Plant development: hidden networks

Leaf venation, as a resistor, to optimize a switchable IR absorber

Leaf vascular patterns are the mechanisms and mechanical support for the transportation of fluidics for photosynthesis and leaf development properties. Vascular hierarchical networks in leaves have far-reaching functions in optimal transport efficiency of functional fluidics. Embedding leaf morphogenesis as a resistor network is significant in the optimization of a translucent thermally functional material. This will enable regulation through pressure equalization by diminishing flow pressure variation. This paper investigates nature's vasculature networks that exhibit hierarchical branching scaling applied to microfluidics. To enable optimum potential for pressure drop regulation by algorithm design. This code analysis of circuit conduit optimization for transport fluidic flow resistance is validated against CFD simulation, within a closed loop network. The paper will propose this self-optimization, characterization by resistance seeking targeting to determine a microfluidic network as a resistor. To advance a thermally function material as a switchable IR absorber.

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.

Pattern formation of leaf veins by the positive feedback regulation between auxin flow and auxin efflux carrier

The generation of vascular pattern formation in plants is an interesting process of pattern formation in organisms. It is well known that the plant hormone auxin is involved in plant vascular differentiation and that the PIN1 protein, an auxin efflux carrier, localizes to one side of the cell membrane. Several hypotheses have been proposed to explain the formation of leaf venation. One is the canalization hypothesis that is based on the assumption that a positive feedback regulation exists between the flow of a signal molecule and the capacity of its flow. Here, we attempted to integrate the canalization hypothesis and experimental data. We investigated models of the positive feedback regulation between the auxin flow and PIN1 localization. Model 1, with conserved PIN1 amount in each cell, can generate a branching pattern similar to that of plant leaf venation. We introduced the diffusible enhancer "e" into the model as unknown factor. The obtained patterns show a quasi-periodic distribution of auxin flow paths, when the model dynamics includes domain growth. In order to understand the early initiation process that generates an inhomogeneity from an almost homogeneous distribution, we introduced model 2, a simplified version of model 1. Model 2 can generate inhomogeneity with a parameter dependency similar to that of model 1. To analyse parameter condition required for pattern development, approximated equations are obtained from model 2. The isocline analysis of the equations without spatial structure shows that the inhomogeneous distribution occurs from an almost homogeneous distribution. This parameter condition for generating inhomogeneity is consistent with the results of models 1 and 2.

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.

Vascular patterning and leaf shape

Morphogenesis of leaf shape and formation of the major elements of leaf vasculature are temporally coordinated during leaf development. Current analyses of mutant phenotypes provide strong support for the role of auxin signaling in vascular pattern formation and indicate that leaf shape and vasculature are developmentally coupled. Two other mechanisms that may contribute to the regulation of these processes are a diffusion-reaction system and long-distance signaling of informational macromolecules.