pith. sign in

arxiv: 1907.02730 · v1 · pith:TDME3ZWDnew · submitted 2019-07-05 · 🧬 q-bio.TO

Systems biology approach to the origin of the tetrapod limb

Koh Onimaru , Luciano Marcon This is my paper

Pith reviewed 2026-05-25 02:01 UTC · model grok-4.3

classification 🧬 q-bio.TO
keywords systems biologyfin-to-limb transitiontetrapod limb originevolutionary developmental biologymorphological evolutiongene regulatory networkscomputational modelingdevelopmental non-linearity
0
0 comments X

The pith

An integrative systems biology approach supplies a mechanical explanation for the fin-to-limb transition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews comparative studies of fins and limbs and presents an approach that combines mechanistic theory, computational modeling, and in vivo experiments. This method accounts for how similar genomic sequences produce different morphologies through the nonlinear interactions of genes and cells in multicellular systems. The central result is a mechanical account of the differences between fish fins and tetrapod limbs that addresses long-standing questions of skeletal homology. The authors conclude that counter-intuitive gene dynamics make such combined methods necessary for understanding evolutionary changes in body form.

Core claim

The authors describe their integrative approach as providing a mechanical explanation for the morphological difference between fish fins and tetrapod limbs. This explanation helps resolve the debate over anatomical homology between the skeletal elements of fins and limbs, and it illustrates why purely sequence-based comparisons are insufficient for multicellular evolution.

What carries the argument

The integrative systems biology approach that combines mechanistic theory, computational modeling, and in vivo experiments to handle developmental non-linearity.

If this is right

  • The approach accounts for how shared genomes generate diverse morphologies via nonlinear multicellular dynamics.
  • It supplies a concrete mechanical basis for resolving homology questions between fins and limbs.
  • Similar integrative methods become necessary whenever gene interactions produce counter-intuitive developmental outcomes.
  • Purely genetic or descriptive comparisons are insufficient to explain evolutionary transitions in body plan.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same modeling framework could be tested on other evolutionary transitions that involve changes in appendage structure.
  • It implies that future studies of morphological evolution should prioritize experiments that directly confront model predictions rather than sequence data alone.
  • If the mechanical explanation holds, it would predict specific gene-interaction changes that distinguish limbs from fins across additional vertebrate lineages.

Load-bearing premise

The assumption that the described combination of theory, modeling, and experiments actually supplies the mechanical explanation for the observed fin-limb differences.

What would settle it

Direct comparison showing that the computational models fail to predict the skeletal outcomes observed in targeted in vivo gene-interaction experiments on fin and limb development.

Figures

Figures reproduced from arXiv: 1907.02730 by Koh Onimaru, Luciano Marcon.

Figure 1
Figure 1. Figure 1: The history of comparative study of fins and limbs. a, The tetrapod limb. b, A pectoral fin of the small-spotted catshark. c, Metapterygial axes. d, Shubin and Alberch’s scheme of a mouse forelimb, adapted from Shubin & Alberch, 1986 [6]. e, The expression patterns of Hoxd genes in mouse limb buds, adapted from Tarchini & Duboule 2006 [11]. hu, humerus; ul, ulna; ra, radial; uln, ulnare; d1-d5, digit 1-5. … view at source ↗
Figure 2
Figure 2. Figure 2: PD patterning in limb development. a, Saunders’s AER experiments, adapted from Saunders 1948 [27]. B, The progress zone model, adapted from Tabin & Wolpert 2007 [30]. PZ, progress zone. C, The expression pattern of Meis1/2, Hoxa11, and Hoxa13 in mouse limb buds, based on Marcader et al., 2009 [31]. D, in silico simulation of the two-signal model. Reproduced from Uzkudun et al., 2015 [32]. The AER is a thic… view at source ↗
Figure 3
Figure 3. Figure 3: Positional information theory of the ZPA. a, b, Schemes of polority potential in a normal chick wing (a) and Saundars’ ZPA graft experiment (b). Adapted from Saunders JW, Gasseling 1968 and Wolpert 1969 [28, 29]. c, Mouse genetics on AP patterning. Left panel, a mouse limb bud with SHH and GLI3 repressor (GLI3R) gradients, based on Riddle et al., 1993 and Wang et al., 2000 [43, 46]. Right panel, the autopo… view at source ↗
Figure 4
Figure 4. Figure 4: An example of the Turing mechanism. The top four panels show simulation results of the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Computer modeling of limb and fin development. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

