Modelling Plant Hormone Gradients

Abstract

Cellular patterning in the Arabidopsis root is coordinated via a localised auxin concentration maximum in the root tip, requiring the regulated expression of specific genes. The activities of plant hormones such as auxin, ethylene and cytokinin depend on cellular context and exhibit either synergistic or antagonistic interactions. Due to the complexity and nonlinearity of spatiotemporal interactions between both hormones and gene expression in root development, modelling plant hormone gradients requires a systems approach in which experimental data and modelling analysis are closely combined. Modelling therefore allows a predictive interrogation of highly complex and nonintuitive interactions between components in the system. Important factors to be considered when modelling hormone gradients include the construction of a hormonal crosstalk network, the formulation of kinetic equations and the construction of an in silico root map. A modelling approach enables the analysis of relationships between multiple hormone gradients, predictions on how hormone gradients emerge under the action of hormonal crosstalk, and the prediction and elucidation of experimental results from mutant roots.

Key Concepts

  • Patterning in Arabidopsis root development is coordinated via a localised auxin concentration maximum in the root tip, requiring the regulated expression of specific genes.
  • The activities of plant hormones such as auxin, ethylene, cytokinin, abscisic acid, gibberellin and brassinosteroids depend on cellular context and exhibit either synergistic or antagonistic interactions.
  • Auxin concentration and the associated regulatory and target genes are regulated by diverse interacting hormones and gene expression and therefore cannot change independently of the various crosstalk components in space and time.
  • Other hormone concentrations, such as ethylene and cytokinin concentrations, and expression of the associated regulatory and target genes are also interlinked.
  • Modelling plant hormone gradients requires a systems approach where experimental data and modelling analysis are closely combined.
  • A hormonal crosstalk network describes the regulatory relationships between hormones and their associated genes.
  • A kinetic equation can be formulated for any regulatory relationship following thermodynamic and kinetic principles.
  • Construction of an in silico root map enables the study of multicellular cell–cell communications in Arabidopsis root development.
  • Modelling hormone gradients enables the analysis of relationships between multiple hormone gradients, predictions on how hormone gradients emerge under the action of hormonal crosstalk, and the prediction and elucidation of experimental results from mutant roots.
  • Modelling auxin gradients can also incorporate different mechanisms of polar auxin transport and the interaction of hormone gradients and root growth.

Keywords: Arabidopsis; root development; hormone gradients; hormonal crosstalk; mathematical modelling; kinetics; in silico root map; gene expression; metabolic regulation; systems biology

Figure 1. The hormonal crosstalk network constructed based on experimental data. Symbols: Auxin: auxin hormone, ET: ethylene, CK: cytokinin, PINm: PIN mRNA, PINp: PIN protein, PLSm: POLARIS mRNA, PLSp: POLARIS protein, X: downstream ethylene signalling, Ra*: active form of auxin receptor, Ra: inactive form of auxin receptor, Re*: active form of ethylene receptor, ETR1. Re: inactive form of ethylene receptor, ETR1, CTR1*: active form of CTR1, CTR1: inactive form of CTR1, AUX1m: AUX1 mRNA, AUX1p: AUX1 protein. Reproduced with permission from Moore et al. (2015a) © John Wiley and Sons.
Figure 2. Methodology for formulating kinetic equations based on experimental data. A kinetic equation can be formulated for any regulatory relationship following thermodynamic and kinetic principles.
Figure 3. Root structure and construction of an in silico root map. (a) A simple rectangular multicellular root showing the developmental regions and the different tissue layers. EZ: elongation zone; MZ: meristematic zone; COL: columella; QC: quiescent centre. (b) An example matrix of grid points, which code for a MZ cell tier in the root map. Cell files: E: epidermal/cortex; P: pericycle; V: vascular. Grid point codes: 0, cytosol; 1, 2 and 3, cell wall grid points. PIN protein is cycled from the nearest neighbour cytosolic grid point to the cell wall grid points using different rate constants: 1: low, 2: medium, 3: high.
Figure 4. Modelled colour maps demonstrating concentration gradients for auxin, ethylene and cytokinin hormones, and the PIN and AUX1 auxin carrier proteins in the root. Selected expanded views show species gradients in detail. EZ: elongation zone; MZ: meristematic zone; COL: columella; QC: quiescent centre. Red arrows indicate the location of the expanded views in each colour map.
Figure 5. Modelling predictions for the average auxin concentration in different cell types or tissues. (a) Individual auxin profiles showing the average auxin concentration down the longitudinal axis of the root for the three different cell types (epidermal, pericycle and vascular cells), indicating that the auxin maximum is predominantly established in the central vascular tissues at or close to the quiescent centre (QC). (b) Average auxin concentrations relative to the QC in different regions of the root, with the maximum occurring in the QC region. QC: quiescent centre; COL: columella; STE: stele; END: endodermis; CO: cortex; EP: epidermis; MZ: meristematic zone; EZ: elongation zone.
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References

Abley K, Barbier De Reuille P, Strutt D, et al. (2013) An intracellular partitioning‐based framework for tissue cell polarity in plants and animals. Development 140: 2061–2074.

