Diversity of woodland strawberry inflorescences arises from heterochrony regulated by TERMINAL FLOWER 1 and FLOWERING LOCUS T.

A vast variety of inflorescence architectures have evolved in angiosperms. Here, we analyze the diversity and development of the woodland strawberry (Fragaria vesca) inflorescence. Contrary to historical classifications, we show that it is a closed thyrse: a compound inflorescence with determinate primary monopodial axis and lateral sympodial branches, thus combining features of racemes and cymes. We demonstrate that this architecture is generated by 2 types of inflorescence meristems differing in their geometry. We further show that woodland strawberry homologs of TERMINAL FLOWER 1 (FvTFL1) and FLOWERING LOCUS T (FvFT1) regulate the development of both the racemose and cymose components of the thyrse. Loss of functional FvTFL1 reduces the number of lateral branches of the main axis and iterations in the lateral branches but does not affect their cymose pattern. These changes can be enhanced or compensated by altering FvFT1 expression. We complement our experimental findings with a computational model that captures inflorescence development using a small set of rules. The model highlights the distinct regulation of the fate of the primary and higher-order meristems, and explains the phenotypic diversity among inflorescences in terms of heterochrony resulting from the opposite action of FvTFL1 and FvFT1 within the thyrse framework. Our results represent a detailed analysis of thyrse architecture development at the meristematic and molecular levels.

The hidden diversity of vascular patterns in flower heads.

Vascular systems are intimately related to the shape and spatial arrangement of the plant organs they support. We investigate the largely unexplored association between spiral phyllotaxis and the vascular system in Asteraceae flower heads. We imaged heads of eight species using synchrotron-based X-ray micro-computed tomography and applied original virtual reality and haptic software to explore head vasculature in three dimensions. We then constructed a computational model to infer a plausible patterning mechanism. The vascular system in the head of the model plant Gerbera hybrida is qualitatively different from those of Bellis perennis and Helianthus annuus, characterized previously. Cirsium vulgare, Craspedia globosa, Echinacea purpurea, Echinops bannaticus, and Tanacetum vulgare represent variants of the Bellis and Helianthus systems. In each species, the layout of the main strands is stereotypical, but details vary. The observed vascular patterns can be generated by a common computational model with different parameter values. In spite of the observed differences of vascular systems in heads, they may be produced by a conserved mechanism. The diversity and irregularities of vasculature stand in contrast with the relative uniformity and regularity of phyllotactic patterns, confirming that phyllotaxis in heads is not driven by the vasculature.

Phyllotactic patterning of gerbera flower heads.

Phyllotaxis, the distribution of organs such as leaves and flowers on their support, is a key attribute of plant architecture. The geometric regularity of phyllotaxis has attracted multidisciplinary interest for centuries, resulting in an understanding of the patterns in the model plants Arabidopsis and tomato down to the molecular level. Nevertheless, the iconic example of phyllotaxis, the arrangement of individual florets into spirals in the heads of the daisy family of plants (Asteraceae), has not been fully explained. We integrate experimental data and computational models to explain phyllotaxis in Gerbera hybrida We show that phyllotactic patterning in gerbera is governed by changes in the size of the morphogenetically active zone coordinated with the growth of the head. The dynamics of these changes divides the patterning process into three phases: the development of an approximately circular pattern with a Fibonacci number of primordia near the head rim, its gradual transition to a zigzag pattern, and the development of a spiral pattern that fills the head on the template of this zigzag pattern. Fibonacci spiral numbers arise due to the intercalary insertion and lateral displacement of incipient primordia in the first phase. Our results demonstrate the essential role of the growth and active zone dynamics in the patterning of flower heads.

Phyllotaxis without symmetry: what can we learn from flower heads?

Phyllotaxis is commonly considered in the context of circular meristems or receptacles, yet non-circular (fasciated) structures also give rise to new primordia and organs. Here we investigate phyllotactic patterns in fasciated flower heads in the Asteraceae plant family. We begin by surveying the phenomenon of fasciation. We then show that phyllotactic patterns in fasciated heads can be generated by removing the inessential assumption of circularity from the previously published model of gerbera heads. To characterize these patterns, we revisit the conceptual framework in which phyllotactic patterns are commonly described. We note that some notions, in particular parastichies and parastichy numbers, maintain their significance in non-circular phyllotaxis, whereas others, in particular the divergence angle, need to be extended or lose their role. These observations highlight a number of open problems related to phyllotaxis in general, which may be elucidated by studies of fasciated heads.

