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Modeling cytoskeleton

self-assembly

Dimitrios Vavylonis

Department of Physics, Lehigh University

BIOS 10Lehigh University

Oct 30, 2009

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How does the cell achieveinternal organization?

How is it regulated?

Can we model cell structure and dynamics?

Cell organization

http://mgl.scripps.edu/people/goodsell/gallery/patterson.html

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Thermal and viscous forces are very

large on the scale of proteins

secm/9|proteinv

The result of this is diffusion

t= 0 t= 3 psec = 3 10-12 sec

in this time the protein travels

0.027 nm

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computer picks arandom direction (up/down/left/right)

with equal probability at each step

(a Monte Carlo method)

drunkards walk

Modeling diffusion: random walk on a lattice

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Brownian motion, continued

Diffusion coefficient D for a protein in the cell ~ 4 Pm2/sec

0 steps 100 steps 1000 steps

x(t) = constant (D t)1/2

x(t)

t= 0 fraction of a sec several sec

5 Pm

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Polymerization of proteins to filaments

Kovar, Harris, Mahaffy, Higgs, Pollard

Cell, 124 423 (2006)

D ~D/2 ~D/3

+ cross-links rigid, stationary cytoskeleton

Alberts et al, MBOC

actin filament

actin

monomers

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Microtubule filaments and cell organization

Alberts et al, MBOC

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Search and capture of chromosomes

by microtubules during mitosis

dividing cell

dynamic instability

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GTP-cap model of dynamic instability

Alberts et al, MBOC

GDP-tubulin

GTP-tubulin

cap

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GTP-cap toy model

GTP-tubulin monomers

diffuse in the cytoplasm

at concentration c

microtubule filament

hydrolysis at blue/red interface, rate khydrok+c

kcat

k-

Gillespie algorithm (a Monte Carlo method)1. pick an event at random according to rate constants

(polymerization, depolymerization, hydrolysis)

2. update configuration and time

krescue

GDP-tubulinGTP-tubulin

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Numerical simulations of the model

large GTP-tubulin monomer concentrations

small GTP-tubulin monomer concentrations

example of length

trajectory at small

concentrations:

Time (sec)

subu

nits

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Insights from simple model

time (sec)

su

bunits

other trajectories averageelongation rate

monomer

concentration

0

catastrophe

and rescue

region

c*

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Models of chromosome search and capture

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fission yeast

Wu lab, Ohio State Univ. 2007

Neuron growth

actin

Forscher lab, Yale Univ.

budding yeastAmberg Mol. Biol. Cell (1998)

Actin filaments and cell shape changes

actin patches actin cables

motile fibroblast (GFP-actin)Watanabe lab, Kyoto Univ.

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Actin polymerization: driving force for cellular motions

5 nm

barbed endpointed end

Svitkina et al J. Cell Biol. 139 397(1997)

Watanabe and Mitchison,Science, 295 8 (2002)

fibroblast

EGFP-actin

~5 Pm

movie

duration 156 sec

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Actin network within a motile cell

Svitkina et al. J. Cell Biol. 139 397(1997)

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Motility of cancer cells causes metastasis

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http://www.nytimes.com/2009/06/09/science/09cell.html

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Low concentrations of markers: actin speckles

Numerical simulations

of actin turnover based

on analysis of speckleimages

(ongoing project)

Naoki Watanabe, Kyoto University

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CHD-GFP

binds to sides of

actin filaments

spindle poles

Spb1Jian-Qiu Wu (Pollard lab, Yale Univ 2007)

Vavylonis, Wu, et al. Science 2008

Actin Cytoskeleton in Cell Division

fission yeast cdc25-22cell

Zhou and WangMol. Biol. Cell2008

GFP-actin kidney cell

Pollard and Earnshaw, Cell Biology (2002)

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Contractile ring assembles from ~ 63 myosin II nodes in ~ 10 min

