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B C Goodwin

Publications and source records attributed to B C Goodwin.

At least 19 recordsLinked to original sources
PubMed1990

Drosophila segmentation: supercomputer simulation of prepattern hierarchy.

Spontaneous prepattern formation in a two level hierarchy of reaction-diffusion systems is simulated in three space co-ordinates and time, mimicking gap gene and primary pair-rule gene expression. The model rests on the idea of Turing systems of the second kind, in which one prepattern generates position dependent rate constants for a subsequent reaction-diffusion system. Maternal genes are assumed responsible for setting up gradients from the anterior and posterior ends, one of which is needed to stabilize a double period prepattern suggested to underly the read out of the gap genes. The resulting double period pattern in turn stabilizes the next prepattern in the hierarchy, which has a short wavelength with many characteristics of the stripes seen in actual primary pair-rule gene expression. Without such hierarchical stabilization, reaction-diffusion mechanisms yield highly patchy short wave length patterns, and thus unreliable stripes. The model yields seven stable stripes located in the middle of the embryo, with the potential for additional expression near the poles, as observed experimentally. The model does not rely on specific chemical reaction kinetics, rather the effect is general to many such kinetic schemes. This makes it robust to parameter changes, and it has good potential for adapting to size and shape changes as well. The study thus suggests that the crucial organizing principle in early Drosophila embryogenesis is based on global field mechanisms, not on particular local interactions.

Animals↗
PubMed1990

Spatial harmonics and pattern specification in early Drosophila development. Part I. Bifurcation sequences and gene expression.

Molecular probes have now provided an unprecedented wealth of detail revealing the changing spatial patterns of gene products in early Drosophila development. This is examined for dynamic properties which might provide insights into the underlying behaviour of the patterning process. What emerges is that transcripts and protein products of members of the major categories of zygotically active genes involved in segmentation pass through transient spatial patterns that are suggestive of harmonic sequences arising from spatial frequency-doubling bifurcations. That is to say, these patterns are typically periodic in space and show a doubling in the number of domains of spatial expression as development proceeds. One of these patterns reflects the primary functional role of the gene in the establishment of the spatial pattern. The different categories of segmentation gene pass through these transients at different rates, those with the longest functional wavelength progressing most slowly. Each gene in a category has its own unique phase relationship to other members, as well as particular variations on the harmonic sequence theme. The result is that the developing embryo experiences a spatial hierarchy of phase-shifted patterning influences that span the range from the whole embryo to single segments, providing progressively more spatial resolution in the patterning process. The characteristic transients and the dynamic relationships between genes of the different categories suggest that gene products expressed in longer-wavelength patterns act as bifurcation parameters on the dynamic system generating the next shorter wavelength category. Such parametric influences are known to result in frequency-doubling bifurcations in Turing reaction-diffusion systems. A general model is proposed of a hierarchically-nested set of quasi-autonomous dynamic systems involving gene activities that can generate the progressively finer spatial order that emerges during embryogenesis. This model has implications for the general stability properties of evolving epigenetic systems.

Animals↗
PubMed1990

Spatial harmonics and pattern specification in early Drosophila development. Part II. The four colour wheels model.

