Pith. sign in

REVIEW 3 major objections 5 minor 88 references

Signaling gradients in surface dynamics as basis for planarian regeneration

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper argues that polarity-preserving planarian regeneration is driven by wound-edge stem cells sensing the slope of a wnt-related gradient, not its level, and that a reaction–diffusion model built on this gradient-sensing boundary…

desk verdict The gradient-sensing mechanism is new and the reduction is solid, but the printed boundary terms have the wrong sign — the full model as written would regenerate tail at the anterior wound. read the letter →

arxiv 1908.04253 v2 pith:A3TXL5SE submitted 2019-08-12 q-bio.QM nlin.AOnlin.PS

Arnd Scheel , Angela Stevens , Christoph Tenbrock This is my paper · ORCID
classification q-bio.QMnlin.AOnlin.PS MSC 92C1535K5735Q92
keywords planarianregenerationreaction-diffusionmodeldynamicboundaryconditionswntgradientsensingpolaritypreservationcuttingandgraftingexperimentstristabilityreduction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper attempts to show that a compact reaction–diffusion model can reproduce planarian regeneration, with head and tail formed in the correct orientation even from fragments as small as half a percent of the worm. Its key move is to let stem cells at a wound edge read the direction (slope) of a wnt-related signal gradient rather than its absolute concentration, and to implement this as dynamic boundary conditions at the two ends of a one-dimensional body. The authors claim this is the only reacting-and-diffusing-species model that reproduces most cutting and grafting experiments, because it preserves polarity over body sizes spanning two orders of magnitude. If the claim holds, it supplies a minimal biological mechanism: the residual gradient left in a fragment, read at the cut surface, is enough to tell each end which pole to make.

What carries the argument

The load-bearing object is the dynamic (Wentzell) boundary compartment: a thin finite-size region at each body edge with its own concentrations and kinetics, coupled to the bulk through diffusive flux and containing an extra wound-healing source that differentiates stem cells according to the sign of $\partial_\nu w$ (Eqs. (3.8)–(3.15)). This boundary sensor provides the positive feedback—a small rise in boundary $w$ strengthens the gradient, which strengthens head/tail differentiation, which in turn raises boundary $w$—that makes the unpolarized trunk state unstable and starts regeneration. It also separates the model from Turing-style wavelength selection and from French-flag reading of absolute wnt levels; the reduced analysis distills the action to a scalar equation for $w$ whose stability boundaries predict when regeneration fails.

What would settle it

A concrete test: in an amputated fragment, image a wnt/β-catenin reporter in the first hours after cutting and compare the differentiation fate of cells at the two wounds with the signed slope of the reporter near each wound. If cells at a wound facing a flat or inverted residual gradient still reliably make the correct head or tail, the gradient-sensing mechanism is falsified. A model-level falsifier also exists: the linear stability calculation in Section 4.4 predicts that the unpolarized state is unstable only when the boundary feedback coefficients satisfy $\tau/\varepsilon > 1/\gamma + \sqrt{2}$ in the scalar reduction; measuring these rates and testing whether regeneration still occurs despite stability would settle the mechanism.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that polarity-preserving regeneration can be organized entirely by gradient sensing at body edges, without any cell reading the absolute level of a morphogen. In the model, a long-range wnt-related signal $w$ sits in a monotone gradient from head to tail. After a cut, the remaining fragment keeps a piece of that gradient, and stem cells in a thin boundary compartment at each wound differentiate into head or tail cells according to the sign of the normal derivative $\partial_\nu w$, through terms such as $\tau(1-h)(1-d)\chi^\varepsilon_{>\theta}(\partial_\nu w)$ for head and the mirror term for tail. The resulting dynamics regenerate correct poles from tiny trunk fragments and remain robust as the domain grows; the authors also show analytically that replacing the dynamic boundary conditions by instantaneous Robin-type conditions destroys regeneration, because the positive feedback between the boundary value of $w$ and the bulk gradient is lost.

Load-bearing premise

The load-bearing premise is that stem cells at a fresh wound can measure the sign (or small thresholded value) of the spatial slope of the wnt-related gradient and turn that into head-versus-tail differentiation; the paper postulates this sensing step rather than deriving it from a molecular mechanism or direct measurement.

