1
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Liu Z, Chao Y, Zheng Z, Zhu L. Spontaneous oscillation of an active filament under viscosity gradients. SOFT MATTER 2024; 20:3845-3853. [PMID: 38651457 DOI: 10.1039/d4sm00095a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We investigate the effects of uniform viscosity gradients on the spontaneous oscillations of an elastic, active filament in viscous fluids. Combining numerical simulations and linear stability analysis, we demonstrate that a viscosity gradient increasing from the filament's base to tip destabilises the system, facilitating its self-oscillation. This effect is elucidated through a reduced-order model, highlighting the delicate balance between destabilising active forces and stabilising viscous forces. Additionally, we reveal that while a perpendicular viscosity gradient to the filament's orientation minimally affects instability, it induces asymmetric ciliary beating, thus generating a net flow along the gradient. Our findings offer new insights into the complex behaviours of biological and artificial filaments in complex fluid environments, contributing to the broader understanding of filament dynamics in heterogeneous viscous media.
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Affiliation(s)
- Zhaorong Liu
- Department of Mechanical Engineering, National University of Singapore, 117575, Singapore.
| | - Youchuang Chao
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China
| | - Zhijun Zheng
- CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China
| | - Lailai Zhu
- Department of Mechanical Engineering, National University of Singapore, 117575, Singapore.
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2
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Link KG, Guy RD, Thomases B, Arratia PE. Effect of fluid elasticity on the emergence of oscillations in an active elastic filament. J R Soc Interface 2024; 21:20240046. [PMID: 38774961 DOI: 10.1098/rsif.2024.0046] [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: 06/02/2023] [Accepted: 03/20/2024] [Indexed: 07/31/2024] Open
Abstract
Many microorganisms propel themselves through complex media by deforming their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, the passive elastic response from deformations of the flagellum and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there are limited data on how systematic changes in elasticity alter the beat. This work analyses a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip of a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in the bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number and thus provides a possible mechanistic understanding of the experimental observations.
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Affiliation(s)
- Kathryn G Link
- Department of Mathematics, University of California , Davis, CA 95616, USA
| | - Robert D Guy
- Department of Mathematics, University of California , Davis, CA 95616, USA
| | - Becca Thomases
- Department of Mathematical Sciences, Smith College , Northampton, MA 01063, USA
| | - Paulo E Arratia
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania , Philadelphia, PA 19104, USA
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3
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Moradi M, Shklyaev OE, Balazs AC. Integrating chemistry, fluid flow, and mechanics to drive spontaneous formation of three-dimensional (3D) patterns in anchored microstructures. Proc Natl Acad Sci U S A 2024; 121:e2319777121. [PMID: 38437554 PMCID: PMC10945754 DOI: 10.1073/pnas.2319777121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Accepted: 01/17/2024] [Indexed: 03/06/2024] Open
Abstract
Enzymatic reactions in solution drive the convection of confined fluids throughout the enclosing chambers and thereby couple the processes of reaction and convection. In these systems, the energy released from the chemical reactions generates a force, which propels the fluids' spontaneous motion. Here, we use theoretical and computational modeling to determine how reaction-convection can be harnessed to tailor and control the dynamic behavior of soft matter immersed in solution. Our model system encompasses an array of surface-anchored, flexible posts in a millimeter-sized, fluid-filled chamber. Selected posts are coated with enzymes, which react with dissolved chemicals to produce buoyancy-driven fluid flows. We show that these chemically generated flows exert a force on both the coated (active) and passive posts and thus produce regular, self-organized patterns. Due to the specificity of enzymatic reactions, the posts display controllable kaleidoscopic behavior where one regular pattern is smoothly morphed into another with the addition of certain reactants. These spatiotemporal patterns also form "fingerprints" that distinctly characterize the system, reflecting the type of enzymes used, placement of the enzyme-coated posts, height of the chamber, and bending modulus of the elastic posts. The results reveal how reaction-convection provides concepts for designing soft matter that readily switches among multiple morphologies. This behavior enables microfluidic devices to be spontaneously reconfigured for specific applications without construction of new chambers and the fabrication of standalone sensors that operate without extraneous power sources.
