Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments

Chakrabarti, Brato; Saintillan, David

doi:10.1103/physrevfluids.4.043102

Cited by 62 publications

(130 citation statements)

References 63 publications

(159 reference statements)

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“…We will aim to evaluate the accuracy of a recent regularized singularity representation [40,53,54], as used by Ishimoto and Gaffney [41] to simulate population-level behaviors of spermatozoa confined to a plane, in particular considering its natural extension to motion in three spatial dimensions. Here we briefly recapitulate the key principles of the methodology, and direct the reader to the original publications [40,41,53,54] for further details.…”

Section: E Coarse-grained Singularity Representations Of Swimmersmentioning

confidence: 99%

Pairwise hydrodynamic interactions of synchronized spermatozoa

2019

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The journey of mammalian spermatozoa in nature is well-known to be reliant on their individual motility. Often swimming in crowded microenvironments, the progress of any single swimmer is likely dependent on their interactions with other nearby swimmers. Whilst the complex dynamics of lone spermatozoa have been well-studied, the detailed effects of hydrodynamic interactions between neighbors remain unclear, with inherent nonlinearity in the pairwise dynamics and potential dependence on the details of swimmer morphology. In this study we will attempt to elucidate the pairwise swimming behaviors of virtual spermatozoa, forming a computational representation of an unbound swimming pair and evaluating the details of their interactions via a high-accuracy boundary element method. We have explored extensive regions of parameter space to determine the pairwise interactions of synchronized spermatozoa, with synchronized swimmers often being noted in experimental observations, and have found that two-dimensional reduced autonomous dynamical systems capture the anisotropic nature of the swimming speed and stability arising from near-field hydrodynamic interactions. Focusing on two initial configurations of spermatozoa, namely those with swimmers located side-by-side or above and below one another, we have found that side-by-side cells attract each other, and the trajectories in the phase plane are well captured by a recently-proposed coarsegraining method of microswimmer dynamics via superposed regularized Stokeslets. In contrast, the above-below pair exhibit a remarkable stable pairwise swimming behavior, corresponding to a stable configuration of the plane autonomous system with swimmers lying approximately parallel to one another. At further reduced swimmer separations we additionally observe a marked increase in swimming velocity over individual swimmers in the bulk, potentially suggesting a competitive advantage to cooperative swimming. These latter observations are not captured by the coarse-grained regularized Stokeslet modeling or simple singularity representations, emphasizing the complexity of near-field cell-cell hydrodynamic interactions and their inherent anisotropy.

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Section: E Coarse-grained Singularity Representations Of Swimmersmentioning

confidence: 99%

Pairwise hydrodynamic interactions of synchronized spermatozoa

2019

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“…Scaling lengths by L, sliding displacement by a, time by the correlation timescale τ 0 = 1/(π 0 + 0 ), elastic forces by B/L 2 , and motor loads by ρf 0 produces four dimensionless groups, of which two are of primary interest: (i) the sperm number Sp = L (8πν/Bτ 0 ) 1/4 , where ν is the viscosity, compares the relaxation time of a bending mode to the motor correlation time; (ii) the activity number µ a = aρf 0 L 2 /B compares motor-induced sliding forces to characteristic elastic forces. The two other dimensionless groups are: µ = Ka 2 L 2 /B and ζ = a/(v 0 τ 0 ) [34]. With these scalings, the dimensionless equations for φ(s, t) read…”

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confidence: 99%

“…where the first two equations are force balances in the tangential and normal directions while the third is the moment balance. The dimensionless tangential and normal drag coefficients c ,⊥ derive from local terms in slender body theory [34] and satisfy c ⊥ /c → 2 for infinitely slender filaments. Hydrodynamic interactions are captured by the disturbance velocity u d , with projections u d t and u d n in the tangential and normal directions, respectively.…”

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confidence: 99%

“…The last term accounts for biochemical noise with ξ(s, t) = 0 and ξ(s, t)ξ(s , t ) = 2Λδ(s − s )δ(t − t ), where Λ is an effective temperature. These governing equations are solved numerically as outlined in [34]. Spontaneous oscillations.-We first describe the dynamics of isolated filaments, with model parameters estimated from experiments [30,33,34]; see Supplemental Information [19] for details.…”

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confidence: 99%

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Hydrodynamic Synchronization of Spontaneously Beating Filaments

Chakrabarti

Saintillan

2019

Phys. Rev. Lett.

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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 anti-phase 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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“…The dotted lines correspond to the prediction obtained by adding O(1) constant to their leading log( ) terms. The solid lines corresponding to the fit to the numerical results are given by equation(50).…”

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confidence: 99%

Elastohydrodynamical instabilities of active filaments, arrays and carpets analyzed using slender body theory

Gopinath

Sangani

2020

Preprint

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The rhythmic motions and wave-like planar oscillations in filamentous soft structures are ubiquitous in biology. Inspired by these, recent work has focused on the creation of synthetic colloid-based active mimics that can be used to move, transport cargo, and generate fluid flows. Underlying the functionality of these mimics is the coupling between elasticity, geometry, dissipation due to the fluid, and active force or moment generated by the system. Here, we use slender body theory to analyze the linear stability of a subset of these -active elastic filaments, filament arrays and filament carpets -animated by follower forces. Follower forces can be external or internal forces that always act along the filament contour. The application of slender body theory enables the accurate inclusion of hydrodynamic effects, screening due to boundaries, and interactions between filaments. We first study the stability of fixed and freely suspended sphere-filament assemblies, calculate neutral stability curves separating stable oscillatory states from stable straight states, and quantify the frequency of emergent oscillations. When shadowing effects due to the physical presence of the spherical boundary are taken into account, the results from the slender body theory differ from that obtained using local resistivity theory. Next, we examine the onset of instabilities in a small cluster of filaments attached to a wall and examine how the critical force for onset of instability and the frequency of sustained oscillations depend on the number of filaments and the spacing between the filaments. Our results emphasize the role of hydrodynamic interactions in driving the system towards perfectly in-phase or perfectly out of phase responses depending on the nature of the instability. Specifically, the first bifurcation corresponds to filaments oscillating inphase with each other. We then extend our analysis to filamentous (line) array and (square) carpets of filaments and investigate the variation of the critical parameters for the onset of oscillations and the frequency of oscillations on the inter-filament spacing. The square carpet also produces a uniform flow at infinity and we determine the ratio of the mean-squared flow at infinity to the energy input by active forces. We conclude by analyzing the bending and buckling instabilities of a straight passive filament attached to a wall and placed in a viscous stagnant flow -a problem related to the growth of biofilms, and also to mechanosensing in passive cilia and microvilli. Taken together, our results provide the foundation for more detailed non-linear analyses of spatiotemporal patterns in active filament systems.

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Spontaneous oscillations, beating patterns, and hydrodynamics of active microfilaments

Cited by 62 publications

References 63 publications

Pairwise hydrodynamic interactions of synchronized spermatozoa

Pairwise hydrodynamic interactions of synchronized spermatozoa

Hydrodynamic Synchronization of Spontaneously Beating Filaments

Elastohydrodynamical instabilities of active filaments, arrays and carpets analyzed using slender body theory

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