Noise-Induced Localized Patterns in Excitable Media: Amplitude versus Persistence

Chau Dao; Chuan-Hsiang Huang; Gia-Wei Chern; Jr-Ming Yang

REVIEW 3 major objections 4 minor 48 references

Noise-Induced Localized Patterns in Excitable Media: Amplitude versus Persistence

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Nucleating a localized excitation needs a fixed total noise dose; amplitude and persistence can be traded.

desk verdict Sound central idea—amplitude and persistence as joint nucleation controls—but the phase diagrams rest on an undefined run-classification rule, so the paper needs revision before it is reproducible. read the letter →

arxiv 2608.10862 v1 pith:K4UPEY54 submitted 2026-08-11 cond-mat.soft

Chau Dao , Jr-Ming Yang , Chuan-Hsiang Huang , Gia-Wei Chern This is my paper · ORCID

classification cond-mat.soft

keywords excitablemediaFitzHugh-Nagumonoise-inducedpatternformationtemporalcorrelationsOrnstein-Uhlenbecknoiseintegratedstrengthlocalizedexcitationpatchesinhibitorresponsetime

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

Transient patches of activity appear spontaneously in many excitable biological systems, but it has been unclear which statistical feature of the fluctuations triggers them. This paper argues that neither instantaneous noise amplitude nor temporal persistence acts alone; the controlling quantity is the integrated noise strength $A=\sigma_\eta^2 \tau_c$, the accumulated stochastic forcing. In a one-dimensional FitzHugh-Nagumo excitable medium, the same localized patch can be nucleated by a short loud fluctuation or by a longer quiet one, provided they deposit the same $A$. The simulations map out three regimes—quiescent, localized pattern-forming, and system-wide alternating—and show that the inhibitor response time $\tau_v$ subsequently decides whether a nucleated excitation stays local or spreads. The result suggests that experiments should characterize intracellular noise by both amplitude and correlation time, not amplitude alone.

What carries the argument

The machinery is a stochastic FitzHugh-Nagumo reaction-diffusion system on a periodic one-dimensional domain, driven by an Ornstein-Uhlenbeck noise field with equal-time rms amplitude $\sigma_\eta$ and correlation time $\tau_c$. The load-bearing identity is the integrated noise strength $A=\sigma_\eta^2 \tau_c$, defined as the time integral of the noise autocorrelation, which collapses amplitude and persistence into a single control parameter. Three complementary parameter sweeps—$\tau_v$ versus $\tau_c$ at fixed $A$, $A$ versus $\tau_c$ at fixed $\tau_v$, and $\tau_v$ versus $\tau_c$ at fixed $\sigma_\eta$—separate amplitude effects from persistence effects. The inhibitor response time $\tau_v$ supplies the second timescale that decides whether an excitation stays localized or becomes system-wide, and a mean-field treatment of the white-noise limit yields a self-consistent estimate of the nonequilibrium quiescent background and a nucleation criterion $\sigma_u \sim (\alpha+\beta-1)/\alpha$.

What would settle it

Run the same model with an explicit excitation detector (for example, activator above 0.5 over at least five percent of the system for at least ten activator time units) and sweep all three parameter planes; if the quiescent-to-pattern boundary no longer follows contours of $A=\sigma_\eta^2 \tau_c$ at fixed $\tau_v$, the amplitude-persistence compensation claim fails.

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Extended reading notes

Core claim

The paper's central claim is that transient localized excitation patches are nucleated by accumulated stochastic forcing rather than by instantaneous amplitude or persistence separately. The identity $A=\sigma_\eta^2 \tau_c$ links the two routes: a short-lived fluctuation with large equal-time rms amplitude and a longer-lived fluctuation with proportionally smaller amplitude deposit the same integrated noise strength and can cross the same excitation threshold. At fixed $A$, increasing the correlation time lowers the instantaneous amplitude and eventually suppresses nucleation; at fixed $\sigma_\eta$, increasing the correlation time adds persistence without the amplitude penalty and strongly promotes nucleation. The opposite trends in these two sweeps are the paper's direct evidence that amplitude and persistence are interchangeable stochastic control parameters. Once a patch is nucleated, its growth, lifetime, and whether it remains local or spreads are governed mainly by the inhibitor response time $\tau_v$, and sufficiently persistent noise can extend a patch's life when $\tau_c \gtrsim \tau_v$.