It is still not understood how similar genomic sequences have generated diverse and spectacular forms during evolution. The difficulty to bridge phenotypes and genotypes stems from the complexity of multicellular systems, where thousands of genes and cells interact with each other providing developmental non-linearity. To understand how diverse morphologies have evolved, it is essential to find ways to handle such complex systems. Here, we review the fin-to-limb transition as a case study for the evolution of multicellular systems. We first describe the historical perspective of comparative studies between fins and limbs. Second, we introduce our approach that combines mechanistic theory, computational modeling, and in vivo experiments to provide a mechanical explanation for the morphological difference between fish fins and tetrapod limbs. This approach helps resolve a long-standing debate about anatomical homology between the skeletal elements of fins and limbs. We will conclude by proposing that due to the counter-intuitive dynamics of gene interactions, integrative approaches that combine computer modeling, theory and experiments are essential to understand the evolution of multicellular organisms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript reviews historical comparative studies of fins and limbs, then introduces an integrative systems biology approach combining mechanistic theory, computational modeling, and in vivo experiments. It claims this approach supplies a mechanical explanation for morphological differences between fish fins and tetrapod limbs and helps resolve the long-standing anatomical homology debate. The paper concludes that non-linear gene interactions in multicellular systems make such combined methods essential for understanding evolutionary morphology.

Significance. If the specific models and experiments were shown to deliver a mechanical explanation, the work would usefully illustrate the application of systems approaches to an evo-devo question. The advocacy for integrative methods aligns with existing practice in the field but does not introduce a novel methodological stance.

major comments (2)
  1. [Abstract / integrative approach section] Abstract and the section describing the integrative approach: the central claim that the combination of mechanistic theory, computational modeling, and in vivo experiments 'provides a mechanical explanation' for fin-limb differences is asserted without any model equations, simulation outputs, experimental protocols, or quantitative results. This absence prevents evaluation of whether the homology debate is actually addressed.
  2. [Fin-to-limb transition section] The section on the fin-to-limb transition: the manuscript states that the approach resolves the homology debate, yet no concrete mapping between modeled mechanical forces and specific skeletal homologies (e.g., stylopod/zeugopod/autopod correspondences) is supplied, leaving the resolution claim unsupported.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful comments on our manuscript. The paper is a perspective and review that introduces an integrative systems biology framework for the fin-to-limb transition rather than presenting new quantitative results. We will revise to clarify the scope of the claims and better indicate where supporting model details appear in related work.

read point-by-point responses

  1. Referee: [Abstract / integrative approach section] Abstract and the section describing the integrative approach: the central claim that the combination of mechanistic theory, computational modeling, and in vivo experiments 'provides a mechanical explanation' for fin-limb differences is asserted without any model equations, simulation outputs, experimental protocols, or quantitative results. This absence prevents evaluation of whether the homology debate is actually addressed.

    Authors: We agree that the manuscript does not contain the model equations, simulation outputs, or experimental protocols, as its purpose is to review historical comparative studies and propose the integrative approach as a way forward. The concrete mechanical explanations and quantitative results from applying this approach are described in our prior publications, which we will cite more explicitly. We will revise the abstract and integrative approach section to state that the paper outlines the framework whose application yields the mechanical explanation, rather than asserting that the explanation is delivered within this text. revision: yes

  2. Referee: [Fin-to-limb transition section] The section on the fin-to-limb transition: the manuscript states that the approach resolves the homology debate, yet no concrete mapping between modeled mechanical forces and specific skeletal homologies (e.g., stylopod/zeugopod/autopod correspondences) is supplied, leaving the resolution claim unsupported.

