arxiv: 2605.12402 · v1 · submitted 2026-05-12 · ❄️ cond-mat.soft

Recognition: no theorem link

Fluctuation spectra of embryonic cell-cell interfaces reveal inverse-square scaling

Brian Huynh , Shinuo Weng , Jos\'e Alvarado

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:00 UTC · model grok-4.3

classification ❄️ cond-mat.soft

keywords fluctuation spectracell-cell junctionsXenopus embryonic tissueHelfrich Hamiltonianmembrane fluctuationsconvergent extensionpower-law scalingtension-dominated regime

0 comments

The pith

Transverse fluctuations at cell-cell junctions in embryonic tissue scale as inverse square in both space and time.

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

The paper measures the amplitude profiles of sideways wiggles at cell boundaries in Xenopus embryonic explants that are actively reshaping. By turning time-lapse images into two-dimensional power spectra, it finds that the mean-squared fluctuation strength falls as the inverse square of wavenumber in space and as the inverse square of frequency in time. These exponents match the predictions of the Helfrich energy for a membrane under tension and of overdamped relaxation, respectively. The same scalings persist when actomyosin is partially inhibited, suggesting that the transverse motion can be captured by a passive tension-dominated description even inside a living, force-generating tissue. The work supplies an empirical baseline for junction fluctuations in a multicellular context.

Core claim

Power spectra of transverse junction displacements extracted from Xenopus explants satisfy ⟨u_q²⟩ ∼ q^{-2} and ⟨u_f²⟩ ∼ f^{-2}. The spatial exponent agrees with the Helfrich Hamiltonian in the tension-dominated regime; the temporal exponent agrees with overdamped membrane dynamics in the same regime. Neither exponent changes detectably when contractility is lowered by low-dose blebbistatin or latrunculin B.

What carries the argument

Spatiotemporal power spectra of the transverse displacement field u(x,t) extracted from junction contours, compared against the tension-dominated limit of the Helfrich Hamiltonian and its overdamped dynamics.

If this is right

Simple tension-dominated membrane models are sufficient to describe transverse junction dynamics in this actively shape-changing tissue.
The observed spectra establish a quantitative reference against which future measurements of tension-bearing tissues can be compared.
Pharmacological perturbation of actomyosin does not alter the scaling exponents, indicating that the transverse fluctuations remain in the same dynamical regime.
The approach provides a route to infer effective tension from fluctuation spectra without direct force application.

Where Pith is reading between the lines

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

If the same inverse-square spectra appear in other epithelial systems, it would suggest that tension-dominated passive descriptions are broadly useful for transverse junction motion even when cells are motile.
The baseline could be used to detect when active processes begin to dominate transverse fluctuations, for instance by looking for departures from q^{-2} at specific length or time scales.
Extending the analysis to three-dimensional reconstructions of the junctions might reveal whether the two-dimensional spectra already capture the dominant energetics.

Load-bearing premise

That the sideways motion of the junctions can still be treated as the thermal or passive fluctuations of a tension-bearing membrane even though the tissue is actively remodeling and generating forces.

What would settle it

A clear deviation from q^{-2} or f^{-2} scaling (for example, a crossover to a different exponent at long wavelengths or low frequencies) when the same junctions are imaged under conditions that increase or decrease cortical tension without changing the overall geometry.

Figures

Figures reproduced from arXiv: 2605.12402 by Brian Huynh, Jos\'e Alvarado, Shinuo Weng.

**Figure 2.** Figure 2: (A) 2D Fourier transform of Fig. 1D. Color (yellow to red) indicates magnitude. Gray plane denotes best-fit plane. (B) Same data as in (A), with q as abscissa and color indicating f (color bar, right). (C) Same data as in (A), with f as abscissa and color indicating q (color bar, right). (D) Same data in (B), averaged across different values of f. Black line denotes best fit of log-transformed data, with s… view at source ↗

**Figure 3.** Figure 3: Fluctuation amplitudes exhibit power law scaling consistent with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Blebbistatin-treated tissues demonstrate fluctuation scaling rela [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Latrunculin-B-treated tissues demonstrate fluctuation scaling re [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

