Reversal of Flagella Wave Propagation Controlled

by Asymmetric Dynein Dynamics

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Feng Ling, Yi Man, Eva Kanso

University of Southern California

APS DFD 2019

Flagella and Cilia in the Wild

  • Cilia and Flagella can generate wildly different kinds of waveform
  • Typically, the swimming direction of the organism dictates that most flagella and cilia should assume a Base-to-Tip waveform
  • Certain organisms (e.g. Tryponosome L. mexicana) can use Tip-to-Base waves to swim tail first, but can also exhibit anterograde Base-to-Tip waves

Conserved Internal Structures

  • Despite the diversity of wave shapes and waveform directions, most motile cilia and flagella (Eukaryotic) assume the '9+2' axoneme structure
  • Axoneme is the force generating component of cilia and flagella:
    • Dynein motors causes sliding between microtubule doublets, and resistance to this sliding produces bending of the entire structure

Experiments with Tryponosomes

  • Recent experiments* have shown that reversal of Tryponosome flagellum wave directions can be induced by the proximal to distal asymmetry in the Dynein distribution.
  • Specifically, a mutant without outer Dynein arms in its distal tip only will prefer Base-to-Tip waveforms over the typical Tip-to-Base waveforms

Wild Type

Mutant

Proximal

Distal

*Edwards et al., PNAS (2018)

Press ↓ key for their results

Wild Type

Tip-to-Base

Mixed/Static

Base-to-Tip

Intermittent T2B

26%

22%

50%

2%

Mutant

1%

1%

54%

44%

Observed Waveforms

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*Edwards et al., PNAS (2018)

Tug-of-War Model of Flagellum

  • Flagellum centerline is modeled as an elastic filament moving in Stokes' fluid and is coupled to the Dynein dynamics
  • Two populations (n+ and n-) of Dynein motors will bend the flagellum in opposite directions
  • Dynein dynamics is modeled by the Langevin equations where a parameter α controls the attachment rate and work with geometric feedback to determine detachment rates

Model Capability

  • This model* can encode different types of geometric feedback models⁺ (e.g. sliding control, curvature control) and different boundary conditions⁰ (e.g. clamped, hinged end)
  • Given geometry and dynein activity, flagellum waves are typically dominated by ones that travel in a fixed direction, if the attachment rate α is a constant

*Oriola et al., R. S. Interface (2017)

⁺Chakrabarti & Saintillan, PRF (2019)

⁰Man, Ling, & Kanso, Phil. Trans. B (2019)

Direction Reversal under Sliding Con

  • Interestingly, given a fixed set of geometric and activity parameters, this model of flagellum can still produce tip-to-base waves, base-to-tip waves, as well as some mixed state depending on how the baseline Dynein attachment rate α changes along the filament !
\partial\alpha/\partial s=0
\partial\alpha/\partial s<0
\partial\alpha/\partial s>0

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Sperm# = 10, activity# = 8000.

Press ↓ key for biologically relevant values

Sperm# = 10, activity# = 8000.

Press ↓ key for biologically relevant values

Sperm# = 10, activity# = 8000.

Press ↓ key for biologically relevant values

Dynein Activity Number

Sperm Number

But There's More... (following are preliminary results)

  • Linearized model can directly predict the dominant flagellum wave direction under infinitesimal perturbations
  • Changes in ∂α/∂s will not reverse the direction of flagellum wave propagation under curvature feedback only*
  • Currently, the most favored geometric feedback mechanism for cilia and flagella is the geometric-clutch model, which can be think of as a mixture of sliding and curvature control under small deformations
  • We can study effects of ∂α/∂s under both sliding and curvature Control

*phase lag of curvature feedback determines wave directions, see Riedel-Kruse et al., HFSP J. (2007)

⁺Bayly & Wilson, R.S. Interface (2015)

Press ↓ key for a taste of these results

Transition Landscape for Sliding Ctrl

Dynein Activity Number

Base-to-Tip

Tip-to-Base

∂α/∂s

Sliding Control + Curvature Control

Base-to-Tip

Tip-to-Base

∂α/∂s

Dynein Activity Number

Dynein Activity Number

APS DFD 2019 M03.24: Reversal of Flagellar Wave Propagation is Controlled by Proximal to Distal Asymmetry in Molecular Motor Dynamics

By Feng Ling

APS DFD 2019 M03.24: Reversal of Flagellar Wave Propagation is Controlled by Proximal to Distal Asymmetry in Molecular Motor Dynamics

APS DFD 2019 M03.24 for abstract see https://meetings.aps.org/Meeting/DFD19/Session/M03.24

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