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How multiscale curvature couples forces to cellular functions

Nature Reviews Physics volume 6, pages 246–268 (2024)Cite this article

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Abstract

Among the physicochemical cues in the cellular microenvironment that orchestrate cell processes, the different levels of curvature in the extracellular matrix and intrinsic to the tissues play a pivotal role in the spatiotemporal control of key cellular functions. Curvature influences multicellular organization and contributes to the onset of specific human diseases. This Review outlines how physical parameters used to describe the balance of forces in cells and tissues shed light on the mechanism of curvature sensing of cells across different length scales. We provide a summary of progress in delineating the fundamental mechanobiological characteristics of curvature sensing across various scales, emphasizing key challenges in the field. Additionally, we explore the potential of vertex model approaches to uncover critical physical elements involved in the mechanical regulation of curved tissues and the construction of functional architectures at the collective level. Finally, we examine how changes in curvature can influence transcriptional regulation through a reorganization of cytoskeletal forces acting on the nucleus, thereby facilitating the development of specific human diseases.

Key points

  • Cells interact with the curved surfaces of many organs and, at a lower scale, with the rounded features of the extracellular matrix, which inherently links geometric form and biological function.

  • The curvature of the extracellular matrix influences vital cellular processes by defining physical boundary conditions across multiple scales.

  • Multicellular tissues are active materials, and curved patterns in tissues emerge from stress fields generated by intrinsic forces coupled with extrinsic constraints.

  • The regulation of cellular shape and tension by curvatures at various length scales activates specific mechanotransduction pathways that synergistically determine downstream cellular functions.

  • Changes in the balance of cellular forces required to adapt to curved environments can have dramatic consequences, promoting the emergence of various human diseases.

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Fig. 1: Forces acting at the tissue scale.
Fig. 2: Mechanisms of tissue curvature generation and vertex models.
Fig. 3: In-plane curvature at cellular and tissue scales.
Fig. 4: Multiscale out-of-plane curvatures.
Fig. 5: Nuclear curvosensing on concave and convex substrates.

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Acknowledgements

The authors apologize to all authors whose work could not be included owing to space constraints. S.G. acknowledges funding from FEDER Prostem Research Project no. 1510614 (Wallonia DG06), the F.R.S.-FNRS Epiforce Project no. T.0092.21, the F.R.S.-FNRS Cellsqueezer Project no. J.0061.23, the F.R.S.-FNRS Optopattern Project no. U.NO26.22, Programme Wallon d’Investissement Région Wallone pour les instruments d’imagerie (INSTIMAG UMONS #1910169) and the Interreg MAT(T)ISSE project, which is financially supported by Interreg France-Wallonie-Vlaanderen (Fonds Européen de Développement Régional, FEDER-ERDF). M.L. is financially supported by a WBI.World Scholarship Fellowship from the Wallonia-Brussels International (WBI) Excellence Grants Programme. A.R. acknowledges funding from the Swiss National Fund for Research Grants nos 31003A_149975, 31003A_173087 and 31003A_200793, and the European Research Council Synergy Grant no. 951324_R2-TENSION. The authors want to thank the NCCR Chemical Biology for constant support during this project. C.T. acknowledges support from the French National Research Agency, Grant no. ANR-22-CE13-0015-01 for the project ‘CurvEDyn’.

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Authors and Affiliations

  1. Department of Biochemistry, University of Geneva, Geneva, Switzerland

    Marine Luciano & Aurélien Roux

  2. CNRS, INSA Lyon, Ecole Centrale de Lyon, Universite Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Villeurbanne, France

    Caterina Tomba

  3. National Center of Competence in Research in Chemical Biology, University of Geneva, Geneva, Switzerland

    Aurélien Roux

  4. Mechanobiology & Biomaterials Group, Research Institute for Biosciences, CIRMAP, University of Mons, Mons, Belgium

    Sylvain Gabriele

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  1. Marine Luciano
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M.L., C.T., A.R. and S.G. conceptualized the article. Figure designs were generated by all authors and further edited by M.L. and S.G. All authors contributed substantially to the writing, the discussion of the content and approved the final content.

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Glossary

Adherens junction

Component of the cell–cell junction in multicellular organisms in which cadherin receptors bridge neighbouring plasma membranes via their homophilic interactions. Adherens junction provides strong mechanical attachment between neighbouring cells through the linkage of their cytoplasmic face to the actin cytoskeleton.

BAR-domain protein

Highly conserved protein dimerization domains that occur in many proteins involved in membrane dynamics and act as connecting links between actin dynamics and membrane rearrangements in all eukaryotes. BAR domains preferentially bind to curved membrane regions.

Chromatin

Complex of genomic DNA with proteins called histones that forms chromosomes within the nucleus of eukaryotic cells.

Durotaxis

Guidance of cell migration by rigidity gradients, which arise from differential structural properties of the extracellular matrix. Most cells migrate up rigidity gradients (that is, in the direction of greater stiffness) but some cell types have been reported to migrate down rigidity gradients (known as negative durotaxis).

Epithelial tissues

Single-cell monolayers that separate tissues or cavities from their environment.

