On the generation of force required for actin-based motility

doi:10.1038/s41598-024-69422-3

. 2024 Aug 8;14(1):18384.

doi: 10.1038/s41598-024-69422-3.

On the generation of force required for actin-based motility

Alberto Salvadori^{1

2}, Claudia Bonanno³, Mattia Serpelloni^{3

4}, Robert M McMeeking^{3

5

6

7}

Affiliations

¹ The Mechanobiology Research Center, UNIBS, 25123, Brescia, Italy. alberto.salvadori@unibs.it.
² Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123, Brescia, Italy. alberto.salvadori@unibs.it.
³ The Mechanobiology Research Center, UNIBS, 25123, Brescia, Italy.
⁴ Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123, Brescia, Italy.
⁵ Materials and Mechanical Engineering Departments, University of California, Santa Barbara, CA, 93106, USA.
⁶ School of Engineering, University of Aberdeen, King's College, Aberdeen, AB24 3UE, UK.
⁷ INM - Leibniz Institute for New Materials, Campus D2 2, Saarbruecken, Germany.

PMID: 39117762
PMCID: PMC11310465
DOI: 10.1038/s41598-024-69422-3

On the generation of force required for actin-based motility

Alberto Salvadori et al. Sci Rep. 2024.

. 2024 Aug 8;14(1):18384.

doi: 10.1038/s41598-024-69422-3.

Authors

Alberto Salvadori^{1

2}, Claudia Bonanno³, Mattia Serpelloni^{3

4}, Robert M McMeeking^{3

5

6

7}

Affiliations

¹ The Mechanobiology Research Center, UNIBS, 25123, Brescia, Italy. alberto.salvadori@unibs.it.
² Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123, Brescia, Italy. alberto.salvadori@unibs.it.
³ The Mechanobiology Research Center, UNIBS, 25123, Brescia, Italy.
⁴ Department of Mechanical and Industrial Engineering, Università degli Studi di Brescia, via Branze 38, 25123, Brescia, Italy.
⁵ Materials and Mechanical Engineering Departments, University of California, Santa Barbara, CA, 93106, USA.
⁶ School of Engineering, University of Aberdeen, King's College, Aberdeen, AB24 3UE, UK.
⁷ INM - Leibniz Institute for New Materials, Campus D2 2, Saarbruecken, Germany.

PMID: 39117762
PMCID: PMC11310465
DOI: 10.1038/s41598-024-69422-3

Abstract

The fundamental question of how forces are generated in a motile cell, a lamellipodium, and a comet tail is the subject of this note. It is now well established that cellular motility results from the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone around the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed, departing from the well-known theory of Larché-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.

Keywords: Actin-based motility; Chemo-transport-mechanics; Continuum mechanics; Finite elements; High performance computing.

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Conflict of interest statement

The authors declare no competing interests.

Figures

**Figure 1**
A 3D picture of the molecular components required for actin-based motility of Listeria monocytogenes.

**Figure 2**
Schematic representation of volume increment and protrusion upon the structural arrangement of monomers after polymerization of the dense actin filament network in lamellipodia (brown). The sparser actin network in the lamella is represented in purple. Scale bar, 1 $μ$ m. Inspired by.

**Figure 3**
Transient evolution of $c_{F}$ in time for different values of $Ω_{f}$ and $k_{f}^{*}$ , at $c_{G}^{0} = 2.42$ moles $m^{- 3}$ .

**Figure 4**
Simulation of the actin comet tail (colored) in Listeria monocytogenes (gray). (a) Mises stress; (b) actin concentration evolution in time at point A. In the simulations, the influence lengthscale of the signal is taken as $ℓ = 1.00 μ m$ .

**Figure 5**
(a) Transient evolution of $c_{F}$ in time, for $Ω_{F} = 0.25$ $m^{3}$ ${moles}^{- 1}$ , $k_{f}^{*} = 0.05$ $s^{- 1}$ , and $c_{G}^{0} = 2.42$ moles $m^{- 3}$ ; (b) Evolution of the network velocity in time, for $Ω_{F} = 0.25$ $m^{3}$ ${moles}^{- 1}$ , $k_{f}^{*} = 0.05$ $s^{- 1}$ , and $c_{G}^{0} = 2.42$ moles $m^{- 3}$ . After an initial rapid development, the velocity is in agreement with the data, highlighted by the shaded strip. Data reported in correspond to the violet band ( $85 \pm 68 nm / \min$ ).

