High-pressure freezing of spermiogenic nuclei supports a dynamic chromatin model for the histone-to-protamine transition.

In this study, we present for the first time a description of the dynamic chromatin changes that occur during spermiogenesis in the internally fertilizing caenogastropod mollusc Nucella lamellosa. Chromatin condensation in developing sperm cells in some animals, such as the model biological system used here, involves the histone-to-protamine transition and proceeds through a patterning stage from granules to fibers to lamellae. This may be due to the physicochemical phenomenon of phase separation by spinodal decomposition, a dynamic mechanism known to generate pattern. This hypothesis is based entirely on published transmission electron microscopy photomicrographs using conventional fixation technology. We now report that spermatid nuclear patterning and subsequent condensation in testis of Nucella lamellosa fixed by high-pressure freezing and freeze substitution (HPF/FS) is similar to that in glutaraldehyde-fixed testis, and can be related to the processing of sperm nuclear basic proteins (SNBPs).

Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions.

BACKGROUND AND AIMS: A study is made by computation of the interplay between the pattern formation of growth catalysts on a plant surface and the expansion of the surface to generate organismal shape. Consideration is made of the localization of morphogenetically active regions, and the occurrence within them of symmetry-breaking processes such as branching from an initially dome-shaped tip or meristem. Representation of a changing and growing three-dimensional shape is necessary, as two-dimensional work cannot distinguish, for example, formation of an annulus from dichotomous branching. METHODS: For the formation of patterns of chemical concentrations, the Brusselator reaction-diffusion model is used, applied on a hemispherical shell and generating patterns that initiate as surface spherical harmonics. The initial shape is hemispherical, represented as a mesh of triangles. These are combined into finite elements, each made up of all the triangles surrounding each node. Chemical pattern is converted into shape change by moving nodes outwards according to the concentration of growth catalyst at each, to relieve misfits caused by area increase of the finite element. New triangles are added to restore the refinement of the mesh in rapidly growing regions. KEY RESULTS: The postulated mechanism successfully generates: tip growth (or stalk extension by an apical meristem) to ten times original hemisphere height; tip flattening and resumption of apical advance; and dichotomous branching and higher-order branching to make whorled structures. Control of the branching plane in successive dichotomous branchings is tackled with partial success and clarification of the issues. CONCLUSIONS: The representation of a growing plant surface in computations by an expanding mesh that has no artefacts constraining changes of shape and symmetry has been achieved. It is shown that one type of pattern-forming mechanism, Turing-type reaction-diffusion, acting within a surface to pattern a growth catalyst, can generate some of the most important types of morphogenesis in plant development.

Dynamic regulation of growing domains for elongating and branching morphogenesis in plants.

With their continuous growth, understanding how plant shapes form is fundamentally linked to understanding how growth rates are controlled across different regions of the plant. Much of a plant's architecture is generated in shoots and roots, where fast growth in tips contrasts with slow growth in supporting stalks. Shapes can be determined by where the boundaries between fast- and slow-growing regions are positioned, determining whether tips elongate, branch, or cease to grow. Across plants, there is a diversity in the cell wall chemistry through which growth operates. However, prototypical morphologies, such as tip growth and branching, suggest there are common dynamic constraints in localizing chemical growth catalysts. We have used Turing-type reaction-diffusion mechanisms to model this spatial localization and the resulting growth trajectories, characterizing the chemistry-growth feedback necessary for maintaining tip growth and for inducing branching. The mechanism defining the boundaries between fast- and slow-growing regions not only affects tip shape, it must be able to form new boundaries when the pattern-forming dynamics break symmetry, for instance in the branching of a tip. In previous work, we used an arbitrary concentration threshold to switch between two dynamic regimes of the growth catalyst in order to define growth boundaries. Here, we present a chemical dynamic basis for this threshold, in which feedback between two pattern-forming mechanisms controls the extent of the regions in which fast growth occurs. This provides a general self-contained mechanism for growth control in plant morphogenesis (not relying on external cues) which can account for both simple tip extension and symmetry-breaking branching phenomena.

Analysis of pattern precision shows that Drosophila segmentation develops substantial independence from gradients of maternal gene products.