    Authors: The text currently asserts that the approach helps resolve the homology debate without supplying the explicit mappings in this manuscript. Those mappings arise from the modeling component of the approach and are developed in our related studies. We will revise the fin-to-limb transition section to describe the approach as enabling such mappings and thereby offering a route to resolving the debate, while removing any implication that the resolution is completed here. Additional citations to the modeling work will be added. revision: yes

Circularity Check

0 steps flagged

No circularity; review paper presents no derivations or equations

full rationale

The manuscript is a review outlining historical comparative studies and advocating an integrative approach (mechanistic theory + modeling + experiments) to explain fin-limb differences. No equations, fitted parameters, predictions, or derivation chains appear in the abstract or described content. The central claim rests on the standard position that non-linear gene interactions require combined methods, without reducing any result to self-definition, self-citation load-bearing, or renaming. This is self-contained against external benchmarks with no load-bearing internal reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.0 · 5700 in / 1079 out tokens · 30656 ms · 2026-05-25T02:01:06.430268+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

110 extracted references · 110 canonical work pages

  1. [1]

    Genetica

    Alberch P (1991) From genes to phenotype: dynamical systems and evolvability. Genetica

    work page 1991

  2. [2]

    Philos Trans R Soc B, 237:37–72

    Turing AM (1952) The Chemical Basis of Morphogenesis. Philos Trans R Soc B, 237:37–72

    work page 1952

  3. [3]

    Princeton university press

    Wagner GP (2014) Homology, genes and evolutionary innovation. Princeton university press

    work page 2014

  4. [4]

    John van V oorst , Paternoster Row., London

    Owen R (1848) On the archetype and homologies of the vertebrate skeleton. John van V oorst , Paternoster Row., London

    work page

  5. [5]

    Mayr E (1982) The growth of biological thought: Diversity, Evolution, and Inheritance

    work page 1982

  6. [6]

    Evol Biol 20:318–390

    Shubin NH, Alberch P (1986) A morphogenetic approach to the origin and basic organization of the tetrapod limb. Evol Biol 20:318–390

    work page 1986

  7. [7]

    Gegenbaur C (1865) Untersuchungen zur vergleichenden anatomie der wirbeltiere. V ol. II. Wilhelm Engelmann, Leipzig

    work page

  8. [8]

    Jarvik E (1980) Basic structure and evolution of vertebrates. V ol. 2. Academic Press Inc. (London) LTD., London

    work page 1980

  9. [9]

    Anat Anz 44:24–27

    Watson DMS (1913) On the primitive tetrapod limb. Anat Anz 44:24–27

    work page 1913

  10. [10]

    Acta Zool

    Holmgren N (1952) An embryological analysis of the mammalian carpus and its bearing upon the question of the origin of the tetrapod limb. Acta Zool. 33:1–115

    work page 1952

  11. [11]

    Dev Cell 10:93–103

    Tarchini B, Duboule D (2006) Control of Hoxd genes’ collinearity during early limb development. Dev Cell 10:93–103. https://doi.org/10.1016/j.devcel.2005.11.014

    work page doi:10.1016/j.devcel.2005.11.014 2006

  12. [12]

    In: Hall BK (ed) Fins into Limbs: Evolution, Development, and Transformation

    Wagner GP, Larsson HCE (2007) Fins and limbs in the study of evolutionary novelties. In: Hall BK (ed) Fins into Limbs: Evolution, Development, and Transformation. The University of Chicago Press, pp 49–61

    work page 2007

  13. [13]

    BioEssays 24:460–465

    Cohn MJ, Lovejoy CO, Wolpert L, Coates MI (2002) Branching, segmentation and the metapterygial axis: Pattern versus process in the vertebrate limb. BioEssays 24:460–465. https://doi.org/10.1002/bies.10088

    work page doi:10.1002/bies.10088 2002

  14. [14]

