding plant roots. Here we achieve a connection between root growth and hormone distribution by extending a model of root tip growth, which describes the tip as a string of dividing and expanding cells. In contrast to a former model, a biophysical growth equation relates the cell wall extensibility, the osmotic potential and the yield threshold to the relative growth rate. This equation is used in combination with a refined hormone model including active auxin transport. The model assumes that the wall extensibility is determined by the concentration of a wall enzyme, whose production and degradation are assumed to be controlled by auxin and cytokinin. Investigation of the effects of auxin on the relative growth rate distribution thus becomes possible. Solving the equations numerically allows us to test the reaction of the model to changes in auxin production. Results are validated with measurements found in literature.

Effective diffusion rates and cross-correlation analysis of “acid growth” data

“…A hormone model of primary root growth in which the wall extensibility is determined by the concentration of a wall enzyme (unspecified by the authors), whose production and degradation are assumed to be controlled by auxin and cytokinin, was proposed by Chavarria-Krauser et al (2005). Additionally, the role of new class of plant hormones, strigolactones (SLs), was postulated in this process (de Saint Germain et al 2013;Marzec and Muszynska 2015).…”

Multiscale modelling of auxin transport in the plant-root elongation zone

“…Delbarre et al (1996Delbarre et al ( , 1994) measured the passive-diffusion membrane permeability in tobacco cells as 0.14 − 0.18 cm h −1 and the majority of previous modelling studies use estimates around these values (Chavarrıa-Krauser et al 2005;Goldsmith et al 1981;Heisler and Jönsson 2006;Jönsson et al 2006;Kramer 2004Kramer , 2009Swarup et al 2005); thus following Swarup et al (2005), we set P I AAH = 0.2 cm h −1 = 0.56 µm s −1 . Experimental values for the membrane permeabilities due to the influx and efflux carriers have not been well characterised.…”

“…Early studies (Goldsmith et al 1981;Martin et al 1990;Mitchison 1980b) considered only a single line of cells, with auxin diffusion within the cytoplasms and with passive and carrier-mediated transport across the cell membranes; these showed how the efflux carriers increase the tissue-scale auxin flux. More recent studies have considered more complex tissue geometries and have incorporated apoplastic diffusion Jönsson et al 2006;Kramer 2004;Laskowski et al 2008;Swarup et al 2005), saturable carrier-mediated transport (de Reuille et al 2006;Feugier et al 2005;Jönsson et al 2006;Merks et al 2007;Smith et al 2006), cytoplasmic structure (Kramer 2004;Perrine-Walker et al 2010), cell growth (Chavarrıa-Krauser et al 2005;Grieneisen et al 2007;Jönsson et al 2006;Mironova et al 2010;Stoma et al 2008), auxin production and degradation (Feugier and Iwasa 2006;Feugier et al 2005;Perrine-Walker et al 2010;Heisler and Jönsson 2006;Jönsson et al 2006;Smith et al 2006;Stoma et al 2008) and dynamics of the efflux carriers Jönsson et al 2006;Kramer 2009;Merks et al 2007;Mironova et al 2010;Stoma et al 2008).…”

Multiscale Systems Analysis of Root Growth and Development: Modeling Beyond the Network and Cellular Scales

“…Multiscale models have addressed the transport of several hormones, including auxin (Swarup et al, 2005;Grieneisen et al, 2007), gibberellin (Band et al, 2012a), and cytokinin (Chavarria-Krauser et al, 2005). These models of gibberellin and cytokinin have supposed passive diffusion between adjacent cells, taking the simplest assumption, which may require revision as biological knowledge increases (Cedzich et al, 2008).…”

“…Due to the predicted auxin distribution ( Figure 2B), their model simulates cell's division and growth dynamics in the meristem and elongation zone, capturing the gradual expansion of the meristem over the first 8 d after germination and the reduction in meristem size after root excision. Chavarria-Krauser et al (2005) modeled the growth dynamics at the root tip, supposing that the ratio between auxin and cytokinin governs the production and degradation of a remodeling enzyme, which in turn regulates cell growth and division. Considering root developmental responses, Lucas et al (2008b), in predicting lateral root initiation, considered a pool of auxin at the root tip that is consumed by root gravitropic bending and/or emergence.…”