Filopodia

Slender and finger-like projections that extend from the leading edge of migrating cells. They are filled with bundled actin filaments and are involved in cell migration, cell–cell communication and sensing the environment.

Focal adhesions

Multiprotein site within cells that mechanically interact the extracellular matrix (cell outside) with the actin cytoskeleton (cell inside).

Gene transcription

Process of copying a segment of DNA sequence into an RNA molecule. This process can be divided in three steps: initiation, elongation and termination.

Histone

Family of positively charged proteins that associate with DNA and help condense it into chromatin.

Hypotonic shocks

Refer to an environmental medium that has a lower concentration of solutes than the cytoplasm, inducing a flow of water into the cell and a sudden modification of its osmotic pressure.

Lamellipodia

Thin projection that extends from the leading edge of a migrating cell and contains a quasi-2D actin mesh. These projections on the leading edge are involved in cell migration and exploration of the environment.

Laplace law

The pressure of a bubble with fixed surface tension varies inversely with its radius of curvature.

Manifold

A topological space M for which every point x has a neighbourhood homeomorphic to Euclidean space. In simple terms, it is a mathematical concept describing a space that appears flat similar to ordinary Euclidean space when you zoom in close enough but can have a more complicated overall shape such as a curved shaped.

Mechanosensing

Molecular process through which cells or cellular components translate mechanical forces or deformations into biochemical signals.

Mechanotransduction

Cellular responses to changes in the mechanical environment, including forces, deformations or mechanical properties.

Membrane tension

Local characteristic of the membrane, delineating the stretching–compression elastic stresses at each point along the membrane surface. This involves examining an infinitesimal element of the membrane plane, isolated by an imaginary boundary. Mechanical tension is the force exerted on the unit length of this imaginary boundary by the surrounding membrane, acting tangentially to the membrane plane.

Mesenchymal stem cells (MSCs)

Type of multipotent stromal cell that can differentiate into various cell types, such as osteoblasts (bone cells), chondrocytes (cartilage cells) and adipocytes (fat cells).

Microvilli

Finger-like projections of ~1–2 µm in length that extend from the surface of epithelial cells lining, for instance, the small intestine, kidney tubules and the inner ear. Microvilli are filled with bundled actin filaments and are involved in a wide variety of functions, including absorption, secretion, cellular adhesion and mechanotransduction.

Molecular clutch model

Concept that describes the flexible transmission of forces generated by the flow of actin filaments to adhesion sites, allowing cells to exert a spatially and temporally regulated grip on the substrate. It has a crucial role in the mechanical connection between the actin flow and cell adhesion complexes during cell migration.

Nematic order

Refers to a state of molecular alignment observed in cellular populations such as fibroblasts, akin to the alignment seen in liquid crystals. In this state, molecular entities exhibit a preferred directionality without long-range positional order.

Osmotic pressure

Pressure caused by a difference in the amounts of solutes (or molecules) between solutions (or fluids) separated by a semipermeable membrane.

Second harmonic generation microscopy

A second-order coherent process is employed, up-converting two lower energy photons precisely to twice the incident frequency (half the wavelength) of an excitation laser. This nonlinear imaging technique has proven effective in the specific and sensitive visualization of endogenous extracellular matrix components, such as collagen fibres, across diverse sample types.

Signal transduction

Process by which cells receive, interpret and respond to extracellular forces and signals. This intricate communication system involves the transmission of molecular signals through a series of events, ultimately leading to a cellular response or change in behaviour.

Tessellation

Repeating pattern that covers a 2D surface without overlaps or gaps using one or more geometric shapes, called tiles, with no overlaps and no gaps.

Transcription

Process by which the information in a strand of DNA is copied into a new molecule of messenger RNA.

Vertex models

A class of mathematical models that treat cells as individual objects, represented by polygons in two dimensions and polyhedra in three dimensions. Epithelial tissues are modelled as a connected mesh of these polygons or polyhedral elements, and mechanical forces are applied to the vertices of these geometric structures.

Villus and crypt domains

Two distinct regions of the intestinal epithelium, which play important roles in nutrient uptake and tissue regeneration, respectively. The villus is a finger-like projection lined with absorptive enterocytes, secretory enteroendocrine cells and goblet cells. The crypt is a pocket-like invagination located at the base of the villus that houses the intestinal stem cell niche.

Viscoelasticity

Rheological property of biological tissues and materials that present elastic properties and viscous properties, which allow for timescale-dependent deformation when subjected to mechanical stress.

Yes-associated protein

Yes-associated protein, also known as YAP, is a mechanosensitive transcriptional co-activator protein that associates with several DNA-binding proteins to drive gene transcription. YAP activity is regulated by many kinase cascade pathways and proteins through phosphorylation. Phosphorylated YAP can be sequestered in the cytoplasm and then degraded by the ubiquitin–proteasome system, whereas unphosphorylated YAP translocates to the nucleus, where it performs a series of functions. YAP and its paralogue, transcriptional co-activator with PDZ-binding motif (TAZ), are the major downstream effectors of the Hippo pathway.

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Luciano, M., Tomba, C., Roux, A. et al. How multiscale curvature couples forces to cellular functions. Nat Rev Phys 6, 246–268 (2024). https://doi.org/10.1038/s42254-024-00700-9

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