1. 1 Ανάπτυξη στοχαστικού μαθηματικού μοντέλου για την προσομοίωση πειραμάτων ανάκτησης φθορισμού μετά από φωτολεύκανση με σκοπό την μελέτη των κινητικών ιδιοτήτων σημασμένων πρωτεϊνών [http://www.api.com/lifescience/dv-QLM.html]

2. 2 PRESENTATION OUTLINE  FRAP Introduction Introduction Deterministic Modeling Deterministic Modeling Stochastic Modeling Stochastic Modeling Comparison of the two methods Comparison of the two methods Analysis of GFP-GR kinetics Analysis of GFP-GR kinetics

3. 3 Definition: A live-cell-imaging technique used to study the extensive networks of protein–protein interactions that regulate cellular processes. Technique: A pulse of high-intensity light is used to irreversibly photobleach a population of fluorophores in a target region FRAP: INTRODUCTION [Nature, 2004]

4. 4 FRAP: RECOVERY CURVE Reaction:kon,koff Diffusion:Df [http://www.bio.davidson.edu/Courses/Molbio/FRAPx/FRAP.html]

5. 5 FRAP: DETERMINISTIC MODELING Pure Diffusion Almost all proteins are free, Recovery=diffusion Effective Diffusion Reactions faster than diffusion Recovery=slowed down diffusion Reaction Dominant Diffusion faster than reactions Recovery=reactions rates [Sprague et al, 2004]

6. 6 FRAP: STOCHASTIC MODELING I Model: Diffusion is seen as a Brownian random motion (Simulation with Monte Carlo methods) GFP diffuses with no preferred direction due to random collisions with surrounding molecules Application: nuclear mobility of a GFP-tagged glucocorticoid receptor (GFP-GR) in nuclei of both normal and ATP- depleted cells.Does it binds to the nuclear matrix (3-dimensional filamentous protein )? [Brown R, 1828] Brownian motion of DNA-tethered beads Brownian motion of DNA-tethered beads [http://www.bio.brandeis.edu/~gelles/movies.html]

7. 7 FRAP: STOCHASTIC MODELING II Model: Reaction is seen as stochastic biochemical pathway (Simulation with Monte Carlo methods) 1. What is the time that a new reaction will happen? 2. What is the next most probable reaction? 3. What will be the change of reactant species after a reaction has occurred? [Gillespie D, 1977]

8. 8 FRAP: STOCHASTIC MODELING III

9. 9 FRAP: DETERMINISTIC VERSUS STOCHASTIC MODELING

10. 10 FRAP: STUDYING THE NUCLEAR MOBILITY OF A GFP-GR I Population statisticsPopulation statistics Tendency towards reaction equilibrium (entropy!)Tendency towards reaction equilibrium (entropy!)

11. 11 FRAP: STUDYING THE NUCLEAR MOBILITY OF A GFP-GR II

12. 12 FRAP: STUDYING THE NUCLEAR MOBILITY OF A GFP-GR III

13. 13 FRAP: STUDYING THE NUCLEAR MOBILITY OF A GFP-GR IV

14. 14 FRAP: STUDYING THE NUCLEAR MOBILITY OF A GFP-GR V

15. 15 FRAP: WHAT MORE CAN STOCHASTIC SIMULATION OFFER  Firmer physical basis  Richer information  Expensive implementation

16. 16 ACKNOWLEDGEMENTS  ΙΚΥ  TUGRAZ, AUSTRIA