Phyllotaxis: is the golden angle optimal for light capture?

Phyllotactic patterns are some of the most conspicuous in nature. To create these patterns plants must control the divergence angle between the appearance of successive organs, sometimes to within a fraction of a degree. The most common angle is the Fibonacci or golden angle, and its prevalence has led to the hypothesis that it has been selected by evolution as optimal for plants with respect to some fitness benefits, such as light capture. We explore arguments for and against this idea with computer models. We have used both idealized and scanned leaves from Arabidopsis thaliana and Cardamine hirsuta to measure the overlapping leaf area of simulated plants after varying parameters such as leaf shape, incident light angles, and other leaf traits. We find that other angles generated by Fibonacci-like series found in nature are equally optimal for light capture, and therefore should be under similar evolutionary pressure. Our findings suggest that the iterative mechanism for organ positioning itself is a more likely target for evolutionary pressure, rather than a specific divergence angle, and our model demonstrates that the heteroblastic progression of leaf shape in A. thaliana can provide a potential fitness benefit via light capture.

A Model of Differential Growth-Guided Apical Hook Formation in Plants.

Differential cell growth enables flexible organ bending in the presence of environmental signals such as light or gravity. A prominent example of the developmental processes based on differential cell growth is the formation of the apical hook that protects the fragile shoot apical meristem when it breaks through the soil during germination. Here, we combined in silico and in vivo approaches to identify a minimal mechanism producing auxin gradient-guided differential growth during the establishment of the apical hook in the model plant Arabidopsis thaliana Computer simulation models based on experimental data demonstrate that asymmetric expression of the PIN-FORMED auxin efflux carrier at the concave (inner) versus convex (outer) side of the hook suffices to establish an auxin maximum in the epidermis at the concave side of the apical hook. Furthermore, we propose a mechanism that translates this maximum into differential growth, and thus curvature, of the apical hook. Through a combination of experimental and in silico computational approaches, we have identified the individual contributions of differential cell elongation and proliferation to defining the apical hook and reveal the role of auxin-ethylene crosstalk in balancing these two processes.

A common developmental program can produce diverse leaf shapes.

Eudicot leaves have astoundingly diverse shapes. The central problem addressed in this paper is the developmental origin of this diversity. To investigate this problem, we propose a computational model of leaf development that generalizes the largely conserved molecular program for the reference plants Arabidopsis thaliana, Cardamine hirsuta and Solanum lycopersicum. The model characterizes leaf development as a product of three interwoven processes: the patterning of serrations, lobes and/or leaflets on the leaf margin; the patterning of the vascular system; and the growth of the leaf blade spanning the main veins. The veins play a significant morphogenetic role as a local determinant of growth directions. We show that small variations of this model can produce diverse leaf shapes, from simple to lobed to compound. It is thus plausible that diverse shapes of eudicot leaves result from small variations of a common developmental program.

Integration of transport-based models for phyllotaxis and midvein formation.

The plant hormone auxin mediates developmental patterning by a mechanism that is based on active transport. In the shoot apical meristem, auxin gradients are thought to be set up through a feedback loop between auxin and the activity and polar localization of its transporter, the PIN1 protein. Two distinct molecular mechanisms for the subcellular polarization of PIN1 have been proposed. For leaf positioning (phyllotaxis), an "up-the-gradient" PIN1 polarization mechanism has been proposed, whereas the formation of vascular strands is thought to proceed by "with-the-flux" PIN1 polarization. These patterning mechanisms intersect during the initiation of the midvein, which raises the question of how two different PIN1 polarization mechanisms may work together. Our detailed analysis of PIN1 polarization during midvein initiation suggests that both mechanisms for PIN1 polarization operate simultaneously. Computer simulations of the resulting dual polarization model are able to reproduce the dynamics of observed PIN1 localization. In addition, the appearance of high auxin concentration in our simulations throughout the initiation of the midvein is consistent with experimental observation and offers an explanation for a long-standing criticism of the canalization hypothesis; namely, how both high flux and high concentration can occur simultaneously in emerging veins.