~ 40 myosin II (Myo2p) molecules/node

~ 2 formin Cdc12p dimers/nodeWu and Pollard, Science 2005

Rlc1p-3GFP

Vavylonis, Wu, Hao, OShaughnessy, Pollard,

Science 2008

spinning disk confocal microscopy

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Actin meshwork establishes connections among nodes

red: nodes (Rlc1-RFP1)green: actin filaments (GFP-CHD)

cdc25-22cellsradial projection

0

2SR

arclengths

data: Wu (2007, 2008)

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actin filamentpolymerization

m/sec2.0~ P

actin filament capture

nm100~cr

traction on filamentsbetween nodes

pNF 4t

lifetime of connections

lifetime of filaments

sec20~

sec20~

Dynamic reestablishment of connections plasticity of network

Search, capture, pull and release model

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Simulations with search, capture, pull and release

30x time lapse,

20min

Simulated radial projection

red: nodes

green: actin

0 2SR experiment:

x model reproduces many observed features

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Dependence on parameter values

red: nodes

green: actin filaments

m/sec2.0 Ppolv

m/sec04.0 Ppo lv

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Hachet and Simanis, Genes and Development, 2008

Formin Mutant: clump formation

Wild type: robust ring formation

Some mutant cells form clumps

ring

clumps

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Clump formation kinetics

d

l

Qtclump

1|

Qt /1* |

Qdrcv2

00'|

22

orcQdD|

2/1*** )(Dttvl

00

*

/ rldrl

0t

clump size ~ r0

vrtclump /0

A B

Node

rootmean

square

displaceme

nt

time(Qt)

B: Slope 1(clump formation)

*l

*t

0r

A: Slope (diffusion)

clumpt

0.1 1 100.01

0.01

0.1

Monte Carlo Simulation of 2D bulk of nodes

Scaling arguments:

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Actin meshwork in the middle of a dividing yeast cell

4D confocal microscopy experiments (Jian-Qiu Wu, Ohio State)

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skeletonization(ridge point detection)

Tracking of polymerizing

actin filaments in vitro

Li et al. (ISBI 2009, MICCAI 2009)

Actin filament network in the middle of

dividing cell

Systematic image analysis of actin in cells and in vitro

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Pom1p

??

Mid1p

cytoplasmic

concentrtation

gradients?

Cell polarization and establishment of cell center

Padte et al. Curr. Biol 2006

Celton-Morizur et al. J. Cell Sci. 2006

Wu et al Dev Cell 2003

wildtype

Padte et al. Curr. Biol 2006

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Martin and Chang, Dev. Cell, 8, 479 (2006)

Kamasaki et al., Nature Cell Biol., 7, 916, (2005).

actin cables: bundles of actin

filaments

nucleated by formin For3pretrograde flow

Formin For3p and actin cable assembly

EM: bundles of ~ 10 actinfilaments

1.7 Pm

short filaments ~ 100 subunits

actin filament: 370 sub/Pm

Yang and Pon PNAS (2002)

v ~ 0.3 m/sec ~ 110 actin subunits/seP

budding yeast

cables nucleated

by forminsBnr1p, Bni1p

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3D actin cable turnover model

(based on model proposed by Martin and Chang)

~ 50

depends on actin polymerization

Wang and Vavylonis, PloS ONE(2008)

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Fluorescence recovery after For3p photobleaching

Martin and Chang (2006)

comparison of simulated recovery to experiment:

LatA: sequesters actin

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Acknowledgments

Nikola Ojkic, Matthew Smith, Tyler Drake

Hui Wang, Alex Veksler, Eddy Yusuf

Department of Physics,

Lehigh University

Xiaolei Huang, Tian Shen, Hongsheng LiDepartment of Computer Science,

Lehigh University

Naoki Watanabe

Department of Pharmacology

Kyoto University

Jian-Qiu Wu

Department of Molecular Genetics,Ohio State University

Thomas Pollard

Department of Molecular, Cellular and Developmental Biology,

Yale University

Support: HFSP, NIH, Lehigh University