How can dynamic kinetochore movements result in stable kinetochore

cluster positioning in metaphase?

EXPERIMENTS

Dynamic Kinetochore Movements

Metaphase Kinetochore Clustering

?

COMPUTERSIMULATION

Dynamic Kinetochore Movements

Metaphase Kinetochore Clustering

A Model for Regulationof Kinetochore Dynamics

A Model for Regulation

of Kinetochore Dynamics

Direct New Experimentation

Develop Hypotheses for

Mutant Phenotypes

Account for Stochastic variation using quantitative

analysis

Building a model: Budding Yeast Spindle Geometry

Leng

th (

µm

)

Time (minutes)

“Catastrophe”

“Rescue”

A Stochastic Simulation: Kinetochore Microtubule “Dynamic Instability”

Vg

Vs

kc

kr

Evaluating Model Predictions: Model Convolution

0 0 0 1 0 0 0 1 0 0 0 00 0 0 0 0 10 0 0 0 1 0 …

…

Simulation Results Simulated Fluorescent Kinetochore and SPB Markers

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 Fluorescent Kinetochore and Spindle

Pole Body Markers

Evaluating Model Predictions: Model Convolution

Quantitative MicroscopePoint Spread Function

-0.4-0.20+0.2+0.4 μm

-0.4-0.4-0.2-0.200+0.2+0.2+0.4 μm+0.4 μm

Measured Background Noise

Final Simulated Image

Can Microtubule Dynamic Instability Explain Kinetochore

Congression in Budding Yeast?

Experimentally Observed

Theoretically Predicted

?

2 µm

Constant Parameters of Kinetochore Microtubule Dynamic Instability

Sprague et al., Biophysical J., 2003

Catastrophe Frequency (kc) = Rescue Frequency (kr)UNIFORM DISTRIBUTION

Unequal Catastrophe and Rescue FrequenciesEXPONENTIAL DISTRIBUTION

EXPERIMENTAL RESULTS: Peak in kinetochore fluorescence midway between poles and equator

Can only get peaks here

Not here

Right PoleLeft Pole

Not here

Constant Parameters of Kinetochore Microtubule Dynamic Instability

Spatial Gradient Model for Catastrophe Frequency

Spatial Gradient Model for Catastrophe Frequency

Experimental Image

E Catastrophe Gradient

Catastrophe Gradient Simulated Image

0.032

0.034

0.036

0.038

0.04

0.042

0.044

0.046

0.048

0 0.2 0.4 0.6 0.8 1

Normalized Position in Spindle, x/L

F

ract

ion

Cse4

-GF

P F

luo

resc

ence

Experimentally Observed Metaphase Spindles, n=56

Simulated Catastrophe Gradient Model (p<.01)

Cse4-GFP Fluorescence Recovery After Photobleaching (FRAP) Experiment

Cse4-GFP FRAP Experiment: Simulation Results

*Experimental data from Pearson et al., Curr Biol (2004)

Catastrophe Gradient-Tension Rescue Model

13 2

POLE

POLE

Simulated Sister Kinetochore Position Tracking

Catastrophe Gradient Model

…Add Tension-Dependent Rescue

POLE

POLE

Cse4-GFP FRAP Experiment: Simulation Results

*Experimental data from Pearson et al., Curr Biol (2004)

Spatial Catastrophe Gradient Model with Tension-Dependent Rescue Frequency

Experimental Image

Simulated Image

0.032

0.034

0.036

0.038

0.04

0.042

0.044

0.046

0.048

0 0.2 0.4 0.6 0.8 1

Normalized Position in Spindle, x/L

F

ract

ion

of

To

tal

Sp

ind

le C

se4-

GF

P

Flu

ore

scen

ce

Experimentally Observed Metaphase Spindles, n=56

Simulated Catastrophe Gradient with Tension-Based RescueModel p=.55

GFP-Tubulin FRAP Experiment

Simulated kMT DynamicsSimulated Tubulin

FRAP Recovery (Spindle-Half)

GFP-Tubulin FRAP Experiment: Simulation Results

*Experimental data from Maddox et al., Nature Cell Biol (2000)

Tubulin FRAP Experiment Constrains Growth and Shrinking Velocities in Model

GFP-Tubulin FRAP by Spindle Position: Preliminary Simulation Results

Tubulin FRAP by Spindle Position Experiment Constrains all Dynamic Instability Parameters in Model

0

20

40

60

80

100

120

140

160

180

0 0.1 0.2 0.3 0.4Normalized Spindle Position (Pole--Equator)

FR

AP

Hal

f-T

ime

(sec

)

experimental n=16

simulation, kMT dynamics only, n=16, CatastropheGradient with Tension-Dependent Rescue Model

What would the model predict for a mutant lacking tension at the

kinetochore?

Mutant Spindles:Loss of Tension at the Kinetochore

Spring Constant = 0

Mutant Cell Experiment: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=0.11

EXPERIMENTAL SIMULATION

CONCLUSIONMetaphase kinetochore congression in budding yeast may be mediated by a

catastrophe gradient, and depend on tension between sister kinetochores.

SIMULATED METAPHASE CONGRESSION

SIMULATED LOSS OF TENSION

A Model for Regulation

of Kinetochore Dynamics

Direct New Experimentation

Develop Hypotheses for

Mutant Phenotypes

Account for Stochastic variation using quantitative

analysis

FUTURE DIRECTIONS

Extra slides

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

Model Experiment

Deconvolution

Convolution

Steady-State “Metaphase” Spindle(Length 1.6-1.9 µm)

Non-Steady StateEarly Metaphase Spindle

(Length 1.1-1.5 µm)

Quantitative Analysis of Spindle Fluorescence Images:Steady State Cse4-GFP Distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Spindle Length

p va

lue

(μm)

0.032

0.034

0.036

0.038

0.04

0.042

0.044

0.046

0.048

0.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized Position in Spindle, x/L

Frac

tion

of T

otal

Spi

ndle

Cse

4-G

FP

Fluo

resc

ence

Pro-metaphase Spindles, n=39

Metaphase Spindles, n=56

Metaphase Reference Distribution

“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

Loss of Tension at the Kinetochore

Control Spindle (with Chromosome Replication)

Replication Deficient Spindle

Bipolar Attachment at Kinetochore Monopolar Attachment at Kinetochore