1. Stochastic Model of Microdomain Formation in Biological Membranes Audi Byrne May 19 th 2005 MPB Retreat Biomathematics Study Group

2. Anne Kenworthy Lab 2004-2005 Kimberly Drake Shawn Goodwin Carl Rogers Minchul Kang

3. The micro-organization of lipids and proteins within the cell membrane is an open question. We investigate: (1) Clustering mechanisms which would result in distinct protein organizations and (2) Ways in which FRET could be used to distinguish among these possibilities in native cell membranes. Overview The Lipid Raft Hypothesis

4.  The cell membrane phase separates into liquid- ordered domains and liquid-disordered domains.  Liquid-Ordered Domains - “lipid rafts” - enriched in glycosphingolipids and cholesterol - act to compartmentalize membrane proteins: involved in signal transduction, protein sorting and membrane transport.

5. Heetderks and Weiss Lipid-Lipid Interactions Gel Domains: Phospholipids with long, ordered chains Fluid Domains: Phospholipids with short, disordered chains Cholesterol : Gel domains form a liquid ordered phase Domain Formation In Model Membranes

6. 1. Building a Model for Membrane Partitioning - What conditions (model rules) result in phase separation of lipids?

7. Model Components I Different Lipid Species Different lipid species are assigned different labels ‘  ’. Plasma Membrane NxN Square Lattice Every node is occupied by a single lipid. (10 4 - 10 6 lipids)

8. Plasma Membrane

9. Lipid 1

10. Plasma Membrane Lipid 2 Lipid 1

11. Plasma Membrane Lipid 2 Lipid 1 Lipid 3

12. Plasma Membrane Lipid 2 Lipid 1 Lipid 3

13. Model Components II Every pair of lipid types is assigned an “interface energy”. Lipid Interaction Lattice Energy The total energy of the system is defined as the sum of the interface energies of all adjacent nodes on the lattice. 0 <   1  2 < 1 Example Like lipids:  = 0 Unlike lipids:  = 1

14. Lipid Diffusion Lipids diffuse by stochastic random walk in a way which decreases system energy by the Metropolis algorithm: Neighboring lipids switch locations if switching decreases the energy of the system. Otherwise, the switch is permitted only if the local temperature is high enough. (random variable)

15. Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6

16. Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6 Neighbor Switch

17. Example Unlike Lipids δ =1 Lipid-Lipid Interface Energies Like Lipids δ=0 Local Interface Energy = 6 Neighbor Switch Local Interface Energy = 3

18. Simulation Results Random Initial Conditions

19. Simulation Results

20. 2. Application of the Phase Separation Model - What predictions does the model make for different lipid-lipid interactions? - Can FRET be used to distinguish among different lipid-lipid interactions?

21. A 3-Lipid Mixture: Lipid 1 and Lipid 2 occur in 1:1 ratio. Lipid 1 does not mix with Lipid 2 or Lipid 3. What does the model predict as the coupling energy between Lipid 3 and Lipid 2 is varied? Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 From A to C, interface energies between Lipid 2 and Lipid 3 increase.

22. Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 Lipid 2Lipid 1Lipid 3

23. Example A Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 Lipid 2Lipid 1Lipid 3

24. Example A Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 Example B Lipid 2Lipid 1Lipid 3

25. Example A Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 Example BExample C Lipid 2Lipid 1Lipid 3

26. Example A 30% Lipid 3 Example A: Lipid3 Partitions Within Lipid2 Example B: Lipid3 Partitions Slightly Within Lipid2 Example C: Lipid3 Doesn’t Partition Within Lipid2 Example BExample C Lipid 2Lipid 1Lipid 3

27. Interface Energies of L2 and L3 Decrease → Lipid 3 Concentration Increases → [1%,10%,30%] Example C Example B Example A

28. Modeling FRET Lipids are randomly labeled with “donors” and “acceptors” that can undergo “FRET”. FRET Efficiency = (# Actual Transfers) / (# Possible Transfers) = (Acceptor Fluorescence) / (Acceptor + Donor Fluorescence) Fluorescence Resonance Energy Transfer Electronic excitation energy is transferred from one protein (the donor) to another (the acceptor) over very small (<10 nm) distances due to their dipole-dipole interaction. FRET efficiency is proportional to the inverse sixth power of the distance between the proteins.

29. Labeling Lipid 3 “Expt” 1 Results: Distinguishing Models With FRET Y-axis: FRET efficiency X-axis: Lipid3 concentration Blue = L3 Partitions Well into L2 Purple = L3 Partitions Somewhat Pink = L3 Doesn’t Partition into L2

30. Labeling Lipid 3Labeling Lipid 3 with donors and Lipid 2 with acceptors “Expt” 1“Expt” 2 Results: Distinguishing Models With FRET Y-axis: FRET efficiency X-axis: Lipid3 concentration Blue = L3 Partitions Well into L2 Purple = L3 Partitions Somewhat Pink = L3 Doesn’t Partition into L2

31. Labeling Lipid 3Labeling Lipid 3 with donors and Lipid 2 with acceptors Labeling Lipid 3 with donors and Lipid 1 with acceptors “Expt” 1“Expt” 2“Expt” 3 Results: Distinguishing Models With FRET Y-axis: FRET efficiency X-axis: Lipid3 concentration Blue = L3 Partitions Well into L2 Purple = L3 Partitions Somewhat Pink = L3 Doesn’t Partition into L2

32. Conclusion FRET can distinguish between model predictions and modeling can be used to suggest the most sensitive experimental approach. Future Directions Model protein and add protein-lipid interactions. Develop models for other raft mechanisms.

33. Thank you