    Development 122:1449–1466

    Nelson CE, Morgan B a, Burke AC, et al (1996) Analysis of Hox gene expression in the chick limb bud. Development 122:1449–1466. https://doi.org/10.1038/342767a0

    work page doi:10.1038/342767a0 1996

  15. [15]

    C., Falkenstein H, Renucci A, et al (1989) Coordinate expression of the murine Hox-5 complex homoeobox-containing genes during limb pattern formation

    Dolle P, Izpisua-Belmonte, J. C., Falkenstein H, Renucci A, et al (1989) Coordinate expression of the murine Hox-5 complex homoeobox-containing genes during limb pattern formation. Nature 342:767–772

    work page 1989

  16. [16]

    Nature 388:639–648

    Shubin N, Tabin C, Carroll S (1997) Fossils, genes and the evolution of animal limbs. Nature 388:639–648

    work page 1997

  17. [17]

    Nature 375:678–681

    Sordino P, van der Hoeven F, Duboule D (1995) Hox gene expression in teleost fins and the origin of vertebrate digits. Nature 375:678–681

    work page 1995

  18. [18]

    Nature 447:473–476

    Davis MC, Dahn RD, Shubin NH (2007) An autopodial-like pattern of Hox expression in the fins of a basal actinopterygian fish. Nature 447:473–476. https://doi.org/10.1038/nature05838

    work page doi:10.1038/nature05838 2007

  19. [19]

    PLoS One 2:e754

    Freitas R, Zhang G, Cohn MJ (2007) Biphasic Hoxd gene expression in shark paired fins reveals an ancient origin of the distal limb domain. PLoS One 2:e754

    work page 2007

  20. [20]

    Sci Rep 6:

    Tulenko FJ, Augustus GJ, Massey JL, et al (2016) HoxD expression in the fin-fold compartment of basal gnathostomes and implications for paired appendage evolution. Sci Rep 6:. https://doi.org/10.1038/srep22720

    work page doi:10.1038/srep22720 2016

  21. [21]

    Dev Biol 322:220–233

    Ahn D, Ho RK (2008) Tri-phasic expression of posterior Hox genes during development of pectoral fins in zebrafish: implications for the evolution of vertebrate paired appendages. Dev Biol 322:220–233

    work page 2008

  22. [22]

    Nature 537:225–228

    Nakamura T, Gehrke AR, Lemberg J, et al (2016) Digits and fin rays share common developmental histories. Nature 537:225–228. https://doi.org/10.1038/nature19322

    work page doi:10.1038/nature19322 2016

  23. [23]

    Proc R Soc B Biol Sci 284:20162780

    Tulenko FJ, Massey JL, Holmquist E, et al (2017) Fin-fold development in paddlefish and catshark and implications for the evolution of the autopod. Proc R Soc B Biol Sci 284:20162780. https://doi.org/10.1098/rspb.2016.2780

    work page doi:10.1098/rspb.2016.2780 2017

  24. [24]

    Dev Cell 23:1219–1229

    Freitas R, Gómez-Marín C, Wilson JM, et al (2012) Hoxd13 Contribution to the Evolution of Vertebrate Appendages. Dev Cell 23:1219–1229. https://doi.org/10.1016/j.devcel.2012.10.015

    work page doi:10.1016/j.devcel.2012.10.015 2012

  25. [25]

    Annu Rev Earth Planet Sci 37:163–179

    Clack JA (2009) The fin to limb transition: new data, interpretations, and hypotheses from paleontology and developmental biology. Annu Rev Earth Planet Sci 37:163–179. https://doi.org/10.1146/annurev.earth.36.031207.124146

    work page doi:10.1146/annurev.earth.36.031207.124146 2009

  26. [26]

    Elife 4:e07048

    Onimaru K, Kuraku S, Takagi W, et al (2015) A shift in anterior–posterior positional information underlies the fin-to-limb evolution. Elife 4:e07048. https://doi.org/10.7554/eLife.07048.001

    work page doi:10.7554/elife.07048.001 2015

  27. [27]

