Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions (original) (raw)

A mathematical basis for plant patterning derived from physico-chemical phenomena

BioEssays : news and reviews in molecular, cellular and developmental biology, 2013

The position of leaves and flowers along the stem axis generates a specific pattern, known as phyllotaxis. A growing body of evidence emerging from recent computational modeling and experimental studies suggests that regulators controlling phyllotaxis are chemical, e.g. the plant growth hormone auxin and its dynamic accumulation pattern by polar auxin transport, and physical, e.g. mechanical properties of the cell. Here we present comprehensive views on how chemical and physical properties of cells regulate the pattern of leaf initiation. We further compare different computational modeling studies to understand their scope in reproducing the observed patterns. Despite a plethora of experimental studies on phyllotaxis, understanding of molecular mechanisms of pattern initiation in plants remains fragmentary. Live imaging of growth dynamics and physicochemical properties at the shoot apex of mutants displaying stable changes from one pattern to another should provide mechanistic insights into organ initiation patterns.

The role of chemical dynamics in plant morphogenesis1

Biochemical Society Transactions, 2010

In biological development, the generation of shape is preceded by the spatial localization of growth factors. Localization, and how it is maintained or changed during the process of growth, determines the shapes produced. Mathematical models have been developed to investigate the chemical, mechanical and transport properties involved in plant morphogenesis. These synthesize biochemical and biophysical data, revealing underlying principles, especially the importance of dynamics in generating form. Chemical kinetics has been used to understand the constraints on reaction and transport rates to produce localized concentration patterns. This approach is well developed for understanding de novo pattern formation, pattern spacing and transitions from one pattern to another. For plants, growth is continual, and a key use of the theory is in understanding the feedback between patterning and growth, especially for morphogenetic events which break symmetry, such as tip branching. Within the c...

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis

PloS one, 2018

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn m...

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

The International Journal of Developmental Biology, 2006

Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tipgrowing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.

Expression of pattern in plants: combining molecular and calculus-based biophysical paradigms

American Journal of Botany, 1999

Pattern formation in plant meristems occurs across a broad scale. At the topographical level (large scale), tissue folding in the meristem is responsible for the initiation of new organs in specific phyllotactic patterns and also determines organ shape. At the cellular level (small scale), oriented cell division and microtubule-based cellulose reinforcement control cell pattern and growth direction. I argue here that structural specification at each scale is highly efficient if the pertinent gene activity is manifested in two complementary biophysical categories. At large scale, one category is the tendency of the formative tissue to fold with a certain spatial periodicity determined by its material properties (e.g., bending stiffness from cellulose content). This latent tendency is formalized in a differential equation for physical buckling. The second category at this scale comprises boundary conditions that specify how the latent tendency is manifested as topography: whether tissue humps occur as whorls or Fibonacci spirals. This versatile combinatorial format accounts for the relative stability of alternative organ patterning as well as alternative organ shaping (e.g., stamens vs. carpels). It also accounts for the structural shifts seen in normal development and after mutation or chemical/physical intervention. At small scale, the latent differential activity is the tendency for groups of dividing cells to co-align their cytoskeletons. The curvature of the surface opposes this tendency. The least curved part of a new primordium is its quasicylindrical midportion. There, by aligning microtubules and cellulose coherently around the organ, a new growth direction is set. Thus large-scale buckling produces curvature variation, which, in turn, affects the localization and orientation of the cytoskeleton. This scheme for the coherent production of diverse geometrical features, involving calculus at two structural levels, is supported by complex organogenetic responses to simple physical intervention. Also, many morphological alternatives, wild type vs. mutant, reflect single changes in parameters in this differential-integral format.

Spatial pattern formation in the flower of Arabidopsis thaliana: mathematical modeling

Doklady biological sciences : proceedings of the Academy of Sciences of the USSR, Biological sciences sections / translated from Russian

The research into the genetic control of flower formation is a rapidly evolving field of plant developmental biology. An ABC model of the genetic control of floral morphogenesis based on the studies of Arabidopsis thaliana mutants [1] envisaged the flower structure as a pattern comprising four organ whorls, with the particular organ development in each whorl specified by the combined activities of several genes. The expression of the A class genes APETALA1 ( AP1 ) and APETALA2 ( AP2 ) determines for the development of sepals (whorl 1). The development of carpels (whorl 4) is specified by the C class gene AGAMOUS ( AG ). The combined activities of the A and C genes together with the B genes APETALA3 ( AP 3 ) and PISTILLATA ( PI ) specify the development of petals and stamens (whorls 2 and 3, respectively). The ABC model postulates that the mutations in these genes would change the organ specificity in particular whorls. In several ABC mutants, the number of flower organs is changed; therefore a hypothesis was put forward that these genes specify both the identity of flower organs and flower organ initiation [2]. However, the mechanism of such specification is poorly understood. When working out the mathematical model of floral development based on the ABC-model postulates, we found that the existing evidence on the functions of the ABC genes did not sufficiently clarify the nature of changes in the arrangement of flower organs in the mutants. It follows that the processes that determine spatial pattern formation in the flower must be studied in more detail .

Computational Morphodynamics: A Modeling Framework to Understand Plant Growth

Annual Review of Plant Biology, 2010

Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions that provide further insight into the processes involved, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental challenges: (a) to understand the feedback between mechanics of growth and chemical or molecular signaling, and (b) to design models that span and integrate single cell behavior with tissue development. We review different approaches to model plant growth and discuss a variety of model types that can be implemented to demonstrate how the interplay between computational modeling and experimentation can be used to explore the morphodynamics of plant development. 12.1 Review in Advance first posted online on February 1, 2010. (Changes may still occur before final publication online and in print.) Changes may still occur before final publication online and in print.

The possible role of reaction–diffusion in leaf shape

Proceedings of the Royal …, 2000

We consider mechanisms that may determine certain simple leaf shapes. Compared with other aspects of plant morphogenesis, such as phyllotaxis or spiral leaf arrangement, rather little is known about leafshape-determining mechanisms. We develop mathematical models for the gross pattern of leaf shape based on reaction^di¡usion systems. These models are consistent with what is known about factors that might determine leaf shape. They show that diverse leaf shapes may be obtained from a single reactiond i¡usion system. This has implications in terms of both convergent and divergent evolution. The models make predictions that can be tested experimentally. We predict the form of pre-patterns of growth promoters in leaf primordia of di¡erent sizes when the morphogens either di¡use into the primordia or are produced locally. We also predict the e¡ects on leaf shape of removing parts of primordia at di¡erent times. The models can also predict the e¡ects on leaf shape of the topical application of activators and inhibitors to leaf primordia.

Computational models of plant development and form

The use of computational techniques increasingly permeates developmental biology, from the acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division patterns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computational modelers.

Modeling of Branching Patterns in Plants

Bulletin of Mathematical Biology, 2008

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model which seems to be in agreement with biological observations.