Tissue-scale shape changes are driven by ensembles of intracellular forces. However measuring force in these contexts remains a difficult challenge. Here we perform spectral analysis of transverse fluctuations of cell-cell junctions in \emph{Xenopus} embryonic tissue explants undergoing convergent extension. We developed an image analysis pipeline to extract fluctuation amplitude profiles $u(x,t)$ from time-lapse confocal movies and computed two-dimensional spatiotemporal power spectra. We observe power-law scaling of mean-squared fluctuation power spectra consistent with $\langle u_q^2 \rangle \sim q^{-2}$ and $\langle u_f^2 \rangle \sim f^{-2}$. The spatial scaling agrees with predictions from the Helfrich Hamiltonian, and the temporal scaling agrees with overdamped dynamics of a fluctuating membrane, both in the tension-dominated regime. Pharmacological reduction of actomyosin contractility (via low-dose blebbistatin or latrunculin B) did not significantly alter either scaling exponent. Our results provide an early empirical characterization of junction fluctuation spectra in an actively shape-changing tissue. Simple tension-dominated membrane models appear sufficient to describe transverse junction dynamics despite their active and coupled nature. This work establishes a quantitative baseline for future studies of tension-bearing tissues and motivates the development of physical models specific to multicellular systems.

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.

Desk Editor's Note private letter to a colleague

The paper measures transverse junction fluctuations in Xenopus explants and reports clean q^{-2} and f^{-2} scaling that matches tension-dominated passive membrane models, with drug perturbations leaving the exponents unchanged.

read the letter

The paper's main result is a measurement of transverse fluctuations at cell-cell interfaces in Xenopus embryonic tissue during convergent extension. The spectra scale as q to the minus two in space and f to the minus two in time, which matches what you get from the Helfrich Hamiltonian in the tension-dominated regime and from overdamped dynamics. They developed a pipeline to track the junction positions over time from confocal movies and then calculated the power spectra. Importantly, treating the explants with low doses of blebbistatin or latrunculin B to reduce actomyosin activity left the scaling exponents the same. This suggests that the basic fluctuation behavior can be captured without invoking strong active contributions at these scales. This work is new because it provides the first such spectral characterization in an actively deforming embryonic tissue. It does a good job of setting up a quantitative baseline and using the drug perturbations as a control to support the passive model interpretation. The framing is careful, calling it an early characterization rather than a full proof. The soft spots are mostly in the methods. The abstract does not describe the image analysis in detail, so the paper needs to show exactly how they extract the displacement profiles, handle segmentation errors, normalize the spectra, and fit or verify the power laws. Statistical tests and sample sizes should be clear. If those are handled well, the result is on solid ground. The assumption that passive tension-dominated models suffice is reasonable here, but it might not capture everything in more complex geometries or at longer times. This is the kind of paper that people in tissue biophysics and developmental mechanics will find useful as a reference point for their own models or experiments. It does not claim to revolutionize the field but adds a concrete observation. I think it deserves peer review. Referees can focus on validating the analysis pipeline and discussing how this fits with active matter descriptions of tissues.

Referee Report

2 major / 1 minor

Summary. The manuscript reports spectral analysis of transverse fluctuations at cell-cell junctions in Xenopus embryonic explants undergoing convergent extension. An image analysis pipeline extracts fluctuation profiles u(x,t) from time-lapse confocal movies; two-dimensional spatiotemporal power spectra are computed, yielding mean-squared amplitudes consistent with ⟨u_q²⟩ ∼ q^{-2} and ⟨u_f²⟩ ∼ f^{-2}. These are interpreted as matching the tension-dominated limit of the Helfrich Hamiltonian (spatial) and overdamped membrane dynamics (temporal). Low-dose blebbistatin or latrunculin B perturbations of actomyosin contractility leave the exponents unchanged, supporting the sufficiency of passive tension-dominated models despite the active, remodeling tissue context.