    J Exp Zool 108:363–403

    Saunders JW (1948) The proximo-distal sequence of origin of the parts of the chick wing and the role of the ectoderm. J Exp Zool 108:363–403. https://doi.org/10.1002/jez.1401080304

    work page doi:10.1002/jez.1401080304 1948

  28. [28]

    In: Epithelial Mesenchymal Interactions

    Saunders JW, Gasseling MT (1968) Ectodermal-mesenchymal interactions in the origin of limb symmetry. In: Epithelial Mesenchymal Interactions. pp 78–97

    work page 1968

  29. [29]

    J Theor Biol 25:1–47

    Wolpert L (1969) Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25:1–47

    work page 1969

  30. [30]

    Genes Dev 21:1433–1442

    Tabin C, Wolpert L (2007) Rethinking the proximodistal axis of the vertebrate limb in the molecular era. Genes Dev 21:1433–1442. https://doi.org/10.1101/gad.1547407

    work page doi:10.1101/gad.1547407 2007

  31. [31]

    Int J Dev Biol 53:1483–1494

    Mercader N, Selleri L, Criado LM, et al (2009) Ectopic Meis1 expression in the mouse limb bud alters P-D patterning in a Pbx1-independent manner. Int J Dev Biol 53:1483–1494

    work page 2009

  32. [32]

    Mol Syst Biol 11:815–815

    Uzkudun M, Marcon L, Sharpe J (2015) Data-driven modelling of a gene regulatory network for cell fate decisions in the growing limb bud. Mol Syst Biol 11:815–815. https://doi.org/10.15252/msb.20145882

    work page doi:10.15252/msb.20145882 2015

  33. [33]

    Nature 244:492–496

    Summerbell D, Lewis JH, Wolpert L (1973) Positional Information in chick limb morphogenesis. Nature 244:492–496. https://doi.org/10.1038/244492a0

    work page doi:10.1038/244492a0 1973

  34. [34]

    Science 264:104–107

    Fallon JF, López A, Ros MA, et al (1994) FGF-2: Apical ectodermal ridge growth signal for chick limb development. Science 264:104–107. https://doi.org/10.1126/science.7908145

    work page doi:10.1126/science.7908145 1994

  35. [35]

    Cell 75:579–587

    Niswander L, Tickle C, V ogel A, et al (1993) FGF-4 replaces the apical ectodermal ridge and directs outgrowth and patterning of the limb. Cell 75:579–587. https://doi.org/10.1016/0092- 8674(93)90391-3

    work page doi:10.1016/0092- 1993

  36. [36]

    Development 114:755–768

    Niswander L, Martin GR (1992) Fgf-4 expression during gastrulation, myogenesis, limb and tooth development in the mouse. Development 114:755–768

    work page 1992

  37. [37]

    Biochem Biophys Res Commun 204:882–888

    Ohuchi H, Yoshioka H, Tanaka A, et al (1994) Involvement of androgen-induced growth factor (FGF-8) gene in mouse embryogenesis and morphogenesis. Biochem Biophys Res Commun 204:882–888. https://doi.org/10.1006/bbrc.1994.2542

    work page doi:10.1006/bbrc.1994.2542 1994

  38. [38]

    Mech Dev 48:129–138

    Heikinheimo M, Lawshé A, Shackleford GM, et al (1994) Fgf-8 expression in the post- gastrulation mouse suggests roles in the development of the face, limbs and central nervous system. Mech Dev 48:129–138. https://doi.org/10.1016/0925-4773(94)90022-1

    work page doi:10.1016/0925-4773(94)90022-1 1994

  39. [39]

    Nature 418:539–544

    Dudley AT, Ros MA, Tabin CJ (2002) A re-examination of proximodistal patterning during vertebrate limb development. Nature 418:539–544. https://doi.org/10.1038/nature00945

    work page doi:10.1038/nature00945 2002

  40. [40]

