Stable spatial gradients of cytoskeleton assembly regulators David Odde University of Minnesota

Microtubule Structure

Length (µm) Time (minutes) “Catastrophe” “Rescue” Microtubule “Dynamic Instability” (DI) VgVg VsVs kckc krkr see VanBuren et al., PNAS USA (2002)

Microtubules in Mitosis

Mitotic Spindle spindle pole body chromosome kinetochore kinetochore microtubule spindle pole body 1.5 µm In yeast: ~40 MTs µm In animal cells: ~1000 MTs Interpolar microtubule

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

Length (µm) Time (minutes) “Catastrophe” “Rescue” Microtubule “Dynamic Instability” (DI) VgVg VsVs kckc krkr

Point Spread Function (PSF) A point source of light is spread via diffraction through a circular aperture Modeling needs to account for PSF μm

Simulated Image Obtained by Convolution of PSF and GWN with Original Distribution Original Fluorophore Distribution 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 SE

Results: DI Only Model 1000 nm

Results: DI Only Model

Alternative Models

Microtubule Chemotaxis Immobile Kinase Mobile Phosphatase Microtubule A: Phosphorylated ProteinStabilizes MTs B: Unphosphorylated ProteinDestabilizes MTs Concentration Position MT Attractant MT Repellant X=0 X=L k* Surface reaction B-->A k Homogeneous reaction A-->B

Microtubule Chemotaxis:Op18 Immobile Plx1 Mobile PP2A Microtubule A: Op18-hi-P B: Op18-low-PDestabilizes MTs Concentration Position Op18-hi-P Op18-low-P Chromatin

Microtubule Chemotaxis: RanGTP Immobile RCC1 Mobile RanGAP Microtubule A: RanGTPStabilizes MTs B: RanGDP Concentration Position RanGTP RanGDP Chromatin

Model for Chemotactic Gradients of Phosphoprotein State Fick’s Second Law with First-Order Homogeneous Reaction (A->B) B.C. 1: Surface reaction at x=0 (B->A) B.C. 2: No net flux at x=L Conservation of phosphoprotein

Predicted Concentration Profile If k= 1 s -1, D= m 2 /s, and L=10 µm, then  =3

Model Predictions: Effect of Homogeneous Reaction Rate

Model Predictions: Effect of Surface Reaction Rate

Microtubule Chemotaxis: RanGTP Immobile RCC1 Mobile RanGAP Microtubule A: RanGTPStabilizes MTs B: RanGDP Concentration Position RanGTP RanGDP Chromatin

Results: Chemical Gradient and Polar Ejection Force Models 1000 nm

Cse4 end of simulation, mutant “Tension” model Left Half Spindle Right Half Spindle Figure 2

Cse4 End of Simulation, wild-type, “Gradient-Only” Model Right Half Spindle Left Half Spindle Figure 4

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

X X X Y Z Y Simulated Actin Filament Dendritic Branching Simulated Image of Actin Filament Dendritic Branching Model-Convolution: Application to Dendritic Actin Filament Branching

Simulated Image Obtained by Model-Convolution of Original Distribution Original Fluorophore Distribution Image Obtained by Deconvolution of Simulated Image Potential Pitfalls of Deconvolution

Acknowledgements Whitaker Foundation National Science Foundation

Comparing Models to Microscopy Molecular TheoryMolecular Reality Microscopic Observations Model Predictions ??? Fluorescence Microscope Computer Simulation