Editorial extensions

If this is right

  • A fragment cut from the trunk, head, or tail region regenerates head at the original head-facing edge and tail at the other, with polarity preserved across body sizes from $L=0.005$ to $L=40$ in simulations.
  • Grafting reproduces the observed either-or outcome: donor head tissue placed near the host head merges and vanishes, while the same tissue placed far from the host head persists and can organize a second axis.
  • Absolute levels of wnt signaling are not used for polarity in the early regeneration stages, so equally small fragments from different body regions behave alike despite very different local wnt concentrations.
  • During uniform growth the pattern is maintained for moderate growth speeds; if dilution makes the wnt gradient shallower than the sensing threshold, the head is lost and a second tail replaces it.
  • Regeneration begins as an instability of the gradientless trunk state, and near the boundary between recovery and failure the model predicts oscillatory wnt concentrations before the gradient collapses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct experimental test of the paper's mechanism would be to image wnt/β-catenin reporters at a fresh wound and ask whether differentiation direction correlates with the slope of the gradient on the two sides of the cut, rather than with the local concentration.
  • Because the paper identifies a finite-size boundary compartment as mathematically necessary (dynamic rather than Robin conditions), it implies that a distinct 'pole' tissue with its own kinetics should be experimentally detectable at planarian body edges; failure to find such a compartment would undercut the model.
  • The conservation of wnt signaling across planarians and hydra suggests the gradient-sensing boundary mechanism could be tested in hydra as well, where the same type of head/foot grafting experiments have been quantified.
  • If the gradient-sensing rule is really generic, it might be implemented in synthetic tissues or organoids by engineering cells that measure a morphogen slope at an artificial boundary, providing an engineering route to polarity control.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces a reaction-diffusion model for planarian regeneration along the anterior-posterior axis. The model tracks stem, head, and tail cell densities together with short-range head/tail signals and a long-range wnt-related signal w. Dynamics in the bulk are supplemented by Wentzell-type dynamic boundary conditions on a boundary compartment, where stem-cell differentiation into head or tail cells is switched by the sign of the normal derivative of w. The authors report numerical simulations of homeostasis, cutting, grafting, and growth, and claim correct reproduction of the main experiments with preservation of polarity over orders of magnitude in body size. The second half of the paper derives reduced two-species and scalar models, analyzes stability of the unpolarized state, and argues that dynamic boundary conditions are necessary for regeneration while Robin-type conditions fail. The paper also predicts oscillations near the threshold of regeneration failure.

Significance. If the central claim is correct, the model offers a minimal, analytically tractable mechanism for polarity-preserving regeneration that does not rely on Turing-type wavelength selection and that scales over large size changes. The explicit model reduction to an order-parameter equation and to a scalar equation, plus the stability analysis in Section 4.4, is a genuine strength: it identifies a concrete positive-feedback loop through boundary sensing and explains why dynamic boundary conditions are qualitatively different from instantaneous Robin conditions. The scalar model's oscillatory instability is a falsifiable prediction. However, the significance is conditional on resolving the sign inconsistency in the sensing terms and on demonstrating that the reported outcomes are robust rather than fine-tuned to near-critical parameter values. As written, the central claim is not supported by the printed equations.

major comments (3)
  1. [Section 3.2, Eqs. (3.13)-(3.15)] The signs in the gradient-sensing terms are inverted relative to the stated head/tail convention. In the healthy gradient and in the cutting initial condition (3.16), w increases from left to right, so w_x>0. At the left boundary x=-L the outward normal derivative is ∂ν w = -w_x <0, so the indicator χ^ε_{<-θ}(∂ν w) in Eq. (3.15) is active and χ^ε_{>θ}(∂ν w) in Eq. (3.14) is inactive. The written model therefore produces tail cells at the anterior wound and head cells at the posterior wound, which is the opposite of the experimental polarity the paper claims to reproduce. This is not a minor labeling issue: for a trunk fragment with h=d=0, the wrong Ψ term is unsuppressed and drives differentiation in the wrong direction. The reduced model in Eq. (4.5) uses the opposite sign convention (Ψ_c^± contains χ^ε_{>θ}(-∂ν w|±L) for the +1/head state), so the full and reduced systems are internally inconsistent. Either the full model in Section 3 has a sign typo that also affects the reported simulations, or the simulations were generated with a different system than the one printed. In either case, the central demonstration of Section 3.3 is not supported by the equations as written.
  2. [Sections 3.3 and 4.3] The paper repeatedly claims robust behavior for a wide range of parameter values, but the simulation parameters are explicitly chosen close to critical values. Section 3.3 states: 'Our choices of parameters are close to the critical values, where head and tail regions neither shrink nor expand.' Section 4.3 chooses κ=0.577, which is within 0.001 of the Maxwell point κ*=1/√3≈0.5774 identified in Section 4.2. For a bistable or tristable front system, operating at the Maxwell point makes the size and persistence of grafted head/tail regions highly sensitive to small parameter perturbations. The paper does not provide a systematic parameter scan, a phase diagram, or a basin-of-attraction study. Without such evidence, the qualitative statements about 'robustness' in Section 2.2 and the abstract cannot be distinguished from fine-tuning of the reported simulations.
  3. [Sections 1, 2.2, and 3.3] The abstract and introduction claim that the model 'correctly reproduces' cut and graft experiments and that it is the only reacting-diffusing-species model able to do so. The evidence consists of a small number of simulations with hand-picked initial conditions and no quantitative comparison to experimental data such as regeneration times, minimum fragment sizes, or the observed frequencies of two-headed versus two-tailed outcomes. The paper itself notes in Section 2.2 that the model cannot produce a bias between two-headed and two-tailed animals because head and tail are treated symmetrically. The claims should be softened to 'is consistent with the qualitative outcomes of selected experiments,' and the uniqueness claim should either be removed or supported by a systematic comparison with the models discussed in Section 2.4.
minor comments (5)
  1. [Eq. (3.15)] The second sensing function is labeled Ψ_w but should be Ψ_d, consistent with Eq. (3.12) and the surrounding text.
  2. [Title and formatting] The title contains a typo: 'planari an' should be 'planarian.' There are also repeated spacing errors in the text, e.g., 'Differential equations' and 'inhomegeneous Dirichlet boundary conditions' in Section 3.2.
  3. [Section 4.2] The text writes 'critical “Mawell” point' but should read 'Maxwell point.'
  4. [Section 3.3] The numerical simulations are not accompanied by code or data availability statements, and the parameter values in Table 1 are presented without a sensitivity analysis. Providing the simulation code would substantially improve reproducibility, especially given the sign inconsistency noted above.
  5. [Section 5] The statement that gradient sensing is 'necessary' to reproduce robust preservation of polarity is presented as a conclusion, but the paper only demonstrates sufficiency of the proposed mechanism. The wording should be adjusted to reflect that this is a conjecture supported by the reduced-model analysis, not a proven necessity.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the gradient-sensing mechanism is an openly stated modeling postulate, with one minor non-load-bearing self-citation. A printed sign error would reverse the claimed polarity, but that is a correctness issue, not circularity.