    Science 332:1083–1086

    Cooper KL, Hu JK-H, ten Berge D, et al (2011) Initiation of proximal-distal patterning in the vertebrate limb by signals and growth. Science 332:1083–1086

    work page 2011

  41. [41]

    Science 332:1086–1088

    Roselló-Díez A, Ros M a, Torres M (2011) Diffusible signals, not autonomous mechanisms, determine the main proximodistal limb subdivision. Science 332:1086–1088. https://doi.org/ 10.1126/science.1199489

    work page doi:10.1126/science.1199489 2011

  42. [42]

    In: Seminars in Cell and Developmental Biology

    Delgado I, Torres M (2016) Gradients, waves and timers, an overview of limb patterning models. In: Seminars in Cell and Developmental Biology. Elsevier, pp 109–115

    work page 2016

  43. [43]

    Cell 75:1401–1416

    Riddle RD, Johnson RL, Laufer E, Tabin C (1993) Sonic hedgehog mediates the polarizing activity of the ZPA. Cell 75:1401–1416. https://doi.org/10.1016/0092-8674(93)90626-2

    work page doi:10.1016/0092-8674(93)90626-2 1993

  44. [44]

    Development 122:1225–1233

    Marigo V , Scott MP, Johnson RL, et al (1996) Conservation in hedgehog signaling: induction of a chicken patched homolog by Sonic hedgehog in the developing limb. Development 122:1225–1233

    work page 1996

  45. [45]

    Dev Biol 236:421–435

    Chiang C, Litingtung Y , Harris MP, et al (2001) Manifestation of the limb prepattern: limb development in the absence of sonic hedgehog function. Dev Biol 236:421–435. https://doi.org/10.1006/dbio.2001.0346

    work page doi:10.1006/dbio.2001.0346 2001

  46. [46]

    Cell 100:423–434

    Wang B, Fallon J, Beachy P (2000) Hedgehog-regulated processing of Gli3 produces an anterior/posterior repressor gradient in the developing vertebrate limb. Cell 100:423–434. https://doi.org/10.1016/S0092-8674(00)80678-9

    work page doi:10.1016/s0092-8674(00)80678-9 2000

  47. [47]

    Dev Biol 182:42–51

    Masuya H, Sagai T, Moriwaki K, Shiroishi T (1997) Multigenic control of the localization of the zone of polarizing activity in limb morphogenesis in the mouse. Dev Biol 182:42–51

    work page 1997

  48. [48]

    Science 298:827–830

    Te Welscher P, Zuniga A, Kuijper S, et al (2002) Progression of vertebrate limb development through SHH-mediated counteraction of GLI3. Science 298:827–830. https://doi.org/10.1126/science.1075620

    work page doi:10.1126/science.1075620 2002

  49. [49]

    Nature 418:979–983

    Litingtung Y , Li Y , Fallon JF, Chiang C (2002) Shh and Gli3 are dispensable for limb skeleton formation but regulate digit number and identity. Nature 418:979–983. https://doi.org/10.1038/nature01033

    work page doi:10.1038/nature01033 2002

  50. [50]

    Nat Rev Mol Cell Biol 8:

    Newman SA (2007) The Turing mechanism in vertebrate limb patterning. Nat Rev Mol Cell Biol 8:. https://doi.org/10.1038/nrm1830-c1

    work page doi:10.1038/nrm1830-c1 2007

  51. [51]

    Tickle C (2006) Making digit patterns in the vertebrate limb. Nat. Rev. Mol. Cell Biol. 7:45– 53

    work page 2006

  52. [52]

    Mech Dev 122:1218–1233

    McGlinn E, Van Bueren KL, Fiorenza S, et al (2005) Pax9 and Jagged1 act downstream of Gli3 in vertebrate limb development. Mech Dev 122:1218–1233. https://doi.org/doi:10.1016/ j.mod.2005.06.012

    work page 2005

  53. [53]

