Mechanical tuning of mammalian sperm behaviour by hyperactivation, rheology and substrate adhesion: a numerical exploration

Ishimoto, Kenta; Gaffney, Eamonn A.

doi:10.1098/rsif.2016.0633

Cited by 35 publications

(38 citation statements)

References 53 publications

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“…Stable swimming is only possible when the Hamiltonian symmetry is broken (such as in the case where weak fluid viscoelasticity is included (Yazdi et al 2015)). Wall potential forces, included in numerical studies (Ishikawa & Pedley 2007;Spagnolie & Lauga 2012;Ishimoto & Gaffney 2016), give rise to an additional velocity perpendicular to the wall given by…”

Section: Discussionmentioning

confidence: 99%

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

Ishimoto

Crowdy

2017

J. Fluid Mech.

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Induction of flow is commonly used to control the migration of a microswimmer in a confined system such as a microchannel. The motion of a swimmer, in general, is governed by nonlinear equations due to non-trivial hydrodynamic interactions between the flow and the swimmer near a wall. This paper derives analytical expressions for the equations of motion governing a circular treadmilling swimmer in simple shear near a no-slip wall by combining the reciprocal theorem for Stokes flow with an exact solution for the dragging problem of a cylinder near a wall. We demonstrate that the reduced dynamical system possesses a Hamiltonian structure, which we use to show that the swimmer cannot migrate stably at a constant distance from a wall but only exhibit periodic oscillatory motion along the wall, or to escape from it. A treadmilling swimmer with the lowest two treadmilling modes is investigated in detail by means of a bifurcation analysis of the reduced dynamical system. It is found that the swimming direction of oscillatory motion is clarified by the sign of the Hamiltonian in the absence of flow, and that the induction of the flow suppresses upstream migration but aligns swimmer orientations in downstream migration. These results could inform strategies for the transport and control of micro-organisms and micromachines.

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Section: Discussionmentioning

confidence: 99%

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

Ishimoto

Crowdy

2017

J. Fluid Mech.

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“…In order to capture the effects of such surface forces, including the effects of contact with the boundary, we can include short-range repulsive boundary forces of steric origin, given per unit surface area and scaling in strength with the ratio of fluid viscosity and dimensional beating period, μ/T d . Following Ishimoto and Gaffney [45], we explicitly give the force per unit area in dimensional form as…”

Section: Repulsive Boundary Forcesmentioning

confidence: 99%

Response of monoflagellate pullers to a shearing flow: A simulation study of microswimmer guidance

et al. 2018

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Microscale swimming may be intuited to be dominated by background flows, sweeping away any untethered bodies with the prevalent flow direction. However, it has been observed that many microswimmers utilize ambient flows as guidance cues, in some cases resulting in net motion upstream, contrary to the dominant background fluid direction and our accompanying intuition. Thus the hydrodynamic response of small-scale motile organisms requires careful analysis of the complex interaction between swimmer and environment. Here we investigate the effects of a Newtonian shear flow on monoflagellated swimmers with specified body symmetry, representing, for instance, the Leishmania mexicana promastigote, a parasitic hydrodynamic puller that inhabits the microenvironment of a sandfly vector midgut and is the cause of a major and neglected human tropical disease. We observe that a lack of symmetry-breaking cellular geometry results in the periodic tumbling of swimmers in the bulk, with the rotations exhibiting a linear response to changes in shearing rate enabling analytic approximation. In order to draw comparisons with the better-studied pushers, we additionally consider virtual Leishmania promastigotes in a confined but typical geometry, that of a no-slip planar solid boundary, and note that in general stable guided taxis is not exhibited amongst the range of observed behaviors. However, a repulsive boundary gives rise to significant continued taxis in the presence of shearing flow, a phenomenon that may be of particular pertinence to the infective lifecycle stage of such swimmers subject to the assumption of a Newtonian medium. We finally propose a viable and general in vitro method of controlling microswimmer boundary accumulation using temporally evolving background shear flows, based on the analysis of phase-averaged dynamics and verified in silico.

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“…This is representative of the range of beat forms observed in experiments (Dresdner & Katz, 1981;Drobnis et al, 1988;Guerrero et al, 2011;Ooi et al, 2014;Suarez & Dai, 1992;Woolley & Vernon, 2001). Similar to previous models (Ishimoto & Gaffney, 2016;Omori & Ishikawa, 2016;Smith et al, 2009b), we assume that the two wave amplitudes are related via the chirality parameter α where B = αA for 0 ≤ α ≤ 1. Here, α = 0 corresponds to the planar case and α = 1 corresponds to the helical case.…”

Section: Calcium and Curvature Dynamicsmentioning

confidence: 99%

“…In these models, the flagellar beat form is an emergent property. Another approach is to prescribe the flagellar beat form (Curtis et al, 2012;Ishimoto & Gaffney, 2016;Ishimoto et al, 2017). In all of these modeling studies, regardless of how the flagellar beat form is modeled, the observed sperm trajectory is an emergent property of the coupled system accounting for the fluid dynamics and the swimmer.…”

Section: Introductionmentioning

confidence: 99%

“…Of the many modeling studies related to sperm motility, only a handful of models have attempted to consider the role of calcium dynamics on flagellar bending. Models have incorporated the effect of calcium indirectly by prescribing different waveforms for an activated (low calcium, symmetric waveform) or hyperactivated (high calcium, asymmetric waveform) sperm, without including any calcium dynamics directly in the model, to investigate emergent trajectories and interactions with a wall (Curtis et al, 2012;Ishimoto & Gaffney, 2016;Ishimoto et al, 2017;Olson & Fauci, 2015). Another modeling approach has been to directly couple the sperm motility to either a temporal or spatiotemporal evolving calcium concentration via an asymmetric calcium dependent curvature model where flagellar bending was planar (2D) (Olson et al, 2011;Olson, 2013;Simons et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

Carichino

Olson

2018

Mathematical Medicine and Biology: A Journal of the IMA

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Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The signaling pathways by which calcium increases within the flagellum are well established. However, the exact mechanisms of how calcium regulates flagellar bending are still under investigation. We extend our previous model of planar flagellar bending by developing a fluid-structure interaction model that couples the three-dimensional motion of the flagellum in a viscous, Newtonian fluid with the evolving calcium concentration. The flagellum is modeled as a Kirchhoff rod: an elastic rod with preferred curvature and twist. The calcium dynamics are represented as a one-dimensional reaction-diffusion model on a moving domain, the centerline of the flagellum. The two models are coupled assuming that the preferred curvature and twist of the sperm flagellum depend on the local calcium concentration. To investigate the effect of calcium on sperm motility, we compare model results of flagellar bend amplitude and swimming speed for three cases: planar, helical (spiral with equal amplitude in both directions), and quasi-planar (spiral with small amplitude in one direction). We observe that for the same parameters, the planar swimmer is faster and a turning motion is more clearly observed when calcium coupling is accounted for in the model. In the case of flagellar bending coupled to the calcium concentration, we observe emergent trajectories that can be characterized as a hypotrochoid for both quasi-planar and helical bending.

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Mechanical tuning of mammalian sperm behaviour by hyperactivation, rheology and substrate adhesion: a numerical exploration

Cited by 35 publications

References 53 publications

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

Dynamics of a treadmilling microswimmer near a no-slip wall in simple shear

Response of monoflagellate pullers to a shearing flow: A simulation study of microswimmer guidance

Emergent three-dimensional sperm motility: coupling calcium dynamics and preferred curvature in a Kirchhoff rod model

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