Adamowski M and Friml J (2015) PIN‐dependent auxin transport: action, regulation, and evolution. The Plant Cell 27: 20–32.

Band LR, Úbeda‐Tomás S, Dyson RJ, et al. (2012) Growth‐induced hormone dilution can explain the dynamics of plant root cell elongation. Proceedings of the National Academy of Sciences of the USA 109: 7577–7582.

Band LR, Wells DM, Fozard JA, et al. (2014) Systems analysis of auxin transport in the Arabidopsis root apex. The Plant Cell 26: 862–875.

Barbier de Reuille P, Routier‐Kierzkowska AL, Kierzkowski D, et al. (2015) MorphoGraphX: a platform for quantifying morphogenesis in 4D. eLife 4: e05864. DOI: 10.7554/eLife.05864.

Bennett MJ, Marchant A, Green HG, May ST, et al. (1996) Arabidopsis AUX1gene: a permease‐like regulator of root gravitropism. Science 273: 948–950.

Bennett T, Hines G and Leyser O (2014) Canalization: what the flux? Trends in Genetics 30: 41–48.

van Berkel K, de Boer RJ, Scheres B and ten Tusscher K (2013) Polar auxin transport: models and mechanisms. Development 140: 2253–2268.

Bishopp A, Lehesranta S, Vaten V, et al. (2011) Phloem‐transported cytokinin regulates polar auxin transport and maintains vascular pattern in theroot meristem. Current Biology 21: 927–932.

Blilou I, Xu J, Wildwater M, et al. (2005) The PIN auxin efflux facilitator network controls growth and patterning in Arabidopsis roots. Nature 433: 39–44.

Chapman EJ and Estelle M (2009) Mechanism of auxin‐regulated gene expression in plants. Annual Review of Genetics 43: 265–285.

De Rybel B, Adibi M, Breda AS, et al. (2014) Integration of growth and patterning during vascular tissue formation in Arabidopsis. Science 345: 1255215.

De Vos D, Vissenberg K, Broeckhove J, et al. (2014) Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root? PLoS Computational Biology 10: e1003910.

Fàbregas N, Formosa‐Jordan P, Confraria A, et al. (2015) Auxin influx carriers control vascular patterning and xylem differentiation in Arabidopsis thaliana. PLoS Genetics 11 (4): e1005183. DOI: 10.1371/journal.pgen.1005183.

Garay‐Arroyo A, De La Paz SM, Garcıa‐Ponce B, et al. (2012) Hormone symphony during root growth and development. Developmental Dynamics 241: 1867–1885.

Grieneisen VA, Xu J, Marée AFM, et al. (2007) Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 449: 1008–1013.

Grunewald W and Friml J (2010) The march of the PINs: developmental plasticity by dynamic polar targeting in plant cells. The EMBO Journal 29: 2700–2714.

Hill K, Porco S, Lobet G, et al. (2013) Root systems biology: integrative modeling across scales, from gene regulatory networks to the rhizosphere. Plant Physiology 163: 1487–1503.

Jones B and Ljung K (2011) Auxin and cytokinin regulate each other's levels via a metabolic feedback loop. Plant Signal and Behavior 1: 6(6).

Klipp E, Liebermeister W, Wierling C, et al. (2009) Systems Biology, a Text Book. Weinheim: WILEY‐VCH Verlag GmbH & Co. KgaA.

Kramer EM, Rutschow HL and Mabie SS (2011) AuxV: a database of auxin transport velocities. Trends in Plant Science 16: 461–463.

Leskovac V (2003) Comprehensive enzyme kinetics. Kluwer Academic/Plenum: Publishers.

Liu JL, Mehdi S, Topping J, Tarkowski P and Lindsey K (2010) Modelling and experimental analysis of hormonal crosstalk in Arabidopsis. Molecular Systems Biology 6: 373.

Liu JL, Mehdi S, Topping J, Friml J and Lindsey K (2013) Interaction of PLS and PIN and hormonal crosstalk in Arabidopsis root development. Frontiers in Plant Science 4: 75.

Liu J, Rowe J and Lindsey K (2014) Hormonal crosstalk for root development: a combined experimental and modelling perspective. Frontiers in Plant Science 5: 116.

Ljung K (2013) Auxin metabolism and homeostasis during plant development. Development 140: 943–950.

Mahonen AP, ten Tusscher K, Siligato R, et al. (2014) PLETHORA gradient formation mechanism separates auxin responses. Nature 515: 125–129.

Moore S, Zhang X, Mudge A, et al. (2015a) Spatiotemporal modelling of hormonal crosstalk explains the level and patterning of hormones and gene expression in Arabidopsis thaliana wildtype and mutant roots. New Phytologist. DOI: 10.1111/nph.13421.

