David Odde Dept. of Biomedical Engineering University of Minnesota
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Transcript of David Odde Dept. of Biomedical Engineering University of Minnesota
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Model-Convolution Approach to Modeling Green Fluorescent
Protein Dynamics: Application to Yeast Cell Division
David OddeDept. of Biomedical Engineering
University of Minnesota
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Mitotic Spindle
spindle pole
chromosomes
kinetochore
1.7 µmIn budding yeast:
~40 MTs10-20 µm
In animal cells:
~1000 MTs
interpolarmicrotubule
- -
+++
+
kinetochore microtubule
bifunctionalplus-end motors
+ +
spindle pole
COMPRESSION
TENSION
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Microtubule Dynamic Instability
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Leng
th (µ
m)
Time (minutes)
“Catastrophe”
“Rescue”
Microtubule “Dynamic Instability”
Vg
Vs
kc
kr
Hypothesis: The kinetochore modulates the DI parameters
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Can only get peaks here
Not here
MT Length Distribution for Pure Dynamic Instability
Right PoleLeft Pole
1.7
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Budding Yeast Spindle Geometry
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Congression in S. cerevisiae
P PEQ
Green=Cse4-GFP kMT Plus Ends
Red=Spc29-CFP kMT Minus Ends
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“Experiment-Deconvolution”vs. “Model-Convolution”
Model ExperimentDeconvolution
Convolution
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Point Spread Function (PSF)
• A point source of light is spread via diffraction through a circular aperture
• Modeling needs to account for PSF
-0.4-0.20+0.2+0.4 μm
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Simulated Image Obtainedby Model-Convolution of
Original Distribution
Original FluorophoreDistribution
Image Obtained by Deconvolution
of Simulated Image
Potential Pitfalls of Deconvolution
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Cse4-GFP Fluorescence Distribution
Experimentally Observed
Theoretically Predicted
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Dynamic Instability Only Model
Sprague et al., Biophysical J., 2003
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Modeling ApproachModel
Probability that themodel is consistent with the data
ParameterSpace
(a1, a2, a3,…aN)<Cutoff?
Experimental Data yes
no
Accept ModelParameterSpace
Reject ModelParameterSpace
Accept ModelParameterSpace
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Modeling ApproachModel assumptions:1) Metaphase kinetochore microtubule dynamics
are at steady-state (not time-dependent)2) One microtubule per kinetochore3) Microtubules never detach from kinetochores4) Parameters can be:• Constant• Spatially-dependent (relative to poles)• Spatially-dependent (relative to sister
kinetochore)
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“Microtubule Chemotaxis” in a Chemical Gradient
ImmobileKinase
MobilePhosphatase
A: Phosphorylated ProteinB: Dephosphorylated Protein
k*Surface reaction B-->A
kHomogeneous reaction A-->B
KinetochoreMicrotubules
- +
ImmobileKinase
MT Destabilizer
Position
Concentration
X=0 X=L
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Could tension stabilize kinetochore microtubules?
Tension
Kip3
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Distribution of Cse4-GFP: Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue
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Model Combinations
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123
Catastrophe Gradient-Tension Rescue Model
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Conclusions
• Congression in budding yeast is mediated by:– Spatially-dependent catastrophe
gradient– Tension between sister kinetochore-
dependent rescue• Model-convolution can be a useful
tool for comparing fluorescent microscopy data to model predictions
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Acknowledgements
• Melissa Gardner, Brian Sprague (Uof M)• Chad Pearson, Paul Maddox,
Kerry Bloom,Ted Salmon (UNC-CH)
• National Science Foundation• Whitaker Foundation• McKnight Foundation
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Simulated Image Obtainedby Convolution of PSF and GWN
with Original Distribution
Original FluorophoreDistribution
Model-Convolution
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Kinetochore MT Lengths in Budding Yeast
Experimentally Observed
Theoretically Predicted
?