Load-bearing premise

All three phase diagrams rely on an unstated operational rule for what counts as a noise-induced excitation—no activator threshold, minimum lifetime, or spatial extent is specified—so a different detection rule would move the reported phase boundaries.

Editorial extensions

If this is right

Cells with different sources or sizes of molecular fluctuations could still show similar protrusion dynamics, as long as amplitude and persistence compensate to the same integrated noise strength.
Gaussian white noise alone can support transient localized patterns at sufficiently large $A$, so finite temporal correlation is not a prerequisite for patch formation.
Because $A$ controls nucleation while $\tau_v$ controls spread, an excitable network can be switched from local to system-wide activity by changing only inhibitor kinetics while leaving the noise fixed.
Patch lifetime and size should increase roughly linearly with $\tau_v$ throughout the pattern-forming regime, giving a quantitative observable for experiments.
Weak but persistent perturbations could drive an excitable signaling system across threshold with less collateral effect than a strong brief stimulus.

Reading between the lines

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

Editorial: the phase-boundary analysis implies a quantitative nucleation-rate prediction—probability per site per unit time should depend on $A$ through the variance $\sigma_u^2$ computed in the mean-field treatment—though the paper does not derive such a rate.
Editorial: the same amplitude-persistence tradeoff may extend to non-Gaussian or spatially correlated noise if the controlling variable is still the integrated autocorrelation, but the paper does not test that case.
Editorial: because the patch-detection rule is not specified, the exact location of the quiescent-pattern boundary is convention-dependent; an explicit detector would convert the phase diagrams into a sharper falsifiable prediction.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First, the thing to know: this paper has a real idea—parameterizing the noise by integrated strength A = σ_η² τ_c and showing that white noise alone can nucleate localized patches, with persistence acting as a second control—but the central phase diagrams are built on a run-classification rule the authors never state. That is not a minor omission; it is the instrument reading used for every boundary in Fig. 2.

What is actually new: the systematic interpolation between white and Ornstein-Uhlenbeck noise, the explicit contrast between fixed-A and fixed-σ_η sweeps, and the demonstration that τ_v (inhibitor response) sets patch size and lifetime independently of how the noise is parameterized. The paper is honest about the relationship to Hecht et al. [47,48], and the model itself is standard FHN with additive OU noise. The mean-field appendix is crude but gives a concrete criterion (σ_u ~ (α+β−1)/α) that could be checked. The numerics use 50 runs per point; error bars are absent, but for phase diagrams of this kind that is workable if the detection rule were fixed.

The soft spots are, in order of severity. First, the missing definition of 'noise-induced excitation': no threshold on u, no minimum lifetime, no minimum spatial extent. The stress-test note is right that a lax vs strict detector would shift the boundaries and could even change the compensation claim. The authors say in the captions that colors are 'percentage of runs exhibiting noise-induced excitation,' but never say what that means operationally. Second, the appendix claims 'excellent numerical agreement' for the mean-field background without showing a comparison plot. Third, no code or data are provided; the patch statistics in Appendix C are also expressed as percentages without thresholds.

The definitional link A = σ_η² τ_c is not a circularity problem: it is a parameterization choice, and the phase diagrams are independent simulation evidence. The qualitative regimes and the contrasting trends in Figs. 2(a) and (c) are robust enough to believe, but I would not want to cite the quantitative boundary A_c(τ_c) until the detection rule is specified.

For whom: stochastic reaction-diffusion and cell-signaling modelers. It deserves a serious referee, but the referee should push hard on the operational definition and, ideally, get the code and data. My verdict: conditional accept, not reject.

