Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves

[2410.12213] Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences > Pattern Formation and Solitons arXiv:2410.12213 (nlin) [Submitted on 16 Oct 2024 ( v1 ), last revised 5 Nov 2025 (this version, v4)] Title: Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves Authors: Jack M. Hughes , Saar Modai , Leah Edelstein-Keshet , Arik Yochelis View a PDF of the paper titled Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves, by Jack M. Hughes and Saar Modai and Leah Edelstein-Keshet and Arik Yochelis View PDF HTML (experimental) Abstract: Eukaryotic cells demonstrate a wide variety of dynamic patterns of filamentous actin (F-actin) and its regulators. Some of these patterns play important roles in cell functions, such as distinct motility modes, which motivate this study. We devise a mass-conserved reaction-diffusion model for active and inactive Rho-GTPase and F-actin in the cell cortex. The mass-conserved Rho-GTPase system promotes F-actin, which feeds back to inactivate the former. We study the model on a 1D periodic domain (edge of thin sheet-like cell) using bifurcation theory in the framework of spatial dynamics, complemented with numerical simulations. Among several discussed bifurcations, the analysis centers on the study of the codimension-2 long wavelength and finite wavenumber Hopf instability, in which we describe a rich structure of steady wave-pinning states (a.k.a. mesas, obeying the Maxwell construction), propagating coherent solutions (fronts and excitable pulses), and travelling and standing waves, all distinguished by mass conservation regimes and classified by domain sizes. Specifically, we highlight the unexpected conditions for bistability between steady wave-pinning and travelling wave states on moderate domain sizes, i.e., unfolding through domain length. These results uncover and exemplify possible mechanisms of coexistence, robustness, and transitions between distinct cellular motility modes, including directed migration, turning, and ruffling. More broadly, the results indicate that non-gradient reaction-diffusion models comprising mass conservation have distinct pattern formation mechanisms that motivate further investigations, such as the unfolding of codimension-3 instabilities and T-points. Comments: 47 pages, 25 figures Subjects: Pattern Formation and Solitons (nlin.PS) ; Cell Behavior (q-bio.CB) MSC classes: 92C17, 37G15, 37M20, 37N25, 58J55, 35K57 Cite as: arXiv:2410.12213 [nlin.PS] (or arXiv:2410.12213v4 [nlin.PS] for this version) https://doi.org/10.48550/arXiv.2410.12213 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SIAM J. Applied Dynamical Systems, 25(2), pp. 789--835. (2026) Related DOI : https://doi.org/10.1137/25M1737717 Focus to learn more DOI(s) linking to related resources Submission history From: Jack Hughes [ view email ] [v1] Wed, 16 Oct 2024 04:14:37 UTC (5,211 KB) [v2] Thu, 27 Feb 2025 21:29:22 UTC (6,211 KB) [v3] Sun, 14 Sep 2025 05:56:17 UTC (5,555 KB) [v4] Wed, 5 Nov 2025 00:13:29 UTC (6,313 KB) Full-text links: Access Paper: View a PDF of the paper titled Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves, by Jack M. Hughes and Saar Modai and Leah Edelstein-Keshet and Arik Yochelis View PDF HTML (experimental) TeX Source view license Current browse context: nlin.PS < prev | next > new | recent | 2024-10 Change to browse by: nlin q-bio q-bio.CB References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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