dimitrios vavylonis - lehigh universityinbios21/pdf/fall2008/vavylonis... · 2010. 10. 13. ·...
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Modeling cytoskeleton self assembly
Dimitrios VavylonisDepartment of Physics, Lehigh University
October 31, 2008
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● How does the cell achieve internal 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 << protein size ~ 4 nm
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computer picks arandom direction (up/down/left/right)with equal probability at each step
(a “Monte Carlo” method)“drunkard’s 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 μm2/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 μm
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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 chromosomesby 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 monomersdiffuse 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)
subu
nits
other trajectories average elongation rate
monomerconcentration
0catastropheand rescue
region
c*
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Models of chromosome search and capture
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Cytokinesis
Pollard and Earnshaw, “Cell Biology” (2002)
~50 μm
Ring assembly involves ~ 50 or more protein components.How do protein molecules assemble in a ring?What is the mechanistic pathway?How is it coordinated and controlled?How does the ring exert the required force?
5 nm actinmonomers
actinfilament
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time
15 μm
Fission yeast is a a model organism for the study of cytokinesis
nucleus
cell tipcell tip
contractilering
yeastsbuild rigid cell wallsaround them
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Contractile ring assembles from ~ 63 nodes in ~ 10 min
~ 40 myosin II (Myo2p) molecules/node~ 2 formin Cdc12p dimers/node Wu and Pollard, Science 2005
Rlc1p-3GFP
Vavylonis, Wu, Hao, O’Shaughnessy, Pollard, Science 2008
spinning disk confocal microscopy
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Actin filament meshwork establishes connections among nodes
red: nodes (Rlc1-RFP1)green: actin filaments (GFP-CHD)
radial projection
02π
Rar
c le
ngth
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Lateral contraction model
Wu, Sirotkin, Kovar, Lord, Beltzner, Kuhn, Pollard J. Cell Biol. 2006
node
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time
Model with static connections condenses nodes into clumps!
numerical simulation
pattern and dynamics of connections is important
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15x time lapse10 minutes
each frame: average of 6
Nodes move in stochastic manner, making many starts, stops and changes of direction
nm/sec30≈v
sec20≈τ
typical node speed
typical duration
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Evidence for dynamic actin meshwork growing out of nodes
4x time lapse (0.3 s/frame)GFP-CHD (binds actin filaments), Rlc1p-tdTomato (nodes)
single confocal slice
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actin filamentpolymerization
m/sec2.0~ μ
actin filament capture
nm 100~cr
traction on filaments between nodes
pNF 4≥
lifetime of connections
lifetime of filamentssec 20~
sec 20~
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 projectionred: nodesgreen: actin
0 2πR experiment:
• model reproduces many observed features
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Actin Dynamics in Cell Motility
frame-to-frame = 1 secmovie lasts 600 sec
5 μm
Diez, Gerisch, Anderson, Muller-Taubenberger, Bretschneider PNAS, 102, 7601 (2005)
Total internal reflectionfluorescence microscopy(TIRFM)
Dictyostelium response tochemoattractant
fluorescent LimE-GFP (binds actin filaments)
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Dynamic Actin NetworkLamellipodiumSvitkina et alJ. Cell Biol. 139 397 (1997)
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Motility of cancer cells causes metastasis
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Green Fluorescent Protein (GFP) and Biological Imaging
greenfluorescent
spots
Aequorea Victoria
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1994
gene gene fused to GFP gene
Live cells become fluorescent
The cell makes its own fluorophore
GFP can be expressed in a different species and remains fluorescent
Tsien lab, UCSD
many more colors:
+ photoconvertible GFP etc.
Chalfie et al. (Columbia)