A plausible molecular interpretation of the polar coordinate model with a centripetal degeneracy of distinctive field values

I have attempted to interpret, in molecular terms, the polar coordinate model for epimorphic regulation, revised to accommodate the rigorouslyheld constraints of the polar coordinate system (Sibatani, 1981). If the angular coordinate of the field value is represented by a physical variable in the form of a proportion function, R, to be defined as the intensity ratio of two morphogen curves, then R can stay unchanged along any radius mapped on the actual space, while the intensity of the two morphogens together approaches zero towards the field centre, satisfying the requirement of the centripetal degeneracy of the distinctive angular field values. Implications of this idea are discussed in theoretical and molecular terms as well as in respect of interpretations of some experimental data.     

The rule of normal neighbors: A hypothesis for morphogenetic pattern regulation

The rule of normal neighbors, a generalization of the polar coordinate model of V. French, P. J. Bryant, and S. V. Bryant (1976, Science193, 969–981), can predict topological features of epimorphic regeneration without ascribing a particular coordinate system of positional values to cells. The rule correctly predicts the types and symmetries of structures which regenerate after grafting operations on the distal segments of crayfish legs. The rule of normal neighbors should be valid for any regenerating system in which short-range interactions between cells near the site of wound healing suffice to restore normal structures. Two criteria for defining “minimal regeneration” are proposed: (1) a “shortest-path rule” which generalizes the corresponding rule in the polar coordinate model; and (2) a “minimal free energy” hypothesis.     

Simpler rules for epimorphic regeneration: The polar-coordinate model without polar coordinates

The polar-coordinate model of French, Bryant & Bryant (1976) describes epimorphic regeneration in insects and amphibians, and correctly predicts some surprising phenomena. Their model rests on two main rules. It is shown here that the first of these, the Rule of Intercalation, expresses a requirement that the pattern of positional values of the cells shall be continuous, and that the other, the Rule of the Complete Circle, is not an independent hypothesis, but simply a consequence of the continuity requirement. The formulation of the rules in terms of continuity is coordinate-free and applicable in any number of dimensions: polar coordinates do not have the fundamental significance attached to them by French, Bryant & Bryant (1976), nor are there any grounds to think that the system of positional values in an amphibian limb is two-dimensional. Some simple topology helps to clarify the concepts and prove these points. The phenomena codified by French et al. are to be expected in any epimorphically regenerative organ whose pattern of growth and pattern of positional values are defined by a maintained system of diffusible chemical signals.     

A polar co-ordinate system for positional information in the vertebrate neural retina

Pattern formation in many developing systems has been traditionally understood in terms of a prior signalling of positional information along mutually orthogonal axes, thus setting up a Cartesian co-ordinate grid. Existing data from the vertebrate neural retina has here been reinterpreted in terms of a non-Cartesian system. Results bearing on regeneration and duplication in eye fragments, “axial determination” and polarity alterations in fused eye fragments are considered and interpreted in terms of a polar co-ordinate system. On this model the position of each region of the retina is defined by a co-ordinate (radial) expressing distance from the centre and another (circumferential) expressing position around the circumference. The radial co-ordinate accords with the radial nature of retinal growth and it is possible that the spatially ordered sequence of cell divisions may itself specify the sequence of radial positions. The circumferential co-ordinate, unlike the radial counterpart, is specified in interaction with the extra-ocular tissue such that it may be oriented in the embryo with reference to a primary embryo Cartesian grid. The ability of the model to account for ultrastructural findings, problematic for the Cartesian model, is discussed.     

两栖肢场的插值再生和图式调节

French-Bryant-Bryant的增生场图式调节机制被合理地作了修正,从而自洽地测决了同侧嫁接和异侧嫁接致生正常重肢的形成问题:(1)指出细胞插值生长和远向变换约束之间的平衡是一种自发对称性破损机制,会导致全区捷径插值被分区捷径插值局部地(在异侧嫁接)或整体地(在同侧嫁接)取代,分别在全区和分区极大周值差位置致生重肢.(2)关于重肢的手性和细胞来源的理论预测与实验结果吻合.(3)对于异常重肢的结构复杂性也提出了一种可行的解释.     

Morphogenetic interactions occurring between blastemas and stumps after exchanging blastemas between normal and double-half forelimbs in the axolotl, Ambystoma mexicanum.

