Complex morphogenesis of surfaces: theory and experiment on coupling of reaction-diffusion patterning to growth.

Reaction-diffusion theory for pattern formation is considered in relation to processes of biological development in which there is continuous growth and shape change as each new pattern forms. This is particularly common in the plant kingdom, for both unicellular and multicellular organisms. In addition to the feedbacks in the chemical dynamics, there is then another loop linking size and shape changes with the reaction-diffusion patterning of growth controllers in the growing region. In studies by computation, the codes must incorporate, alongside the usual solvers of the partial differential dynamic equations, a versatile growth code, to express any kind of shape change. We have found that regulation of shape change in particular ways (e.g. to make narrow-angle branchings) demands new features in our chemical mechanisms. Our growth algorithm is for a surface growing tangentially, but moving outward and changing shape to accommodate the extra area. This is potentially applicable both to the tunica layer of multicellular plant meristems and to the growing tip of the cell surface, e.g. in the morphogenesis of single-celled chlorophyte algae which display branching processes: whorl formation in Acetabularia (Dasycladales) and repeated dichotomous branching in Micrasterias (Desmidiaceae). For computational studies, a hemispherical shell is a reasonable idealization of the initial shape. We describe results of two types of study: (1) Pattern formation by three reaction-diffusion models, with contrasted nonlinearities, on the hemispherical shell, particularly to find conditions for robust formation of annular pattern or pattern for dichotomous branching, both of which are common in plants. (2) Sequential dichotomous branchings in a system growing and changing in shape from the hemispherical start.

Whorl morphogenesis in the dasycladalean algae: the pattern formation viewpoint.

The dasycladalean algae produce diverse whorled structures, among which the best known are the vegetative and reproductive whorls of Acetabularia acetabulum. In this paper, we review the literature pertaining to the origin of these structures. The question is addressed in terms of the necessary pattern-forming events and the possible mechanisms involved, an outlook we call the pattern formation viewpoint. The pattern-forming events involved in the morphogenesis of the vegetative and reproductive whorls of Acetabularia have been used to define five and six morphogenetic stages, respectively. We discuss three published mechanisms which account, at least in part, for the pattern-forming events. The mechanisms are mechanical buckling of the cell wall, reaction-diffusion of morphogen molecules along the cell membrane, and mechanochemical interactions between Ca2+ ions and the cytoskeleton in the cytosol. The numerous differences between these mechanisms provide experimental grounds to test their validity. To date, the results of these experiments point towards reaction diffusion as the most likely patterning mechanism. Finally, we consider the evolutionary origin of the vegetative and reproductive whorls and provide mechanistic explanations for some of the major evolutionary advances.

Suppression of positional errors in biological development.

Cells in developing embryos behave according to their positions in the organism, and therefore seem to be receiving 'positional information'. A widespread view of the mechanism for this is that each cell responds locally to the concentration level of some extracellular chemical which is distributed in a spatial gradient. For molecules conveying and receiving the positional signal, concentrations are likely to be low enough that, per individual cell, only a few thousand molecules may be involved. Fluctuations to be expected in these numbers (Poisson distribution) could readily lead to errors up to a few percent of embryo length in the reading of position. This is an intolerable level of error for some developmental pattern-forming events. Embryos must have means of suppressing such errors. We maintain that this requires communication between cells, and illustrate this by using the reaction part of two well-known Turing-type reaction-diffusion models as the local gradient reader. We show that switching on diffusion in these models leads to adequate suppression of positional errors.

Definition of TCR recognition sites on Ld-tum- complexes.