Moore S, Zhang X, Liu J and Lindsey K (2015b) Some fundamental aspects of modelling auxin patterning in the context of auxin‐ethylene‐cytokinin crosstalk. Plant Signaling and Behavior, DOI: 10.1080/15592324.2015.1056424.

Naseem M, Philippi N, Hussain A, et al. (2012) Integrated systems view on networking by hormones in Arabidopsis immunity reveals multiple crosstalk for cytokinin. The Plant Cell 24: 1793–1814.

Nordstrom A, Tarkowski P, Tarkowska D, et al. (2004) Auxin regulation of cytokinin biosynthesis in Arabidopsis thaliana: a factor of potential importance for auxin–cytokinin‐regulated development. Proceedings of the National Academy of Sciences of the USA 101: 8039–8044.

Peer WA, Blakeslee JJ, Yang H and Murphy AS (2011) Seven things we think we know about auxin transport. Molecular Plant 4: 487–504.

Péret B, Swarupa K, Fergusonet A, et al. (2012) AUX/LAX genes encode a family of auxin influx transporters that perform distinct functions during Arabidopsis development. The Plant Cell 24: 2874–2885.

Petrasek J, Mravec J, Bouchard RD, et al. (2006) PIN proteins perform a rate‐limiting function in cellular auxin efflux. Science 312: 914–918.

Rutschow HL, Baskin TI and Kramer EM (2011) Regulation of solute flux through plasmodesmata in the root meristem. Plant Physiology 155: 1817–1826.

Ruzicka K, Ljung K, Vanneste S, et al. (2007) Ethylene regulates root growth through effects on auxin biosynthesis and transport‐dependent auxin distribution. The Plant Cell 19: 2197–2212.

Sabatini S, Sabatini S, Beis D, et al. (1999) An auxin‐dependent distal organizer of pattern and polarity in the Arabidopsis root. Cell 99: 463–472.

Sauro HM (2011) Enzyme Kinetics for Systems Biology. Seattle: Ambrosius Publishing.

Schaller GE, Bishopp A and Kieber JJ (2015) The yin‐yang of hormones: cytokinin and auxin interactions in plant development. The Plant Cell 27: 44–63.

Shi Y, Tian S, Hou L, et al. (2012) Ethylene signaling negatively regulates freezing tolerance by repressing expression of CBF and type‐A ARR genes in Arabidopsis. The Plant Cell 24: 2578–2595.

Stepanova AN, Jun J, Likhacheva AV and Alonso JM (2007) Multilevel interactions between ethylene and auxin in Arabidopsis roots. The Plant Cell 19: 2169–2185.

Swarup R, Perry P, Hagenbeek D, et al. (2007) Ethylene upregulates auxin biosynthesis in Arabidopsis seedlings to enhance inhibition of root cell elongation. The Plant Cell 19: 2186–2196.

Tanimoto M, Roberts K and Dolan L (1995) Ethylene is a positive regulator of root‐hair development in Arabidopsis thaliana. The Plant Journal 8: 943–948.

To JP, Haberer G, Ferreira FJ, et al. (2004) Type‐A Arabidopsis response regulators are partially redundant negative regulators of cytokinin signaling. The Plant Cell 16: 658–671.

Vanneste S and Friml J (2009) Auxin: a trigger for change in plant development. Cell 136: 1005–1016.

Voß U, Bishopp A, Farcot E and Bennett MJ (2014) Modelling hormonal response and development. Trends in Plant Science 19: 311–319.

Vogel JP, Woeste KE, Theologis A and Kieber JJ (1998) Recessive and dominant mutations in the ethylene biosynthetic gene ACS5 of Arabidopsis confer cytokinin insensitivity and ethylene overproduction, respectively. Proceedings of the National Academy of Sciences of the USA 95: 4766–4771.

Yoshida S, Barbier de Reuille P, Lane B, et al. (2014) Genetic control of plant development by overriding a geometric division rule. Developmental Cell 29: 75–87.

Further Reading

Kieber JJ and Schaller GE (2014) Cytokinins. The Arabidopsis Book 11: e0168. DOI: 10.1199/tab.0168.

Klipp E, Liebermeister W, Wierling C, et al. (2009) Systems Biology, a Text Book. Weinheim: WILEY‐VCH Verlag GmbH & Co. KgaA.

Leskovac V (2003) Comprehensive Enzyme Kinetics. New York: Kluwer Academic/Plenum Publishers.

Sauro HM (2011) Enzyme Kinetics for Systems Biology. Ambrosius Publishing.

Zhao Y (2014) Auxin biosynthesis. The Arabidopsis Book 11: e0173. DOI: 10.1199/tab.0173.

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Moore, Simon, Zhang, Xiaoxian, Liu, Junli, and Lindsey, Keith(Oct 2015) Modelling Plant Hormone Gradients. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0023733]