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Affiliation(s)
- Moslem Moradi
- Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, PA15261
| | - Oleg E. Shklyaev
- Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, PA15261
| | - Anna C. Balazs
- Department of Chemical Engineering, University of Pittsburgh, Pittsburgh, PA15261
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4
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Wan KY. Active oscillations in microscale navigation. Anim Cogn 2023; 26:1837-1850. [PMID: 37665482 PMCID: PMC10769930 DOI: 10.1007/s10071-023-01819-5] [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: 05/22/2023] [Revised: 07/27/2023] [Accepted: 08/12/2023] [Indexed: 09/05/2023]
Abstract
Living organisms routinely navigate their surroundings in search of better conditions, more food, or to avoid predators. Typically, animals do so by integrating sensory cues from the environment with their locomotor apparatuses. For single cells or small organisms that possess motility, fundamental physical constraints imposed by their small size have led to alternative navigation strategies that are specific to the microscopic world. Intriguingly, underlying these myriad exploratory behaviours or sensory functions is the onset of periodic activity at multiple scales, such as the undulations of cilia and flagella, the vibrations of hair cells, or the oscillatory shape modes of migrating neutrophils. Here, I explore oscillatory dynamics in basal microeukaryotes and hypothesize that these active oscillations play a critical role in enhancing the fidelity of adaptive sensorimotor integration.
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Affiliation(s)
- Kirsty Y Wan
- Living Systems Institute, University of Exeter, Stocker Road, Exeter, EX4 4QD, UK.
- Department of Mathematics and Statistics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK.
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5
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Lough W, Weibel DB, Spagnolie SE. Self-buckling and self-writhing of semi-flexible microorganisms. SOFT MATTER 2023; 19:7349-7357. [PMID: 37740382 DOI: 10.1039/d3sm00572k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
The twisting and writhing of a cell body and associated mechanical stresses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a flagellar orientation field, we derive the Euler-Poincaré equations governing the dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium Proteus mirabilis. A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. These studies highlight a practical requirement for the stiffness of bacteria below which self-buckling occurs and cell motility becomes ineffective.
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Affiliation(s)
- Wilson Lough
- Department of Physics, University of Wisconsin-Madison, Madison, WI 53706, USA.
| | - Douglas B Weibel
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Saverio E Spagnolie
- Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, WI 53706, USA
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
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6
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Krishnamurthy D, Prakash M. Emergent programmable behavior and chaos in dynamically driven active filaments. Proc Natl Acad Sci U S A 2023; 120:e2304981120. [PMID: 37406100 PMCID: PMC10334789 DOI: 10.1073/pnas.2304981120] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 05/16/2023] [Indexed: 07/07/2023] Open
Abstract
How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.
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Affiliation(s)
| | - Manu Prakash
- Department of Bioengineering, Stanford University, Stanford, CA94305
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7
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Wang C, Zhou Y, Yang X, Chen Y, Shen Y, Luo M. Conformation and dynamics of a tethered active polymer chain. Phys Rev E 2022; 106:054501. [PMID: 36559343 DOI: 10.1103/physreve.106.054501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2022] [Accepted: 10/13/2022] [Indexed: 11/05/2022]
Abstract
The conformational and dynamical properties of a tethered semiflexible polymer chain under tangential active force (f_{a}) are studied by using the Langevin dynamics simulation method. The head of the polymer is fixed near an infinite flat surface at z=0. The polymer is equilibrated first at f_{a}=0 and then subjected to the active force. Under the influence of the active force, the polymer is gradually compressed. Specially, for large f_{a} and large bending rigidity (k_{b}), the polymer is buckled into a quasihelical structure rotating around the z axis at the steady state. It is found that both the radius of the quasihelical structure (R) and the angular velocity of the rotation (ω) are nearly independent of the polymer length (N), but show scaling relations with f_{a} and k_{b}, i.e., R∝f_{a}^{-1/3}k_{b}^{1/3} and ω∝f_{a}^{4/3}k_{b}^{-1/3}, which are explained by simple dynamical models. Before reaching the steady state, it is further found that the buckling velocity of the polymer is proportional to f_{a} but roughly independent of k_{b} and N, then the buckling time (t_{b}) can be described by a scaling relation t_{b}∝Nf_{a}^{-1}. The underlying mechanism of the buckling process is revealed.