An intracellular partitioning-based framework for tissue cell polarity in plants and animals.

Tissue cell polarity plays a major role in plant and animal development. We propose that a fundamental building block for tissue cell polarity is the process of intracellular partitioning, which can establish individual cell polarity in the absence of asymmetric cues. Coordination of polarities may then arise through cell-cell coupling, which can operate directly, through membrane-spanning complexes, or indirectly, through diffusible molecules. Polarity is anchored to tissues through organisers located at boundaries. We show how this intracellular partitioning-based framework can be applied to both plant and animal systems, allowing different processes to be placed in a common evolutionary and mechanistic context.

Auxin-driven patterning with unidirectional fluxes.

The plant hormone auxin plays an essential role in the patterning of plant structures. Biological hypotheses supported by computational models suggest that auxin may fulfil this role by regulating its own transport, but the plausibility of previously proposed models has been questioned. We applied the notion of unidirectional fluxes and the formalism of Petri nets to show that the key modes of auxin-driven patterning-the formation of convergence points and the formation of canals-can be implemented by biochemically plausible networks, with the fluxes measured by dedicated tally molecules or by efflux and influx carriers themselves. Common elements of these networks include a positive feedback of auxin efflux on the allocation of membrane-bound auxin efflux carriers (PIN proteins), and a modulation of this allocation by auxin in the extracellular space. Auxin concentration in the extracellular space is the only information exchanged by the cells. Canalization patterns are produced when auxin efflux and influx act antagonistically: an increase in auxin influx or concentration in the extracellular space decreases the abundance of efflux carriers in the adjacent segment of the membrane. In contrast, convergence points emerge in networks in which auxin efflux and influx act synergistically. A change in a single reaction rate may result in a dynamic switch between these modes, suggesting plausible molecular implementations of coordinated patterning of organ initials and vascular strands predicted by the dual polarization theory.

A division in PIN-mediated auxin patterning during organ initiation in grasses.

The hormone auxin plays a crucial role in plant morphogenesis. In the shoot apical meristem, the PIN-FORMED1 (PIN1) efflux carrier concentrates auxin into local maxima in the epidermis, which position incipient leaf or floral primordia. From these maxima, PIN1 transports auxin into internal tissues along emergent paths that pattern leaf and stem vasculature. In Arabidopsis thaliana, these functions are attributed to a single PIN1 protein. Using phylogenetic and gene synteny analysis we identified an angiosperm PIN clade sister to PIN1, here termed Sister-of-PIN1 (SoPIN1), which is present in all sampled angiosperms except for Brassicaceae, including Arabidopsis. Additionally, we identified a conserved duplication of PIN1 in the grasses: PIN1a and PIN1b. In Brachypodium distachyon, SoPIN1 is highly expressed in the epidermis and is consistently polarized toward regions of high expression of the DR5 auxin-signaling reporter, which suggests that SoPIN1 functions in the localization of new primordia. In contrast, PIN1a and PIN1b are highly expressed in internal tissues, suggesting a role in vascular patterning. PIN1b is expressed in broad regions spanning the space between new primordia and previously formed vasculature, suggesting a role in connecting new organs to auxin sinks in the older tissues. Within these regions, PIN1a forms narrow canals that likely pattern future veins. Using a computer model, we reproduced the observed spatio-temporal expression and localization patterns of these proteins by assuming that SoPIN1 is polarized up the auxin gradient, and PIN1a and PIN1b are polarized to different degrees with the auxin flux. Our results suggest that examination and modeling of PIN dynamics in plants outside of Brassicaceae will offer insights into auxin-driven patterning obscured by the loss of the SoPIN1 clade in Brassicaceae.

Modelling biomechanics of bark patterning in grasstrees.