Referee Report

3 major / 4 minor

Summary. The paper studies a one-dimensional FitzHugh-Nagumo reaction-diffusion system driven by Ornstein-Uhlenbeck noise, with the integrated noise strength A = σ_η^2 τ_c as the primary control parameter. By sweeping the inhibitor response time τ_v, the noise correlation time τ_c, the noise amplitude σ_η, and A, the authors report three dynamical regimes: quiescent, spatially extended alternating, and pattern-forming with transient localized excitation patches. The central claim is that localized patches can be nucleated either by short-lived fluctuations with large instantaneous amplitude or by weaker fluctuations that persist longer, and that these two routes are unified through the integrated noise strength A, while the inhibitor response time determines whether an excitation remains local or spreads system-wide. The paper includes a qualitative mechanism based on threshold crossing, a mean-field treatment of the nonequilibrium quiescent background in the white-noise limit, and appendices documenting the numerical scheme and patch size/lifetime statistics.

Significance. If the central claim holds, the paper gives a simple and potentially useful organizing principle for noise-induced localized patterns in excitable media: amplitude and persistence of fluctuations act as joint nucleation controls, with the inhibitor time scale controlling the fate of a nucleated excitation. The phase diagrams are falsifiable predictions, and the white-noise limit result (localized patterns without temporal correlations) is a clear, nontrivial message for a broad readership. The paper also connects to concrete biological phenomena, such as Ras-PI3K patches, which increases its significance. However, the reproducibility of the quantitative results is currently compromised by an underspecified run-classification rule, the absence of error bars, and an unverified claim of excellent mean-field agreement; these gaps must be addressed before the manuscript can support its quantitative conclusions.

major comments (3)

[Dynamical phases; Fig. 2] The phase diagrams in Fig. 2 color-code the percentage of 50 runs exhibiting "noise-induced excitation," but the manuscript never defines the operational classifier: it does not state the threshold on u, the minimum spatial extent, the minimum lifetime, or the rule that distinguishes a localized excitation patch from the spatially extended alternating phase. Since the quiescent-pattern boundary in Fig. 2(a), the critical curve A_c(τ_c) in Fig. 2(b), and the contrasting trends in Fig. 2(c) are all read off this undefined observable, a different detector could shift the boundaries or even change the monotonicity of A_c(τ_c). Please specify the exact detection rule (including thresholds and any cooldown/merging conditions), and provide the detection code or a precise pseudocode description so that the amplitude-persistence compensation result is reproducible.
[Dynamical phases; Fig. 2 and Fig. 6] Each phase point is based on 50 independent runs, but no error bars, confidence intervals, or statistical uncertainties are reported for the percentage of runs classified as excited. The white dashed phase boundaries in Fig. 2 are also introduced without a stated contouring rule or threshold percentage. For a stochastic classification, the binomial uncertainty on a 50-run percentage is sizable near the boundaries, so the monotonicity claim for A_c(τ_c) and the crossover arrows in Figs. 2(a) and 2(c) cannot currently be distinguished from detector and sampling effects. Please add error bars or at least report the classification threshold and the number of runs per point, and state how the boundary curves were constructed.
[Appendix B] Appendix B states that the mean-field estimates "have excellent numerical agreement with the simulated results," but no comparison plot, table, or quantitative error metric is provided. Because the approximations (spatially Gaussian u, negligible covariance between u^2 and v, small δv) are introduced ad hoc, this agreement claim is the only evidence that the nonequilibrium background calculation is quantitatively reliable. Please add a direct comparison of μ_u, μ_v, and σ_u^2 against simulation results as functions of A, and state the numerical values or relative errors supporting the "excellent agreement" wording.

minor comments (4)