See this image and copyright information in PMC

References

1. Borisy, G. G. & Svitkina, T. M. Actin machinery: Pushing the envelope. Curr. Opin. Cell Biol.12(1), 104–112 (2000). 10.1016/S0955-0674(99)00063-0 - DOI - PubMed
1. Pantaloni, D., Le Clainche, C. & Carlier, M.-F. Mechanism of actin-based motility. Science292(5521), 1502–1506 (2001). 10.1126/science.1059975 - DOI - PubMed
1. Blanchoin, L., Boujemaa-Paterski, R., Sykes, C. & Plastino, J. Actin dynamics, architecture, and mechanics in cell motility. Physiol. Rev.94(1), 235–263 (2014). 10.1152/physrev.00018.2013 - DOI - PubMed
1. Marston, D. J. & Goldstein, B. Actin-based forces driving embryonic morphogenesis in caenorhabditis elegans. Curr. Opin. Genet. Dev.16(4), 392–398 (2006). 10.1016/j.gde.2006.06.002 - DOI - PubMed
1. Barrasa-Ramos, S., Dessalles, C., Hautefeuille, M. & Barakat A. Mechanical regulation of the early stages of angiogenesis. J. R. Soc. Interface19(20220360) (2022). - PMC - PubMed

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[1] Borisy, G. G. & Svitkina, T. M. Actin machinery: Pushing the envelope. Curr. Opin. Cell Biol.12(1), 104–112 (2000). 10.1016/S0955-0674(99)00063-0 - DOI - PubMed

[2] Borisy, G. G. & Svitkina, T. M. Actin machinery: Pushing the envelope. Curr. Opin. Cell Biol.12(1), 104–112 (2000). 10.1016/S0955-0674(99)00063-0 - DOI - PubMed

[3] Pantaloni, D., Le Clainche, C. & Carlier, M.-F. Mechanism of actin-based motility. Science292(5521), 1502–1506 (2001). 10.1126/science.1059975 - DOI - PubMed

[4] Pantaloni, D., Le Clainche, C. & Carlier, M.-F. Mechanism of actin-based motility. Science292(5521), 1502–1506 (2001). 10.1126/science.1059975 - DOI - PubMed

[5] Blanchoin, L., Boujemaa-Paterski, R., Sykes, C. & Plastino, J. Actin dynamics, architecture, and mechanics in cell motility. Physiol. Rev.94(1), 235–263 (2014). 10.1152/physrev.00018.2013 - DOI - PubMed

[6] Blanchoin, L., Boujemaa-Paterski, R., Sykes, C. & Plastino, J. Actin dynamics, architecture, and mechanics in cell motility. Physiol. Rev.94(1), 235–263 (2014). 10.1152/physrev.00018.2013 - DOI - PubMed

[7] Marston, D. J. & Goldstein, B. Actin-based forces driving embryonic morphogenesis in caenorhabditis elegans. Curr. Opin. Genet. Dev.16(4), 392–398 (2006). 10.1016/j.gde.2006.06.002 - DOI - PubMed

[8] Marston, D. J. & Goldstein, B. Actin-based forces driving embryonic morphogenesis in caenorhabditis elegans. Curr. Opin. Genet. Dev.16(4), 392–398 (2006). 10.1016/j.gde.2006.06.002 - DOI - PubMed

[9] Barrasa-Ramos, S., Dessalles, C., Hautefeuille, M. & Barakat A. Mechanical regulation of the early stages of angiogenesis. J. R. Soc. Interface19(20220360) (2022). - PMC - PubMed

[10] Barrasa-Ramos, S., Dessalles, C., Hautefeuille, M. & Barakat A. Mechanical regulation of the early stages of angiogenesis. J. R. Soc. Interface19(20220360) (2022). - PMC - PubMed

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On the generation of force required for actin-based motility

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On the generation of force required for actin-based motility

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