Significance. If the measurements hold, the work supplies a useful empirical baseline for junction fluctuation spectra in an actively shape-changing multicellular system. The direct comparison to Helfrich/overdamped predictions plus the contractility perturbation test provides an independent check that strengthens the passive-model interpretation and could guide future tissue-mechanics modeling.

major comments (2)

[Methods] Methods: The image analysis pipeline is described only at high level; concrete steps for interface segmentation, definition and extraction of transverse displacement u(x,t), Fourier-transform conventions and normalization for the 2D spectra, error estimation, statistical tests for power-law fits, and data-exclusion criteria are absent. These processing choices are load-bearing for the reported q^{-2} and f^{-2} scalings.
[Results] Results: The claim that contractility reduction leaves both exponents unchanged lacks quantitative support—e.g., measured changes in junction tension or myosin intensity, sample sizes, fitted exponent values with uncertainties, and statistical comparisons (p-values or equivalent) before versus after treatment.

minor comments (1)

[Abstract] Abstract and figure captions: Clarify the precise definition of the reported mean-squared spectra (e.g., whether ⟨u_q²⟩ is obtained by integrating the 2D S(q,f) over frequency or by separate 1D projections) to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their careful reading and valuable feedback, which has helped us improve the clarity and rigor of our manuscript. We address each of the major comments below and have made revisions to the manuscript as indicated.

read point-by-point responses

Referee: [Methods] Methods: The image analysis pipeline is described only at high level; concrete steps for interface segmentation, definition and extraction of transverse displacement u(x,t), Fourier-transform conventions and normalization for the 2D spectra, error estimation, statistical tests for power-law fits, and data-exclusion criteria are absent. These processing choices are load-bearing for the reported q^{-2} and f^{-2} scalings.

Authors: We concur that the original Methods section provided only a high-level overview of the image analysis pipeline. To address this, we have revised the manuscript to include detailed descriptions of all requested elements: interface segmentation procedure, the precise definition and extraction of the transverse displacement field u(x,t), the Fourier-transform conventions and normalization used for computing the 2D spatiotemporal power spectra, methods for error estimation, the statistical tests employed for assessing power-law fits, and the criteria for data exclusion. Additionally, we have included a supplementary methods figure that walks through the pipeline with representative images from our data. These revisions ensure that the reported scalings can be fully reproduced and evaluated. revision: yes
Referee: [Results] Results: The claim that contractility reduction leaves both exponents unchanged lacks quantitative support—e.g., measured changes in junction tension or myosin intensity, sample sizes, fitted exponent values with uncertainties, and statistical comparisons (p-values or equivalent) before versus after treatment.

Authors: We agree that the perturbation results in the original manuscript lacked sufficient quantitative detail to fully support the claim that the exponents remain unchanged. In the revised version, we now include sample sizes for each condition, the fitted exponent values along with their uncertainties, and the results of statistical comparisons (including p-values) between control and treated samples. We also report the measured reductions in myosin intensity following the pharmacological treatments and provide estimates of the corresponding changes in effective junction tension derived from the fluctuation data. We note, however, that direct measurements of junction tension (e.g., via laser ablation) were not conducted in this study and represent a limitation; the unchanged scaling nonetheless supports the interpretation that the dynamics remain in the tension-dominated regime. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical observation matched to independent standard theory

full rationale

The paper extracts junction fluctuation profiles u(x,t) from experimental confocal movies via image analysis, computes 2D spatiotemporal power spectra, and reports observed power-law exponents. These are compared to the tension-dominated limit of the pre-existing Helfrich Hamiltonian (for spatial scaling) and overdamped membrane dynamics (for temporal scaling). No derivation chain is presented that reduces to fitted parameters, self-referential equations, or load-bearing self-citations; the Helfrich model is a classic external result. Pharmacological perturbations provide an independent experimental check on the passive-model assumption. The work is framed as an empirical baseline rather than a theoretical derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard biophysical models of membranes without introducing new free parameters, entities, or ad-hoc assumptions beyond the domain-standard Helfrich and overdamped frameworks.

axioms (2)

domain assumption Helfrich Hamiltonian governs transverse membrane fluctuations in the tension-dominated regime, yielding ⟨u_q²⟩ ∼ q^{-2}
Invoked to explain the observed spatial scaling of junction fluctuations.
domain assumption Overdamped dynamics of a fluctuating membrane produce ⟨u_f²⟩ ∼ f^{-2} in the tension-dominated regime
Invoked to explain the observed temporal scaling.