We analyze the relation between maternal gradients and segmentation in Drosophila, by quantifying spatial precision in protein patterns. Segmentation is first seen in the striped expression patterns of the pair-rule genes, such as even-skipped (eve). We compare positional precision between Eve and the maternal gradients of Bicoid (Bcd) and Caudal (Cad) proteins, showing that Eve position could be initially specified by the maternal protein concentrations but that these do not have the precision to specify the mature striped pattern of Eve. By using spatial trends, we avoid possible complications in measuring single boundary precision (e.g., gap gene patterns) and can follow how precision changes in time. During nuclear cleavage cycles 13 and 14, we find that Eve becomes increasingly correlated with egg length, whereas Bcd does not. This finding suggests that the change in precision is part of a separation of segmentation from an absolute spatial measure, established by the maternal gradients, to one precise in relative (percent egg length) units.

Possible mechanisms for early and intermediate stages of sperm chromatin condensation patterning involving phase separation dynamics.

During spermiogenesis in some internally fertilizing molluscs and insects, the post-meiotic spermatid nucleus develops via a sequence of complex patterns of the nuclear contents (chromatin and nucleoplasm) on the way to final chromatin condensation. We have examined the TEM data on these sequences for three species: Philaenus spumarius(a homopteran insect), Murex brandaris (a gastropod mollusc), and Eledone cirrhosa(a cephalopod mollusc). For each of these, spatially quantitative study reveals a constant spacing between pattern repeats through changes from granular to fibrillar to lamellar pattern, followed finally by a shrinkage of the spacing. Therefore we distinguish a "patterning" stage followed by a "condensation" stage. The former appears to demand a dynamic explanation, because there is no sign of structural connections to establish the part of the spacing that crosses the nucleoplasm. We consider types of dynamic mechanism, and show that for "nanostructural" dimensions (tens of nanometers as pattern spacing) reaction-diffusion dynamics are quite inappropriate, but that separation of two fluid phases by a mechanism similar to what is known as "spinodal decomposition" is a very attractive possibility.

Spatially quantitative control of the number of cotyledons in a clonal population of somatic embryos of hybrid larch Larix x leptoeuropaea.

BACKGROUND AND AIMS: Many conifer embryos, both in natural seeds and in clonal populations of somatic embryos, display variability in the number of cotyledons. In hybrid larch, Larix x leptoeuropaea (synonymous with L. x marschlinsii Coaz), such variability has previously been reported in somatic embryos, together with a decrease in the average cotyledon number when benzyladenine (BA) is applied exogenously. Described here is a spatially quantitative study with the aim of throwing some light on the way cotyledon number is determined, and hence the mechanism of cotyledon formation. METHODS: Stock cultures of embryogenic tissue were maintained and later made embryogenically active by standard methods. Development through cotyledon formation was followed by optical microscopy with quantitative measurement of embryo diameter and number of cotyledons. SEMs of representative stages and cotyledon numbers were done for purposes of illustration in this account. Existing mathematics of waveforms on a disc were cast into a form suitable to compare with the quantitative data. RESULTS: The number of cotyledons is linearly related to the diameter of the apical surface of the embryo (which approximates a circular disc) at the time of first appearance of the cotyledon primordia. This linearity is a constant-spacing phenomenon between adjacent primordia. Addition of BA to the medium restricts the range of apical diameters without changing inter-cotyledon spacing. Slope/intercept ratio of the linear plot matches expectation for initiation of cotyledon pattern as a harmonic waveform on a circular disc. CONCLUSIONS: The entire pattern of cotyledon primordia arises as a single entity coordinated by a mechanism with wave-forming properties. This is explicable by diverse mechanisms, especially either mechanical buckling ('biophysical') or reaction-diffusion kinetics ('physicochemical').

Reaction-diffusion models of growing plant tips: bifurcations on hemispheres.

We study two chemical models for pattern formation in growing plant tips. For hemisphere radius and parameter values together optimal for spherical surface harmonic patterns of index l = 3, the Brusselator model gives an 84% probability of dichotomous branching pattern and 16% of annular pattern, while the hyperchirality model gives 88% probability of dichotomous branching and 12% of annular pattern. The models are two-morphogen reaction-diffusion systems on the surface of a hemispherical shell, with Dirichlet boundary conditions. Bifurcation analysis shows that both models give possible mechanisms for dichotomous branching of the growing tips. Symmetries of the models are used in the analysis.