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Hickey DJ, Golestanian R, Vilfan A. Nonreciprocal interactions give rise to fast cilium synchronization in finite systems. Proc Natl Acad Sci U S A 2023; 120:e2307279120. [PMID: 37756336 PMCID: PMC10556628 DOI: 10.1073/pnas.2307279120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Accepted: 08/14/2023] [Indexed: 09/29/2023] Open
Abstract
Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.
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Affiliation(s)
- David J. Hickey
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
| | - Ramin Golestanian
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OxfordOX1 3PU, United Kingdom
| | - Andrej Vilfan
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, 37077Göttingen, Germany
- Department of Condensed Matter Physics, Jožef Stefan Institute, 1000Ljubljana, Slovenia
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Hickey D, Vilfan A, Golestanian R. Ciliary chemosensitivity is enhanced by cilium geometry and motility. eLife 2021; 10:66322. [PMID: 34346311 DOI: 10.7554/elife.66322] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 08/03/2021] [Indexed: 11/13/2022] Open
Abstract
Cilia are hairlike organelles involved in both sensory functions and motility. We discuss the question of whether the location of chemical receptors on cilia provides an advantage in terms of sensitivity and whether motile sensory cilia have a further advantage. Using a simple advection-diffusion model, we compute the capture rates of diffusive molecules on a cilium. Because of its geometry, a non-motile cilium in a quiescent fluid has a capture rate equivalent to a circular absorbing region with ∼4× its surface area. When the cilium is exposed to an external shear flow, the equivalent surface area increases to ∼6×. Alternatively, if the cilium beats in a non-reciprocal way in an otherwise quiescent fluid, its capture rate increases with the beating frequency to the power of 1/3. Altogether, our results show that the protruding geometry of a cilium could be one of the reasons why so many receptors are located on cilia. They also point to the advantage of combining motility with chemical reception.
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Affiliation(s)
- David Hickey
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen, Germany
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen, Germany.,J. Stefan Institute, Ljubljana, Slovenia
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen, Germany.,Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdom
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R Ferreira R, Fukui H, Chow R, Vilfan A, Vermot J. The cilium as a force sensor-myth versus reality. J Cell Sci 2019; 132:132/14/jcs213496. [PMID: 31363000 DOI: 10.1242/jcs.213496] [Citation(s) in RCA: 49] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Cells need to sense their mechanical environment during the growth of developing tissues and maintenance of adult tissues. The concept of force-sensing mechanisms that act through cell-cell and cell-matrix adhesions is now well established and accepted. Additionally, it is widely believed that force sensing can be mediated through cilia. Yet, this hypothesis is still debated. By using primary cilia sensing as a paradigm, we describe the physical requirements for cilium-mediated mechanical sensing and discuss the different hypotheses of how this could work. We review the different mechanosensitive channels within the cilium, their potential mode of action and their biological implications. In addition, we describe the biological contexts in which cilia are acting - in particular, the left-right organizer - and discuss the challenges to discriminate between cilium-mediated chemosensitivity and mechanosensitivity. Throughout, we provide perspectives on how quantitative analysis and physics-based arguments might help to better understand the biological mechanisms by which cells use cilia to probe their mechanical environment.
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Affiliation(s)
- Rita R Ferreira
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, 67404 Illkirch, France.,Centre National de la Recherche Scientifique, UMR7104, 67404 Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, U1258, 67404 Illkirch, France.,Université de Strasbourg, 67404 Illkirch, France
| | - Hajime Fukui
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, 67404 Illkirch, France.,Centre National de la Recherche Scientifique, UMR7104, 67404 Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, U1258, 67404 Illkirch, France.,Université de Strasbourg, 67404 Illkirch, France
| | - Renee Chow
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, 67404 Illkirch, France.,Centre National de la Recherche Scientifique, UMR7104, 67404 Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, U1258, 67404 Illkirch, France.,Université de Strasbourg, 67404 Illkirch, France
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Department of Living Matter Physics, 37077 Göttingen, Germany .,J. Stefan Institute, 1000 Ljubljana, Slovenia
| | - Julien Vermot
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, 67404 Illkirch, France .,Centre National de la Recherche Scientifique, UMR7104, 67404 Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, U1258, 67404 Illkirch, France.,Université de Strasbourg, 67404 Illkirch, France
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Ferreira RR, Vilfan A, Jülicher F, Supatto W, Vermot J. Physical limits of flow sensing in the left-right organizer. eLife 2017; 6. [PMID: 28613157 PMCID: PMC5544429 DOI: 10.7554/elife.25078] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2017] [Accepted: 06/13/2017] [Indexed: 12/20/2022] Open
Abstract
Fluid flows generated by motile cilia are guiding the establishment of the left-right asymmetry of the body in the vertebrate left-right organizer. Competing hypotheses have been proposed: the direction of flow is sensed either through mechanosensation, or via the detection of chemical signals transported in the flow. We investigated the physical limits of flow detection to clarify which mechanisms could be reliably used for symmetry breaking. We integrated parameters describing cilia distribution and orientation obtained in vivo in zebrafish into a multiscale physical study of flow generation and detection. Our results show that the number of immotile cilia is too small to ensure robust left and right determination by mechanosensing, given the large spatial variability of the flow. However, motile cilia could sense their own motion by a yet unknown mechanism. Finally, transport of chemical signals by the flow can provide a simple and reliable mechanism of asymmetry establishment. DOI:http://dx.doi.org/10.7554/eLife.25078.001
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Affiliation(s)
- Rita R Ferreira
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, Illkirch, France.,Centre National de la Recherche Scientifique, Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, Illkirch, France.,Université de Strasbourg, Illkirch, France
| | | | - Frank Jülicher
- Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany
| | - Willy Supatto
- Laboratory for Optics and Biosciences, Ecole Polytechnique, Centre National de la Recherche Scientifique (UMR7645), Institut National de la Santé et de la Recherche Médicale (U1182) and Paris Saclay University, Palaiseau, France
| | - Julien Vermot
- Institut de Génétique et de Biologie Moléculaire et Cellulaire, Illkirch, France.,Centre National de la Recherche Scientifique, Illkirch, France.,Institut National de la Santé et de la Recherche Médicale, Illkirch, France.,Université de Strasbourg, Illkirch, France
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Brumley DR, Polin M, Pedley TJ, Goldstein RE. Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin. J R Soc Interface 2016; 12:20141358. [PMID: 26040592 PMCID: PMC4528573 DOI: 10.1098/rsif.2014.1358] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour—possibly influenced by both mechanical interactions and direct biological regulation—is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.
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Affiliation(s)
- Douglas R Brumley
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Marco Polin
- Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
| | - Timothy J Pedley
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
| | - Raymond E Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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Golestanian R, Ramaswamy S. Active matter. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:67. [PMID: 23807470 DOI: 10.1140/epje/i2013-13067-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2013] [Accepted: 06/04/2013] [Indexed: 06/02/2023]
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