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Affiliation(s)
- Chao Wang
- Department of Physics, Taizhou University, Taizhou 318000, Zhejiang, China
| | - Yanli Zhou
- Department of Physics, Taizhou University, Taizhou 318000, Zhejiang, China
| | - Xiao Yang
- Department of Physics, Taizhou University, Taizhou 318000, Zhejiang, China
| | - Yingcai Chen
- Department of Physics, Taizhou University, Taizhou 318000, Zhejiang, China
| | - Yifan Shen
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China
| | - Mengbo Luo
- Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang, China
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8
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Woodhams LG, Shen Y, Bayly PV. Generation of ciliary beating by steady dynein activity: the effects of inter-filament coupling in multi-filament models. J R Soc Interface 2022; 19:20220264. [PMID: 35857924 PMCID: PMC9257587 DOI: 10.1098/rsif.2022.0264] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2022] [Accepted: 06/20/2022] [Indexed: 09/05/2023] Open
Abstract
The structure of the axoneme in motile cilia and flagella is emerging with increasing detail from high-resolution imaging, but the mechanism by which the axoneme creates oscillatory, propulsive motion remains mysterious. It has recently been proposed that this motion may be caused by a dynamic 'flutter' instability that can occur under steady dynein loading, and not by switching or modulation of dynein motor activity (as commonly assumed). In the current work, we have built an improved multi-filament mathematical model of the axoneme and implemented it as a system of discrete equations using the finite-element method. The eigenvalues and eigenvectors of this model predict the emergence of oscillatory, wave-like solutions in the absence of dynein regulation and specify the associated frequencies and waveforms of beating. Time-domain simulations with this model illustrate the behaviour predicted by the system's eigenvalues. This model and analysis allow us to efficiently explore the potential effects of difficult to measure biophysical parameters, such as elasticity of radial spokes and inter-doublet links, on the ciliary waveform. These results support the idea that dynamic instability without dynamic dynein regulation is a plausible and robust mechanism for generating ciliary beating.
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Affiliation(s)
- Louis G. Woodhams
- Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130-4899, USA
| | - Yenan Shen
- Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
| | - Philip V. Bayly
- Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO 63130-4899, USA
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9
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Omori T, Munakata S, Ishikawa T. Self-sustaining oscillation of two axonemal microtubules based on a stochastic bonding model between microtubules and dynein. Phys Rev E 2022; 106:014402. [PMID: 35974562 DOI: 10.1103/physreve.106.014402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 06/17/2022] [Indexed: 06/15/2023]
Abstract
The motility of cilia and flagella plays important physiological roles, and there has been a great deal of research on the mechanisms underlying the motility of molecular motors. Although recent molecular structural analyses have revealed the components of the ciliary axoneme, the mechanisms involved in the regulation of dynein activity are still unknown, and how multiple dyneins coordinate their movements remains unclear. In particular, the mode of binding for axonemal dynein has not been elucidated. In this study, we constructed a thermodynamic stochastic model of microtubule-dynein coupling and reproduced the experiments of Aoyama and Kamiya on the minimal component of axonemal microtubule-dynein. We then identified the binding mode of axonemal dynein and clarified the relationship between dynein activity distribution and axonemal movement. Based on our numerical results, the slip-bond mechanism agrees quantitatively with the experimental results in terms of amplitude, frequency, and propagation velocity, implying that axial microtubule-dynein coupling may follow a slip-bond mechanism. Moreover, the frequency and propagation velocity decayed in proportion to the fourth power of microtubule length, and the critical load of the trigger for the oscillation agreed well with Euler's critical load.
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Affiliation(s)
- T Omori
- Department of Finemechanics, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
| | - S Munakata
- Department of Biomedical Engineering, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
| | - T Ishikawa
- Department of Finemechanics, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
- Department of Biomedical Engineering, Tohoku University, Aramaki Aoba 6-6-01, Sendai, Miyagi Japan
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10
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Wang C, Tang H, Zhang X. Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics. BIOINSPIRATION & BIOMIMETICS 2022; 17:041002. [PMID: 35443232 DOI: 10.1088/1748-3190/ac68ba] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 04/20/2022] [Indexed: 06/14/2023]
Abstract
Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.
