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B C Goodwin

Publications and source records attributed to B C Goodwin.

At least 19 recordsLinked to original sources
PubMed2001

A cellular oscillator model for periodic pattern formation.

In this paper, we present a model for pattern formation in developing organisms that is based on cellular oscillators (CO). An oscillatory process within cells serves as a developmental clock whose period is tightly regulated by cell autonomous or non-autonomous mechanisms. A spatial pattern is generated as a result of an initial temporal ordering of the cell oscillators freezing into spatial order as the clocks slow down and stop at different times or phases in their cycles. We apply a CO model to vertebrate somitogenesis and show that we can reproduce the dynamics of periodic gene expression patterns observed in the pre-somitic mesoderm. We also show how varying somite lengths can be generated with the CO model. We then discuss the model in view of experimental evidence and its relevance to other instances of biological pattern formation, showing its versatility as a pattern generator.

Animals↗
PubMed2000

The life of form. Emergent patterns of morphological transformation.

The problem of biological form remains unresolved despite the known details of gene activities in embryonic development. Segmentation is discussed in connection with observed gene activities and the question of generic regularities across phyla. The sciences of complexity and nonlinear dynamics are considered as contexts for the exploration of constraints at both the level of genetic networks and morphogenesis. A new model of morphogenetic constraints coupled to dynamic attractors is proposed as an approach to the question--how to unite the contingencies of evolutionary genetic changes with the emergent regularities of organismic morphologies?

Animals↗
PubMed1997

Temporal organization and disorganization in organisms.

The study of biological rhythms has always been a highly interdisciplinary field of research, one that is constantly breaking new ground. Developments during the past 10 years are transforming our ideas about the dynamics of physiological regulation in two ways: (i) homeostasis is really homeodynamics, with sophisticated but robust patterns of hierarchically nested rhythms covering several orders of magnitude in the frequency domain; (ii) there is much more irregularity than previously believed in processes as basic as the heart rate, suggesting either a chaotic generator, a complex pattern of interacting systems with different frequencies, or possibly both. This behavior is consistent with that expected of organisms as complex adaptive systems.

Acclimatization↗
PubMed1993

Is morphogenesis an intrinsically robust process?

Because morphogenesis is dynamically complex, involving many processes operating over different spatial and temporal scales, it is generally assumed that the stability and repeatability of development depends primarily upon accurate control over parameter values i.e. a precise genetic program. However, it is possible that the dynamic coupling between the different mechanisms involved in development reduces the choices available to the system because of bias in successive symmetry-breaking events. Evidence for such stable cascades in morphogenetic processes is described, and a general argument is presented for morphogenesis as an intrinsically robust process. The evolutionary implications of the hypothesis are considerable.

Acetabularia↗
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↗
PubMed1980

Experiments on developing limb buds of the axolotl Ambystoma mexicanum.

Various experiments were performed on the limb buds of axolotls to compare the behaviour of amphibian limbs with that previously reported for chick limbs. Following removal of the tip or whole limb bud, extensive powers of regulation were observed since complete limbs always formed. Similarly after distal to proximal grafts intercalary regulation occurred to produce perfect limbs and after proximal to distal grafts serial repetitions resulted. Transplantation and rotation of limb buds to reverse either the dorso-ventral, antero-posterior or both axes resulted in the induction of supernumerary limbs in a large proportion of cases. Such regulatory behaviour of axolotl limb buds is in contrast to the mosaic nature of chick limbs and as a result, theories such as the progress-zone theory which have been formulated on the basis of data from chick limbs are not relevant to general principles of vertebrate limb development. Possible reasons for the diverse behaviour between the two systems are discussed.

Ambystoma↗