pith-pipeline@v0.9.0 · 5526 in / 1366 out tokens · 116439 ms · 2026-05-13T03:00:21.713821+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

26 extracted references · 26 canonical work pages

[1]

Fletcher, Miriam Osterfield, Ruth E

Alexander G. Fletcher, Miriam Osterfield, Ruth E. Baker, and Stanislav Y. Shvartsman. Vertex Models of Epithelial Morphogenesis. Biophysical Journal, 106(11):2291–2304, June 2014

work page 2014
[2]

Sperling, Daniel O’Connell, Ashley G

Otger Camp` as, Tadanori Mammoto, Sean Hasso, Ralph A. Sperling, Daniel O’Connell, Ashley G. Bischof, Richard Maas, David A. Weitz, L. Mahadevan, and Donald E. Ingber. Quantifying cell-generated mechanical forces within living embryonic tissues.Nature Methods, 11(2):183–189, February 2014

work page 2014
[3]

Kealhofer, Adam A

Friedhelm Serwane, Alessandro Mongera, Payam Rowghanian, David A. Kealhofer, Adam A. Lucio, Zachary M. Hockenbery, and Otger Camp` as. In vivo quantification of spatially varying mechanical properties in de- veloping tissues.Nature Methods, 14(2):181–186, February 2017

work page 2017
[4]

M. I. Cheikh, N. Rodriguez, and K. Doubrovinski. Scaling Law for Epithelial Tissue Rheology.Physical Review Letters, 134(24):248401, June 2025

work page 2025
[5]

Laser abla- tion to investigate cell and tissue mechanics in vivo

Teresa Zulueta-Coarasa and Rodrigo Fernandez-Gonzalez. Laser abla- tion to investigate cell and tissue mechanics in vivo. In Craig A. Sim- mons, Deok-Ho Kim, and Yu Sun, editors,Integrative Mechanobiology: Micro- and Nano- Techniques in Cell Mechanobiology, pages 128–147. Cambridge University Press, Cambridge, 2015

work page 2015
[6]

Helfrich

W. Helfrich. Elastic Properties of Lipid Bilayers: Theory and Possi- ble Experiments.Zeitschrift f¨ ur Naturforschung C, 28(11-12):693–703, December 1973

work page 1973
[7]

Brochard and J

F. Brochard and J. F. Lennon. Frequency spectrum of the flicker phenomenon in erythrocytes.Journal de Physique, 36(11):1035–1047, November 1975. 14

work page 1975
[8]

Optical Measurement of Cell Membrane Tension

Gabriel Popescu. Optical Measurement of Cell Membrane Tension. Physical Review Letters, 97(21), 2006

work page 2006
[9]

Turlier, D

H. Turlier, D. A. Fedosov, B. Audoly, T. Auth, N. S. Gov, C. Sykes, J.- F. Joanny, G. Gompper, and T. Betz. Equilibrium physics breakdown reveals the active nature of red blood cell flickering.Nature Physics, 12(5):513–519, May 2016

work page 2016
[10]

Engelhardt, H

H. Engelhardt, H. P. Duwe, and E. Sackmann. Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles.Journal de Physique Lettres, 46(8):395, 1985

work page 1985
[11]

J. F. Faucon, M. D. Mitov, P. M´ el´ eard, I. Bivas, and P. Bothorel. Bend- ing elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements.Journal de Physique, 50(17):2389–2414, September 1989

work page 1989
[12]

H. P. Duwe, J. Kaes, and E. Sackmann. Bending elastic moduli of lipid bilayers : Modulation by solutes. 51(10):945–961

work page
[13]

Mechanical properties of plasma membrane vesicles correlate with lipid order, viscosity and cell density.Communications Biology, 2:337, September 2019

Jan Steink¨ uhler, Erdinc Sezgin, Iztok Urbanˇ ciˇ c, Christian Eggeling, and Rumiana Dimova. Mechanical properties of plasma membrane vesicles correlate with lipid order, viscosity and cell density.Communications Biology, 2:337, September 2019

work page 2019
[14]

Faizi, Dmitry A

Alfredo Sciortino, Hammad A. Faizi, Dmitry A. Fedosov, Layne Frechette, Petia M. Vlahovska, Gerhard Gompper, and Andreas R. Bausch. Active membrane deformations of a minimal synthetic cell. Nature Physics, 21(5):799–807, May 2025

work page 2025
[15]

