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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

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Mitotic Spindle spindle pole chromosomes kinetochore 1.7 µm In budding yeast: ~40 MTs 10-20 µm In animal cells: ~1000 MTs interpolar microtubule -- + + + + kinetochore microtubule bifunctional plus-end motors ++ spindle pole COMPRESSION TENSION

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Microtubule Dynamic Instability

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Length (µm) Time (minutes) “Catastrophe” “Rescue” Microtubule “Dynamic Instability” VgVg VsVs kckc krkr Hypothesis: The kinetochore modulates the DI parameters

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Can only get peaks here Not here MT Length Distribution for Pure Dynamic Instability Right PoleLeft Pole 1.7

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Budding Yeast Spindle Geometry

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Congression in S. cerevisiae P P EQ Green=Cse4-GFPkMT Plus Ends Red=Spc29-CFPkMT Minus Ends

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

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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

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

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Cse4-GFP Fluorescence Distribution Experimentally Observed Theoretically Predicted

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Dynamic Instability Only Model Sprague et al., Biophysical J., 2003

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Modeling Approach Model Probability that the model is consistent with the data Parameter Space (a 1, a 2, a 3,…a N )

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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)

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“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

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Could tension stabilize kinetochore microtubules? Tension Kip3

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

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Model Combinations

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123 Catastrophe Gradient-Tension Rescue Model

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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

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Acknowledgements Melissa Gardner, Brian Sprague (Uof M) Chad Pearson, Paul Maddox, Kerry Bloom,Ted Salmon (UNC-CH) National Science Foundation Whitaker Foundation McKnight Foundation

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

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

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Catastrophe Gradient Model Frequency (min -1 ) Normalized Spindle Position Sprague et al., Biophys. J., 2003

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Distribution of Cse4-GFP: Catastrophe Gradient Model

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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

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Cse4-GFP FRAP: Modeling and Experiment Catastrophe Gradient Simulation Experiment

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Cse4-GFP FRAP: Modeling and Experiment

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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

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Could tension stabilize kinetochore microtubules? Tension Kip3

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Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model

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Experimental Cse4-GFP in Cdc6 mutants WT Cdc6

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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

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

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

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Simulation of Budding Yeast Mitosis Metaphase Anaphase Prometaphase Start with random positions, let simulation reach steady-state Eliminate cohesion, set spring constant to 0

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MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE

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WT Stu2p-depleted Pearson et al., Mol. Biol. Cell, 2003 Stu2p-mediated catastrophe gradient?

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Green Fluorescent Protein

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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

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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

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Sister Kinetochore Microtubule Dynamics

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

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“Directional Instability” Skibbens et al., JCB 1993

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Tension on the kinetochore promotes switching to the growth state? Skibbens and Salmon, Exp. Cell Res., 1997

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Tension Between Sister Kinetochore- Dependent Rescue

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

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Microtubule Dynamic Instability

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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

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Predicted Concentration Profile

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Model Predictions: Effect of Surface Reaction Rate

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Defining “Metaphase” in Budding Yeast

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