Stable spatial gradients of cytoskeleton assembly regulators

David Odde

University of Minnesota

Microtubule Structure

Leng

th (

µm

)

Time (minutes)

“Catastrophe”

“Rescue”

Microtubule “Dynamic Instability” (DI)

Vg

Vs

kc

kr

see VanBuren et al., PNAS USA (2002)

Microtubules in Mitosis

Mitotic Spindle

spindle pole body

chromosome

kinetochore

kinetochoremicrotubule

spindle pole body

1.5 µmIn yeast:

~40 MTs10-20 µm

In animal cells:

~1000 MTs

Interpolarmicrotubule

Hypothesis

Dynamic instability alone is sufficient to explain the observed MT length distribution in the yeast mitotic spindle

Results: Cse4p-GFP Distribution

Experimentally Observed

Theoretically Predicted

?

2 µm

Leng

th (

µm

)

Time (minutes)

“Catastrophe”

“Rescue”

Microtubule “Dynamic Instability” (DI)

Vg

Vs

kc

kr

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 Convolution of PSF and GWN

with Original Distribution

Original FluorophoreDistribution

Model-Convolution

Spindle Geometry

Results: Distribution of Cse4-GFP fluorescence

Experimentally Observed

Theoretically Predicted

Results: Distribution of Cse4-GFP fluorescence

x=0 x=L

QS QSSE

Results: DI Only Model

1000 nm

Results: DI Only Model

Alternative Models

Microtubule Chemotaxis

ImmobileKinase

MobilePhosphatase

Microtubule

A: Phosphorylated Protein Stabilizes MTsB: Unphosphorylated Protein Destabilizes MTs

Concentration

Position

MT Attractant

MT Repellant

X=0 X=L

k*Surface reaction B-->A

kHomogeneous reaction A-->B

Microtubule Chemotaxis:Op18

ImmobilePlx1

MobilePP2A

Microtubule

A: Op18-hi-PB: Op18-low-P Destabilizes MTs

Concentration

Position

Op18-hi-P

Op18-low-P

Chromatin

Microtubule Chemotaxis: RanGTP

ImmobileRCC1

MobileRanGAP

Microtubule

A: RanGTP Stabilizes MTsB: RanGDP

Concentration

Position

RanGTP

RanGDP

Chromatin

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

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

If k= 1 s-1, D=10-11 m2/s, and L=10 µm, then =3

Model Predictions: Effect of Homogeneous 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

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

Microtubule Chemotaxis: RanGTP

ImmobileRCC1

MobileRanGAP

Microtubule

A: RanGTP Stabilizes MTsB: RanGDP

Concentration

Position

RanGTP

RanGDP

Chromatin

Results: Chemical Gradient and Polar Ejection Force Models

1000 nm

Cse4 Bleach @ end of simulation, mutant “Tension” model

LeftHalfSpindle

RightHalfSpindle

Figure 2

Cse4 Bleach @ End of Simulation, wild-type, “Gradient-Only” Model

RightHalfSpindle

LeftHalfSpindle

Figure 4

Mitotic Spindle

Conclusion: Spatial gradients in MT DI parameter(s)may play a role in mediating budding yeast mitotis

F FF F

X

X

X

Y

Z

Y

Simulated Actin FilamentDendritic Branching

Simulated Image of Actin FilamentDendritic Branching

Model-Convolution: Application to Dendritic Actin Filament Branching

Simulated Image Obtainedby Model-Convolution of

Original Distribution

Original FluorophoreDistribution

Image Obtained by Deconvolution

of Simulated Image

Potential Pitfalls of Deconvolution

Acknowledgements

• Whitaker Foundation

• National Science Foundation

Comparing Models to Microscopy

Molecular Theory Molecular Reality

Microscopic Observations

Model Predictions ???

Fluorescence Microscope

Computer Simulation