full rationale

The regeneration mechanism is introduced as an assumption, not inferred from the phenomena: 'We postulate that, as a key ingredient to robust regeneration and preservation of polarity, the production rate Ψ_h/d depends sensitively on the normal derivative of the long-range signal w' (Sec. 3.2). The cutting/grafting/growth simulations solve the full initial-boundary-value problem and exhibit non-obvious behaviors, including failure for small fragments, oscillations near the failure threshold, and instability of Robin-type relaxations, so the demonstrations are not logically identical to the inputs. The reduced model and linearization in Sec. 4.4 are additional analytic content, not a restatement of the boundary term. The only notable self-citation is [76] for the underlying cell-signal formulation and growth laws; it is background and not load-bearing, so at most a minor self-citation. Separately, under the standard outward-normal convention, Eqs. (3.14)-(3.15) assign head production to the posterior wound and tail production to the anterior wound, opposite to the paper's claim; this sign/typo discrepancy is a correctness issue that does not constitute circularity.

Assumptions & free parameters 15 free parameters · 7 assumptions · 2 invented entities

All parameters in Table 1 are chosen by hand from order-of-magnitude reasoning; none are fitted to experimental data with uncertainties. The central gradient-sensing and boundary-compartment postulates lack molecular identification. The analytical results are derived in reduced models and partially confirm the mechanism the authors inserted, though they also yield a falsifiable oscillation prediction.

free parameters (15)
  • Ds = 1
    Stem cell diffusion coefficient; chosen as order one because neoblasts move fairly freely (Section 3.3).
  • Dh = 1e-3
    Head cell diffusivity; chosen small to localize the head region.
  • Dd = 1e-3
    Tail cell diffusivity; chosen small to localize the tail region.
  • Duh and Dud = 1e-2 each
    Short-range signal diffusivities; chosen small relative to wnt diffusion.
  • Dw = 1
    wnt signal diffusivity; chosen large to establish a long-range gradient.
  • ps and eta_s = 100 and 100
    Fast stem cell proliferation and apoptosis rates; justify the quasi-steady assumption s approximately 1.
  • ph, pd, eta_h, eta_d = all 1
    Head and tail differentiation and death rates; equal values enforce reflection symmetry and prevent head-tail bias.
  • r0, r1, r2, r3 = 18, 12, 6, 6
    Short-range signal production and degradation rates; chosen to produce tristability; r0 and r3 sit near the critical values separating expanding from shrinking head and tail regions.
  • pw = 10
    wnt production and degradation rate; fast relative to cell dynamics; authors state differing rates give similar outcomes.
  • tau = 0.5
    Rate of boundary gradient-sensing differentiation; a central parameter for polarity restoration.
  • theta and epsilon = 3 and 2e-3
    Threshold and sharpness of gradient sensing; small epsilon and theta improve recovery but increase noise sensitivity.
  • gamma = 0.3
    Boundary compartment mass fraction; homeostasis and cutting fail for gamma near 0.03.
  • L = 10
    Half-length of simulated body; robustness is claimed for L up to 40 and down to 0.005 but is not systematically demonstrated.
  • kappa (reduced model) = 0.577
    Chosen at the Maxwell point kappa* = 1/sqrt(3) so head and tail regions neither expand nor shrink in grafting; explicit tuning.
  • tau (scalar model) = 50
    Boundary production rate in the scalar model, much larger than tau = 0.5 in the full model; analysis assumes tau much greater than 1.
assumptions (7)
  • domain assumption Cell densities and signals evolve as continuum reaction-diffusion fields on a one-dimensional interval x in [-L, L].
    Section 3.1: ignores 2D/3D anatomy, other body axes, and discrete cell structure; the paper restricts to the anterior-posterior axis.
  • ad hoc to paper The lumped variable w represents the full wnt-related signaling family and obeys degradation by head cells and saturated production by tail cells in Eq. (3.7).
    Section 3.1: w absorbs multiple wnt and beta-catenin pathway components; this is a modeling simplification, not a measured molecular species.
  • ad hoc to paper A finite-size boundary compartment with dynamic (Wentzell) boundary conditions (3.8)-(3.9) describes wound healing at body edges.
    Section 3.2: the compartment and boundary reactions are introduced to represent wound-edge proliferation and differentiation; no tissue-scale derivation is given.
  • ad hoc to paper Stem cells at boundary compartments sense the sign of the normal derivative of w and differentiate accordingly through the Psi functions in (3.13)-(3.15).
    Section 3.2: central polarity mechanism; the paper states it postulates this sensitivity and gives no molecular implementation.
  • domain assumption Quasi-steady-state reductions: stem cell density is constant s approximately 1 and short-range signals u_h and u_d are algebraically slaved to h and d (Section 4.1).
    Section 4.1: justified by separation of time scales (ps and r_j much greater than 1) and supported by numerical observation, not proven for all parameter regimes.
  • domain assumption Head and tail cells have equal kinetics and the system is reflection-symmetric between h and d.
    Section 4.2 and Table 1: this symmetry prevents the experimentally observed head-tail bias; the authors note it as a limitation in Section 5.
  • ad hoc to paper For the scalar model, boundary order parameter c+ adjusts rapidly to sign of the normal derivative of w, excluding grafting and multiple head/tail regions.
    Section 4.5: this reduction is explicitly restricted and formal; it underlies the oscillation prediction.
invented entities (2)
  • Boundary compartment variables U+ with gradient-sensing differentiation kinetics Psi+
    purpose: Represent a thin wound-edge region where stem cells differentiate to head or tail based on the sign of the normal derivative of w; this is the mechanism that preserves polarity in simulations.
    The compartment and Psi functions are model postulates introduced in (3.8)-(3.15); there is no direct experimental measurement of such a compartment or of slope-sensing differentiation, though the authors cite discussions of pole regions.
  • Lumped wnt-related signal w independent evidence
    purpose: Provide a long-range gradient that carries orientation information; produced by tail cells and degraded by head cells.
    A wnt/beta-catenin gradient is supported by cited experiments, but w as a single scalar variable is a lumped idealization, not a measured molecular species.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Signaling gradients in surface dynamics as basis for planarian regeneration." pith.science (2026). https://pith.science/paper/A3TXL5SE

