Dynamic modulation of actomyosin contractility and cortical flow by filament recycling

 

Will McFadden - Feb 8, 2017

Cells reorganize their contents and change shape through a process called cortical flow

Yumura et al. 2013

 

Amoeboid migration

Cell polarization

Ed Munro

 

Berhndt et al. 2012

 

Epithelial spreading

The machinery of cortical flow is the cortical actomyosin cytoskeleton

 

Christopher Beck

cross-linkers

actin filaments

myosin motors

electron micrograph of cortical actin network

The cytoskeletal cortex supports the cell in a web just below the cell surface

Filament cross-linking proteins transiently bind individual actin filaments together

Actin filaments and myosin motors interact to exert forces on the cortex

actin filament

myosin motor

Jonathan Alberts

Filaments in the actomyosin cortex are highly dynamic and turnover rapidly

Actin networks remodel quickly

movie duration 30s

Actin monomers depolymerize rapidly

Robin, McFadden, Yao, Munro 2014

Active fluid theory describes flows of active material like the actomyosin cortex

Passive

Viscosity

Active Stress

myosin

Active fluids explain flow in terms of active stresses and passive viscosities

Passive

Viscosity

Active Stress

\dot{\gamma}=\frac{\sigma}{\eta}
γ˙=ση\dot{\gamma}=\frac{\sigma}{\eta}

flow rate

active stress

viscosity

The active stress and passive viscosity are assumed to arise from molecular properties of cytoskeletal networks

Passive

Viscosity

Active Stress

Cortical flow has been successfully described as an active fluid in which the active stress depends on presence of myosin motors.

Mayer et al. 2010

 

myosin motors

Passive

Viscosity

Active Stress

force imbalance

cortical flows

There's a gulf between the active fluid description and the molecular details

Active fluid theory

Molecular details

Passive

Viscosity

Active Stress

The theory doesn't explain how myosin generates stress or how actin passively deforms

My goal was to construct a minimal model of filaments and motors that could explain the emergence of active stress and passive vicosity.

  • Actin filaments
  • Cross-linking
  • Myosin motors
  • Actin turnover

Actin filaments are semi-flexible polymers with asymmetric compliance

Lenz Gardel Dinner New J Phys 2012

L

Worm-like chain model

soft linear compression

rigid linear extension

L

Mimicking cross-linker dynamics via a frictional interaction between filaments

Mimicking motor activity via an effective force at a subset of intersections

 

Samantha Stam

Lenz Gardel and Dinner New J Phys 2012

linear approximation

active motor

passive cross-linker

motor force

walking rate

These minimal assumptions are sufficient to generate macrocscopic contraction

compressed

extended

Goal: Use molecular scale model to derive macroscopic theory of flow

Passive

Viscosity

Active Stress

Passive

Viscosity

Active Stress

split up the problem

\dot{\gamma}=\frac{\sigma}{\eta}
γ˙=ση\dot{\gamma}=\frac{\sigma}{\eta}

flow rate

First, let's inspect the behavior of the network in the absence of turnover

  • Actin filaments
  • Cross-linking
  • Myosin motors
  • Actin turnover

In the absence of turnover, actin networks exhibit viscous flow on intermediate timescales, but ultimately tear

extensional force

~1/viscosity

Passive

Viscosity

relaxed

extended

In the absence of turnover, active networks build up force,  but they lose connectivity and can't sustain it

Murrell and Gardel 2012

 

in vitro actomyosin contraction

Active Stress

compressed

extended

In both the passive and active case, there is a mechanical reasoning behind the timescales over which force builds up and dissipates.

Active Stress

Passive

Viscosity

This model still hasn't accounted for the dynamic turnover of filaments

cells must turnover their actin to maintain flows

Preventing filament turnover stalls flows and leads to cortical tearing

Dr. Jonathatn Michaux

 

japlakinolide treatments

What happens when I introduce highly simplified filament turnover?