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Affiliation(s)
- Chenglei Wang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Hui Tang
- Research Center for Fluid Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, People's Republic of China
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, Guangdong 518057, People's Republic of China
| | - Xing Zhang
- The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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11
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Collesano L, Guido I, Golestanian R, Vilfan A. Active beating modes of two clamped filaments driven by molecular motors. J R Soc Interface 2022; 19:20210693. [PMID: 34983201 PMCID: PMC8728166 DOI: 10.1098/rsif.2021.0693] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 12/02/2021] [Indexed: 12/11/2022] Open
Abstract
Biological cilia pump the surrounding fluid by asymmetric beating that is driven by dynein motors between sliding microtubule doublets. The complexity of biological cilia raises the question about minimal systems that can re-create similar patterns of motion. One such system consists of a pair of microtubules that are clamped at the proximal end. They interact through dynein motors that cover one of the filaments and pull against the other one. Here, we study theoretically the static shapes and the active dynamics of such a system. Using the theory of elastica, we analyse the shapes of two filaments of different lengths with clamped ends. Starting from equal lengths, we observe a transition similar to Euler buckling leading to a planar shape. When further increasing the length ratio, the system assumes a non-planar shape with spontaneously broken chiral symmetry after a secondary bifurcation and then transitions to planar again. The predicted curves agree with experimentally observed shapes of microtubule pairs. The dynamical system can have a stable fixed point, with either bent or straight filaments, or limit cycle oscillations. The latter match many properties of ciliary motility, demonstrating that a two-filament system can serve as a minimal actively beating model.
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Affiliation(s)
- Laura Collesano
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen 37077, Germany
| | - Isabella Guido
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen 37077, Germany
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen 37077, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK
| | - Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen 37077, Germany
- Jožef Stefan Institute, Ljubljana 1000, Slovenia
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12
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Fatehiboroujeni S, Gopinath A, Goyal S. Three-dimensional nonlinear dynamics of prestressed active filaments: Flapping, swirling, and flipping. Phys Rev E 2021; 103:013005. [PMID: 33601644 DOI: 10.1103/physreve.103.013005] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2020] [Accepted: 12/24/2020] [Indexed: 11/07/2022]
Abstract
Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.
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Affiliation(s)
- Soheil Fatehiboroujeni
- Department of Mechanical Engineering, University of California, Merced, California 95343, USA
| | - Arvind Gopinath
- Department of Bioengineering, University of California, Merced, California 95343, USA
| | - Sachin Goyal
- Department of Mechanical Engineering, University of California, Merced, California 95343, USA and Health Sciences Research Institute, University of California, Merced, California 95343, USA
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13
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Chelakkot R, Hagan MF, Gopinath A. Synchronized oscillations, traveling waves, and jammed clusters induced by steric interactions in active filament arrays. SOFT MATTER 2021; 17:1091-1104. [PMID: 33289748 DOI: 10.1039/d0sm01162b] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
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 for stable synchronization remain a mystery. Inspired by how these biological entities integrate elasticity with molecular motor activity to generate sustained oscillations, a number of synthetic active filament systems have been developed that mimic oscillations of these biological active filaments. Here, we describe the collective dynamics and stable spatiotemporal patterns that emerge in such biomimetic multi-filament arrays, under conditions where steric interactions may impact or dominate the collective dynamics. To focus on the role of steric interactions, we study the system using Brownian dynamics, without considering long-ranged hydrodynamic interactions. The simulations treat each filament as a connected chain of self-propelling colloids. We demonstrate that short-range steric inter-filament interactions and filament roughness are sufficient - even in the absence of inter-filament hydrodynamic interactions - to generate a rich variety of collective spatiotemporal oscillatory, traveling and static patterns. We first analyze the collective dynamics of two- and three-filament clusters and identify parameter ranges in which steric interactions lead to synchronized oscillations and strongly occluded states. Generalizing these results to large one-dimensional arrays, we find rich emergent behaviors, including traveling metachronal waves, and modulated wavetrains that are controlled by the interplay between the array geometry, filament activity, and filament elasticity. Interestingly, the existence of metachronal waves is non-monotonic with respect to the inter-filament spacing. We also find that the degree of filament roughness significantly affects the dynamics - specifically, filament roughness generates a locking-mechanism that transforms traveling wave patterns into statically stuck and jammed configurations. Taken together, simulations suggest that short-ranged steric inter-filament interactions could combine with complementary hydrodynamic interactions to control the development and regulation of oscillatory collective patterns. Furthermore, roughness and steric interactions may be critical to the development of jammed spatially periodic states; a spatiotemporal feature not observed in purely hydrodynamically interacting systems.
