scientific correspondence the dino phenotype is caused by a mutation In a restriction-fragment length poly- in the zebrafish chordin gene, revealing that morphism (RFLP) linkage analysis of more The zebrafish organizer Chordin is an essential component of the than 400 mutant chromosomes, we saw no dorsal organizer. Furthermore, we provide recombination between dino and chordin requires chordino evidence that Chordin and BMPs are antag- (Fig. 1b), indicating that dino and chordin onistic, not only at the protein level but also are within 0.25 centimorgans (cM). The The dorsoventral pattern of vertebrate at the transcriptional level. chordin complementary DNA from dintt250 embryos is established and regulated by Zebrafish Chordin (S. S.-M. & M. H., mutant embryos has a deletion of 104 base opposing gradients of ventralizing bone manuscript in preparation) shows the same pairs, causing a frame-shift predicted to morphogenetic proteins (BMPs) and BMP protein organization as its Xenopus and produce a severely truncated protein (Fig8. antagonists1–3 (such as Chordin2,4, Noggin5,6 Drosophila homologues, Xchd2 and Sog12–14, 1c). This truncated form has only the first and Follistatin7,8 in the frog embryo) respectively(Fig. 1a). A hydrophobic amino- 42 amino acids of the wild-type Chordin secreted by a dorsal organizer. In the terminal sequence is followed by the first protein and completely lacks the cysteine- zebrafish, Danio rerio, mutations in a num- of four cysteine-rich repeats (CR1); the rich repeats. ber of genes that affect dorsoventral pat- remaining three (CR2–4) being towards the Injection of Xenopus chordin messenger terning of the early embryo have been carboxy terminus. The chordin gene is first RNA into dino mutants rescues the mutant identified9,10, but only two, dino and mer- expressed on the dorsal side of the embryo, phenotype, producing viable and fertile cedes, are involved in dorsal specification11, starting before gastrulation (Fig. 2a), when homozygous dino mutant adult fish (Fig. 1 with dino mutants displaying the stronger, the Spemann organizer is thought to gener- d,e,f). This indicates that chordin is not ventralized phenotype. Here we show that ate dorsalizing signals. required after the early stages of develop- ment, as the injected RNA is largely degrad- ed by the end of the gastrulation stage (data not shown). These data indicate that the defects of dino mutant embryos are poten- tially caused by a null mutation in the chordin gene. In view of this genetic rela- tionship, we will refer to both the mutant and the gene as chordino. In mutant embryos, chordino expression is strongly reduced at midgastrula stages (Fig. 2a,b), indicating that chordino expres- sion requires functional Chordino protein. Indeed, the wild-type chordino expression pattern can be rescued in chordino mutants by the injection of both Xenopus chordin mRNA (Fig. 2c) and mRNA encoding a dominant negative BMP receptor (Fig. 2d), whereas over-expression of bmp-4 in wild- type embryos leads to a reduction in chor- dino expression levels similar to those in chordino mutants (data not shown). This suggests that such autoregulation of chor- dino is achieved by an inhibition of antago- Figure 1 a, Schematic representation of Xenopus Chordin, zebrafish Chordin, and Drosophila Sog. Numbers indicate the percentage of amino-acid identity between the respective cysteine-rich domains. b, Linkage analysis, carried out as in ref. 15. Genomic DNA was digested with EcoRI. Lanes 1 and 2: parental DNA from the WIK strain and a heterozygous dino individual in the Tübingen background, respectively. Lanes 3, 6—10: DNA from pools of dino mutant F2 embryos (a total of 136 genome equivalents; 272 mutant chromosomes). Figure 2 a, Wild-type and b, Mutant embryo. & & & Lanes 4 and 5: DNA from pools of sibling F2 embryos ( / and din/ ; 0.5 and 24 genome equivalents, chordino mRNA can be rescued to almost wild-type respectively). c, Predicted structure of dintt250, containing the first 42 wild-type amino acids and 54 additional levels by the injection of mRNA encoding c, Xeno- unrelated residues. Part of the amino-acid sequence of the wild type (left) and mutant protein (right) is pus chordin (Xchd) or d, A dominant-negative BMP shown, with the first four amino acids of CR1 displayed in italics. d, Wild-type embryo at 3 days of develop- receptor (tBr). All embryos are shown in a dorsal ment. e, Sibling dino mutant embryo. Note the small eyes and split ventral tail fin. f, Mutant embryo, rescued view after in situ hybridizations with a chordino anti- by injection of Xenopus chordin mRNA. The ventral tail fin is partially duplicated (arrow), but otherwise the sense probe. a,b,d, 70% epiboly. c, 80% epiboly. embryo appears normal. RNA injections were done as in ref. 3. 