[Reaction-diffusion equations; Fig. 2 caption] The value of τ_u is never specified; the figure captions and parameter lists give α, β, D_u, D_v, τ_v, τ_c, A, and σ_η, but not τ_u or the time step Δt used for the production runs. Please state these values explicitly, since all reported lifetimes and correlation times are quoted in units of τ_u.
[Fig. 5 and Appendix C] The claim that patch lifetime and size "scale linearly with τ_v" is supported only by visual inspection of Fig. 5. Please add linear fits with their slopes, or at least quantitative correlation measures, and include error bars on the averaged patch properties.
[Eq. (3) and Discussion] The statement that amplitude and persistence are "linked through the integrated noise strength" is true by definition because A ≡ σ_η^2 τ_c. The nontrivial empirical content is the phase behavior under the two different parameterizations in Figs. 2(a) and 2(c); the text should state explicitly that the definitional link is not itself a measured result, to avoid overstating the circularity-sensitive part of the claim.
[Appendix A, Eq. (A10)] The notation in the vector term "2βcv1" is ambiguous because the unit vector 1 and the scalar multiplication are not defined; please clarify the notation and also report the fixed-point iteration tolerance and maximum iteration count used in the production runs.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the amplitude–persistence link is an explicit definition (Eq. 3), and the phase boundaries rest on independent simulations.

full rationale

The paper defines the integrated noise strength as A ≡ σ_η^2 τ_c in Eq. (3) and explicitly states that it regards A, rather than σ_η, as the primary control parameter. The abstract sentence that amplitude and persistence 'are linked through the integrated noise strength' is therefore a restatement of an explicit definition, not a derived prediction that is being sold as a measured result. The substantive claim — that strong short-lived fluctuations and weaker persistent fluctuations can both nucleate localized patches — is supported by direct simulation phase diagrams (Fig. 2) whose color encodes the percentage of 50 independent runs exhibiting excitation, and by patch-size/lifetime statistics (Fig. 6). No parameter is fitted to the target result, and the mean-field calculation in Appendix B is a self-consistent linearized estimate compared with simulations, not an input from which the phase diagrams are derived. The paper's self-citations (e.g., refs. 5, 9, 14, 18, 19) appear only as biological background and are not load-bearing for the model, the noise parameterization, or the phase classification. The main weakness is the underspecified run-scoring criterion for 'noise-induced excitation' — no u-threshold, minimum lifetime, or spatial extent is stated — which threatens reproducibility and falsifiability but is not a circularity: it does not make any prediction equal to an input or reduce a derived result to a fit. Under the hard rules, no step in the derivation chain reduces by construction to its own inputs, so the appropriate score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

All parameters are simulation inputs, not fitted to data. The central claim rests on phase diagrams whose classification criterion is not specified, so the numerical ranges and detection rule are load-bearing. The mean-field appendix introduces closure approximations that are observationally motivated rather than derived. No new physical entities are introduced; A is a derived control parameter.

free parameters (3)

α = 0.5, β = 0.7
Chosen model parameters for the inhibitor relaxation and steady state; the phase boundaries and the white-noise criterion σ_u ~ (α + β - 1)/α depend on them, and they are not inferred from data.
D_u = 1, D_v = 5
Diffusion constants chosen to place the system in the inhibitor-diffuses-faster regime; patch length scales in Eq. (5) scale with these values.
Sweep ranges for τ_v, τ_c, A, σ_η and numerical grid (N, L, Δt)
The phase diagrams cover 1 ≤ τ_v ≤ 50, 0.5 ≤ τ_c < 5.5, 0.01 ≤ A ≤ 0.5, and σ_η = 0.5. Exact N, L, Δt, and tolerances are not reported, so the diagrams are not fully reproducible from the text.