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Affiliation(s)
- Raghunath Chelakkot
- Department of Physics, Indian Institute of Technology Bombay, Mumbai, India.
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14
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Stein DB, De Canio G, Lauga E, Shelley MJ, Goldstein RE. Swirling Instability of the Microtubule Cytoskeleton. PHYSICAL REVIEW LETTERS 2021; 126:028103. [PMID: 33512217 PMCID: PMC7616086 DOI: 10.1103/physrevlett.126.028103] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 11/29/2020] [Indexed: 05/12/2023]
Abstract
In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly Drosophila melanogaster have shown a transition from a spatially disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions, we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.
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Affiliation(s)
- David B. Stein
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Gabriele De Canio
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Eric Lauga
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Michael J. Shelley
- Center for Computational Biology, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Courant Institute, New York University, 251 Mercer Street, New York, New York 10012, USA
| | - Raymond E. Goldstein
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
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15
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Guo H, Man Y, Wan KY, Kanso E. Intracellular coupling modulates biflagellar synchrony. J R Soc Interface 2021; 18:20200660. [PMID: 33435844 DOI: 10.1098/rsif.2020.0660] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate Chlamydomonas reinhardtii using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.
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Affiliation(s)
- Hanliang Guo
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA.,Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Yi Man
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Kirsty Y Wan
- Living Systems Institute, University of Exeter, Exeter EX4 4QD, UK
| | - Eva Kanso
- Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
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16
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Tiwari I, Parmananda P, Chelakkot R. Periodic oscillations in a string of camphor infused disks. SOFT MATTER 2020; 16:10334-10344. [PMID: 33237113 DOI: 10.1039/d0sm01393e] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The rhythmic beating motion of autonomously motile filaments has many practical applications. Here, we present an experimental study on a filament made of camphor infused paper disks, stitched together adjacent to each other using nylon thread. The filament displays spontaneous translatory motion when it is placed on the surface of water due to the surface tension gradients created by camphor molecules on the water surface. When this filament is clamped on one end, we obtain regular oscillatory motion instead of translation. The filament shows qualitatively different dynamics at different activity levels, which is controlled by the amount of camphor infused into the paper disks. For a better physical understanding of the filament dynamics, we develop a minimal numerical model involving a semi-flexible filament made of active polar disks, where the polarity is coupled to the instantaneous velocity of the particle. This model qualitatively reproduces different oscillatory modes of the filament. Moreover, our model reveals a rich dynamical state diagram of the system, as a function of filament activity and the coupling strength.
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Affiliation(s)
- Ishant Tiwari
- Department of Physics, Indian Institute of Technology - Bombay, Mumbai, Maharashtra 400076, India.