862 NATURE | VOL 387 | 26 JUNE 1997 Nature © Macmillan Publishers Ltd 1998 scientific correspondence nizing BMP signals which normally act as classical limit has sparked a lively debate. The negative regulators of chordino expression. mathematical theories all assume that the In addition, chordino mutants display a Have quantum scars periodic orbits are isolated, though more dorsally expanded bmp-4 expression than one isolated orbit can scar a single state. domain3, indicating that during normal been observed? Wilkinson et al. have probed the 25 or so development chordino has a negative influ- lowest quantum levels above the ground ence on bmp-4 transcription in dorsolateral Wilkinson et al.1 have reported observations state. By lowering the energy, the phases of regions. Again, this negative regulation of oscillations in the current of a resonant the classical orbits are made small, so that might be mediated by BMPs themselves, tunnelling diode in a magnetic field. They they remain in-phase. Hence, the neigh- which normally act as positive regulators of proposed that this provides the first direct bourhoods of topologically distinct perio8d- their own expression3. experimental evidence for quantum ‘scar- ic orbits become so large that they overlap It has been shown that Xenopus Chordin ring’ in a real chaotic system. But we believe and so cease to be isolated. inhibits the antagonizing Bmp-4 activity by that Wilkinson et al. have not observed In the experiment, the electronic motion direct binding to the Bmp-4 protein, there- quantum scars in the usual sense. They con- is confined by a magnetic field to a cylindri- by preventing receptor activation4. Our data sidered a far-from semiclassical regime cal energy surface whose ends are the two demonstrate that this inhibition at the pro- where current theories of scarring are not barriers of the well. Wilkinson et al. found tein level is potentiated by two synergistic valid. Demonstrating these effects in a solid- that the tunnelling is dominated by four sin- feedback loops which lead to a derepression state device is a tremendous achievement. gle eigenstates, roughly ‘linear’ in shape with of chordino transcription and an inactiva- However, we believe that even in the semi- Nø10 oscillations along the magnetic field. tion of bmp-4 expression. classical limit this type of experiment does However, the energy surface supported only Our findings demonstrate that chordino not go beyond other experiments on atoms nø2–3 oscillations perpendicular to the is required during early dorsoventral pat- in magnetic fields as a probe of scarring. field, so each ‘linear’ eigenstate is supported terning of the zebrafish embryo, where it A quantum particle travelling from A to by a large fraction of the Poincaré surface on functions as an antagonist of ventralizing B experiences all possible paths in between. the emitter wall, including a cluster of short BMP signals. This supports the notion that The wave-like nature of a quantum particle periodic orbits of similar action that traverse mechanisms of early dorsoventral pattern- means that each path has a phase and so the length of the cylinder. ing are conserved between vertebrates and neighbouring paths interfere with each This similarity of action is analogous to invertebrates13. other. The combined contributions of these back and forth motion close to the axis of a Stefan Schulte-Merker paths build up the wavefunction, which pro- long, thin cylinder. Most of the action comes MPI für Entwicklungsbiologie, Spemannstrasse 35, vides a complete description of the quantum from the longitudinal motion, with smaller 72076 Tübingen, Germany dynamics of the particle. At high energies, in differences due to the transverse compo- Kevin J. Lee the semiclassical limit (h- →0), phases associ- nents. The periodic orbits become isolated Howard Hughes Medical Institute, ated with different paths are large. Hence, only when we can resolve the differences in Department of Biochemistry and Molecular neighbouring paths can rapidly fall out of action (typically for n¤10). For small n Biophysics, phase and their contributions cancel by (non-isolated case), sequences of individual Center for Neurobiology and Behavior, destructive interference. When the typical ‘linear’ states, roughly aligned with the mag- Columbia University, New York, motion is a chaotic trajectory, this should netic field, are ubiquitous1,3. These states New York 10032, USA produce wavefunctions with no structure cannot distinguish between the different Andrew P. McMahon other than a random grainy pattern. periodic orbits. The stability parameters of Department of Molecular and Cellular Biology, But Heller2 found that for h- →0, quan- the classical dynamics are essentially irrele- Harvard University, 16 Divinity Avenue, tum states of a chaotic system show ‘scars’, vant, in contrast to an isolated scar. They are Cambridge, Massachusetts 02138, USA concentrations near the paths of unstable, essentially a quantum phenomenon, the so- Matthias Hammerschmidt* isolated periodic orbits (classical orbits called adiabatic separability4, more relevant MPI für Immunbiologie, Stübeweg 51, which retrace themselves and are isolated if in the deep quantum regime than an inter- 79108 Freiburg, Germany there is no other periodic orbit of similar pretation in terms of scars.