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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. In animal cells:. In budding yeast:. 10-20 µm. 1.7 µm. ~1000 MTs. ~40 MTs. Mitotic Spindle. interpolar
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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
In animal cells: In budding yeast: 10-20 µm 1.7 µm ~1000 MTs ~40 MTs Mitotic Spindle interpolar microtubule + COMPRESSION + kinetochore spindle pole spindle pole - - + + TENSION kinetochore microtubule chromosomes + + bifunctional plus-end motors
“Catastrophe” Length (µm) “Rescue” Time (minutes) Microtubule “Dynamic Instability” kc Vg Vs kr Hypothesis: The kinetochore modulates the DI parameters
MT Length Distribution for Pure Dynamic Instability Can only get peaks here Not here 1.7 Left Pole Right Pole
Congression in S. cerevisiae P EQ P Green=Cse4-GFP kMT Plus Ends Red=Spc29-CFP kMT Minus Ends
Deconvolution Convolution “Experiment-Deconvolution”vs. “Model-Convolution” Model Experiment
-0.4 -0.2 0 +0.4 μm +0.2 Point Spread Function (PSF) • A point source of light is spread via diffraction through a circular aperture • Modeling needs to account for PSF
Original Fluorophore Distribution Simulated Image Obtained by Model-Convolution of Original 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 Experimental Data Parameter Space yes Probability that the model is consistent with the data <Cutoff? (a1, a2, a3,…aN) no Accept Model Accept Model Reject Model Parameter Space Parameter Space Parameter Space
Modeling Approach • Model assumptions: • Metaphase kinetochore microtubule dynamics are at steady-state (not time-dependent) • One microtubule per kinetochore • Microtubules never detach from kinetochores • Parameters can be: • Constant • Spatially-dependent (relative to poles) • Spatially-dependent (relative to sister kinetochore)
k k* Surface reaction B-->A Homogeneous reaction A-->B MT Destabilizer Concentration X=L X=0 Position “Microtubule Chemotaxis” in a Chemical Gradient A: Phosphorylated Protein B: Dephosphorylated Protein Kinetochore Microtubules - + Immobile Kinase Immobile Kinase Mobile Phosphatase
Tension Could tension stabilize kinetochore microtubules? Kip3
Distribution of Cse4-GFP: Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue
3 2 1 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
Model-Convolution Original Fluorophore Distribution Simulated Image Obtained by Convolution of PSF and GWN with Original Distribution
Kinetochore MT Lengths in Budding Yeast ? 2 µm Experimentally Observed Theoretically Predicted
Catastrophe Gradient Model Frequency (min-1) Normalized Spindle Position Sprague et al., Biophys. J., 2003
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
MT Destabilizer Concentration X=L X=0 Position Gradients in Phospho-state If k= 50 s-1, D=5 µm2/s, and L=1 µm, then g=3
Tension Tension Could tension stabilize kinetochore microtubules? Kip3
Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model
Cse4-GFP in Cdc6 Cells: No tension between sister kinetochores Catastrophe Gradient with Tension-Dependent Rescue Model (No Tension) Rescue Gradient with Tension-Dependent Catastrophe Model (No Tension) Frequency (min-1) Frequency (min-1) Normalized Spindle Position Normalized Spindle Position
Cse4-GFP in Cdc6 Cells: No tension between sister kinetochores
Rescue Gradient Model Catastrophe or Rescue Frequency (min-1) Normalized Spindle Position
Simulation of Budding Yeast Mitosis Anaphase Prometaphase Metaphase Start with random positions, let simulation reach steady-state Eliminate cohesion, set spring constant to 0
Stu2p-mediated catastrophe gradient? WT Stu2p-depleted Pearson et al., Mol. Biol. Cell, 2003
Prometaphase Spindles and the Importance of Tension in Mitosis “Syntely” M Ipl1-mediated detachment of kinetochores under low tension Dewar et al., Nature 2004 D
MT Length Distributions • Regard MT dynamic instability as diffusion + drift • The drift velocity is a constant given by • For constant Vg, Vs, kc, and kr, the length distribution is exponential Vd<0 exponential decay Vd>0 exponential growth
Model-Convolution Original Fluorophore Distribution Simulated Image Obtained by Convolution of PSF and GWN with Original Distribution
“Directional Instability” Skibbens et al., JCB 1993
Tension on the kinetochore promotes switching to the growth state? Skibbens and Salmon, Exp. Cell Res., 1997
Lack of Equator Crossing in the Catastrophe Gradient with Tension-Rescue Model Catastrophe Gradient with Tension-Rescue Model ~25% FRAP recovery ~5% FRAP recovery