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17
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Man Y, Kanso E. Multisynchrony in Active Microfilaments. PHYSICAL REVIEW LETTERS 2020; 125:148101. [PMID: 33064515 DOI: 10.1103/physrevlett.125.148101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Revised: 07/09/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
Biological microfilaments exhibit a variety of synchronization modes. Recent experiments observed that a pair of isolated eukaryotic flagella, coupled solely via the fluid medium, display synchrony at nontrivial phase lags in addition to in-phase and antiphase synchrony. Using an elastohydrodynamic filament model in conjunction with numerical simulations and a Floquet-type theoretical analysis, we demonstrate that it is possible to reach multiple synchronization states by varying the intrinsic activity of the filament and the strength of hydrodynamic coupling between the two filaments. Then, we derive an evolution equation for the phase difference between the two filaments at weak coupling, and use a Kuramoto-style phase sensitivity analysis to reveal the nature of the bifurcations underlying the transitions between these different synchronized states.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Eva Kanso
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, USA
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18
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Fily Y, Subramanian P, Schneider TM, Chelakkot R, Gopinath A. Buckling instabilities and spatio-temporal dynamics of active elastic filaments. J R Soc Interface 2020; 17:20190794. [PMID: 32316880 DOI: 10.1098/rsif.2019.0794] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
Biological filaments driven by molecular motors tend to experience tangential propulsive forces also known as active follower forces. When such a filament encounters an obstacle, it deforms, which reorients its follower forces and alters its entire motion. If the filament pushes a cargo, the friction on the cargo can be enough to deform the filament, thus affecting the transport properties of the cargo. Motivated by cytoskeletal filament motility assays, we study the dynamic buckling instabilities of a two-dimensional slender elastic filament driven through a dissipative medium by tangential propulsive forces in the presence of obstacles or cargo. We observe two distinct instabilities. When the filament's head is pinned or experiences significant translational but little rotational drag from its cargo, it buckles into a steadily rotating coiled state. When it is clamped or experiences both significant translational and rotational drag from its cargo, it buckles into a periodically beating, overall translating state. Using minimal analytically tractable models, linear stability theory and fully nonlinear computations, we study the onset of each buckling instability, characterize each buckled state, and map out the phase diagram of the system. Finally, we use particle-based Brownian dynamics simulations to show our main results are robust to moderate noise and steric repulsion. Overall, our results provide a unified framework to understand the dynamics of tangentially propelled filaments and filament-cargo assemblies.
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Affiliation(s)
- Yaouen Fily
- Wilkes Honors College, Florida Atlantic University, Jupiter, FL, USA
| | | | - Tobias M Schneider
- Emergent Complexity in Physical Systems Laboratory (ECPS), Ecole Polytechnique Federale de Lausanne, CH 1015 Lausanne, Switzerland
| | | | - Arvind Gopinath
- Department of Bioengineering, University of California Merced, Merced, CA, USA
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19
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Kadam K, Khole VV, Ghosalkar K, Jagtap D, Yarramala DS, Ramachandran B. Thiol based mechanism internalises interacting partners to outer dense fibers in sperm. Free Radic Biol Med 2020; 148:170-181. [PMID: 31923584 DOI: 10.1016/j.freeradbiomed.2019.12.031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 12/04/2019] [Accepted: 12/23/2019] [Indexed: 11/19/2022]
Abstract
The sperm tail outer dense fibres (ODFs) contribute passive structural role in sperm motility. The level of disulphide cross-linking of ODFs and their structural thickness determines flagellar bending curvature and motility. During epididymal maturation, proteins are internalized to modify ODF disulphide cross-linking and enable motility. Sperm thiol status is further altered during capacitation in female tract. This suggests that components in female reproductive tract acting on thiol/disulphides could be capable of modulating the tail stiffness to facilitate modulation of the sperm tail rigidity and waveform en route to fertilization. Understanding the biochemical properties and client proteins of ODFs in reproductive tract fluids will help bridge this gap. Using recombinant ODF2 (aka Testis Specific Antigen of 70 kDa) as bait, we identified client proteins in male and female reproductive fluids. A thiol-based interaction and internalization indicates sperm can harness reproductive tract fluids for proteins that interact with ODFs and likely modulate the tail stiffness en route to fertilization.
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Affiliation(s)
- Kaushiki Kadam
- Department of Gamete Immunobiology, National Institute for Research in Reproductive Health, J.M Street, Parel, Mumbai, 400012, India.