The P911 variant of the P815 mastocytoma was shown by Lurquin et al. (Cell 58:293, 1989) to elicit rapid tumor rejection in a syngeneic host. This rejection was mediated by Ld-restricted cytotoxic T lymphocytes (CTL) for which targets could be sensitized by the synthetic peptide designated tum- (P91A-.12-24). In a previous study, T cell clones specific for Ld-tum- complexes displayed very restricted TCR usage and a characteristic TCR motif in the V alpha CDR3 region, predicted to interact with peptide. However, in contrast to the majority of Ld peptide ligands that are nonamers, the tum- peptide is a 13-mer and its sequence does not fit the Ld binding motif. Thus, to define shorter versions of the tum- 13-mer and residues involved in TCR recognition, nonamer derivatives were synthesized and compared in several different binding and functional assays. From these comparisons, the peptide TQNHRALDL was found to be the optimal nonamer. CTL recognition of Ala-substituted analogues of this peptide indicated that the His and Arg residues at positions 4 and 5 are important for TCR contact. We propose that these basic residues of the tum- peptide interact with the previously defined acidic residues in the CDR3 region of several TCR known to recognize Ld-tum- complexes.

A polymorphic residue in the amino terminal alpha 1 hemi-domain of the mouse Ld class I molecule affects its assembly and surface expression.

In comparison to Dd and most other mouse major histocompatibility complex class I molecules, the Ld molecule is poorly expressed on the cell surface, has a lower affinity for beta 2-microglobulin and is trafficked more slowly to the cell surface. Previous studies using Ld-Dd exon-shuffled constructs and the chimeric Ddm1 molecules suggested that the Ld alpha 1 domain was responsible for this phenotype. Two constructs, one containing an Ld-Dd hemi-exon-shuffled alpha 1 exon and the other containing a Dd-Ld hemi-exon-shuffled alpha 1 exon, were inserted into either Ld or Dd to replace the intact alpha 1 exon. These constructs were transfected into mouse L cells. Flow cytometric analyses of the resulting transfectants indicate that the Dd-Ld alpha 1/Ld molecules, similar to the Dd alpha 1/Dd alpha 2/Ld molecules, were expressed at a higher level on the cell surface than either the Ld-Dd alpha 1/Ld molecules or intact Ld molecules. Analyses of the molecules in lysates suggested that a higher proportion of the Dd-Ld alpha 1/Ld molecules, like the Dd alpha 1/Dd alpha 2/Ld molecules, as compared to the Ld-Dd alpha 1/Ld and intact Ld molecules were assembled as detected by alpha 2 domain-reactive monoclonal antibodies. Pulse-chase and lysate stability studies suggested that the lower steady state levels of assembled Ld-Dd alpha 1 molecules resulted from a slower assembly rate rather than instability. Collectively, these studies suggest that residues in the amino terminal half of the Ld alpha 1 domain are responsible for its inefficient assembly, probably leading to its low cell surface expression. To determine which polymorphic residues in the amino terminal alpha 1 hemi-domain might influence this phenotype, several Ld point mutants, in which a Dd amino terminal alpha 1 hemi-domain residue was substituted into the corresponding position of Ld, were analysed. These analyses suggested that, while the residue at position 9 has only a slight effect on beta 2-microglobulin association, it has a striking effect on assembly and cell surface expression.

Association of Ld-restricted peptides with the wild-derived mouse Lw16 MHC class I molecule.