@misc{pith2026190804253,
  author       = {Pith},
  title        = {Pith review of: Signaling gradients in surface dynamics as basis for planarian regeneration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A3TXL5SE}},
  note         = {Machine review of arXiv:1908.04253}
}
read the original abstract

We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized signals that guide stem cell differentiation. Orientation and positional information is encoded in the dynamics of a long range wnt-related signaling gradient. We motivate our model in relation to experimental data and demonstrate how it correctly reproduces cut and graft experiments. In particular, our system improves on previous models by preserving polarity in regeneration, over orders of magnitude in body size during cutting experiments and growth phases. Our model relies on tristability in cell density dynamics, between head, trunk, and tail. In addition, key to polarity preservation in regeneration, our system includes sensitivity of cell differentiation to gradients of wnt-related signals %measured relative to the tissue surface. This process is particularly relevant in a small tissue layer close to wounds during their healing, and modeled here in a robust fashion through dynamic boundary conditions.

Figures

Figures reproduced from arXiv: 1908.04253 by the authors.

Figure 4
Figure 4. for the reduced model and confirm to some extent the ob [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 2.1
Figure 2.1. Typical experiments and their representations [PITH_FULL_IMAGE:figures/full_fig_p006_2_1.png] view at source ↗
Figure 3
Figure 3. for a schematic representation of the indicator function [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (13 more)
Figure 3.1
Figure 3.1. Figure 3.1: Schematic plot of the indicator functions [PITH_FULL_IMAGE:figures/full_fig_p013_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: Equilibrium profiles showing a linear wnt-signaling profile, head and tail cells concentrated near boundaries, stem cell concentrations with small deviations from constant, and chemical signals closely following head and tail-cell concentrations, respectively. Note t…
Figure 3.3
Figure 3.3. Figure 3.3: Growing and shrinking of head and tail cell regio [PITH_FULL_IMAGE:figures/full_fig_p014_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Regeneration after cutting experiments: cutti [PITH_FULL_IMAGE:figures/full_fig_p015_3_4.png]
Figure 3.5
Figure 3.5. Figure 3.5: Regeneration after grafting head tissue into ce [PITH_FULL_IMAGE:figures/full_fig_p016_3_5.png]
Figure 3.6
Figure 3.6. Figure 3.6: Regeneration after grafting multiple head and t [PITH_FULL_IMAGE:figures/full_fig_p016_3_6.png]
Figure 3.7
Figure 3.7. Figure 3.7: For slow and moderate growth speeds, the concentrat [PITH_FULL_IMAGE:figures/full_fig_p017_3_7.png]
Figure 4.1
Figure 4.1. Figure 4.1: Schematic of the reduction from cell type to orde [PITH_FULL_IMAGE:figures/full_fig_p019_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: Simulations of the reduced model (4.3)—(4.6) wi [PITH_FULL_IMAGE:figures/full_fig_p020_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Simulations of the reduced model (4.3)—(4.6) wi [PITH_FULL_IMAGE:figures/full_fig_p020_4_3.png]
Figure 4
Figure 4. Figure 4: shows recovery from small fragments cut from center- [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]
Figure 4.4
Figure 4.4. Figure 4.4: Simulations of the scalar model (4.14) with init [PITH_FULL_IMAGE:figures/full_fig_p022_4_4.png]
Figure 4.5
Figure 4.5. Figure 4.5: Simulations of the scalar model (4.14) with init [PITH_FULL_IMAGE:figures/full_fig_p023_4_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

88 extracted references · 80 canonical work pages

  1. [1]

