Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell...

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Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering University of Minnesota

Transcript of Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell...

Page 1: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Model-Convolution Approach to Modeling Green Fluorescent

Protein Dynamics: Application to Yeast Cell Division

David Odde

Dept. of Biomedical Engineering

University of Minnesota

Page 2: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 3: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Microtubule Dynamic Instability

Page 4: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Leng

th (

µm

)

Time (minutes)

“Catastrophe”

“Rescue”

Microtubule “Dynamic Instability”

Vg

Vs

kc

kr

Hypothesis: The kinetochore modulates the DI parameters

Page 5: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Can only get peaks here

Not here

MT Length Distribution for Pure Dynamic Instability

Right PoleLeft Pole

1.7

Page 6: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Budding Yeast Spindle Geometry

Page 7: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Congression in S. cerevisiae

P PEQ

Green=Cse4-GFP kMT Plus Ends

Red=Spc29-CFP kMT Minus Ends

Page 8: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

“Experiment-Deconvolution”vs. “Model-Convolution”

Model Experiment

Deconvolution

Convolution

Page 9: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 10: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Simulated Image Obtainedby Model-Convolution of

Original Distribution

Original FluorophoreDistribution

Image Obtained by Deconvolution

of Simulated Image

Potential Pitfalls of Deconvolution

Page 11: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Cse4-GFP Fluorescence Distribution

Experimentally Observed

Theoretically Predicted

Page 12: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Dynamic Instability Only Model

Sprague et al., Biophysical J., 2003

Page 13: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Modeling ApproachModel

Probability that themodel is consistent with the data

ParameterSpace

(a1, a2, a3,…aN)

<Cutoff?

Experimental Data yes

no

Accept Model

ParameterSpace

Reject Model

ParameterSpace

Accept Model

ParameterSpace

Page 14: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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)

Page 15: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

“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

Page 16: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Could tension stabilize kinetochore microtubules?

Tension

Kip3

Page 17: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Distribution of Cse4-GFP: Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue

Page 18: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Model Combinations

Page 19: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

123

Catastrophe Gradient-Tension Rescue Model

Page 20: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 21: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Acknowledgements

• Melissa Gardner, Brian Sprague (Uof M)

• Chad Pearson, Paul Maddox, Kerry Bloom,Ted Salmon (UNC-CH)

• National Science Foundation

• Whitaker Foundation

• McKnight Foundation

Page 22: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Simulated Image Obtainedby Convolution of PSF and GWN

with Original Distribution

Original FluorophoreDistribution

Model-Convolution

Page 23: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Kinetochore MT Lengths in Budding Yeast

Experimentally Observed

Theoretically Predicted

?

2 µm

Page 24: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Catastrophe Gradient Model

Fre

quen

cy (

min

-1)

Normalized Spindle Position

Sprague et al., Biophys. J., 2003

Page 25: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Distribution of Cse4-GFP: Catastrophe Gradient Model

Page 26: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 27: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Cse4-GFP FRAP: Modeling and Experiment

Catastrophe Gradient Simulation

Experiment

Page 28: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Cse4-GFP FRAP: Modeling and Experiment

Page 29: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Gradients in Phospho-state

1.0

0.8

0.6

0.4

0.2

0.0

Con

cen

trati

on

, 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

Page 30: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Could tension stabilize kinetochore microtubules?

TensionTension

Kip3

Page 31: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model

Page 32: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Experimental Cse4-GFP in Cdc6 mutants

WT Cdc6

Page 33: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Cse4-GFP in Cdc6 Cells: No tension between sister kinetochores

Rescue Gradient with Tension-Dependent Catastrophe Model (No Tension)

Normalized Spindle Position

Fre

quen

cy (

min

-1)

Catastrophe Gradient with Tension-Dependent Rescue Model (No Tension)

Fre

quen

cy (

min

-1)

Normalized Spindle Position

Page 34: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 35: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Rescue Gradient Model

Normalized Spindle Position

Ca

tast

rop

he

or

Re

scu

e F

requ

enc

y (m

in-1)

Page 36: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Simulation of Budding Yeast Mitosis

Metaphase AnaphasePrometaphase

Start with randompositions, let simulationreach steady-state

Eliminate cohesion,set spring constant to 0

Page 37: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE

Page 38: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

WT Stu2p-depleted

Pearson et al., Mol. Biol. Cell, 2003

Stu2p-mediated catastrophe gradient?

Page 39: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Green Fluorescent Protein

Page 40: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.
Page 41: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 42: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.
Page 43: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.
Page 44: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 45: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Sister Kinetochore Microtubule Dynamics

Page 46: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Simulated Image Obtainedby Convolution of PSF and GWN

with Original Distribution

Original FluorophoreDistribution

Model-Convolution

Page 47: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

“Directional Instability”

Skibbens et al., JCB 1993

Page 48: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Tension on the kinetochore promotes switching to the growth state?

Skibbens and Salmon, Exp. Cell Res., 1997

Page 49: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Tension Between Sister Kinetochore-Dependent Rescue

kr kroeF

Page 50: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Catastrophe Gradient withTension-Rescue Model

Lack of Equator Crossing in the CatastropheGradient with Tension-Rescue Model

~25% FRAP recovery ~5% FRAP recovery

Page 51: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Microtubule Dynamic Instability

Page 52: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

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

Page 53: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Predicted Concentration Profile

where

Y cA cT

X x L

kL2

D

A*e2

e2 1 * 1 e2 B*

e2 1 * 1 e2 * k

*LD

Y Ae X BeX

Page 54: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Model Predictions: Effect of Surface Reaction Rate

1.0

0.8

0.6

0.4

0.2

0.0

Con

cen

trati

on

, Y

1.00.80.60.40.20.0

Position, X

Page 55: Model-Convolution Approach to Modeling Green Fluorescent Protein Dynamics: Application to Yeast Cell Division David Odde Dept. of Biomedical Engineering.

Defining “Metaphase” in Budding Yeast