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Perez Ipiña E, d’Alessandro J, Ladoux B, Camley BA. Deposited footprints let cells switch between confined, oscillatory, and exploratory migration. Proc Natl Acad Sci U S A 2024; 121:e2318248121. [PMID: 38787878 PMCID: PMC11145245 DOI: 10.1073/pnas.2318248121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Accepted: 04/08/2024] [Indexed: 05/26/2024] Open
Abstract
For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.
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Affiliation(s)
- Emiliano Perez Ipiña
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD21218
| | | | - Benoît Ladoux
- Université Paris Cité, CNRS, Institut Jacques Monod, F-75013Paris, France
| | - Brian A. Camley
- William H. Miller III Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD21218
- Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD21218
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Perez Ipiña E, D'Alessandro J, Ladoux B, Camley BA. Deposited footprints let cells switch between confined, oscillatory, and exploratory migration. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.09.14.557437. [PMID: 37745526 PMCID: PMC10515912 DOI: 10.1101/2023.09.14.557437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2023]
Abstract
For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix. Cells may also deposit extracellular matrix components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cells on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.
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Albers T, Delnoij S, Schramma N, Jalaal M. Billiards with Spatial Memory. PHYSICAL REVIEW LETTERS 2024; 132:157101. [PMID: 38682997 DOI: 10.1103/physrevlett.132.157101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2024] [Accepted: 03/20/2024] [Indexed: 05/01/2024]
Abstract
Many classes of active matter develop spatial memory by encoding information in space. We present a framework based on mathematical billiards, wherein particles remember their past trajectories. Despite its deterministic rules, such a system is strongly nonergodic and exhibits intermittent statistics and complex pattern formation. We show how these features emerge from the dynamic change of topology. Our work illustrates how the dynamics of a single-body system can dramatically change with spatial memory, laying the groundwork to further explore systems with complex memory kernels.
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Affiliation(s)
- Thijs Albers
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Stijn Delnoij
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Nico Schramma
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Maziyar Jalaal
- Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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Chen Y, Chong KL, Liu H, Verzicco R, Lohse D. Buoyancy-driven attraction of active droplets. JOURNAL OF FLUID MECHANICS 2024; 980:jfm.2024.18. [PMID: 38361591 PMCID: PMC7615645 DOI: 10.1017/jfm.2024.18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
For dissolving active oil droplets in an ambient liquid, it is generally assumed that the Marangoni effect results in repulsive interactions, while the buoyancy effects caused by the density difference between the droplets, diffusing product and the ambient fluid are usually neglected. However, it has been observed in recent experiments that active droplets can form clusters due to buoyancy-driven convection (Krüger et al. Eur. Phys. J. E, vol. 39, 2016, pp. 1-9). In this study, we numerically analyze the buoyancy effect, in addition to the propulsion caused by Marangoni flow (with its strength characterized by Péclet number Pe). The buoyancy effects have their origin in (i) the density difference between the droplet and the ambient liquid, which is characterized by Galileo number Ga, and (ii) the density difference between the diffusing product (i.e. filled micelles) and the ambient liquid, which can be quantified by a solutal Rayleigh number Ra. We analyze how the attracting and repulsing behaviour of neighbouring droplets depends on the control parameters Pe, Ga, and Ra. We find that while the Marangoni effect leads to the well-known repulsion between the interacting droplets, the buoyancy effect of the reaction product leads to buoyancy-driven attraction. At sufficiently large Ra, even collisions between the droplets can take place. Our study on the effect of Ga further shows that with increasing Ga, the collision becomes delayed. Moreover, we derive that the attracting velocity of the droplets, which is characterized by a Reynolds number Red, is proportional to Ra1/4/(ℓ/R), where ℓ/R is the distance between the neighbouring droplets normalized by the droplet radius. Finally, we numerically obtain the repulsive velocity of the droplets, characterized by a Reynolds number Rerep, which is proportional to PeRa-0.38. The balance of attractive and repulsive effect leads to Pe ~ Ra0.63, which agrees well with the transition curve between the regimes with and without collision.
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Affiliation(s)
- Yibo Chen
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Kai Leong Chong
- Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, PR China
| | - Haoran Liu
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Roberto Verzicco
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
- Gran Sasso Science Institute - Viale F. Crispi, 7 67100 L’Aquila, Italy
| | - Detlef Lohse
- Physics of Fluids Group, Max Planck Center for Complex Fluid Dynamics and J.M.Burgers Center for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Max Planck Institute for Dynamics and Self-Organisation, Am Fassberg 17, 37077 Göttingen, Germany
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Feng K, Ureña Marcos JC, Mukhopadhyay AK, Niu R, Zhao Q, Qu J, Liebchen B. Self-Solidifying Active Droplets Showing Memory-Induced Chirality. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2300866. [PMID: 37526332 PMCID: PMC10520641 DOI: 10.1002/advs.202300866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 05/20/2023] [Indexed: 08/02/2023]
Abstract
Most synthetic microswimmers do not reach the autonomy of their biological counterparts in terms of energy supply and diversity of motions. Here, this work reports the first all-aqueous droplet swimmer powered by self-generated polyelectrolyte gradients, which shows memory-induced chirality while self-solidifying. An aqueous solution of surface tension-lowering polyelectrolytes self-solidifies on the surface of acidic water, during which polyelectrolytes are gradually emitted into the surrounding water and induce linear self-propulsion via spontaneous symmetry breaking. The low diffusion coefficient of the polyelectrolytes leads to long-lived chemical trails which cause memory effects that drive a transition from linear to chiral motion without requiring any imposed symmetry breaking. The droplet swimmer is capable of highly efficient removal (up to 85%) of uranium from aqueous solutions within 90 min, benefiting from self-propulsion and flow-induced mixing. These results provide a route to fueling self-propelled agents which can autonomously perform chiral motion and collect toxins.
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Affiliation(s)
- Kai Feng
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | | | - Aritra K. Mukhopadhyay
- Institut für Physik Kondensierter MaterieTechnische Universität Darmstadt64289DarmstadtGermany
| | - Ran Niu
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Qiang Zhao
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Jinping Qu
- Key Laboratory of Material Chemistry for Energy Conversion and StorageMinistry of EducationSchool of Chemistry and Chemical EngineeringHuazhong University of Science and TechnologyWuhan430074China
| | - Benno Liebchen
- Institut für Physik Kondensierter MaterieTechnische Universität Darmstadt64289DarmstadtGermany
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Abstract
The out-of-equilibrium dynamics of chemotactic active matter—be it animate or inanimate—is closely coupled to the environment, a chemical landscape shaped by secretions from the motile agents, fuel uptake, or autochemotactic signaling. This gives rise to complex collective effects, which can be exploited by the agents for colony migration strategies or pattern formation. We study such effects using an idealized experimental system: self-propelled microdroplets that communicate via chemorepulsive trails. We present a comprehensive experimental analysis that involves direct probing of the diffusing chemical trails and the trail–droplet interactions and use it to construct a generic theoretical model. We connect these repulsive autochemotactic interactions to the collective dynamics in emulsions, demonstrating a state of dynamical arrest: chemotactic self-caging. A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent–trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other’s trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.
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