    Achermann and T

    J. Achermann and T. Sugiyama. Genetic analysis of developmenta l mechanisms in hydra: X. Morphogenetic potentials of a regeneration-deficient strain (reg-16). Developmental biology, 107(1):13–27, 1985

    1985

  2. [2]

    Adell, F

    T. Adell, F. Cebri` a, and E. Sal´ o. Gradients in planarian regenera tion and homeostasis. Cold Spring Harbor perspectives in biology, 2(1):a000505, 2010

    2010

  3. [3]

    Almuedo-Castillo, A

    M. Almuedo-Castillo, A. Bl¨ aßle, D. M¨ orsdorf, L. Marcon, G. H. Soh, K. W. Rogers, A. F. Schier, and P. M¨ uller. Scale-invariant patterning by size-dependent inhibition of nodal sig nalling. Nature Cell Biology, 20(9):1032–1042, 2018

    2018

  4. [4]

    Almuedo-Castillo, M

    M. Almuedo-Castillo, M. Sureda-G´ omez, and T. Adell. Wnt signaling in planarians: new answers to old questions. International Journal of Developmental Biology , 56(1-2-3):53–65, 2012

    2012

  5. [5]

    W. Alt. Biased random walk models for chemotaxis and related diffus ion approximations. Journal of Mathe- matical Biology, 9(2):147–177, 1980

    1980

  6. [6]

    Bagu˜ n` a

    J. Bagu˜ n` a. Mitosis in the intact and regenerating planarian Dugesia mediterranea n. sp. II. Mitotic studies during regeneration, and a possible mechanism of blastema formation. Journal of Experimental Zoology , 195(1):65–79, 1976

    1976

  7. [7]

    Bagu˜ n` a and R

    J. Bagu˜ n` a and R. Romero. Quantitative analysis of cell types during growth, degrowt h and regeneration in the planarians Dugesia mediterranea and Dugesia tigrina . Springer, 1981

    1981

  8. [8]

    Bagu˜ n` a and R

    J. Bagu˜ n` a and R. Romero. Quantitative analysis of cell types d uring growth, degrowth and regeneration in the planarians Dugesia mediterranea and Dugesia tigrina. In The Biology of the Turbellaria , pages 181–194. Springer, 1981

    1981

Show all 88 references
  1. [9]

    Bagu˜ n` a, R

    J. Bagu˜ n` a, R. Romero, E. Sal´ o, J. Collet, C. Auladell, M. Ribas, M. Riutort, J. Garc ´ ıa-Fern` andez, F. Burgaya, and D. Bueno. Growth, degrowth and regeneration as developmen tal phenomena in adult freshwater planarians. In Experimental embryology in aquatic plants and...

    1990

  2. [10]

    J. Bagu, S. Carranza, M. Pala, C. Ribera, G. Giribet, M. A. Arne do, M. Ribas, and M. Riutort. From morphology and karyology to molecules. new methods for taxonomical identifica tion of asexual populations of freshwater planarians. a tribute to professor mario benazzi. Italian ...

    1999

  3. [11]

    C. R. Bardeen and F. Baetjer. The inhibitive action of the roent gen rays on regeneration in planarians. Journal of Experimental Zoology Part A: Ecological Genetics and Phy siology, 1(1):191–195, 1904. 25

    1904

  4. [12]

    H. R. Bode. Head regeneration in Hydra. Developmental dynamics , 226(2):225–236, 2003

    2003

  5. [13]

    Bowen, T

    I. Bowen, T. Ryder, and J. Thompson. The fine structure of t he planarian Polycelis tenuis Iijima. Protoplasma, 79(1-2):1–17, 1974

    1974

  6. [14]

    Cramer von Laue

    C. Cramer von Laue. Untersuchungen zur dualen Funktion von β -Catenin im Wnt-Signalweg und der Cadherin- vermittelten Zelladh¨ asion bei Hydra. PhD thesis, Technische Universit¨ at, 2004

    2004

  7. [15]

    Cusseddu, L

    D. Cusseddu, L. Edelstein-Keshet, J. Mackenzie, S. Portet, and A. Madzvamuse. A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology , 2018

    2018

  8. [16]

    De Vries, J

    E. De Vries, J. Bagu˜ n` a, and I. Ball. Chromosomal polymorphis m in planarians (Turbellaria, Tricladida) and the plate tectonics of the western Mediterranean. Genetica, 62(3):187–191, 1984

    1984

  9. [17]

    C. M. Elliott, T. Ranner, and C. Venkataraman. Coupled bulk-su rface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM J. Math. Anal. , 49(1):360–397, 2017

    2017

  10. [18]

    P. C. Fife. Models for phase separation and their mathematics. Electron. J. Differential Equations , pages No. 48, 26, 2000

    2000

  11. [19]

    Gagliardi, A

    M. Gagliardi, A. Hernandez, I. J. McGough, and J.-P. Vincent. I nhibitors of endocytosis prevent Wnt/Wingless signalling by reducing the level of basal β -catenin/Armadillo. J Cell Sci , 127(22):4918–4926, 2014

    2014

  12. [20]

    L. Gee, J. Hartig, L. Law, J. Wittlieb, K. Khalturin, T. C. Bosch, and H. R. Bode. β -catenin plays a central role in setting up the head organizer in hydra. Developmental biology, 340(1):116–124, 2010

    2010

  13. [21]

