David Odde Dept. of Biomedical Engineering University of Minnesota

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. 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

3. Microtubule Dynamic Instability

4. “Catastrophe” Length (µm) “Rescue” Time (minutes) Microtubule “Dynamic Instability” kc Vg Vs kr Hypothesis: The kinetochore modulates the DI parameters

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

6. Budding Yeast Spindle Geometry

7. Congression in S. cerevisiae P EQ P Green=Cse4-GFP kMT Plus Ends Red=Spc29-CFP kMT Minus Ends

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

9. -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

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

14. 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)

15. 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

16. Tension Could tension stabilize kinetochore microtubules? Kip3

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

18. Model Combinations

19. 3 2 1 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. Model-Convolution Original Fluorophore Distribution Simulated Image Obtained by Convolution of PSF and GWN with Original Distribution

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

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. 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

30. Tension Tension Could tension stabilize kinetochore microtubules? Kip3

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

32. Experimental Cse4-GFP in Cdc6 mutants WT Cdc6D

33. 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

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

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

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

37. MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE

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

39. Green Fluorescent Protein

41. 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

44. 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

45. Sister Kinetochore Microtubule Dynamics

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

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