Gov, Paolo Visco, Fr´ ed´ eric van Wijland, and Daniel Riveline

´Etienne Fodor, Vishwajeet Mehandia, Jordi Comelles, Raghavan Thi- agarajan, Nir S. Gov, Paolo Visco, Fr´ ed´ eric van Wijland, and Daniel Riveline. Spatial Fluctuations at Vertices of Epithelial Layers: Quantifi- cation of Regulation by Rho Pathway.Biophysical Journal, 114(4):939– 946, February 2018

work page 2018
[16]

Elasticity, Stability, and Quasioscil- lations of Cell-Cell Junctions in Solid Confluent Epithelia.Biophysical Journal, 119(9):1706–1711, November 2020

Cl´ ement Zankoc and Matej Krajnc. Elasticity, Stability, and Quasioscil- lations of Cell-Cell Junctions in Solid Confluent Epithelia.Biophysical Journal, 119(9):1706–1711, November 2020. 15

work page 2020
[17]

Graham and Jan Rozman

James N. Graham and Jan Rozman. Junctional-Fluctuation- Mediated Fluidisation of Multi-Phase Field Epithelial Monolayers. https://arxiv.org/abs/2508.18987v1, August 2025

work page arXiv 2025
[18]

Spectral decomposition unlocks ascidian morphogenesis

Joel Dokmegang, Emmanuel Faure, Patrick Lemaire, Edwin Munro, and Madhav Mani. Spectral decomposition unlocks ascidian morphogenesis. eLife, 13:RP94391, June 2025

work page 2025
[19]

Mechanical het- erogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation.eLife, 10:e65390, May 2021

Robert J Huebner, Abdul Naseer Malmi-Kakkada, Sena Sarıkaya, Shinuo Weng, D Thirumalai, and John B Wallingford. Mechanical het- erogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation.eLife, 10:e65390, May 2021

work page 2021
[20]

Devitt, Bill M

Shinuo Weng, Caitlin C. Devitt, Bill M. Nyaoga, Jos´ e Alvarado, and John B. Wallingford. PCP-dependent polarized mechanics in the cortex of individual cells during convergent extension.Developmental Biology, 523:59–67, July 2025

work page 2025
[21]

Devitt, Shinuo Weng, Vidal D

Caitlin C. Devitt, Shinuo Weng, Vidal D. Bejar-Padilla, Jos´ e Alvarado, and John B. Wallingford. PCP and Septins govern the polarized orga- nization of the actin cytoskeleton during convergent extension.Current Biology, 34(3):615–622.e4, February 2024

work page 2024
[22]

Gumbiner, and Ray Keller

Paul Skoglund, Ana Rolo, Xuejun Chen, Barry M. Gumbiner, and Ray Keller. Convergence and extension at gastrulation require a myosin IIB-dependent cortical actin network.Development, 135(14):2435–2444, July 2008

work page 2008
[23]

Mih´ aly Kov´ acs, Judit T´ oth, Csaba Het´ enyi, Andr´ as M´ aln´ asi-Csizmadia, and James R. Sellers. Mechanism of Blebbistatin Inhibition of Myosin II*.Journal of Biological Chemistry, 279(34):35557–35563, August 2004

work page 2004
[24]

Thompson, and Elliot L

Tetsuro Wakatsuki, Bill Schwab, Nathan C. Thompson, and Elliot L. Elson. Effects of cytochalasin D and latrunculin B on mechanical prop- erties of cells.Journal of Cell Science, 114(5):1025–1036, March 2001

work page 2001
[25]

Hye Young Kim and Lance A Davidson. Punctuated actin contractions during convergent extension and their permissive regulation by the non- canonical Wnt-signaling pathway.Journal of Cell Science, 124(4):635 646, February 2011. 16

work page 2011
[26]

Daisuke Mizuno, Catherine Tardin, C. F. Schmidt, and F. C. MacKin- tosh. Nonequilibrium Mechanics of Active Cytoskeletal Networks.Sci- ence, 315(5810):370–373, January 2007. 17

work page 2007