Genetic control of organ shape and tissue polarity.

The mechanisms by which genes control organ shape are poorly understood. In principle, genes may control shape by modifying local rates and/or orientations of deformation. Distinguishing between these possibilities has been difficult because of interactions between patterns, orientations, and mechanical constraints during growth. Here we show how a combination of growth analysis, molecular genetics, and modelling can be used to dissect the factors contributing to shape. Using the Snapdragon (Antirrhinum) flower as an example, we show how shape development reflects local rates and orientations of tissue growth that vary spatially and temporally to form a dynamic growth field. This growth field is under the control of several dorsoventral genes that influence flower shape. The action of these genes can be modelled by assuming they modulate specified growth rates parallel or perpendicular to local orientations, established by a few key organisers of tissue polarity. Models in which dorsoventral genes only influence specified growth rates do not fully account for the observed growth fields and shapes. However, the data can be readily explained by a model in which dorsoventral genes also modify organisers of tissue polarity. In particular, genetic control of tissue polarity organisers at ventral petal junctions and distal boundaries allows both the shape and growth field of the flower to be accounted for in wild type and mutants. The results suggest that genetic control of tissue polarity organisers has played a key role in the development and evolution of shape.

A complex-valued nonlinear neural adaptive filter with a gradient adaptive amplitude of the activation function.

A complex-valued nonlinear gradient descent (CNGD) learning algorithm for a simple finite impulse response (FIR) nonlinear neural adaptive filter with an adaptive amplitude of the complex activation function is proposed. This way the amplitude of the complex-valued analytic nonlinear activation function of a neuron in the learning algorithm is made gradient adaptive to give the complex-valued adaptive amplitude nonlinear gradient descent (CAANGD). Such an algorithm is beneficial when dealing with signals that have rich dynamical behavior. Simulations on the prediction of complex-valued coloured and nonlinear input signals show the gradient adaptive amplitude, CAANGD, outperforming the standard CNGD algorithm.

Mutational spaces for leaf shape and size.

A key approach to understanding how genes control growth and form is to analyze mutants in which shape and size have been perturbed. Although many mutants of this kind have been described in plants and animals, a general quantitative framework for describing them has yet to be established. Here we describe an approach based on Principal Component Analysis of organ landmarks and outlines. Applying this method to a collection of leaf shape mutants in Arabidopsis and Antirrhinum allows low-dimensional spaces to be constructed that capture the key variations in shape and size. Mutant phenotypes can be represented as vectors in these allometric spaces, allowing additive gene interactions to be readily described. The principal axis of each allometric space reflects size variation and an associated shape change. The shape change is similar to that observed during the later stages of normal development, suggesting that many phenotypic differences involve modulations in the timing of growth arrest. Comparison between allometric mutant spaces from different species reveals a similar range of phenotypic possibilities. The spaces therefore provide a general quantitative framework for exploring and comparing the development and evolution of form.

Evolutionary paths underlying flower color variation in Antirrhinum.

To understand evolutionary paths connecting diverse biological forms, we defined a three-dimensional genotypic space separating two flower color morphs of Antirrhinum. A hybrid zone between morphs showed a steep cline specifically at genes controlling flower color differences, indicating that these loci are under selection. Antirrhinum species with diverse floral phenotypes formed a U-shaped cloud within the genotypic space. We propose that this cloud defines an evolutionary path that allows flower color to evolve while circumventing less-adaptive regions. Hybridization between morphs located in different arms of the U-shaped path yields low-fitness genotypes, accounting for the observed steep clines at hybrid zones.

Evolution through genetically controlled allometry space.

Understanding evolutionary change requires phenotypic differences between organisms to be placed in a genetic context. However, there are few cases where it has been possible to define an appropriate genotypic space for a range of species. Here we address this problem by defining a genetically controlled space that captures variation in shape and size between closely related species of Antirrhinum. The axes of the space are based on an allometric model of leaves from an F2 of an interspecific cross between Antirrhinum majus and Antirrhinum charidemi. Three principal components were found to capture most of the genetic variation in shape and size, allowing a three-dimensional allometric space to be defined. The contribution of individual genetic loci was determined from QTL analysis, allowing each locus to be represented as a vector in the allometric space. Leaf shapes and sizes of 18 different Antirrhinum taxa, encompassing a broad range of leaf morphologies, could be accurately represented as clouds within the space. Most taxa overlapped with, or were near to, at least one other species in the space, so that together they defined a largely interconnected domain of viable forms. It is likely that the pattern of evolution within this domain reflects a combination of directional selection and evolutionary tradeoffs within a high dimensional space.