assumptions (5)

domain assumption FitzHugh-Nagumo dynamics with additive activator noise is a valid minimal model for excitable biological signaling and generic excitable media.
Introduced in the Introduction and generalized in the Discussion; if fluctuations enter through other variables, or in 2D or 3D, the specific regime boundaries may differ.
domain assumption The integrated noise strength A = σ_η^2 τ_c is the relevant accumulated stochastic forcing for nucleation.
Defined in Eq. (3) and used as the primary control parameter throughout; its sufficiency for nucleation is asserted from simulations, not derived from first principles.
ad hoc to paper In the mean-field calculation, u is spatially Gaussian, the covariance between u^2 and v is negligible, and δv fluctuations are small.
Used to close Eqs. (B3) and (B10) in Appendix B; these approximations are justified only by empirical observation of simulations.
domain assumption Fifty runs of duration 500 τ_u per parameter point are representative enough to classify phases.
Every phase diagram point uses 50 runs; no error bars, convergence tests, or worst-case variability are shown.
domain assumption The one-dimensional periodic discretization with D_u Δt / a^2 ≪ 1 approximates the continuum limit.
Assumed in Appendix B for variance formula Eq. (B11); N and L are not stated, so this cannot be checked from the text.

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Cite this review

Pith. "Pith review of Noise-Induced Localized Patterns in Excitable Media: Amplitude versus Persistence." pith.science (2026). https://pith.science/paper/K4UPEY54

@misc{pith2026260810862,
  author       = {Pith},
  title        = {Pith review of: Noise-Induced Localized Patterns in Excitable Media: Amplitude versus Persistence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K4UPEY54}},
  note         = {Machine review of arXiv:2608.10862}
}

read the original abstract

Transient spatially localized activity underlies a broad range of biological processes, yet the statistical property of fluctuations that controls its nucleation remains unclear. We systematically investigate noise-induced dynamics in a spatially extended FitzHugh-Nagumo excitable system and identify three regimes: a quiescent phase, a spatially extended alternating phase, and a pattern-forming phase characterized by transient localized excitation patches. Surprisingly, we find that temporal noise correlations are not required for patch formation: Gaussian white noise produces localized patches when its amplitude is sufficiently large, whereas weaker fluctuations can achieve the same effect when temporal correlations allow them to persist. Our results identify the instantaneous amplitude and the persistence as joint stochastic control parameters for transient pattern formation in excitable media. These distinct quantities are linked through the integrated noise strength, which quantifies the accumulated stochastic forcing available to nucleate an excitation. In addition, the inhibitor response time subsequently determines whether the excitation remains localized or spreads throughout the system.

Figures

Figures reproduced from arXiv: 2608.10862 by the authors.

**Figure 2.** FIG. 2. Noise-induced dynamical phases under three parameterizations of the active noise. Color indicates the percentage of 50 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. Spacetime diagram of the activator field [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 5.** Figure 5: FIG. 5. (a) Patch lifetime (in units of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 6.** Figure 6: FIG. 6. Properties of the noise-induced excitation patches for the three parameter sweeps corresponding to Fig. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

48 extracted references · 44 canonical work pages

[1]

M. G. Vicker, Reaction–diffusion waves of actin filament polymerization/depolymerization in dictyostelium pseu- dopodium extension and cell locomotion, Biophys. Chem. 84, 87 (2000)

work page 2000
[2]

Gerisch, T

G. Gerisch, T. Bretschneider, A. M¨ uller-Taubenberger, E. Simmeth, M. Ecke, S. Diez, and K. Anderson, Mobile actin clusters and traveling waves in cells recovering from actin depolymerization, Biophys. J.87, 3493 (2004)

work page 2004
[3]

O. D. Weiner, W. A. Marganski, L. F. Wu, S. J. Altschuler, and M. W. Kirschner, An actin-based wave generator organizes cell motility, PLOS Biol.5, 1 (2007)

work page 2007
[4]

Asano, A

Y. Asano, A. Nagasaki, and T. Q. Uyeda, Correlated waves of actin filaments and pip3 in dictyostelium cells, Cell Motil.65, 923 (2008)

work page 2008
[5]

Huang, M

C.-H. Huang, M. Tang, C. Shi, P. A. Iglesias, and P. N. Devreotes, An excitable signal integrator couples to an idling cytoskeletal oscillator to drive cell migration, Nat. Cell Biol.15, 1307 (2013)

work page 2013
[6]