    Genes Dev 49:2735–2747

    Peters H, Neubuser A, Kratochwil K, Balling R (1998) Pax9-deficient mice lack pharyngeal pouch derivatives and teeth and exhibit craniofacial and limb abnormalities. Genes Dev 49:2735–2747

    work page 1998

  54. [54]

    Genes Dev 7:2318–2328

    Small KM, Potter SS (1993) Homeotic transformations and limb defects in Hox A11 mutant mice. Genes Dev 7:2318–2328. https://doi.org/10.1101/gad.7.12a.2318

    work page doi:10.1101/gad.7.12a.2318 1993

  55. [55]

    Development 122:2997–3011

    Fromental-Ramain C, Warot X, Messadecq N, et al (1996) Hoxa-13 and Hoxd-13 play a crucial role in the patterning of the limb autopod. Development 122:2997–3011

    work page 1996

  56. [56]

    Science 329:1616–1620

    Kondo S, Miura T (2010) Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329:1616–1620

    work page 2010

  57. [57]

    Springer-Verlag, New York

    Murray JD (2003) Mathematical Biology II - Spatial Models and Biomedical Applications, 3rd ed. Springer-Verlag, New York

    work page 2003

  58. [58]

    Nonlinear programming in complex space: Sufficient conditions and duality

    Murray JD (1982) Parameter space for turing instability in reaction diffusion mechanisms: A comparison of models. J Theor Biol 98:143–163. https://doi.org/10.1016/0022- 5193(82)90063-7

    work page doi:10.1016/0022- 1982

  59. [59]

    https://doi.org/10.1016/0022-5193(74)90128-3

    Bard J, Lauder I (1974) How well does Turing’s theory of morphogenesis work? J Theor Biol 45:501–531. https://doi.org/10.1016/0022-5193(74)90128-3

    work page doi:10.1016/0022-5193(74)90128-3 1974

  60. [60]

    Interface Focus 2:487–496

    Maini PK, Woolley TE, Baker RE, et al (2012) Turing’s model for biological pattern formation and the robustness problem. Interface Focus 2:487–496

    work page 2012

  61. [61]

    Phys Rev E - Stat Nonlinear, Soft Matter Phys 84:

    Butler T, Goldenfeld N (2011) Fluctuation-driven Turing patterns. Phys Rev E - Stat Nonlinear, Soft Matter Phys 84:. https://doi.org/10.1103/PhysRevE.84.011112

    work page doi:10.1103/physreve.84.011112 2011

  62. [62]

    Kybernetik 12:30–

    Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetik 12:30–

    work page 1972

  63. [63]

    https://doi.org/10.1007/BF00289234

    work page doi:10.1007/bf00289234

  64. [64]

    PhilTrans R Soc Lond B 353:543–557

    White KAJ, Gilligan CA (1998) Spatial Heterogeneity in Three-Species, Plant-Parasite- Hyperparasite, Systems. PhilTrans R Soc Lond B 353:543–557

    work page 1998

  65. [65]

    J Theor Biol

    Korvasová K, Gaffney EA, Maini PK, et al (2015) Investigating the Turing conditions for diffusion-driven instability in the presence of a binding immobile substrate. J Theor Biol. https://doi.org/10.1016/j.jtbi.2014.11.024

    work page doi:10.1016/j.jtbi.2014.11.024 2015

  66. [66]

    Elife 5:

    Marcon L, Diego X, Sharpe J, Müller P (2016) High-throughput mathematical analysis identifies turing networks for patterning with equally diffusing signals. Elife 5:. https://doi.org/10.7554/eLife.14022

    work page doi:10.7554/elife.14022 2016

  67. [67]

    Phys Rev X 8:

    Diego X, Marcon L, Müller P, Sharpe J (2018) Key Features of Turing Systems are Determined Purely by Network Topology. Phys Rev X 8:. https://doi.org/10.1103/PhysRevX.8.021071

    work page doi:10.1103/physrevx.8.021071 2018

  68. [68]

