### Feng Ling

Grad Student at USC

Reversal of Flagella Wave Propagation Controlled

by Asymmetric Dynein Dynamics

**Feng Ling**, Yi Man, Eva Kanso

*University of Southern California*

APS DFD 2019

- 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

- 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

- 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

Tip-to-Base

Mixed/Static

Base-to-Tip

Intermittent T2B

**26%**

**22%**

**50%**

**2%**

**1%**

**1%**

**54%**

**44%**

**Tap Me !**

*Edwards et al., PNAS (2018)

- 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*attach**ment rate*and work with geometric feedback to determine detachment rates

- 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)

- 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

Tap the buttons on the right!

Tap me!

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

- 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

Dynein Activity Number

Base-to-Tip

Tip-to-Base

∂α/∂s

Base-to-Tip

Tip-to-Base

∂α/∂s

Dynein Activity Number

Dynein Activity Number

By Feng Ling

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

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