| | - Vrinda V Khole
- Department of Gamete Immunobiology, National Institute for Research in Reproductive Health, J.M Street, Parel, Mumbai, 400012, India
| | - Kanaka Ghosalkar
- Department of Gamete Immunobiology, National Institute for Research in Reproductive Health, J.M Street, Parel, Mumbai, 400012, India
| | - Dhanashree Jagtap
- Structural Biology Department, National Institute for Research in Reproductive Health, J.M Street, Parel, Mumbai, 400012, India
| | - Deepthi S Yarramala
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India
| | - Bini Ramachandran
- Thermo Fisher Scientific India Pvt. Ltd, 403-404, Delphi 'B' Wing, Hiranandani Business Park, Powai, Mumbai, 400076, India
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20
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Nawroth JC, van der Does AM, Ryan (Firth) A, Kanso E. Multiscale mechanics of mucociliary clearance in the lung. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190160. [PMID: 31884926 PMCID: PMC7017338 DOI: 10.1098/rstb.2019.0160] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/08/2019] [Indexed: 12/19/2022] Open
Abstract
Mucociliary clearance (MCC) is one of the most important defence mechanisms of the human respiratory system. Its failure is implicated in many chronic and debilitating airway diseases. However, due to the complexity of lung organization, we currently lack full understanding on the relationship between these regional differences in anatomy and biology and MCC functioning. For example, it is unknown whether the regional variability of airway geometry, cell biology and ciliary mechanics play a functional role in MCC. It therefore remains unclear whether the regional preference seen in some airway diseases could originate from local MCC dysfunction. Though great insights have been gained into the genetic basis of cilia ultrastructural defects in airway ciliopathies, the scaling to regional MCC function and subsequent clinical phenotype remains unpredictable. Understanding the multiscale mechanics of MCC would help elucidate genotype-phenotype relationships and enable better diagnostic tools and treatment options. Here, we review the hierarchical and variable organization of ciliated airway epithelium in human lungs and discuss how this organization relates to MCC function. We then discuss the relevancy of these structure-function relationships to current topics in lung disease research. Finally, we examine how state-of-the-art computational approaches can help address existing open questions. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
| | - Anne M. van der Does
- Department of Pulmonology, Leiden University Medical Center, 2300 RC Leiden, The Netherlands
| | - Amy Ryan (Firth)
- Hastings Center for Pulmonary Research, Division of Pulmonary, Critical Care and Sleep Medicine, Department of Medicine, University of Southern California, Los Angeles, CA 90033, USA
- Department of Stem Cell Biology and Regenerative Medicine, University of Southern California, Los Angeles, CA 90033, USA
| | - Eva Kanso
- Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90033, USA
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21
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Abstract
Cilia, or eukaryotic flagella, are microscopic active filaments expressed on the surface of many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces. Cilia are characterized by a highly conserved and intricate internal structure in which molecular motors exert forces on microtubule doublets causing cilia oscillations. The spatial and temporal regulations of this molecular machinery are not well understood. Several theories suggest that geometric feedback control from cilium deformations to molecular activity is needed. Here, we implement a recent sliding control model, where the unbinding of molecular motors is dictated by the sliding motion between microtubule doublets. We investigate the waveforms exhibited by the model cilium, as well as the associated molecular motor dynamics, for hinged and clamped boundary conditions. Hinged filaments exhibit base-to-tip oscillations while clamped filaments exhibit both base-to-tip and tip-to-base oscillations. We report the change in oscillation frequencies and amplitudes as a function of motor activity and sperm number, and we discuss the validity of these results in the context of experimental observations of cilia behaviour. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Feng Ling
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - Eva Kanso
- Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
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22
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Chakrabarti B, Saintillan D. Hydrodynamic Synchronization of Spontaneously Beating Filaments. PHYSICAL REVIEW LETTERS 2019; 123:208101. [PMID: 31809101 DOI: 10.1103/physrevlett.123.208101] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2019] [Revised: 09/12/2019] [Indexed: 06/10/2023]
Abstract
Using a geometric feedback model of the flagellar axoneme accounting for dynein motor kinetics, we study elastohydrodynamic phase synchronization in a pair of spontaneously beating filaments with waveforms ranging from sperm to cilia and Chlamydomonas. Our computations reveal that both in-phase and antiphase synchrony can emerge for asymmetric beats while symmetric waveforms go in phase, and elucidate the mechanism for phase slips due to biochemical noise. Model predictions agree with recent experiments and illuminate the crucial roles of hydrodynamics and mechanochemical feedback in synchronization.
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Affiliation(s)
- Brato Chakrabarti
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
| | - David Saintillan
- Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
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23
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Anand SK, Chelakkot R, Singh SP. Beating to rotational transition of a clamped active ribbon-like filament. SOFT MATTER 2019; 15:7926-7933. [PMID: 31538995 DOI: 10.1039/c9sm01386e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We present a detailed study of a clamped ribbon-like filament under a compressive active force using Brownian dynamics simulations. We show that a clamped ribbon-like filament is able to capture beating as well as rotational motion under the compressive force. The nature of oscillation is governed by the torsional rigidity of the filament. The frequency of oscillation is almost independent of the torsional rigidity. The beating of the filament gives a butterfly-shaped trajectory of the free-end monomer, whereas rotational motion yields a circular trajectory on a plane. The binormal correlation and the principal component analysis reveal the butterfly, elliptical, and circular trajectories of the free end monomer. We present a phase diagram for different kinds of motion in the parameter regime of compressive force and torsional rigidity.