Regeneration blastemas were exchanged between surgically constructed forelimbs comprised of symmetrical tissues (double-anterior and double-posterior) and normal, unoperated forelimbs. Normal blastemas grafted at the stage of medium bud (MB) onto double-half forelimb stumps regenerated normal skeletal patterns in nearly all cases. Double-half blastemas transplanted at the stage of MB onto normal forelimb stumps did not regenerate complete limb patterns. These results indicate that a double-half blastema cannot be “rescued” by transplantation to a normal stump and that a double-half limb stump does not interfere with the ability of a normal blastema to distally transform. The regeneration blastema possesses sufficient positional information at the stage of MB to permit it to develop autonomously. Supernumerary forelimbs resulted from several types of graft-stump combinations. The location and handedness of these supernumerary limbs are predicted by the rules of a recently presented model for pattern regulation in epimorphic fields [French, V., Bryant, P. J., and Bryant, S. V. (1976). Science193, 969–981].     

Wound healing in the imaginal discs of Drosophila. I. Scanning electron microscopy of normal and healing wing discs.

Scanning electron microscopy was used to investigate the morphology of intact imaginal wing discs of third-instar larvae of Drosophila melanogaster. The disc stalk, nerve and tracheal entries and the surface ultrastructure of the columnar cells, the peripodial membrane cells, and the adepithelial cells are described. The behavior of various fragments of the wing disc during culture in vivo was also studied. After injuring a wing disc by cuts with a tungsten needle, during the first day of culture the epithelium curls and the wound surface contracts. Subsequent closure of the wound in $\text{3}\text{4}$ and $\text{1}\text{4}$ sectors, in fragments generated by straight cuts and in central squares, leads to the confrontations of cells from formerly separate positions, as was proposed in connection with the polar coordinate model of French, Bryant, and Bryant [(1976). Pattern regulation in epimorphic fields. Science193, 969–981]. Wound healing comprises three steps: (1) Cell debris is removed; (2) occasional cell processes span the wound; (3) all cells at the wound edge contact cells on the opposite side. After 2–3 days, a continuous epithelium is re-established. The tissue distortion may lead to transient contacts of the columnar epithelium with the peripodial membrane and with itself. The latter can explain the occasional duplications of structures which, according to the fate map, arise from near the wound edge, and which have been previously reported from cultured imaginal disc fragments. The tissue movements appear to be due to the contractile properties of individual cells.     

Growth during pattern regulation in imaginal discs

Fragments of imaginal discs of Drosophila regenerate or duplicate when they are cultured in vivo. This pattern regulation is generally believed to occur by epimorphosis. That is, cells at the wound edge proliferate and fill in the missing positional values by intercalation. It is suggested that no respecification of the positional values of cells away from the wound edge occurs. I report here data on fragment growth during culture that are incompatible with the epimorphic model. I argue that both respecification of existing cells and the generation of new cells by growth are involved in pattern regulation.     

Developmental constraints and the evolution of vertebrate digit patterns

The skeletal makeup of the digits of 145 hands and feet from species from the four classes of tetrapod vertebrates is analysed. The analysis leads to the conclusion that developmental constraints are very influential in the evolution of vertebrate digit patterns. Furthermore, 98% of the patterns analysed fall within the specific constraints of the Stock & Bryant (1981) version of the polar coordinate model for the formation of digit patterns during development and pattern regulation. Three cases of apparently forbidden morphology are discussed in terms of the phenomenon of differential growth during development.     

Mating strategies of topi bulls: getting in the centre of attention

In lek-breeding ungulates, only some males defend clustered lek territories, and others defend dispersed territories or are nonterritorial. In this study of lekking topi antelopes, Damaliscus lunatus, we measured male mating benefits directly by observing matings and investigated why the alternative mating strategies coexist. A multivariate analysis showed that proximity to the lek centre had an overriding, positive, effect on male mating rate. With increasing distance to the lek centre, proximity of a territory to a drainage line became increasingly important in enhancing male mating success. On the other hand, costs of lekking were suggested by higher hyaena density on leks, relatively poor body condition of lek males, and more frequent agonistic encounters, with central lek males more likely to sustain bleeding wounds than others. Probably as a consequence of the intense competition for central lek territories, males defending such territories were larger than others and, judging from horn wear, they were also older than resource defenders. Not only did males defending central lek territories achieve the highest instantaneous mating rate and resource defenders the lowest, but the same order was also likely for overall lifetime reproductive success when we took territorial tenure into account. These results suggest that male mating strategies are phenotype limited, as demands on male quality increase with proximity to the lek centre. Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.      

