A minimal physical model for curvotaxis driven by curved protein complexes at the cells leading edge

Kumar Sadhu, Raj (author), Luciano, Marine (author), Xi, Wang (author), Martinez-Torres, Cristina (author), Schröder, Marcel (author), Blum, Christoph (author), Tarantola, Marco (author), Villa, Stefano (author), Penič, Samo (author), Iglič, Aleš (author), Beta, Carsten (author), Steinbock, Oliver (author), Bodenschatz, Eberhard (author), Ladoux, Benoît (author), Gabriele, Sylvain (author), Gov, Nir S. (author)

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed “curvotaxis.” The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a “minimal cell” model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

• Language: English
• Keywords: cell motility, curved, proteins, computer simulations, Monte Carlo method
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 1-12
• Numbering: Vol. 121, no. 12, [article no.] e2306818121
• PID: 20.500.12556/RUL-173643
• UDC: 577
• ISSN on article: 1091-6490
• DOI: 10.1073/pnas.2306818121
• COBISS.SI-ID: 191263747
• Publication date in RUL: 19.09.2025

Record is a part of a journal

• Title: Proceedings of the National Academy of Sciences of the United States of America
• Shortened title: Proc Natl Acad USA
• Publisher: National Academy of Sciences
• ISSN: 1091-6490
• COBISS.SI-ID: 2318612

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: mobilnost celice, ukrivljeni proteini, računalniške simulacije, metoda Monte Carlo