ModelConvolution Approach to Modeling Green Fluorescent Protein Dynamics

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 interpolar microtubule + COMPRESSION kinetochore + chromosomes + kinetochore microtubule TENSION + - + spindle pole + bifunctional plus-end motors In animal buddingcells: In yeast: ~1000 ~40 MTs 1. 7 µmµm 10 -20 - spindle pole

Microtubule Dynamic Instability

Microtubule “Dynamic Instability” kc Length (µm) “Catastrophe” Vg Vs “Rescue” kr Time (minutes) 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

Budding Yeast Spindle Geometry

Congression in S. cerevisiae P EQ P Green=Cse 4 -GFP k. MT Plus Ends Red=Spc 29 -CFP k. MT Minus Ends

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

Point Spread Function (PSF) +0. 4 μm +0. 2 0 -0. 2 • A point source of light is spread via diffraction through a circular aperture • Modeling needs to account for PSF -0. 4

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

Cse 4 -GFP Fluorescence Distribution Experimentally Observed Theoretically Predicted

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

Modeling Approach Model Parameter Space (a 1, a 2, a 3, …a. N) Experimental Data yes Probability that the model is consistent with the data <Cutoff? Accept Model Reject Model Parameter Space no

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 A: Phosphorylated Protein B: Dephosphorylated Protein k* Surface reaction B-->A - Kinetochore Microtubules + k Homogeneous reaction A-->B Immobile Kinase Mobile Phosphatase Immobile Kinase MT Destabilizer Concentration X=0 Position X=L

Could tension stabilize kinetochore microtubules? Tension Kip 3

Distribution of Cse 4 -GFP: Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue

Model Combinations

Catastrophe Gradient-Tension Rescue Model 3 2 1

Conclusions • Congression in budding yeast is mediated by: – Spatially-dependent catastrophe gradient – Tension between sister kinetochoredependent 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 • Mc. Knight 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

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

Distribution of Cse 4 -GFP: Catastrophe Gradient Model

Experimental Cse 4 -GFP FRAP • Cse 4 -GFP does not turnover on kinetochore • Kinetochores rarely persist in opposite half-spindle Pearson et al. , Current Biology, in press

Cse 4 -GFP FRAP: Modeling and Experiment Catastrophe Gradient Simulation Experiment

Cse 4 -GFP FRAP: Modeling and Experiment

Gradients in Phospho-state MT Destabilizer Concentration X=0 Position X=L If k= 50 s-1, D=5 µm 2/s, and L=1 µm, then g=3

Could tension stabilize kinetochore microtubules? Tension Kip 3 Tension

Catastophe Gradient with Tension Between Sister Kinetochore-Dependent Rescue Model

Experimental Cse 4 -GFP in Cdc 6 mutants WT Cdc 6 D

Cse 4 -GFP in Cdc 6 Cells: No tension between sister kinetochores Rescue Gradient with Tension-Dependent Catastrophe Model (No Tension) Frequency (min-1) Catastrophe Gradient with Tension. Dependent Rescue Model (No Tension) Normalized Spindle Position

Cse 4 -GFP in Cdc 6 Cells: No tension between sister kinetochores

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

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

MINIMUM ABSOLUTE SISTER KINETOCHORE SEPARATION DISTANCE

Stu 2 p-mediated catastrophe gradient? WT Stu 2 p-depleted Pearson et al. , Mol. Biol. Cell, 2003

Green Fluorescent Protein

Prometaphase Spindles and the Importance of Tension in Mitosis “Syntely” M Ipl 1 -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 Vd>0 exponential decay exponential growth

Sister Kinetochore Microtubule Dynamics

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

Tension Between Sister Kinetochore. Dependent Rescue

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