Previous serological analysis of untreated splenocytes and L cell transfectants expressing the wild-derived mouse major histocompatibility complex (MHC) class I molecule, Lw16, demonstrated the presence of two forms of this molecule in the cell lysates, one reactive with both the alpha 2 domain-reactive monoclonal antibody (mAb) 30-5-7 and the alpha 3 domain-reactive mAb 28-14-8 (30-5-7+ 28-14-8+), and the other reactive with only the latter of the two (30-5-7- 28-14-8+). Furthermore, the analysis suggested the presence of both forms on the cell surface. Due to the similarity of Lw16 to the inbred mouse-derived Ld molecule, we tested a panel of Ld-restricted and control peptides for their ability to bind to Lw16 molecules. Here, we report that two Ld-restricted viral peptides, lymphocytic choriomeningitis virus nucleoprotein (LCMV NP) 118-126 and murine cytomegalovirus (MCMV) pp89 168-176, significantly increase the number of Lw16 molecules on the cell surface as measured by the mAb 28-14-8, and the proportion of those molecules that are recognized by the mAb 30-5-7. This was further supported by an increase in mAb 30-5-7-reactive molecules in L.Lw16 cell lysates following treatment with either of these peptides. Examination of the stability of the different forms on the cell surface suggested that the 30-5-7+ Lw16 molecules induced with these peptides were unstable and probably lost their Ld-restricted peptides to generate 30-5-7- 28-14-8+ molecules; these latter molecules were also unstable. In contrast, putative 30-5-7+ and 30-5-7- 28-14-8+ Lw16 molecules on untreated cells were stable. Together, these results suggest that two Ld-restricted, viral peptides can induce assembly of or stabilize 30-5-7+ 28-14-8+ Lw16 molecules, mimicking endogenous self peptides. However, the association of the Ld-restricted peptides with Lw16 is apparently not optimal, since it results in unstable Lw16 molecules.

Computations of post-inductive dynamics in axolotl heart formation.

This paper reports modelling of heart localization in the axolotl (Ambystoma mexicanum). The region of heart specification in the mesoderm defined by classical induction from the endoderm is larger than the area of final myocardial differentiation. For localizing the area of differentiation within the area of specification, we postulate a reaction-diffusion system that arises within the mesoderm in response to induction from the endoderm. This mechanism generates a spatial pattern for two chemicals, an activator and an inhibitor, corresponding to the area of myocardial differentiation. We postulate a diffusible chemical rescuer, which is absent in the cardiac lethal mutant, and which is a precursor to the reaction-diffusion mechanism. The activator, inhibitor, rescuer, and product of endodermal induction are presented in an enzyme mechanism with rate equations similar to the Gierer-Meinhardt equations. These equations were solved numerically in both one and two spatial dimensions. We have attained quantitative agreement with the experimental data for sizes of tissue regions and for times to heartbeat. Experiments modelled include wild-type heart localization as well as both in vitro and in vivo rescue of cardiac lethal mesoderm with wild-type mesoderm. Based upon the parameters necessary to model heart localization, we make a series of predictions. We predict: a specific profile for the endodermal inducer gradient; the possibility of producing multiple hearts in vivo; and a greater contribution to the heart from the wild-type mesoderm for in vivo transplants with cardiac lethal mesoderm. We make some suggestions as to the possible chemical nature of the substances in the model. We indicate that the inhibitory field and mechanochemical theories are probably not as promising as reaction-diffusion for the mechanism of heart localization.

Kinetic theory of living pattern.

The self-organization whereby developing organisms generate the patterns and spatial relationships of their parts has not been explained on any generally accepted theoretical basis. There is a wide gulf between physical scientists and experimental biologists in their expectations of the kind of theory that is best to pursue. Physical scientists incline towards the power of nonlinear dynamics to generate pattern and are trying evangelistically to interest biologists in this approach.

Stripe selection: an intrinsic property of some pattern-forming models with nonlinear dynamics.

In two-dimensional pattern formation, the genesis of stripped rather than spotted patterns may involve preexisting spatial asymmetries, such as unidirectional gradients or asymmetric shape of the pattern-forming domain. In the absence of such asymmetries, some kinds of nonlinear dynamics still lead to striped rather than spotted patterns. We have studied the latter effect both by extensive computer experiments on a range of nonlinear models and by mathematical analysis. We conclude that, when the dynamic equations are written in terms of departure from the unpatterned state, the presence of nonlinearities which are odd functions of these departures (e.g., cubic terms) together with absence of even nonlinearities (e.g., quadratic terms) ensures stripe formation. In computer experiments, we have studied the dynamics of two-morphogen reaction-diffusion models. The mathematical analysis presented in the Appendix shows that the same property exists in more generalized models for pattern formation in the primary visual cortex.

Magnetic resonance imaging approaching microscopic scale: maturation stages of Acetabularia mediterranea reproductive caps.

