Cell division systems that account for the various arrangements and types of differentiated cells within the secondary phloem of conifers

There are two main types of arrangement of differentiated cells within the radial cell files of secondary phloem in conifer trees. In the C-type arrangement, characteristic of the Cupressaceae, fibre (F), parenchyma (P) and sieve (S) cells are arranged in recurrent groups, such as the “standard” cellular quartet (FSPS). In the P-type arrangement, characteristic of the Pinaceae, there are no fibres and one of the characteristic recurrent arrangements is the cellular sextet (PSSSSS). In addition, in both C-type and P-type arrangements, similar cell types are often organised into tangential bands. A simulation model, based on the theory of L-systems, was devised to account for the determination of these two types of regular and recurrent patterns of differentiated phloem cells. It was based on the supposition that, in the meristematic portion of the phloem domain, there are specific spatio-temporal patterns of periclinal cell division. When new cells are produced, those already present are displaced along the cell file, occupying a predictable number of cellular positions as a result of each round of cell division. Each cellular position is assumed to be associated with a specific value of a morphogen, such as the auxin, indole acetic acid, relevant for vascular differentiation. Using published quantitative data on the distribution auxin across the phloem, and assuming specific threshold values of auxin necessary for the determination of each cell type, it was found that sequences of F, S or P cells developed in accordance with the specific pattern of cell division and the related positional values of auxin experienced by the cells during their displacement through the immediately post-mitotic zone of cell determination. The model accounts not only for the typical C-type and P-type cellular arrangements, but also for certain variant arrangements. It provides a working example of the concepts of positional information and positional value for patterned differentiation within a developing plant tissue. There are similarities between the way groups of phloem cells develop and the differentiation of somites in the embryos of vertebrates.     

Rhythmic plant morphogenesis: Recurrent patterns of idioblast cell production

Most plants are constructed from repeating modular units such as phytomers, merophytes, and cell packets. Even an organism as simple as the filamentous cyanobacterium Anabaena shows recurrent patterns of differentiated cellular structures, notably with respect to its heterocysts. These examples reflect the inherent rhythms established within developmental processes of living organisms. In the present article, attention is paid to repetitious production of idioblasts—isolated cells, or clusters of cells, with an identity different to that of neighbouring cells from which they are derived. In higher plant root tissues, idioblasts are contained within cell packets that grow up from mother cells during the course of a number of cycles of cell production. The heterocysts of Anabaena are also discussed; they, too, are a type of idioblast. The idioblasts of root tissues originate as small cells which result from unequal cell divisions. Such divisions are usually the final ones within a cell packet which has already undergone a number of division cycles and are characteristically located at one or both ends of a packet. The packet end walls are suggested to have a role in regulating division asymmetry. Idioblastic systems discussed are root cortical trichosclereids and diaphragm cells; in their earliest stage, the cells from which lateral root primordia arise are also considered as clusters of idioblasts because they, too, are the products of asymmetric divisions of pericyclic mother cells. The division patterns of all these idioblastic systems were modelled in a consistent way using L-systems, with the assumption that the age of a cell-packet end wall plays a special role in cell determination. This article is dedicated to Vsevelod Ya. Brodsky, doyen of Russian studies of rhythms in cell division and development, who celebrates his 80th birthday on August 4, 2008 This article was presented in original.     

Assessing the effects of architectural variations on light partitioning within virtual wheat–pea mixtures

Background and Aims

Predicting light partitioning in crop mixtures is a critical step in improving the productivity of such complex systems, and light interception has been shown to be closely linked to plant architecture. The aim of the present work was to analyse the relationships between plant architecture and light partitioning within wheat–pea (Triticum aestivum–Pisum sativum) mixtures. An existing model for wheat was utilized and a new model for pea morphogenesis was developed. Both models were then used to assess the effects of architectural variations in light partitioning.

Methods

First, a deterministic model (L-Pea) was developed in order to obtain dynamic reconstructions of pea architecture. The L-Pea model is based on L-systems formalism and consists of modules for ‘vegetative development’ and ‘organ extension’. A tripartite simulator was then built up from pea and wheat models interfaced with a radiative transfer model. Architectural parameters from both plant models, selected on the basis of their contribution to leaf area index (LAI), height and leaf geometry, were then modified in order to generate contrasting architectures of wheat and pea.

Key results

By scaling down the analysis to the organ level, it could be shown that the number of branches/tillers and length of internodes significantly determined the partitioning of light within mixtures. Temporal relationships between light partitioning and the LAI and height of the different species showed that light capture was mainly related to the architectural traits involved in plant LAI during the early stages of development, and in plant height during the onset of interspecific competition.

Conclusions

In silico experiments enabled the study of the intrinsic effects of architectural parameters on the partitioning of light in crop mixtures of wheat and pea. The findings show that plant architecture is an important criterion for the identification/breeding of plant ideotypes, particularly with respect to light partitioning.     

Barley morphology, genetics and hormonal regulation of internode elongation modelled by a relational growth grammar

A multiscaled ecophysiological model of barley (Hordeum vulgare) development is presented here. The model is based on the new formalism of relational growth grammars (RGG), an extension of L-systems, and implemented using the new modelling language XL. It is executable in the interactive modelling platform GroIMP. The model consists of a set of morphogenetic rules, combined with a metabolic regulatory network, which simulates the biosynthesis of gibberellic acid (GA1). GA1 and two of its metabolic precursors are transported along the developing simulated structure. Local concentrations of GA1 determine internode elongation. Furthermore, virtual barley individuals are chosen interactively from a population, based on genotype, and (sexual or asexual) reproduction is simulated. Genotype and phenotype of the population are visualized. Seven Mendelian genes have been implemented in the model so far; some of these directly influence the GA-regulation network. The model exemplifies and validates the new formalism and modelling language. RGG have the capability to represent genetic, metabolic and morphological aspects of plant development and reproduction, all within the same framework.     

BIOCOMPUTATION: Some history and prospects

At first glance, biology and computer science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies. We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science.     

Chromosome numbers in the algae: Phaeophyta II

L-systems provide a method for modelling seaweed branching patterns in terms of simple rules. These rules can be used to generate computer graphics images of an alga's basic architecture, which, of course, is often obscured by adventiltious growth in living plants. L-systems provide a mathematical abstraction that allows us to compare species by focusing on essential differences in their substitution rules rather than relying entirely on the visual appearance of branching patterns. Two species of red algae from closely related genera in the Dasyaceae—Dasya rigidula and Dasysiphonia concinna—are virtually identical in pseudolateral branching detail and appear to diverge solely in terms of pseudolateral position. L-systems models and their graphical representations are presented to demonstrate that the two-dimensional, alternate-distichous pattern of pseudolateral position for Dasysiphonia concinna can be derived in a straightforward way from that of the three-dimensional, spiralled pattern of Dasya rigidula. These models illustrate a case in which generic distinction is based upon an easily observable but relatively trivial feature, differences other than branching pattern being quite subtle.     

The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation

The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.