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Affiliation(s)
- Shalabh K Anand
- Department of Physics, Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India.
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24
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Xu L, Jiang Y. Mathematical Modeling of Mucociliary Clearance: A Mini-Review. Cells 2019; 8:cells8070736. [PMID: 31323757 PMCID: PMC6678682 DOI: 10.3390/cells8070736] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2019] [Revised: 07/12/2019] [Accepted: 07/14/2019] [Indexed: 12/13/2022] Open
Abstract
Mucociliary clearance is an important innate host defense of the mammalian respiratory system, as it traps foreign substances, including pollutants, pathogens, and allergens, and transports them out of the airway. The underlying mechanism of the actuation and coordination of cilia, the interplay between the cilia and mucus, and the formation of the metachronal wave have been explored extensively both experimentally and mathematically. In this mini-review, we provide a survey of the mathematical models of mucociliary clearance, from the motion of one single cilium to the emergence of the metachronal wave in a group of them, from the fundamental theoretical study to the state-of-the-art three-dimensional simulations. The mechanism of cilium actuation is discussed, together with the mathematical simplification and the implications or caveats of the results.
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Affiliation(s)
- Ling Xu
- Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA.
| | - Yi Jiang
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA.
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25
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Man Y, Kanso E. Morphological transitions of axially-driven microfilaments. SOFT MATTER 2019; 15:5163-5173. [PMID: 31215548 DOI: 10.1039/c8sm02397b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The interactions of microtubules with motor proteins are ubiquitous in cellular and sub-cellular processes that involve motility and cargo transport. In vitro motility assays have demonstrated that motor-driven microtubules exhibit rich dynamical behaviors from straight to curved configurations. Here, we theoretically investigate the dynamic instabilities of elastic filaments, with free-ends, driven by single follower forces that emulate the action of molecular motors. Using the resistive force theory at low Reynolds number, and a combination of numerical techniques with linear stability analysis, we show the existence of four distinct regimes of filament behavior, including a novel buckled state with locked curvature. These successive instabilities recapitulate the full range of experimentally-observed microtubule behavior, implying that neither structural nor actuation asymmetry are needed to elicit this rich repertoire of motion.
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Affiliation(s)
- Yi Man
- Department of Aerospace and Mechanical engineering, University of Southern California, CA 90007, USA.
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26
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Vilfan A, Subramani S, Bodenschatz E, Golestanian R, Guido I. Flagella-like Beating of a Single Microtubule. NANO LETTERS 2019; 19:3359-3363. [PMID: 30998020 PMCID: PMC6727605 DOI: 10.1021/acs.nanolett.9b01091] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simultaneously on a microtubule. The tangential forces exerted by a cluster are mostly in the range 0-8 pN toward the microtubule minus end, indicating the action of 1 or 2 kinesin motors. The lateral forces are distributed symmetrically and mainly below 10 pN, while the lateral velocity has a strong peak around zero. Unlike well-known models for flapping filaments, kinesins are found to have a strong "pinning" effect on the beating filaments. Our results suggest new strategies to utilize molecular motors in dynamic roles that depend sensitively on the stress built-up in the system.
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Affiliation(s)
- Andrej Vilfan
- Max Planck Institute
for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Jožef
Stefan
Institute, 1000 Ljubljana, Slovenia
| | - Smrithika Subramani
- Max Planck Institute
for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Eberhard Bodenschatz
- Max Planck Institute
for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Institute
for Dynamics of Complex Systems, Georg-August-University
Göttingen, 37073 Göttingen, Germany
- Laboratory
of Atomic and Solid-State Physics, Cornell
University, Ithaca, New York 14853, United
States
| | - Ramin Golestanian
- Max Planck Institute
for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Rudolf
Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Isabella Guido
- Max Planck Institute
for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
- Phone: +49 (0)551 5176310. Fax: +49 (0)551 5176302. E-mail:
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