BACKGROUND AND AIMS: Bark patterns are a visually important characteristic of trees, typically attributed to fractures occurring during secondary growth of the trunk and branches. An understanding of bark pattern formation has been hampered by insufficient information regarding the biomechanical properties of bark and the corresponding difficulties in faithfully modelling bark fractures using continuum mechanics. This study focuses on the genus Xanthorrhoea (grasstrees), which have an unusual bark-like structure composed of distinct leaf bases connected by sticky resin. Due to its discrete character, this structure is well suited for computational studies. METHODS: A dynamic computational model of grasstree development was created. The model captures both the phyllotactic pattern of leaf bases during primary growth and the changes in the trunk's width during secondary growth. A biomechanical representation based on a system of masses connected by springs is used for the surface of the trunk, permitting the emergence of fractures during secondary growth to be simulated. The resulting fracture patterns were analysed statistically and compared with images of real trees. KEY RESULTS: The model reproduces key features of grasstree bark patterns, including their variability, spanning elongated and reticulate forms. The patterns produced by the model have the same statistical character as those seen in real trees. CONCLUSIONS: The model was able to support the general hypothesis that the patterns observed in the grasstree bark-like layer may be explained in terms of mechanical fractures driven by secondary growth. Although the generality of the results is limited by the unusual structure of grasstree bark, it supports the hypothesis that bark pattern formation is primarily a biomechanical phenomenon.

Model for the regulation of Arabidopsis thaliana leaf margin development.

Biological shapes are often produced by the iterative generation of repeated units. The mechanistic basis of such iteration is an area of intense investigation. Leaf development in the model plant Arabidopsis is one such example where the repeated generation of leaf margin protrusions, termed serrations, is a key feature of final shape. However, the regulatory logic underlying this process is unclear. Here, we use a combination of developmental genetics and computational modeling to show that serration development is the morphological read-out of a spatially distributed regulatory mechanism, which creates interspersed activity peaks of the growth-promoting hormone auxin and the cup-shaped cotyledon2 (CUC2) transcription factor. This mechanism operates at the growing leaf margin via a regulatory module consisting of two feedback loops working in concert. The first loop relates the transport of auxin to its own distribution, via polar membrane localization of the pinformed1 (PIN1) efflux transporter. This loop captures the potential of auxin to generate self-organizing patterns in diverse developmental contexts. In the second loop, CUC2 promotes the generation of PIN1-dependent auxin activity maxima while auxin represses CUC2 expression. This CUC2-dependent loop regulates activity of the conserved auxin efflux module in leaf margins to generate stable serration patterns. Conceptualizing leaf margin development via this mechanism also helps to explain how other developmental regulators influence leaf shape.

Developmental timing in plants.

Plants exhibit reproducible timing of developmental events at multiple scales, from switches in cell identity to maturation of the whole plant. Control of developmental timing likely evolved for similar reasons that humans invented clocks: to coordinate events. However, whereas clocks are designed to run independently of conditions, plant developmental timing is strongly dependent on growth and environment. Using simplified models to convey key concepts, we review how growth-dependent and inherent timing mechanisms interact with the environment to control cyclical and progressive developmental transitions in plants.

The interplay between inflorescence development and function as the crucible of architectural diversity.

BACKGROUND: Most angiosperms present flowers in inflorescences, which play roles in reproduction, primarily related to pollination, beyond those served by individual flowers alone. An inflorescence's overall reproductive contribution depends primarily on the three-dimensional arrangement of the floral canopy and its dynamics during its flowering period. These features depend in turn on characteristics of the underlying branching structure (scaffold) that supports and supplies water and nutrients to the floral canopy. This scaffold is produced by developmental algorithms that are genetically specified and hormonally mediated. Thus, the extensive inflorescence diversity evident among angiosperms evolves through changes in the developmental programmes that specify scaffold characteristics, which in turn modify canopy features that promote reproductive performance in a particular pollination and mating environment. Nevertheless, developmental and ecological aspects of inflorescences have typically been studied independently, limiting comprehensive understanding of the relations between inflorescence form, reproductive function, and evolution. SCOPE: This review fosters an integrated perspective on inflorescences by summarizing aspects of their development and pollination function that enable and guide inflorescence evolution and diversification. CONCLUSIONS: The architecture of flowering inflorescences comprises three related components: topology (branching patterns, flower number), geometry (phyllotaxis, internode and pedicel lengths, three-dimensional flower arrangement) and phenology (flower opening rate and longevity, dichogamy). Genetic and developmental evidence reveals that these components are largely subject to quantitative control. Consequently, inflorescence evolution proceeds along a multidimensional continuum. Nevertheless, some combinations of topology, geometry and phenology are represented more commonly than others, because they serve reproductive function particularly effectively. For wind-pollinated species, these combinations often represent compromise solutions to the conflicting physical influences on pollen removal, transport and deposition. For animal-pollinated species, dominant selective influences include the conflicting benefits of large displays for attracting pollinators and of small displays for limiting among-flower self-pollination. The variety of architectural components that comprise inflorescences enable diverse resolutions of these conflicts.

