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

Mitotic Spindle spindle pole chromosomes kinetochore 1.7 µm In budding yeast: ~40 MTs µm In animal cells: ~1000 MTs interpolar microtubule kinetochore microtubule bifunctional plus-end motors ++ spindle pole COMPRESSION TENSION

Microtubule Dynamic Instability

Length (µm) Time (minutes) “Catastrophe” “Rescue” Microtubule “Dynamic Instability” VgVg VsVs kckc krkr 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 P EQ Green=Cse4-GFPkMT Plus Ends Red=Spc29-CFPkMT Minus Ends

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

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 Model-Convolution of Original Distribution Original Fluorophore Distribution 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 Approach Model Probability that the model is consistent with the data Parameter Space (a 1, a 2, a 3,…a N ) <Cutoff? Experimental Data yes no Accept Model Parameter Space Reject Model Parameter Space Accept Model Parameter Space

Modeling Approach Model assumptions: 1)Metaphase kinetochore microtubule dynamics are at steady-state (not time-dependent) 2)One microtubule per kinetochore 3)Microtubules never detach from kinetochores 4)Parameters can be: Constant Spatially-dependent (relative to poles) Spatially-dependent (relative to sister kinetochore)

“Microtubule Chemotaxis” in a Chemical Gradient Immobile Kinase Mobile Phosphatase A: Phosphorylated Protein B: Dephosphorylated Protein k* Surface reaction B-->A k Homogeneous reaction A-->B Kinetochore Microtubules - + Immobile Kinase 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 Obtained by Convolution of PSF and GWN with Original Distribution Original Fluorophore Distribution Model-Convolution

Kinetochore MT Lengths in Budding Yeast Experimentally Observed Theoretically Predicted ? 2 µm

Catastrophe Gradient Model Frequency (min -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-state If k= 50 s -1, D=5 µm 2 /s, and L=1 µm, then  =3 MT Destabilizer Position Concentration X=0 X=L

Could tension stabilize kinetochore microtubules? Tension 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 Frequency (min -1 ) Catastrophe Gradient with Tension- Dependent Rescue Model (No Tension) Frequency (min -1 ) Normalized Spindle Position

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

Rescue Gradient Model Normalized Spindle Position Catastrophe or Rescue Frequency (min -1 )

Simulation of Budding Yeast Mitosis Metaphase Anaphase Prometaphase Start with random positions, let simulation reach 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 V g, V s, k c, and k r, the length distribution is exponential V d <0exponential decay V d >0exponential growth

Sister Kinetochore Microtubule Dynamics

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

Catastrophe Gradient with Tension-Rescue Model Lack of Equator Crossing in the Catastrophe Gradient with Tension-Rescue Model ~25% FRAP recovery ~5% FRAP recovery

Microtubule Dynamic Instability

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 Sprague et al., Biophys. J., 2003

Predicted Concentration Profile

Model Predictions: Effect of Surface Reaction Rate

Defining “Metaphase” in Budding Yeast