    Gierer and H

    A. Gierer and H. Meinhardt. A theory of biological pattern form ation. Kybernetik, 12(1):30–39, 1972

    1972

  14. [22]

    K. A. Gurley, S. A. Elliott, O. Simakov, H. A. Schmidt, T. W. Holste in, and A. S. Alvarado. Expression of secreted Wnt pathway components reveals unexpected comple xity of the planarian amputation response. Developmental biology, 347(1):24–39, 2010

    2010

  15. [23]

    H¨ arting and A

    S. H¨ arting and A. Marciniak-Czochra. Spike patterns in a reac tion–diffusion ode model with Turing instability. Mathematical Methods in the Applied Sciences , 37(9):1377–1391, 2014

    2014

  16. [24]

    H¨ arting, A

    S. H¨ arting, A. Marciniak-Czochra, and I. Takagi. Stable patt erns with jump discontinuity in systems with Turing instability and hysteresis. Disc. Cont. Dyn. Sys. A. , 38:757–800, 2017

    2017

  17. [25]

    Hobmayer, F

    B. Hobmayer, F. Rentzsch, K. Kuhn, C. M. Happel, C. C. von La ue, P. Snyder, U. Rothb¨ acher, and T. W. Holstein. WNT signalling molecules act in axis formation in the diploblastic m etazoan Hydra. Nature, 407(6801):186–189, 2000

    2000

  18. [26]

    Iijima, Y

    M. Iijima, Y. E. Huang, and P. Devreotes. Temporal and Spatia l Regulation of Chemotaxis. Developmental Cell, 3:469–478, 2002

    2002

  19. [27]

    Kakugawa, P

    S. Kakugawa, P. F. Langton, M. Zebisch, S. A. Howell, T.-H. Cha ng, Y. Liu, T. Feizi, G. Bineva, N. O’Reilly, A. P. Snijders, et al. Notum deacylates Wnt proteins to suppress s ignalling activity. Nature, 519(7542):187–192, 2015

    2015

  20. [28]

    Lengfeld, H

    T. Lengfeld, H. Watanabe, O. Simakov, D. Lindgens, L. Gee, L. Law, H. A. Schmidt, S. ¨Ozbek, H. Bode, and T. W. Holstein. Multiple Wnts are involved in Hydra organizer formation and regeneration. Developmental biology, 330(1):186–199, 2009

    2009

  21. [29]

    Levine and W.-J

    H. Levine and W.-J. Rappel. Membrane-bound Turing patterns. Phys. Rev. E (3) , 72(6):061912, 5, 2005

    2005

  22. [30]

    Y. Li, A. Marciniak-Czochra, I. Takagi, and B. Wu. Steady stat es of fitzhugh-nagumo system with non-diffusive activator and diffusive inhibitor. preprint, 2017. 26

    2017

  23. [31]

    Y. Li, A. Marciniak-Czochra, I. Takagi, B. Wu, et al. Bifurcation analysis of a diffusion-ode model with Turing instability and hysteresis. Hiroshima Mathematical Journal , 47(2):217–247, 2017

    2017

  24. [32]

    D. Lobo, W. S. Beane, and M. Levin. Modeling planarian regenera tion: a primer for reverse-engineering the worm. PLoS Comput Biol , 8(4):e1002481, 2012

    2012

  25. [33]

    H. K. MacWilliams. Hydra transplantation phenomena and the mec hanism of hydra head regeneration: II. Properties of the head activation. Developmental biology, 96(1):239–257, 1983

    1983

  26. [34]

    Marciniak-Czochra

    A. Marciniak-Czochra. Receptor-based models with diffusion-d riven instability for pattern formation in hydra. Journal of Biological Systems , 11(03):293–324, 2003

    2003

  27. [35]

    Marciniak-Czochra

    A. Marciniak-Czochra. Receptor-based models with hysteres is for pattern formation in hydra. Mathematical biosciences, 199(1):97–119, 2006

    2006

  28. [36]

    Marciniak-Czochra, S

    A. Marciniak-Czochra, S. H¨ arting, G. Karch, and K. Suzuki. D ynamical spike solutions in a nonlocal model of pattern formation. Nonlinearity, 31(5):1757–1781, 2018

    2018

  29. [37]

    Marciniak-Czochra, G

    A. Marciniak-Czochra, G. Karch, and K. Suzuki. Instability of T uring patterns in reaction-diffusion-ode systems. Journal of Mathematical Biology , 74(3):583–618, 2017

    2017

  30. [38]

    Marciniak-Czochra, G

    A. Marciniak-Czochra, G. Karch, K. Suzuki, J. Zienkiewicz, et a l. Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ode systems. Differential and Integral Equations , 29(7/8):715–730, 2016

    2016

  31. [39]

    Marciniak-Czochra, M

    A. Marciniak-Czochra, M. Nakayama, I. Takagi, et al. Pattern formation in a diffusion-ode model with hysteresis. Differential and Integral Equations , 28(7/8):655–694, 2015

    2015

  32. [40]

    Meinhardt

    H. Meinhardt. Turing’s theory of morphogenesis of 1952 and th e subsequent discovery of the crucial role of local self-enhancement and long-range inhibition. Interface Focus, 2(4):407–416, 2012

    1952

  33. [41]