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.

Control of bud activation by an auxin transport switch.

In many plant species only a small proportion of buds yield branches. Both the timing and extent of bud activation are tightly regulated to produce specific branching architectures. For example, the primary shoot apex can inhibit the activation of lateral buds. This process is termed apical dominance and is dependent on the plant hormone auxin moving down the main stem in the polar auxin transport stream. We use a computational model and mathematical analysis to show that apical dominance can be explained in terms of an auxin transport switch established by the temporal precedence between competing auxin sources. Our model suggests a mechanistic basis for the indirect action of auxin in bud inhibition and captures the effects of diverse genetic and physiological manipulations. In particular, the model explains the surprising observation that highly branched Arabidopsis phenotypes can exhibit either high or low auxin transport.

Computational Models of Auxin-Driven Patterning in Shoots.

Auxin regulates many aspects of plant development and behavior, including the initiation of new outgrowth, patterning of vascular systems, control of branching, and responses to the environment. Computational models have complemented experimental studies of these processes. We review these models from two perspectives. First, we consider cellular and tissue-level models of interaction between auxin and its transporters in shoots. These models form a coherent body of results exploring different hypotheses pertinent to the patterning of new outgrowth and vascular strands. Second, we consider models operating at the level of plant organs and entire plants. We highlight techniques used to reduce the complexity of these models, which provide a path to capturing the essence of studied phenomena while running simulations efficiently.

Towards aspect-oriented functional--structural plant modelling.

BACKGROUND AND AIMS: Functional-structural plant models (FSPMs) are used to integrate knowledge and test hypotheses of plant behaviour, and to aid in the development of decision support systems. A significant amount of effort is being put into providing a sound methodology for building them. Standard techniques, such as procedural or object-oriented programming, are not suited for clearly separating aspects of plant function that criss-cross between different components of plant structure, which makes it difficult to reuse and share their implementations. The aim of this paper is to present an aspect-oriented programming approach that helps to overcome this difficulty. METHODS: The L-system-based plant modelling language L+C was used to develop an aspect-oriented approach to plant modelling based on multi-modules. Each element of the plant structure was represented by a sequence of L-system modules (rather than a single module), with each module representing an aspect of the element's function. Separate sets of productions were used for modelling each aspect, with context-sensitive rules facilitated by local lists of modules to consider/ignore. Aspect weaving or communication between aspects was made possible through the use of pseudo-L-systems, where the strict-predecessor of a production rule was specified as a multi-module. KEY RESULTS: The new approach was used to integrate previously modelled aspects of carbon dynamics, apical dominance and biomechanics with a model of a developing kiwifruit shoot. These aspects were specified independently and their implementation was based on source code provided by the original authors without major changes. CONCLUSIONS: This new aspect-oriented approach to plant modelling is well suited for studying complex phenomena in plant science, because it can be used to integrate separate models of individual aspects of plant development and function, both previously constructed and new, into clearly organized, comprehensive FSPMs. In a future work, this approach could be further extended into an aspect-oriented programming language for FSPMs.

Constraints of space in plant development.

Like all forms in nature, plants are subject to the properties of space. On the one hand, space prevents configurations that would place more than one component in the same location at the same time. A generalization of this constraint limits proximity and density of organs. On the other hand, space provides a means for a plant to create three-dimensional forms by differentially controlling their growth. This results from a connection between the metric properties of surfaces and their Gaussian curvature. Three strategies used by plants to develop within the constraints of space are presented: expansion to another dimension, egalitarian partitioning of space, and competition for space. These strategies are illustrated with examples of curved surfaces of leaves and petals, self-similar branching structures of compound leaves and inflorescences, and tree architecture. The examples highlight the fundamental role of the constraints of space in plant development, and the complementary role of genetic regulation and space-dependent emergent phenomena in shaping a plant.