 

recycling time

or

turnover time

In passive networks: recycling prevents tearing, and tunes passive viscosity

Passive

Viscosity

Turnover time

Viscosity

Recycling allows active networks to produce sustained stress against a boundary

Sustained Stress

Turnover time

Active Stress

Turnover time tunes viscosity and stress

Next we can generate simulation that combine passive and active networks to see whether we can generate flows

Stress

Turnover time

Turnover time

Viscosity

Recycling allows persistent flows and tunes flow rate

slow turnover

fast turnover

active region
Flow
Time
Turnover time
Flow velocity

Passive

Viscosity

Active Stress

faster turnover

Can we explain the biphasic dependence of flow speed in terms of the dependencies of active stress and passive viscosity?

\dot{\gamma}=\frac{\sigma}{\eta}
γ˙=ση\dot{\gamma}=\frac{\sigma}{\eta}

flow rate

viscosity

active stress

Viscosity

Active Stress

Ratio of active stress and viscosity as a function of turnover time should predict flow speed

\dot{\gamma}=\frac{\sigma}{\eta}
γ˙=ση\dot{\gamma}=\frac{\sigma}{\eta}

flow rate

viscosity

active stress

Because these are simulations, I can vary parameters and remeasure stress and viscosity

\tau_c
τc\tau_c
\tau_a
τa\tau_a
\sigma_m
σm\sigma_m
\eta_c
ηc\eta_c

Viscosity

Active Stress

This basic form of the active stress and viscosity dependence is a general property of these networks

a

We can use this model to understand the phase space of cortical flow

inert
tearing
Elastic to Viscous Transisiton Time 
Turnover Time
Flow Speed
inert
turnover independent flows
flows
\tau_c/\tau_a
τc/τa\tau_c/\tau_a
\tau_r/\tau_a
τr/τa\tau_r/\tau_a

The simulations are predicting a pretty striking transition in flow speed between fast and slow turnover

Turnover time
Flow velocity
very slow turnover

This makes experimental predictions about what would happen as we vary turnover time in real cells

conclusions and future directions

this work offers a theoretical framework for understanding cortical flows

it sets up some experiments to test both  quantitative and qualitative predictions

it might help explain what needs to be controlled to generate synthetic systems

Michele Wittels

Margaret Gardel, Ron Rock, Michael Glotzer, Aaron Dinner

Suggested experimental test

There's also a threshold timescale for turnover's impact on effective viscosity

\tau_c
τc\tau_c

There is an optimum turnover time that maximizes the steady state stress

\tau_a
τa\tau_a
\tau_a
τa\tau_a

Actin and myosin are the powerhouse behind force production in our muscles

myosin

aligned actin

aligned actin

Flows arise from active motor working to rearrange a passive filament network

Passive

Active

Mayer et al. 2010

 

Myosin

Myosin motors generates local stresses which drive flows

Passive

Active

strain thinning and tearing in passive networks being pulled on

position

filament velocity

Mechanical picture agrees with prior theoretical estimates for 2D networks

Head Levine Mackintosh, PRL 2003

I found an estimate for viscosity of networks with cross-link relaxation

\tau_c
τc\tau_c
1/\eta
1/η1/\eta

In passive networks: recycling prevents tearing, and reduces steady state viscosity

position

x velocity

x velocity

no recycling

tau =  10s

To test the theory we generated simulations of polarized networks

x velocity

x velocity

position

1000s

\tau_r
τr\tau_r

33s

active region

What is still missing from our description?

Actin filaments are highly dynamic and undergo regulated filament recycling: a key factor in sustaining cortical flows

cellular mechanisms of filament recycling

complete disassembly takes places in 100 s

Kuey et al. JCB 2008

We developed a method to measure filament recycling rates in vivo

during division

pre-division

Robin et al. 2012

How to make your own shape

How can an organism rearrange itself?

Don Kane (U. Rochester)

theseus

By wmcfadd2

theseus

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