    T. H. Morgan. Experimental studies of the regeneration of Pla naria maculata. Development Genes and Evolution , 7(2):364–397, 1898

  34. [42]

    T. H. Morgan. The control of heteromorphosis in Planaria macu lata. Archiv f¨ ur Entwicklungsmechanik der Organismen, 17(4):683–695, 1904

    1904

  35. [43]

    T. H. Morgan. Polarity considered as a phenomenon of gradatio n of materials. Journal of Experimental Zoology , 2(4):495–506, 1905

    1905

  36. [44]

    Y. Mori, A. Jilkine, and L. Edelstein-Keshet. Wave-pinning and ce ll polarity from a bistable reaction-diffusion system. Biophysical journal , 94(9):3684–3697, 2008

    2008

  37. [45]

    J. D. Murray. Mathematical biology I: An introduction . Interdisciplinary Applied Mathematics, 17. Springer- Verlag, New York, 2002

    2002

  38. [46]

    J. D. Murray. Mathematical biology II: Spatial models and biomedical app lications. Interdisciplinary Applied Mathematics, 18. Springer-Verlag, New York, 2003

    2003

  39. [47]

    P. A. Newmark and A. S. Alvarado. Not your father’s planarian: a classic model enters the era of functional genomics. Nature Reviews Genetics , 3(3):210–219, 2002

    2002

  40. [48]

    K. Noda. Reconstitution of dissociated cells of hydra. Zool. Mag., 80:99–101, 1971

    1971

  41. [49]

    N¨ usslein-Volhard and E

    C. N¨ usslein-Volhard and E. Wieschaus. Mutations affecting seg ment number and polarity in Drosophila. Nature, 287(5785):795–801, 1980. 27

    1980

  42. [50]

    H. G. Othmer and E. Pate. Scale-invariance in reaction-diffusion models of spatial pattern formation. Proceedings of the National Academy of Sciences , 77(7):4180–4184, 1980

    1980

  43. [51]

    Owlarn and K

    S. Owlarn and K. Bartscherer. Go ahead, grow a head! A planar ian’s guide to anterior regeneration. Regener- ation, 3(3):139–155, 2016

    2016

  44. [52]

    C. P. Petersen and P. W. Reddien. Smed- β catenin-1 is required for anteroposterior blastema polarity in plana rian regeneration. Science, 319(5861):327–330, 2008

    2008

  45. [53]

    C. P. Petersen and P. W. Reddien. A wound-induced Wnt expres sion program controls planarian regeneration polarity. Proceedings of the National Academy of Sciences , 106(40):17061–17066, 2009

    2009

  46. [54]

    C. P. Petersen and P. W. Reddien. Polarized notum activation at wounds inhibits Wnt function to promote planarian head regeneration. Science, 332(6031):852–855, 2011

    2011

  47. [55]

    Philipp, R

    I. Philipp, R. Aufschnaiter, S. ¨Ozbek, S. Pontasch, M. Jenewein, H. Watanabe, F. Rentzsch, T. W. Holstein, and B. Hobmayer. Wnt/ β -catenin and noncanonical Wnt signaling interact in tissue evaginatio n in the simple eumetazoan Hydra. Proceedings of the National Academy of Sc...

    2009

  48. [56]

    Plickert, V

    G. Plickert, V. Jacoby, U. Frank, W. A. M¨ uller, and O. Mokady. Wnt signaling in hydroid development: formation of the primary body axis in embryogenesis and its subsequ ent patterning. Developmental biology , 298(2):368–378, 2006

    2006

  49. [57]

    Randolph

    H. Randolph. The regeneration of the tail in Lumbriculus. Journal of Morphology , 7(3):317–344, 1892

  50. [58]

    Randolph

    H. Randolph. Observations and experiments on regeneration in planarians. Development Genes and Evolution , 5(2):352–372, 1897

  51. [59]

    R¨ atz and M

    A. R¨ atz and M. R¨ oger. Turing instabilities in a mathematical mod el for signaling networks. J. Math. Biol. , 65(6-7):1215–1244, 2012

    2012

  52. [60]

    R¨ atz and M

    A. R¨ atz and M. R¨ oger. Symmetry breaking in a bulk-surface r eaction-diffusion model for signalling networks. Nonlinearity, 27(8):1805–1827, 2014

    2014

  53. [61]

    P. W. Reddien. Constitutive gene expression and the specificat ion of tissue identity in adult planarian biology. Trends in Genetics , 27(7):277–285, 2011

    2011

  54. [62]

    P. W. Reddien and A. S. Alvarado. Fundamentals of planarian reg eneration. Annu. Rev. Cell Dev. Biol. , 20:725–757, 2004

    2004

  55. [63]

    Reuter, M

    H. Reuter, M. M¨ arz, M. C. Vogg, D. Eccles, L. Gr ´ ıfol-Bold´ u,D. Wehner, S. Owlarn, T. Adell, G. Weidinger, and K. Bartscherer. β -catenin-dependent control of positional information along the A P body axis in planarians involves a teashirt family member. Cell Reports , 10...