The reproductive cap of the giant single-celled alga Acetabularia mediterranea (or A. acetabulum) has rays tapering from a width of about 400 microns at the circumference of the cap to about 30 microns at their junction with the stalk of the cell. This is ideal geometry for testing the current limits of spatial resolution of proton magnetic resonance imaging. In this work, resolution of features down to 40 microns is achieved. Maturation of the cap rays involves a major cytoplasmic reorganization, from continuous cytoplasm and a central vacuole in each ray to bundles of cysts surrounded by aqueous solution. This work shows that an intermediate stage in the change can be highlighted in images by relaxation time (T1) contrasting.

Theoretical aspects of stripe formation in relation to Drosophila segmentation.

Many aspects of Drosophila segmentation can be discussed in one-dimensional terms as a linear pattern of repeated elements or cell states. But the initial metameric pattern seen in the expression of pair-rule genes is fully two-dimensional, i.e. a pattern of stripes. Several lines of evidence suggest a kinetic mechanism acting globally during the syncytial blastoderm stage may be responsible for generating this pattern. The requirement that the mechanism should produce stripes, not spots or some other periodic pattern, imposes preconditions on this act, namely (1) sharp anterior and posterior boundaries that delimit the pattern-forming region, and (2) an axial asymmetrizing influence in the form of an anteroposterior gradient. Models for Drosophila segmentation generally rely on the gradient to provide positional information in the form of concentration thresholds that cue downstream elements of a hierarchical control system. This imposes restrictions on how such models cope with experimental disturbances to the gradient. A shallower gradient, for example, means fewer pattern elements. This need not be the case if the gradient acts through a kinetic mechanism like reaction-diffusion that involves the whole system. It is then the overall direction of the gradient that is important rather than specific concentration values.(ABSTRACT TRUNCATED AT 250 WORDS)

What is the status of reaction-diffusion theory thirty-four years after turing?

Physicochemical explanations of phenomena are divisible into three classes: structure, equilibrium and kinetics. For the phenomena of biological development, many physical scientists have the preconception that the explanations must turn out to be principally kinetic. In this class of theory, reaction-diffusion is by far the most extensively developed, and is worthy of attention both for its own sake and because many of its features well exemplify the nature of the broader field of kinetic theory. Reaction-diffusion should be thought of as a class, rather than a species, of theory. This review addresses three aspects: first, the general nature of the two-morphogen interaction as first proposed by Turing and incorporated in many later models; second, the specifics of these later models and their probable relative scope; third, the current state of attempts to identify the chemical nature of morphogens. It is concluded that reaction-diffusion in particular, and kinetic theory in general, are now slowly emerging from the almost total neglect by biologists which reaction-diffusion suffered for its first 20 years.

Evaluation of home glucose measuring devices.

A large number of glucose-monitoring systems suitable for home use are now available. The Glucochek, an early model (Mk I) and a later (Mk II), the Stan Clark RAHC, the Glucometer, and 20-800 BM glycemie strips were evaluated with regard to accuracy, precision, model variability and operator variability before a particular system was recommended for patient use. Whole blood glucose, on samples samples taken in the Diabetic Clinic of The Royal Melbourne Hospital, Melbourne, was measured with the system under test and in the Biochemistry Department. Accuracy was indicated by the mean of the differences between the two results, and precision by the standard deviation of these differences-the closer these results to zero, the better the system. The 20-800 BM Glycemia strips gave the best results in the hands of an experienced operator, but showed the greatest interoperator differences. These differences decreased when a machine-based system was employed. The Glucochek Mk I did not perform satisfactorily. All the systems tested showed a marked decrease in accuracy and precision when blood glucose levels were greater than 15.0 mmol/L. These results show that a machine is not a necessary part of a home glucose-monitoring system; that patients on home glucose-monitoring must be trained and their results checked against a reference method initially and, ideally, at regular intervals; that home glucose-monitoring in patients with marked hyperglycaemia unreliable.