Modelling of Plant Growth and Development

Anne‐Gaëlle Rolland‐Lagan, University of Ottawa, Ottawa, Ontario, Canada

Published online: March 2009

DOI: 10.1002/9780470015902.a0020107

The development of an organism results from complex interactions between biophysical and biochemical processes and is very dynamic. Therefore the mechanisms at play are best studied using computer simulations. The large amount of molecular data on multiple aspects of plant development and advances in plant imaging make it possible to use simulation modelling as a tool to complement experimental studies. For instance, models of gene regulation networks can predict genetic interactions, which can later be tested experimentally. Models of pattern formation in the root and the shoot based on the transport of the plant hormone auxin can simulate the localization of proteins involved in auxin efflux as well as generating realistic profiles of auxin distribution. Models are also starting to incorporate growth and the role of mechanical forces in development, which should provide a link between molecular biology studies and biophysics.

Key concepts

  • Plant development is highly dynamic as pattern formation and growth occur concurrently.
  • Modelling studies which can account for observed experimental data suggest genetic interactions in space can generate spatial patterns during plant development in a similar way to reaction-diffusion mechanisms initially postulated in the middle of the twentieth century.
  • Models of the relation between auxin gradient and root growth suggests the plant hormone auxin acts similarly to a morphogen. In the case of auxin the response to the morphogen may affect the morphogen gradient. This feedback mechanism can generate patterns similar to reaction diffusion and may account for phyllotaxis and leaf vein pattern formation. Experimental data is still needed to link models of auxin-regulated pattern formation with gene regulatory networks.
  • Mechanical forces affect growth and pattern formation. Methodologies are being developed to model the biomechanics of growth and integrate patterning through chemical and physical processes at various scales of organization.

Keywords: plant development; growth; pattern formation; modelling; simulation

Figure 1. Mechanisms for pattern formation. (a) Local autocatalysis and long-range inhibition mechanism: An activator activates itself and also activates an inhibitor (red arrows). The inhibitor inhibits activator production (blue arrow). The inhibitor diffuses faster than the activator (represented by gradients in activator and inhibitor boxes). Activator and inhibitors are both degraded at a certain rate. The system can be started through a background homogeneous production of activator. The reactions at play combined with the fact that the inhibitor diffuses faster than the activator (long-range inhibition) generates spatial patterns of activator and inhibitor distributions. (b) The French flag model was built to show how a gradient of a morphogen can be interpreted by cells so that different morphogen concentrations c will lead to different cellular states. The purple gradient represents morphogen concentrations along a band of tissue. This gradient is interpreted by cells. For high morphogen concentrations (c>threshold 1) cells differentiate into ‘blue’, for medium concentrations (threshold 2<cc
Figure 2. Modelling a gene regulation network. (a) A hypothetical gene regulation network is represented as set of nodes, which represent the entities studied (e.g. genes, proteins, small molecules). In this example nodes represent genes A, B, C and D. Nodes are connected by directed arrows representing the interactions between entities. Pointed and flat arrows represent positive and negative regulation, respectively. (b) A set of initial conditions (time t0) specify the state of each node. Interaction rules are then applied iteratively to update node states: the state at iteration tn+1 is based on the state at iteration tn. The rules may be described using different types of formalisms, which can be continuous or discrete, deterministic or stochastic. The system eventually converges towards a steady state, which can be fixed or periodic (the system repeatedly cycles through a finite number of states). In this simple example a boolean formalism is used so that states of genes can only be 0 (‘off’: no gene expression) or 1 (‘on’: the gene is expressed). At t0, only D is ‘on’. D activates A so that both A and D are on at t1. At t2 A, B and D are ‘on’ and the system has reached a fixed steady state. Adapted from Alvarez-Buylla et al. (2007).
Figure 3. A role for reaction-diffusion mechanisms in plant pattern formation. (a) Regulation network and reaction diffusion model of trichome formation (based on Benitez et al., 2007). A set of activator genes (GL3, GL1, TTG1, EGL3) code for proteins which form an activator complex. This complex activates TRY and CPC which inhibit the activator complex. The activator is postulated to activate itself. The model is equivalent to a reaction-diffusion model where TRY/CPC is considered an inhibitor complex. The activator complex activates GL2 transcription which leads to trichome differentiation. Spatial patterns of high activator concentrations therefore generate trichome patterns. (b) Modelling WUS expression domain using reaction-diffusion. A longitudinal section of the SAM is shown with the domain of expression of WUS and other genes known (CLV3, CLV1) or postulated (predicted gene L1) to affect WUS expression. Jönsson et al. (2005) propose a model whereby a reaction-diffusion mechanism would generate a spatial pattern of an activator that would activate WUS expression. However, a postulated gene expressed in the epidermal layer (termed L1 here) would code for a mobile signal repressing WUS. (a) and (b): Red arrows indicate positive regulation and blue arrows negative regulation.
Figure 4. Model principles for mechanisms of auxin-mediated patterning. (a) auxin distribution at the root tip is controlled by the tissue-specific subcellular localization of PIN proteins involved in auxin efflux. Modelling studies (Grieneisen et al., 2007) propose this maintains a gradient of auxin which then affects root growth in a concentration dependant way. Simplified auxin gradient as suggested by modelling is shown in blue. Darker blue indicates higher auxin concentrations. Black arrows show routes of auxin transport which reflect experimentally characterized subcellular polarities of PIN proteins: auxin moves in an ‘inverted fountain’. (b) Models of auxin-mediated patterning are based on the feedback relation between auxin transport and auxin distribution. auxin can affect PIN expression and localization (through intermediate gene regulation), which in turn affects auxin distribution and local concentrations. Models incorporating growth also include an effect of auxin on growth. This effect may be reciprocal as growth affects the domain size and shape where patterning processes take place.
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Related Sub-Topics:

Intracellular and Extracellular Signalling | Growth and Synthesis | Developmental Models | Plant Cell Differentiation | Plant Cell Growth | Plant Development | Plant Genetics and Molecular Biology
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Article Title: Modelling of Plant Growth and Development
 
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Rolland‐Lagan, Anne‐Gaëlle(Mar 2009) Modelling of Plant Growth and Development. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0020107]