Y. Arai, T. Shibata, S. Matsuoka, M. J. Sato, T. Yanagida, and M. Ueda, Self-organization of the phos- phatidylinositol lipids signaling system for random cell migration, Proc. Natl. Acad. Sci. U.S.A.107, 12399 (2010)

work page 2010
[7]

Allard and A

J. Allard and A. Mogilner, Traveling waves in actin dy- namics and cell motility, Curr. Opin. Cell Biol.25, 107 (2013)

work page 2013
[8]

Taniguchi, S

D. Taniguchi, S. Ishihara, T. Oonuki, M. Honda- Kitahara, K. Kaneko, and S. Sawai, Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells, Proc. Natl. Acad. Sci. U.S.A.110, 5016 (2013)

work page 2013

Show all 48 references

[9]

Xiong, C.-H

Y. Xiong, C.-H. Huang, P. A. Iglesias, and P. N. De- vreotes, Cells navigate with a local-excitation, global- inhibition-biased excitable network, Proc. Natl. Acad. Sci. U.S.A.107, 17079 (2010)

2010
[10]

Nishikawa, M

M. Nishikawa, M. H¨ orning, M. Ueda, and T. Shibata, Excitable signal transduction induces both spontaneous and directional cell asymmetries in the phosphatidylinos- itol lipid signaling system for eukaryotic chemotaxis, Bio- phys. J.106, 723 (2014)

2014
[11]

P. J. M. van Haastert, I. Keizer-Gunnink, and A. Ko- rtholt, Coupled excitable ras and f-actin activation medi- ates spontaneous pseudopod formation and directed cell movement, Mol. Biol. Cell28, 922 (2017)

2017
[12]

P. N. Devreotes, S. Bhattacharya, M. Edwards, P. A. Iglesias, T. Lampert, and Y. Miao, Excitable signal trans- duction networks in directed cell migration, Annu. Rev. Cell Dev. Biol.33, 103 (2017)

2017
[13]

Matsuoka, K

S. Matsuoka, K. Iwamoto, D. Y. Shin, and M. Ueda, Spontaneous signal generation by an excitable system for cell migration, Front. Cell Dev. Biol.12(2024)

2024
[14]

H. Zhan, S. Bhattacharya, H. Cai, P. A. Iglesias, C.-H. Huang, and P. N. Devreotes, An excitable ras/pi3k/erk signaling network controls migration and oncogenic transformation in epithelial cells, Dev. Cell.54, 608 (2020)

2020
[15]

Y. Miao, S. Bhattacharya, T. Banerjee, B. Abubaker- Sharif, Y. Long, T. Inoue, P. A. Iglesias, and P. N. Devreotes, Wave patterns organize cellular protrusions and control cortical dynamics, Mol. Syst. Biol.15, MSB188585 (2019)

2019
[16]

K. Aoki, Y. Kumagai, A. Sakurai, N. Komatsu, Y. Fujita, C. Shionyu, and M. Matsuda, Stochastic erk activation induced by noise and cell-to-cell propagation regulates cell density-dependent proliferation, Mol. Cell.52, 529 (2013)

2013
[17]

J. G. Albeck, G. B. Mills, and J. S. Brugge, Frequency- modulated pulses of erk activity transmit quantitative proliferation signals, Mol. Cell.49, 249 (2013)

2013
[18]

J.-M. Yang, S. Bhattacharya, H. West-Foyle, C.-F. Hung, T.-C. Wu, P. A. Iglesias, and C.-H. Huang, Integrating chemical and mechanical signals through dynamic cou- pling between cellular protrusions and pulsed erk activa- tion, Nat. Commun.9, 4673 (2018)

2018
[19]

H. Zhan, D. S. Pal, J. Borleis, Y. Deng, Y. Long, C. Janetopoulos, C.-H. Huang, and P. N. Devreotes, Self-organizing glycolytic waves tune cellular metabolic states and fuel cancer progression, Nat. Commun.16, 5563 (2025)

2025
[20]

Sanchez-Vega, M

F. Sanchez-Vega, M. Mina, J. Armenia, W. K. Chatila, A. Luna, K. C. La,et al., Oncogenic signaling pathways in the cancer genome atlas, Cell173, 321 (2018)