    2015

  56. [64]

    J. C. Rink. Stem Cells, Patterning and Regeneration in Planarians: Sel f-Organization at the Organismal Scale , pages 57–172. Springer, New York, 2018

    2018

  57. [65]

    Sal´ o and J

    E. Sal´ o and J. Bagu˜ n` a. Regeneration and pattern formation in planarians. Development, 83(1):63–80, 1984

    1984

  58. [66]

    Sal´ o and J

    E. Sal´ o and J. Bagu˜ n` a. Cell movement in intact and regenerating planarians. Quantitation using chromosomal, nuclear and cytoplasmic markers. Development, 89(1):57–70, 1985

    1985

  59. [67]

    F. V. Santos. Studies on transplantation in Planaria. Biological Bulletin , 57(3):188–197, 1929

    1929

  60. [68]

    M. L. Scimone, S. W. Lapan, and P. W. Reddien. A forkhead tran scription factor is wound-induced at the planarian midline and required for anterior pole regeneration. PLoS Genet , 10(1):e1003999, 2014. 28

    2014

  61. [69]

    Sherratt, P

    J. Sherratt, P. Maini, W. J¨ ager, and W. M¨ uller. A receptor based model for pattern formation in hydra. Forma, 10(2):77–95, 1995

    1995

  62. [70]

    Shimizu, Y

    H. Shimizu, Y. Sawada, and T. Sugiyama. Minimum tissue size requir ed for hydra regeneration. Developmental biology, 155(2):287–296, 1993

    1993

  63. [71]

    S. Shostak. Inhibitory gradients of head and foot regenerat ion in Hydra viridis. Developmental biology, 28(4):620– 635, 1972

    1972

  64. [72]

    L. R. Smales and H. D. Blankespoor. The epidermis and sensory o rgans of Dugesia tigrina (Turbellaria: Tricla- dida). Cell and Tissue Research , 193(1):35–40, 1978

    1978

  65. [73]

    St¨ uckemann, J

    T. St¨ uckemann, J. P. Cleland, S. Werner, H. T.-K. Vu, R. Baye rsdorf, S.-Y. Liu, B. Friedrich, F. J¨ ulicher, and J. C. Rink. Antagonistic Self-Organizing Patterning Systems Contr ol Maintenance and Regeneration of the Anteroposterior Axis in Planarians. Developmental Cell ,...

    2017

  66. [74]

    Sureda-G´ omez, J

    M. Sureda-G´ omez, J. M. Mart ´ ın-Dur´ an, and T. Adell. Localization of planarian β -CATENIN-1 reveals multiple roles during anterior-posterior regeneration and organogenesis . Development, 143(22):4149–4160, 2016

    2016

  67. [75]

    Tasaki, N

    J. Tasaki, N. Shibata, O. Nishimura, K. Itomi, Y. Tabata, F. Son , N. Suzuki, R. Araki, M. Abe, K. Agata, et al. ERK signaling controls blastema cell differentiation during planarian re generation. Development, 138(12):2417– 2427, 2011

    2011

  68. [76]

    Tenbrock

    C. Tenbrock. Mathematical models for regeneration on the ex ample of planarians. PhD-Thesis, University of M¨ unster (WWU), Germany, 2017

    2017

  69. [77]

    A. M. Turing. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B , 1952

    1952

  70. [78]

    D. M. Umulis. Analysis of dynamic morphogen scale invariance. Journal of The Royal Society Interface , 6(41):1179–1191, 2009

    2009

  71. [79]

    D. M. Umulis and H. G. Othmer. Mechanisms of scaling in pattern fo rmation. Development, 140(24):4830–4843, 2013

    2013

  72. [80]

    G. Webster. Studies on pattern regulation in hydra. Development, 16(1):123–141, 1966

    1966

  73. [81]

    Wenemoser, S

    D. Wenemoser, S. W. Lapan, A. W. Wilkinson, G. W. Bell, and P. W. R eddien. A molecular wound response program associated with regeneration initiation in planarians. Genes & Development , 26(9):988–1002, 2012

    2012

  74. [82]

    Wenemoser and P

    D. Wenemoser and P. W. Reddien. Planarian regeneration involve s distinct stem cell responses to wounds and tissue absence. Developmental biology, 344(2):979–991, 2010

    2010

  75. [83]

    Werner, T

    S. Werner, T. St¨ uckemann, M. Beir´ an Amigo, J. C. Rink, F. J¨ ulicher, and B. M. Friedrich. Scaling and regeneration of self-organized patterns. Phys. Rev. Lett. , 114:138101, Apr 2015

    2015

  76. [84]

    O. K. Wilby and G. Webster. Experimental studies on axial polarit y in hydra. Development, 24(3):595–613, 1970

    1970

  77. [85]

    J. N. Witchley, M. Mayer, D. E. Wagner, J. H. Owen, and P. W. Re ddien. Muscle cells provide instructions for planarian regeneration. Cell reports , 4(4):633–641, 2013

    2013

  78. [86]

    L. Wolpert. Positional information and the spatial pattern of c ellular differentiation. Journal of Theoretical Biology, 25(1):1 – 47, 1969

    1969

  79. [87]

    L. Wolpert. Positional Information and Pattern Formation in De velopment. Developmental Genetics , 1994

    1994

  80. [88]

    Wurtzel, L

    O. Wurtzel, L. E. Cote, A. Poirier, R. Satija, A. Regev, and P. W . Reddien. A generic and cell-type-specific wound response precedes regeneration in planarians. Developmental Cell , 35(5):632–645, 2015. 29

    2015

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.