Collective specification of cellular development

Of Cells, Strands, and Networks: Auxin and the Patterned Formation of the Vascular System

Throughout plant development, vascular cells continually form from within a population of seemingly equivalent cells. Vascular cells connect end to end to form continuous strands, and vascular strands connect at both or either end to form networks of exquisite complexity and mesmerizing beauty. Here we argue that experimental evidence gained over the past few decades implicates the plant hormone auxin-its production, transport, perception, and response-in all the steps that lead to the patterned formation of the plant vascular system, from the formation of vascular cells to their connection into vascular networks. We emphasize the organizing principles of the cell- and tissue-patterning process, rather than its molecular subtleties. In the picture that emerges, cells compete for an auxin-dependent, cell-polarizing signal; positive feedback between cell polarization and cell-to-cell movement of the polarizing signal leads to gradual selection of cell files; and selected cell files differentiate into vascular strands that drain the polarizing signal from the neighboring cells. Although the logic of the patterning process has become increasingly clear, the molecular details remain blurry; the future challenge will be to bring them into razor-sharp focus.

The plant body as a network of semi-autonomous agents: a review

Plants can solve amazingly difficult tasks while adjusting their growth and development to the environment. They can explore and exploit several resources simultaneously, even when the distributions of these vary in space and time. The systematic study of plant behaviour goes back to Darwin's book The power of movement in plants. Current research has highlighted that modularity is a key to understanding plant behaviour, as the production, functional specialization and death of modules enable the plant to adjust its movement to the environment. The adjustment is assisted by a flow of information and resources among the modules. Experiments have yielded many results about these processes in various plant species. Theoretical research, however, has lagged behind the empirical studies, possibly owing to the lack of a proper modelling framework that could encompass the high number of components and interactions. In this paper, I propose such a framework on the basis of network theory, viewing the plant as a group of connected, semi-autonomous agents. I review some characteristic plant responses to the environment through changing the states of agents and/or links. I also point out some unexplored areas, in which a dialogue between plant science and network theory could be mutually inspiring. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

The arrangement of lateral veins along the midvein of leaves is not related to leaf phyllotaxis

Positions of leaves along a stem usually adhere to a genetically determined, species-specific pattern known as a leaf phyllotaxis. We investigated whether the arrangement of lateral secondary veins along primary midveins adhered to a species-specific pattern that resembled an alternate or opposite phyllotaxis. We analyzed the venation of temperate dicotyledonous species from different taxonomic groups and chose 18 woody and 12 herbaceous species that have reticulated leaf venation. The arrangement of the lateral veins was neither alternate nor opposite for any of the species. Lateral vein arrangements were instead mixtures of symmetric and asymmetric patterns. Our results show that lateral vein arrangements are related neither to stem-level leaf phyllotaxis (alternate vs. opposite) nor to life form (woody vs. herbaceous). Our results are therefore generally consistent with the canalization hypothesis that the locations of lateral veins are not completely specified genetically prior to leaf formation.

Coordination of cell polarity and the patterning of leaf vein networks

During development, the behavior of cells in tissues is coordinated along specific orientations or directions by coordinating the polar localization of components in those cells. The coordination of such cell polarity is perhaps nowhere more spectacular than in developing leaves, where the polarity of hundreds of cells is coordinated in the leaf epidermis and inner tissue to pattern vein networks. Available evidence suggests that the spectacular coordination of cell polarity that patterns vein networks is controlled by auxin transport and levels, and by genes that have been implicated in the polar localization of auxin transporters.

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.

Polarity, continuity, and alignment in plant vascular strands

Plant vascular cells are joined end to end along uninterrupted lines to connect shoot organs with roots; vascular strands are thus polar, continuous, and internally aligned. What controls the formation of vascular strands with these properties? The "auxin canalization hypothesis"-based on positive feedback between auxin flow through a cell and the cell's capacity for auxin transport-predicts the selection of continuous files of cells that transport auxin polarly, thus accounting for the polarity and continuity of vascular strands. By contrast, polar, continuous auxin transport-though required-is insufficient to promote internal alignment of vascular strands, implicating additional factors. The auxin canalization hypothesis was derived from the response of mature tissue to auxin application but is consistent with molecular and cellular events in embryo axis formation and shoot organ development. Objections to the hypothesis have been raised based on vascular organizations in callus tissue and shoot organs but seem unsupported by available evidence. Other objections call instead for further research; yet the inductive and orienting influence of auxin on continuous vascular differentiation remains unique.

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.

Back to the future: evolution of computational models in plant morphogenesis

There has been a recent surge of studies in plant biology that combine experimental data with computational modeling. Here, we categorize a diversity of theoretical models and emphasize the need to tailor modeling approaches to the questions at hand. Models can start from biophysical or purely heuristic basic principles, and can focus at several levels of biological organization. Recent examples illustrate that this entire spectrum can be useful to understand plant development, and point to a future direction where more approaches are combined in fruitful ways--either by proving the same result with different basic principles or by exploring interactions across levels, in the so-called multilevel models.

Towards the systems biology of auxin-transport-mediated patterning

Polar auxin transport intimately connects plant cell polarity and multicellular patterning. Through the transport of the small molecule indole-3-acetic acid, plant cells integrate their polarities and communicate the degree of their polarization. In this way, they generate an apical-basal axis that serves as a positional reference anchoring subsequent patterning events. Research in recent years has brought the molecular mechanisms underlying auxin perception and auxin transport to light. This knowledge has been used to derive spectacular molecular visualization tools and animated computer simulations, which are now allied in a joint systems biology effort towards a mathematical description of auxin-transport-mediated patterning processes.

