Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays

Chelakkot, Raghunath; Hagan, Michael F.; Gopinath, Arvind

doi:10.1039/d0sm01162b

Cited by 22 publications

(11 citation statements)

References 63 publications

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“…When the vinegar eels are engaged in metachronal waves, the organisms are often touching each other. Chelakkot et al [21] simulated steric interactions between active and elastic filaments in arrays and found that short-ranged steric inter-filament interactions can account for formation of collective patterns such as metachronal waves. Because undulation frequency of C. elegans is slower when under mechanical load imposed by the environment, we assume that steric interactions in our vinegar eels reduce the phase velocity of oscillation.…”

Section: Oscillator Models For Traveling Wavesmentioning

confidence: 99%

“…One approach to modeling metachronal wave formation in cilia or flagella is to model them as flexible filaments that os-cillate or beat when alone. Self-organized metachronal waves then arise due to hydrodynamic [8,11,13,14,[17][18][19][20] or steric [21] interactions between neighboring filaments. Even though a filament can bend and flex, its behavior can approximately be described with an angle or phase which specifies the position of its moving tip (e.g., [13,14]).…”

Section: Introductionmentioning

confidence: 99%

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Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

Quillen,

Peshkov,

Wright

et al. 2021

Preprint

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At high concentration, free swimming nematodes known as vinegar eels (Tubatrix aceti), collectively exhibit metachronal waves near a boundary. We find that the frequency of the collective traveling wave is lower than that of the freely swimming organisms. We explore models based on a chain of oscillators with nearest neighbor interactions that inhibit oscillator phase velocity. The phase of each oscillator represents the phase of the motion of the eel's head back and forth about its mean position. A strongly interacting directed chain model mimicking steric interactions between organisms robustly gives traveling wave states and can approximately match the observed wavelength and oscillation frequency of the observed traveling wave. We predict body shapes assuming that waves propagate down the eel body at a constant speed. The phase oscillator model that impedes eel head overlaps also reduces close interactions throughout the eel bodies.

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Section: Oscillator Models For Traveling Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

Quillen,

Peshkov,

Wright

et al. 2021

Preprint

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“…Such structures have also been studied in simulation in the context of active dipolar particles representing autophoretic colloids [29,30], as well as swimming microorganisms [31] such as magnetotactic bacteria [32]. In related theoretical studies, constrained or bundled chains of self-propelling colloidal particles [33][34][35][36] have also been shown to exhibit collective instabilities. Elasticity mediated interactions are seen to play critical roles, with the competition between mechanical interactions, steric interactions and activity determining the eventual dynam-ical behavior.…”

Section: Introductionmentioning

confidence: 99%

Collective states of active particles with elastic dipolar interactions

Bose¹,

Noerr²,

Gopinathan³

et al. 2022

Preprint

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Many types of mammalian cells exert active contractile forces and mechanically deform their elastic substrate, to accomplish biological functions such as cell migration. These substrate deformations provide a mechanism by which cells can sense other cells, leading to long-range mechanical inter-cell interactions and possible self-organization. Here, we treat cells as noisy motile particles that exert contractile dipolar stresses on elastic substrates as they move. By combining this minimal model for the motility of individual cells with a linear elastic model that accounts for substrate-mediated cellcell interactions, we examine emergent collective states that result from the interplay of cell motility and long-range elastic dipolar interactions. In particular, we show that particles self-assemble into flexible, motile chains which can cluster to form diverse larger-scale compact structures with polar order. By computing key structural and dynamical metrics, we distinguish between the collective states at weak and strong elastic interactions, as well as at low and high motility. We also show how these states are affected by confinement -an important characteristic of the complex mechanical micro-environment inhabited by cells. Our model predictions are generally applicable to active matter with dipolar interactions ranging from biological cells to synthetic colloids endowed with electric or magnetic dipole moments.

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“…While the appearance of MWs across various systems is extremely robust, the microscopic physics and interactions that result in their emergence are not fully understood ( 11 ). Plausible physical mechanisms include mechanical coupling through the anchoring membrane ( 12 ), local steric interactions within dense arrays ( 13 ), and large-scale fluid motion that induces long-range coupling among cilia ( 14 ). Many models coarse grain the internal mechanics and the fluid–structure interactions by approximating cilia as spheres driven on compliant orbits ( 6 , 15 – 22 ).…”

mentioning

confidence: 99%

A multiscale biophysical model gives quantized metachronal waves in a lattice of beating cilia

Chakrabarti

Fürthauer

Shelley

2022

Proc. Natl. Acad. Sci. U.S.A.

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Motile cilia are slender, hair-like cellular appendages that spontaneously oscillate under the action of internal molecular motors and are typically found in dense arrays. These active filaments coordinate their beating to generate metachronal waves that drive long-range fluid transport and locomotion. Until now, our understanding of their collective behavior largely comes from the study of minimal models that coarse grain the relevant biophysics and the hydrodynamics of slender structures. Here we build on a detailed biophysical model to elucidate the emergence of metachronal waves on millimeter scales from nanometer-scale motor activity inside individual cilia. Our study of a one-dimensional lattice of cilia in the presence of hydrodynamic and steric interactions reveals how metachronal waves are formed and maintained. We find that, in homogeneous beds of cilia, these interactions lead to multiple attracting states, all of which are characterized by an integer charge that is conserved. This even allows us to design initial conditions that lead to predictable emergent states. Finally, and very importantly, we show that, in nonuniform ciliary tissues, boundaries and inhomogeneities provide a robust route to metachronal waves.

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Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays

Abstract: Autonomous active, elastic filaments that interact with each other to achieve cooperation and synchrony underlie many critical functions in biology. The mechanisms underlying this collective response and the essential ingredients...

Cited by 22 publications

References 63 publications

Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions

Collective states of active particles with elastic dipolar interactions

A multiscale biophysical model gives quantized metachronal waves in a lattice of beating cilia

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