2 µm
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Catastrophe Gradient Model
Freq
uenc
y (m
in-1)
Normalized Spindle Position
Sprague et al., Biophys. J., 2003
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Distribution of Cse4-GFP: Catastrophe Gradient Model
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Experimental Cse4-GFP FRAP
•Cse4-GFP does not turnover on kinetochore
•Kinetochores rarely persist in opposite half-spindle
Pearson et al., Current Biology, in press
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Cse4-GFP FRAP: Modeling and Experiment
Catastrophe Gradient Simulation
Experiment
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Cse4-GFP FRAP: Modeling and Experiment
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Gradients in Phospho-state1.0
0.8
0.6
0.4
0.2
0.0
Conc
entra
tion,
Y
1.00.80.60.40.20.0
Position, X
If k= 50 s-1, D=5 µm2/s, and L=1 µm, then =3
MT Destabilizer
Position
Concentration
X=0 X=L
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Could tension stabilize kinetochore microtubules?
TensionTension
Kip3
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Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model
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Experimental Cse4-GFP in Cdc6 mutants
WT Cdc6
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Cse4-GFP in Cdc6 Cells: No tension between sister kinetochores
Rescue Gradient with Tension-Dependent Catastrophe Model (No Tension)
Normalized Spindle Position
Freq
uenc
y (m
in-1)
Catastrophe Gradient with Tension-Dependent Rescue Model (No Tension)
Freq
uenc
y (m
in-1)
Normalized Spindle Position
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Cse4-GFP in Cdc6 Cells: No tension between sister kinetochores
0.022
0.023
0.024
0.025
0.026
0.027
0.028
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized Spindle Position
Frac
tion
Fluo
resc
ence
Experimental cdc6 mutants- No Replication (n=27)Catastrophe Gradient with Tension-Dep. Rescue (No Tension); p=0.11Rescue Gradient with Tension-Dep. Catastrophe (No Tension); p<<.01
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Rescue Gradient Model
Normalized Spindle Position
Cat
astro
phe
or R
escu
e Fr
eque
ncy
(min
-1)
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Simulation of Budding Yeast Mitosis
Metaphase AnaphasePrometaphase
Start with randompositions, let simulationreach steady-state
Eliminate cohesion,set spring constant to 0
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MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE
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WT Stu2p-depleted
Pearson et al., Mol. Biol. Cell, 2003
Stu2p-mediated catastrophe gradient?
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Green Fluorescent Protein
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M
D
Prometaphase Spindles and the Importance of Tension in Mitosis
“Syntely”
Ipl1-mediated detachment of kinetochores under low tension
Dewar et al., Nature 2004
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MT Length Distributions•Regard MT dynamic instability as diffusion + drift•The drift velocity is a constant given by
•For constant Vg, Vs, kc, and kr, the length distribution is exponential
p x ~ eVdDx
Vd<0 exponential decayVd>0 exponential growth
Vd x Lg Lstc
Vg tg Vststg ts
Vgkc
Vs kr1kc
1kr
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Sister Kinetochore Microtubule Dynamics
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Simulated Image Obtainedby Convolution of PSF and GWN
with Original Distribution
Original FluorophoreDistribution
Model-Convolution
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“Directional Instability”
Skibbens et al., JCB 1993
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Tension on the kinetochore promotes switching to the growth state?
Skibbens and Salmon, Exp. Cell Res., 1997
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Tension Between Sister Kinetochore-Dependent Rescue
kr kroeF
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Catastrophe Gradient withTension-Rescue Model
Lack of Equator Crossing in the CatastropheGradient with Tension-Rescue Model
~25% FRAP recovery ~5% FRAP recovery
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Microtubule Dynamic Instability
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Model for Chemotactic Gradients of Phosphoprotein State
cAt
D 2cAx2
kcA Fick’s Second Law with First-Order HomogeneousReaction (A->B)
DcAx x0
k *cB 0 B.C. 1: Surface reaction at x=0 (B->A)
DcAx xL
0 B.C. 2: No net flux at x=L
cA cB cT Conservation of phosphoprotein
Sprague et al., Biophys. J., 2003
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Predicted Concentration Profile
where
Y cA cTX x L
kL2
D
A*e2
e2 1 * 1 e2 B*
e2 1 * 1 e2 * k
*LD
Y Ae X BeX
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Model Predictions: Effect of Surface Reaction Rate
1.0
0.8
0.6
0.4
0.2
0.0
Conc
entra
tion,
Y
1.00.80.60.40.20.0
Position, X
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Defining “Metaphase” in Budding Yeast