    Bull Math Biol 61:1093–1120

    Crampin EJ, Gaffney EA, Maini PK (1999) Reaction and diffusion on growing domains: Scenarios for robust pattern formation. Bull Math Biol 61:1093–1120. https://doi.org/10.1006/bulm.1999.0131

    work page doi:10.1006/bulm.1999.0131 1999

  69. [69]

    BioSystems

    Pecze L (2018) A solution to the problem of proper segment positioning in the course of digit formation. BioSystems. https://doi.org/10.1016/j.biosystems.2018.04.005

    work page doi:10.1016/j.biosystems.2018.04.005 2018

  70. [70]

    Science 338:1476–1480

    Sheth R, Marcon L, Bastida MF, et al (2012) Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism. Science 338:1476–1480. https://doi.org/10.1126/science.1226804

    work page doi:10.1126/science.1226804 2012

  71. [71]

    Cell Syst 1:408–416

    Hiscock TW, Megason SG (2015) Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies. Cell Syst 1:408–416. https://doi.org/10.1016/j.cels.2015.12.001

    work page doi:10.1016/j.cels.2015.12.001 2015

  72. [72]

    Development 142:409–419

    Hiscock TW, Megason SG (2015) Mathematically guided approaches to distinguish models of periodic patterning. Development 142:409–419. https://doi.org/10.1242/dev.107441

    work page doi:10.1242/dev.107441 2015

  73. [73]

    Dev Evol 75–98

    Goodwin BC, Trainor LEH (1983) The ontogeny and phylogeny of the pendactyl limb. Dev Evol 75–98

    work page 1983

  74. [74]

    J Theor Biol 52:199–217

    Wilby OK, Ede DA (1975) A model generating the pattern of cartilage skeletal elements in the embryonic chick limb. J Theor Biol 52:199–217. https://doi.org/https://doi.org/10.1016/0022-5193(75)90051-X

    work page doi:10.1016/0022-5193(75)90051-x 1975

  75. [75]

    Science 205:662–668

    Newman SA, Frisch HL (1979) Dynamics of skeletal pattern formation in developing chick limb. Science 205:662–668

    work page 1979

  76. [76]

    J Theor Biol 121:505–508

    Othmer HG (1986) On the Newman-Frisch model of limb chondrogenesis. J Theor Biol 121:505–508. https://doi.org/10.1016/S0022-5193(86)80105-9

    work page doi:10.1016/s0022-5193(86)80105-9 1986

  77. [77]

    J Embryol Exp Morphol 12:339 LP – 356

    Ede DA, Kelly WA (1964) Developmental abnormalities in the trunk and limbs of the <em>talpid</em><sup>3</sup> mutant of the fowl. J Embryol Exp Morphol 12:339 LP – 356

    work page 1964

  78. [78]

    Dev Dyn 203:187–197

    Francis‐West PH, Robertson KE, Ede DA, et al (1995) Expression of genes encoding bone morphogenetic proteins and sonic hedgehog in talpid (ta3) limb buds: Their relationships in the signalling cascade involved in limb patterning. Dev Dyn 203:187–197. https://doi.org/10.1002/aja.1002030207

    work page doi:10.1002/aja.1002030207 1995

  79. [79]

    J R Soc Interface 2:237–253

    Chaturvedi R, Huang C, Kazmierczak B, et al (2005) On multiscale approaches to three- dimensional modelling of morphogenesis. J R Soc Interface 2:237–253. https://doi.org/10.1098/rsif.2005.0033

    work page doi:10.1098/rsif.2005.0033 2005

  80. [80]

    Proc R Soc B Biol Sci 271:1713–1722

    Hentschel HGE, Glimm T, Glazier JA, Newman SA (2004) Dynamical mechanisms for skeletal pattern formation in the vertebrate limb. Proc R Soc B Biol Sci 271:1713–1722. https://doi.org/10.1098/rspb.2004.2772

    work page doi:10.1098/rspb.2004.2772 2004

Showing first 80 references.