david odde dept. of biomedical engineering university of minnesota
DESCRIPTION
Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division. David Odde Dept. of Biomedical Engineering University of Minnesota. In animal cells:. In budding yeast:. 10-20 µm. 1.7 µm. ~1000 MTs. ~40 MTs. Mitotic Spindle. interpolar - PowerPoint PPT PresentationTRANSCRIPT
Model-Convolution Approach to Modeling Green Fluorescent
Protein Dynamics: Application to Yeast Cell Division
David OddeDept. of Biomedical Engineering
University of Minnesota
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
Microtubule Dynamic Instability
Leng
th (µ
m)
Time (minutes)
“Catastrophe”
“Rescue”
Microtubule “Dynamic Instability”
Vg
Vs
kc
kr
Hypothesis: The kinetochore modulates the DI parameters
Can only get peaks here
Not here
MT Length Distribution for Pure Dynamic Instability
Right PoleLeft Pole
1.7
Budding Yeast Spindle Geometry
Congression in S. cerevisiae
P PEQ
Green=Cse4-GFP kMT Plus Ends
Red=Spc29-CFP kMT Minus Ends
“Experiment-Deconvolution”vs. “Model-Convolution”
Model ExperimentDeconvolution
Convolution
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
Simulated Image Obtainedby Model-Convolution of
Original Distribution
Original FluorophoreDistribution
Image Obtained by Deconvolution
of Simulated Image
Potential Pitfalls of Deconvolution
Cse4-GFP Fluorescence Distribution
Experimentally Observed
Theoretically Predicted
Dynamic Instability Only Model
Sprague et al., Biophysical J., 2003
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
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)
“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
Could tension stabilize kinetochore microtubules?
Tension
Kip3
Distribution of Cse4-GFP: Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue
Model Combinations
123
Catastrophe Gradient-Tension Rescue Model
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
Acknowledgements
• Melissa Gardner, Brian Sprague (Uof M)• Chad Pearson, Paul Maddox,
Kerry Bloom,Ted Salmon (UNC-CH)
• National Science Foundation• Whitaker Foundation• McKnight Foundation
Simulated Image Obtainedby Convolution of PSF and GWN
with Original Distribution
Original FluorophoreDistribution
Model-Convolution
Kinetochore MT Lengths in Budding Yeast
Experimentally Observed
Theoretically Predicted
?
2 µm
Catastrophe Gradient Model
Freq
uenc
y (m
in-1)
Normalized Spindle Position
Sprague et al., Biophys. J., 2003
Distribution of Cse4-GFP: Catastrophe Gradient Model
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
Cse4-GFP FRAP: Modeling and Experiment
Catastrophe Gradient Simulation
Experiment
Cse4-GFP FRAP: Modeling and Experiment
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
Could tension stabilize kinetochore microtubules?
TensionTension
Kip3
Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model
Experimental Cse4-GFP in Cdc6 mutants
WT Cdc6
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
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
Rescue Gradient Model
Normalized Spindle Position
Cat
astro
phe
or R
escu
e Fr
eque
ncy
(min
-1)
Simulation of Budding Yeast Mitosis
Metaphase AnaphasePrometaphase
Start with randompositions, let simulationreach steady-state
Eliminate cohesion,set spring constant to 0
MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE
WT Stu2p-depleted
Pearson et al., Mol. Biol. Cell, 2003
Stu2p-mediated catastrophe gradient?
Green Fluorescent Protein
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
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
Sister Kinetochore Microtubule Dynamics
Simulated Image Obtainedby Convolution of PSF and GWN
with Original Distribution
Original FluorophoreDistribution
Model-Convolution
“Directional Instability”
Skibbens et al., JCB 1993
Tension on the kinetochore promotes switching to the growth state?
Skibbens and Salmon, Exp. Cell Res., 1997
Tension Between Sister Kinetochore-Dependent Rescue
kr kroeF
Catastrophe Gradient withTension-Rescue Model
Lack of Equator Crossing in the CatastropheGradient with Tension-Rescue Model
~25% FRAP recovery ~5% FRAP recovery
Microtubule Dynamic Instability
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
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
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
Defining “Metaphase” in Budding Yeast