A three-dimensional representation for base composition of protein-coding DNA sequences

Multi-dimensional scaling is applied to our codon space data on the protein coding sequences of DNA from a wide variety of organisms in an attempt to find the smallest number of parameters which will accurately represent these sequences. I find that a three-dimensional representation is satisfactory. One of the three resulting co-ordinates separates eukaryotes and their associated viruses from prokaryotes and their associated phages, while an orthogonal co-ordinate separates those organisms capable of synthesizing proteins (eukaryotes and prokaryotes) from those not so capable (viruses and phages). Mitochondria show no relation in our plots to any of these groups.     

Radial intercalation is regulated by the Par complex and the microtubule-stabilizing protein CLAMP/Spef1

The directed movement of cells is critical for numerous developmental and disease processes. A developmentally reiterated form of migration is radial intercalation; the process by which cells move in a direction orthogonal to the plane of the tissue from an inner layer to an outer layer. We use the radial intercalation of cells into the skin of Xenopus laevis embryos as a model to study directed cell migration within an epithelial tissue. We identify a novel function for both the microtubule-binding protein CLAMP and members of the microtubule-regulating Par complex during intercalation. Specifically, we show that Par3 and aPKC promote the apical positioning of centrioles, whereas CLAMP stabilizes microtubules along the axis of migration. We propose a model in which the Par complex defines the orientation of apical migration during intercalation and in which subcellular localization of CLAMP promotes the establishment of an axis of microtubule stability required for the active migration of cells into the outer epithelium.     

Quantifying Two-Dimensional Filamentous and Invasive Growth Spatial Patterns in Yeast Colonies

The top-view, two-dimensional spatial patterning of non-uniform growth in a Saccharomyces cerevisiae yeast colony is considered. Experimental images are processed to obtain data sets that provide spatial information on the cell-area that is occupied by the colony. A method is developed that allows for the analysis of the spatial distribution with three metrics. The growth of the colony is quantified in both the radial direction from the centre of the colony and in the angular direction in a prescribed outer region of the colony. It is shown that during the period of 100–200 hours from the start of the growth of the colony there is an increasing amount of non-uniform growth. The statistical framework outlined in this work provides a platform for comparative quantitative assays of strain-specific mechanisms, with potential implementation in inferencing algorithms used for parameter-rate estimation.     

Non-random organization of the Biomphalaria glabrata genome in interphase Bge cells and the spatial repositioning of activated genes in cells co-cultured with Schistosomamansoni

Biomphalaria glabrata is a major intermediate host for the parasitic trematode Schistosoma mansoni, a causative agent of human schistosomiasis. To decipher the molecular basis of this host-parasite interaction, the Bge embryonic cell line provides a unique in vitro model system to assess whether interactions between the snail and parasite affect the cell and genome biology in either organism. The organization of the B. glabrata genome in Bge cells was studied using image analysis through positioning territories of differently sized chromosomes within cell nuclei. The snail chromosome territories are similar in morphology as well as in non-random radial positioning as those found in other derived protostome and deuterostome organisms. Specific monitoring of four gene loci, piwi, BgPrx, actin and ferritin, revealed non-random radial positioning of the genome. This indicates that specific parts of the snail genome reside in reproducible nuclear addresses. To determine whether exposure to parasite is reflected in genome organization, the interphase spatial positioning of genes was assessed after co-culturing Bge cells with either normal or irradiation attenuated miracidia for 30 min to 24 h. The loci of actin and ferritin, genes that are up-regulated in the snail when subjected to infection, were visualized by fluorescence in situ hybridisation (FISH) and their radial nuclear positions i.e. their position in the interphase nucleus with respect to the nuclear edge/envelope, mapped. Interestingly, large scale gene repositioning correlated to temporal kinetics of gene expression levels in Bge cells co-cultured with normal miracidia while irradiated parasites failed to elicit similar gene expression or gene loci repositioning as demonstrated using the ferritin gene. This indicates that normal but not attenuated schistosomes provide stimuli that evoke host responses that are reflected in the host’s nuclear architecture. We believe that this is not only the first time that gene-repositioning studies have been attempted in a mollusc but also demonstrates a parasite influencing the interphase genome organization of its host.     