The origin of the diversity of leaf venation pattern

The leaf venation pattern of plants shows remarkable diversity and species-specificity. However, the mechanism underlying the pattern formation and pattern diversity remains unclear. We developed a mathematical model that is based on the positive feedback regulation between plant hormone auxin and its efflux carrier. This system can generate auxin flow pathways by self-organization from an almost homogeneous state. This result explains a well-known experimental phenomenon referred as to "polar auxin transport." The model can produce diverse leaf venation patterns with spatial regularity under similar conditions to those of leaf development, that is, in the presence of leaf expansion and auxin sink. Final venation patterns are strikingly affected by leaf shape and leaf expansion. These results indicate that the positive feedback regulation between auxin and its efflux carrier is a central dynamic in leaf venation pattern formation. The diversity of leaf venation patterns in plant species is probably due to the differences of leaf shape and leaf expansion pattern.

Maps, books and other metaphors for systems biology

We briefly review the use of metaphors in science and progressively focus on fields from biology and molecular biology to genomics and bioinformatics. We discuss how metaphors are both a tool for scientific exploration and a medium for public communication of complex subjects, by various short examples. Finally, we propose a metaphor for systems biology that provides an illuminating perspective for the ambitious goals of this field and delimits its current agenda.

Modeling plant morphogenesis

Applications of computational techniques to developmental plant biology include the processing of experimental data and the construction of simulation models. Substantial progress has been made in these areas over the past few years. Complex image-processing techniques are used to integrate sequences of two-dimensional images into three-dimensional descriptions of development over time and to extract useful quantitative traits. Large amounts of data are integrated into empirical models of developing plant organs and entire plants. Mechanistic models link molecular-level phenomena with the resulting phenotypes. Several models shed light on the possible properties of active auxin transport and its role in plant morphogenesis.

Reviewing models of auxin canalization in the context of leaf vein pattern formation in Arabidopsis

In both plants and animals vein networks play an essential role in transporting nutrients. In plants veins may also provide mechanical support. The mechanism by which vein patterns are formed in a developing leaf remains largely unresolved. According to the canalization hypothesis, a signal inducing vein differentiation is transported in a polar manner and is channeled into narrow strands. Since inhibition of auxin transport affects venation patterns, auxin is likely to be part of the signal involved. However, it is not clear whether the canalization hypothesis, initially formulated over 25 years ago, is compatible with recent experimental data. In this paper we focus on three aspects of this question, and show that: (i) canalization models can account for an acropetal development of the midvein if vein formation is sink-driven; (ii) canalization models are in agreement with venation patterns resulting from inhibited auxin transport and (iii) loops and discontinuous venation patterns can be obtained assuming proper spacing of discrete auxin sources.

Insulin-like growth factor promotes engraftment, differentiation, and functional improvement after transfer of embryonic stem cells for myocardial restoration

Insulin-like growth factor-1 (IGF-1) promotes myocyte proliferation and can reverse cardiac abnormalities when it is administered in the early fetal stage. Supplementation of a mouse embryonic stem cell (ESC) suspension with IGF-1 might enhance cellular engraftment and host organ-specific differentiation after injection in the area of acute myocardial injury. In the study reported here, we sought to enhance the restorative effect of ESCs in the injured heart by adding IGF-1 to the injected cell population. Green fluorescent protein (GFP)-labeled sv129 ESCs (2.5 x 10(5)) were injected into the ischemic area after left anterior descending (LAD) artery ligation in BalbC mice. Recombinant mouse IGF-1 (25 ng) was added to the cell suspension prior to the injection (n = 5). Echocardiography was performed before organ harvest 2 weeks later. The degree of restoration (ratio of GFP+ to infarct area), expression of cardiac markers by GFP+ cells, inflammatory response, and tumorigenicity were evaluated. Mice with LAD ligation only (n = 5) and ESC transfer without IGF-1 (n = 5) served as controls. ESCs formed viable grafts and improved cardiac function. Left ventricular wall thickness was higher in the IGF-1 group (p = .025). There was a trend toward higher fractional shortening in the IGF-treated group. Histological analysis demonstrated that IGF-1 promoted expression of alpha-sarcomeric actin (p = .015) and major histocompatibility complex class I (p = .01). IGF did not affect the cellular response to the donor cells or tumorigenicity. IGF-1 promotes expression of cardiomyocyte phenotype in ESCs in vivo. It should be considered as an adjuvant to cell transfer for myocardial restoration.

Self-organization of tree form: a model for complex social systems

The branches of a tree can be viewed as redundant organs: they have the same functional roles and the same unlimited developmental potential. The most prominent aspect of tree form, here considered as an example of dynamic self-organization, is the relations among these branches. A branch is a source of information about its size, state and environment. A response to this information is the oriented vascular differentiation which connects the branch with the rest of the plant. A known phytohormone, auxin, is formed by shoot tissues and replaces this orienting influence of a shoot. This accounts for neighboring branches having specific, even competing, effects without any other branch specificity. The same phytohormone also elicits different processes throughout the plant, integrating their occurrence without recourse to a central control. Self-organization requires a positive feedback that enhances the development of a successful branch, and an inhibitory influence that reduces similar branch growth. Both roles could depend on the oriented vascular differentiation that is specified by auxin. Actual tree form at any given time is a transient dynamic state. One reason for this is that competition between branches is a long-term, gradual process. A second reason is that a periodic surfeit of root supplies enhances a seasonal formation of many branches which 'search' environmental possibilities, and most of these branches decline only gradually. The various aspects of tree form could thus depend on remarkably simple and robust principles, requiring only limited genetic information. Much of the necessary information about the details of tree form is generated by a Darwinian-like process of developmental selection, reaching a predictable overall outcome without following any strict plan. It is a case of self-organization in which the component structures, the tree branches, do not move, but do undergo long term developmental changes.