2018
[21]

S. J. Watton and J. Downward, Akt/pkb localisation and 3’ phosphoinositide generation at sites of epithelial cell- matrix and cell-cell interaction, Curr. Biol.9, 433 (1999)

1999
[22]

FitzHugh, Impulses and physiological states in the- oretical models of nerve membrane, Biophys

R. FitzHugh, Impulses and physiological states in the- oretical models of nerve membrane, Biophys. J.1, 445 (1961)

1961
[23]

Nagumo, S

J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IEEE50, 2061 (1962)

1962
[24]

Rinzel and J

J. Rinzel and J. B. Keller, Traveling wave solutions of a nerve conduction equation, Biophys. J.13, 1313 (1973)

1973
[25]

Busch and F

H. Busch and F. Kaiser, Influence of spatiotemporally correlated noise on structure formation in excitable me- dia, Phys. Rev. E67, 041105 (2003)

2003
[26]

A. S. Pikovsky and J. Kurths, Coherence resonance in a noise-driven excitable system, Phys. Rev. Lett.78, 775 (1997)

1997
[27]

H¨ anggi and P

P. H¨ anggi and P. Jung, Colored noise in dynamical sys- tems, inAdv. Chem. Phys., Vol. 89 (John Wiley & Sons,
[28]

M. Kærn, T. C. Elston, W. J. Blake, and J. J. Collins, Stochasticity in gene expression: From theories to phe- notypes, Nat. Rev. Genet.6, 451 (2005)

2005
[29]

J. M. Raser and E. K. O’Shea, Noise in gene expression: Origins, consequences, and control, Science309, 2010 (2005)

2005
[30]

Briat and M

C. Briat and M. Khammash, Noise in biomolecular systems: Modeling, analysis, and control implications, Annu. Rev. Control Robot. Auton. Syst.6, 283 (2023)

2023
[31]

Ramaswamy, The mechanics and statistics of active matter, Annu

S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys.1, 323 (2010)

2010
[32]

M. C. Marchetti, J.-F. Joanny, S. Ramaswamy, T. B. 10 Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrody- namics of soft active matter, Rev. Mod. Phys.85, 1143 (2013)

2013
[33]

Elgeti, R

J. Elgeti, R. G. Winkler, and G. Gompper, Physics of microswimmers—single particle motion and collective behavior: A review, Rep. Prog. Phys.78, 056601 (2015)

2015
[34]

M. E. Cates and J. Tailleur, Motility-induced phase sepa- ration, Annu. Rev. Condens. Matter Phys.6, 219 (2015)

2015
[35]

Bechinger, R

C. Bechinger, R. Di Leonardo, H. L¨ owen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys.88, 045006 (2016)

2016
[36]

Martin, J

D. Martin, J. O’Byrne, M. E. Cates, E. Fodor, C. Nar- dini, J. Tailleur, and F. van Wijland, Statistical mechan- ics of active ornstein-uhlenbeck particles, Phys. Rev. E 103, 032607 (2021)

2021
[37]

active matter

M. te Vrugt, B. Liebchen, and M. E. Cates, Colloquium: What do we mean by “active matter”?, Rev. Mod. Phys. 98, 031001 (2026)

2026
[38]

Brugioni, D.-U

S. Brugioni, D.-U. Hwang, R. Meucci, and S. Boccaletti, Coherence resonance in excitable electronic circuits in the presence of colored noise, Phys. Rev. E71, 062101 (2005)

2005
[39]

Brandstetter, M

S. Brandstetter, M. A. Dahlem, and E. Sch¨ oll, Interplay of time-delayed feedback control and temporally corre- lated noise in excitable systems, Philos. Trans. R. Soc. A 368, 391 (2010)

2010
[40]

Gu and B

A. Gu and B. Wang, Asymptotic behavior of random FitzHugh–Nagumo systems driven by colored noise, Dis- crete Contin. Dyn. Syst. - B23, 1689 (2018)