A Three-dimensional model reconstruction of pole assembly in Bacillus subtilis

In the rod-shaped bacterium Bacillus subtilis, new polar surfaces arise at division through the centripetal synthesis of a centrally located cross-wall. Subsequently, the cross-wall, analogous to a flat annulus, is converted into two inner layers of polar wall as the daughter cells separate. The junction of polar and cylindrical wall is marked by the presence of raised tears or wall bands formed by the splitting apart of the cross-wall at its base. New polar wall formed in this manner accounts for about 15% of the total surface area. The sequence of pole formation has been simulated by means of a generalized conic section based upon the mathematical rotation of a parabola about its longitudinal axis. Four basic measurements describe the stages of pole formation with reference to polar surface area: the equatorial diameter at the wall bands (D_max), the division furrow (D_min), the horizontal distance (h) from the centre of the cross-wall to D_max and the curvature of the nascent polar surfaces. These four parameters were found to yield a close fit to measurements of polar size and shape derived from electron micrographs of cell poles in sectioned organisms. Calculations of pole curvature suggest that both the initial separation of the cross-wall and separation of the daughter cells may occur very rapidly.     

Stereometric craniometry

A method is described whereby three-dimensional co-ordinates of points on a cranium can be recorded in terms of azimuth, elevation and radial distance from a selected point. These co-ordinates can be used to create two-dimensional representations of single crania, the differences between many crania or growth stages of individuals or series of individuals. The co-ordinates can be used in more conventional analytic ways in the same way as cartesian co-ordinates.     

Enhancer-trap detection of expression patterns corresponding to the polar coordinate system in the imaginal discs of Drosophila melanogaster

We have isolated three classes of enhancertrap lines of Drosophila in which lacZ expression patterns in the imaginal discs are consistent with the idea of a polar (radial and angular) coordinate system of positional information. In the first class (HZ76), a circular pattern was expressed transiently during the mid-third instar larval stage when the radial components of the coordinate are probably generated. The expression patterns of the second class (HZ84) were sector-shaped and circular in the leg disc, suggesting a correlation with both radial and angular coordinate values. The expression patterns found in the third class (PZ63 and PZ22) were circular and appeared to reflect radial positional values. Expression in the latter two classes always began in the presumptive dorsal region of the leg disc and gradually spread to the ventral region. These developmental profiles of expression suggested the existence of a centre that initiates patterned gene expression in the presumptive dorsal region of the leg disc. The PZ22 line showed transient expression during tarsal segmentation, suggesting its involvement in tarsal segment formation. We have cloned the PZ22 gene and partially determined its sequence. The deduced amino acid sequence contained a zinc finger motif found in DNA/RNA binding proteins. By in situ hybridization, we determined that the PZ22 gene was transcribed in the leg disc in a pattern identical to that of the lacZ expression. In addition, it was expressed transiently in the embryonic mesoderm during mesoderm segmentation. The PZ22 gene, therefore, may function both in mesodermal segmentation in the embryo and in tarsal segmentation in the imaginal disc.     

The thermodynamics and kinetics of electron transfer in the cytochrome P450cam enzyme system.

In anaerobic environments the first electron transfer in substrate-free P450cam is known to be thermodynamically unfavourable, but in the presence of dioxygen the reduction potential for the reaction shifts positively to make electron transfer thermodynamically favourable. Nevertheless a slower rate of electron transfer is observed in the substrate-free P450cam compared to substrate-bound P450cam. The ferric haem centre in substrate-free P450cam changes from six co-ordinate to five co-ordinate when reduced whereas in substrate-bound P450cam the iron centre remains five co-ordinate in both oxidation states. The slower rate of electron transfer in the substrate-free P450cam is therefore attributed to a larger reorganisation energy as predicted by Marcus theory.     

A new method for determination of parity in optical diffraction patterns from the structures with helical symmetry

In optical diffraction patterns from the structures with helical symmetry, the reflections appear as layer-lines. The Bessel function orders (n) of the layer-lines are not easily determined, because the radial co-ordinates of the principal maxima on the layer-lines cannot be measured precisely. We developed a method to find whether n is even or odd (parity of n) by superposing two identical images of a particle back to back with the two axes aligned. The method was successfully applied to analysis of the structure of straight polyhooks isolated from the mutant SJW880 of Salmonella typhimurium.