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

2. 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

3. Microtubule Dynamic Instability

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

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

6. Budding Yeast Spindle Geometry

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

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

9. 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

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

11. Cse4-GFP Fluorescence Distribution Experimentally Observed Theoretically Predicted

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

13. 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

14. 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)

15. “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

16. Could tension stabilize kinetochore microtubules? Tension Kip3

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

18. Model Combinations

19. 123 Catastrophe Gradient-Tension Rescue Model

20. 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

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

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

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

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

25. Distribution of Cse4-GFP: Catastrophe Gradient Model

26. 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

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

28. Cse4-GFP FRAP: Modeling and Experiment

29. 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

30. Could tension stabilize kinetochore microtubules? Tension Kip3

31. Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model

32. Experimental Cse4-GFP in Cdc6 mutants WT Cdc6 

33. 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

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

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

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

37. MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE

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

39. Green Fluorescent Protein

41. 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

44. 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

45. Sister Kinetochore Microtubule Dynamics

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

47. “Directional Instability” Skibbens et al., JCB 1993

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

49. Tension Between Sister Kinetochore- Dependent Rescue

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

51. Microtubule Dynamic Instability

52. 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

53. Predicted Concentration Profile

54. Model Predictions: Effect of Surface Reaction Rate

55. Defining “Metaphase” in Budding Yeast