We review the evidence presented in Part I showing that transcripts and protein products of maternal, gap, pair-rule, and segment polarity genes exhibit increasingly complex, multipeaked longitudinal waveforms in the early Drosophila embryo. The central problem we address in Part II is the use the embryo makes of these wave forms to specify longitudinal pattern. Based on the fact that mutants of many of these genes generate deletions and mirror symmetrical duplications of pattern elements on length scales ranging from about half the egg to within segments, we propose that position is specified by measuring a "phase angle" by use of the ratios of two or more variables. Pictorially, such a phase angle can be thought of as a colour on a colour wheel. Any such model contains a phaseless singularity where all or many phases, or colours, come together. We suppose as well that positional values sufficiently close to the singularity are meaningless, hence a "dead zone". Duplications and deletions are accounted for by deformation of the cycle of morphogen values occurring along the antero-posterior axis. If the cycle of values surrounds the singularity and lies outside the dead zone, pattern is normal. If the curve transects the dead zone, pattern elements are deleted. If the curve lies entirely on one side of the singularity, pattern elements are deleted and others are duplicated with mirror symmetry. The existence of different wavelength transcript patterns in maternal, gap, pair-rule, and segment polarity genes and the roles of those same genes in generating deletions and mirror symmetrical duplications on a variety of length scales lead us to propose that position is measured simultaneously on at least four colour wheels, which cycle different numbers of times along the anterior-posterior axis. These yield progressively finer grained positional information. Normal pattern specification requires a unique angle, outside of the dead zone, from each of the four wheels. Deformations of the cycle of gene product concentrations yield the deletions and mirror symmetric duplications observed in the mutants discussed. The alternative familiar hypothesis that longitudinal position is specified in an "on" "off" combinatorial code does not readily account for the duplication deletion phenomena.

Animals↗
PubMed1990

Effects of calcium input/output on the stability of a system for calcium-regulated viscoelastic strain fields.

The Goodwin and Trainor model of pattern generation in calcium-regulated strain fields is studied in the case where calcium input and calcium output processes are involved. It is shown that the properties of the original model may still remain provided that the input-output processes are not unstable. In this last case, despite the eventual stabilizing effect of the calcium exchange term, perturbations of the generalized system can grow and lead to inhomogeneous solutions. Applications to cell differentiation and cell growth are discussed.

Acetabularia↗
PubMed1989

Diffusion effects in calcium-regulated strain fields.

The Goodwin-Trainor equations for cellular morphogenesis, based on calcium ion regulation of the visco-elastic properties of the cellular cortex, are generalized to the situation where the concentration of calcium ions (free plus bound) is allowed to change locally. A stability analysis is presented which shows that the generalized equations are also stable against perturbations at low and high wave lengths and may, for certain parameter values, develop instabilities at intermediate wave lengths.

Animals↗
PubMed1984

A further study of the holoblastic cleavage field.

The division of holoblastically cleaving eggs was modelled by Goodwin & Trainor in terms of a minimization principle applied to the generalized surface free energy of a spherical surface, expressed in terms of an order parameter. Their calculations led to a cumulative description of the sequence of horizontal and vertical cleavage lines or planes in terms of the nodal lines of spherical harmonics. In this paper we give a complete treatment, first of the numerical regularities exhibited by holoblastic cleavage resulting in a group-theoretic formulation, and secondly of the calculations which arise from Goodwin & Trainor's model. It is shown mathematically that there is no other cumulative description than the one they produced but that it suffers from certain inaccuracies. We prove that there is an essentially unique non-cumulative description which is more accurate and which predicts the loss of global order after a particular stage which corresponds to that beyond which global biological order itself fails to persist. In the discussion, this is interpreted to mean that the initial global field is superseded by a more local one, in accordance with the biological evidence as observed in the midblastula transition.

Amphibians↗
PubMed1977

Waves and periodic events during primitive streak formation in the chick.

Morphogenetic movements occurring during formation of the primitive streak in the chick embryo are of a periodic nature, with a mean frequency of one pulse every 2.6 min. The period of the oscillatory movement is shown to be temperature-dependent. The onset of these pulses of movement can be seen as a slow wave starting at the posterior end of the embryo and making its way towards the anterior end. An interpretation of this behaviour is discussed.

Animals↗
PubMed1976

An inhibitor of DNA synthesis in erythrocyte-conditioned medium and its separation from haemoglobin.

Erythrocyte-conditioned medium and erythrocyte lysate have been prepared from rat red blood cells. Molecular fractions of the conditioned medium and the lysate are used to test for the presence of erythrocyte chalone in short-term tissue cultures of mouse foetal liver cells. An inhibitor of erythroblast DNA synthesis has been found in the erythrocyte conditioned medium. The inhibitor is not haemoglobin, and it is not found in erythrocyte lysate soluble components.

Animals↗