2018
[41]

Beato, I

V. Beato, I. Sendi˜ na-Nadal, I. Gerdes, and H. Engel, Noise-induced wave nucleations in an excitable chemical reaction, Phys. Rev. E71, 035204 (2005)

2005
[42]

A. G. Balanov, V. Beato, N. B. Janson, H. Engel, and E. Sch¨ oll, Delayed feedback control of noise-induced pat- terns in excitable media, Phys. Rev. E74, 016214 (2006)

2006
[43]

Perc, Spatial coherence resonance in excitable media, Phys

M. Perc, Spatial coherence resonance in excitable media, Phys. Rev. E72, 016207 (2005)

2005
[44]

H. Wang, K. Zhang, and Q. Ouyang, Resonant-pattern formation induced by additive noise in periodically forced reaction-diffusion systems, Phys. Rev. E74, 036210 (2006)

2006
[45]

Das and D

D. Das and D. S. Ray, Dichotomous-noise-induced pat- tern formation in a reaction-diffusion system, Phys. Rev. E87, 062924 (2013)

2013
[46]

M. F. Adamer, H. A. Harrington, E. A. Gaffney, and T. E. Woolley, Coloured noise from stochastic inflows in reaction–diffusion systems, Bull. Math. Biol.82, 44 (2020)

2020
[47]

Hecht, D

I. Hecht, D. A. Kessler, and H. Levine, Transient localized patterns in noise-driven reaction-diffusion systems, Phys. Rev. Lett.104, 158301 (2010)

2010
[48]

Hecht, M

I. Hecht, M. L. Skoge, P. G. Charest, E. Ben-Jacob, R. A. Firtel, W. F. Loomis, H. Levine, and W.-J. Rappel, Acti- vated membrane patches guide chemotactic cell motility, PLoS Comput. Biol.7, e1002044 (2011)

2011

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

M. G. Vicker, Reaction–diffusion waves of actin filament polymerization/depolymerization in dictyostelium pseu- dopodium extension and cell locomotion, Biophys. Chem. 84, 87 (2000)

work page 2000

[2] [2]

Gerisch, T

G. Gerisch, T. Bretschneider, A. M¨ uller-Taubenberger, E. Simmeth, M. Ecke, S. Diez, and K. Anderson, Mobile actin clusters and traveling waves in cells recovering from actin depolymerization, Biophys. J.87, 3493 (2004)

work page 2004

[3] [3]

O. D. Weiner, W. A. Marganski, L. F. Wu, S. J. Altschuler, and M. W. Kirschner, An actin-based wave generator organizes cell motility, PLOS Biol.5, 1 (2007)

work page 2007

[4] [4]

Asano, A

Y. Asano, A. Nagasaki, and T. Q. Uyeda, Correlated waves of actin filaments and pip3 in dictyostelium cells, Cell Motil.65, 923 (2008)

work page 2008

[5] [5]

Huang, M

C.-H. Huang, M. Tang, C. Shi, P. A. Iglesias, and P. N. Devreotes, An excitable signal integrator couples to an idling cytoskeletal oscillator to drive cell migration, Nat. Cell Biol.15, 1307 (2013)

work page 2013

[6] [6]

Y. Arai, T. Shibata, S. Matsuoka, M. J. Sato, T. Yanagida, and M. Ueda, Self-organization of the phos- phatidylinositol lipids signaling system for random cell migration, Proc. Natl. Acad. Sci. U.S.A.107, 12399 (2010)

work page 2010

[7] [7]

Allard and A

J. Allard and A. Mogilner, Traveling waves in actin dy- namics and cell motility, Curr. Opin. Cell Biol.25, 107 (2013)

work page 2013

[8] [8]

Taniguchi, S

D. Taniguchi, S. Ishihara, T. Oonuki, M. Honda- Kitahara, K. Kaneko, and S. Sawai, Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells, Proc. Natl. Acad. Sci. U.S.A.110, 5016 (2013)

work page 2013