1. Protein-membrane association. Theoretical model, Lekner summation A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H.Juffer The University of Oulu Finland-Suomi A.H. Juffer The University of Oulu Finland-Suomi

2. Previous work n W. Xin and A.H. Juffer, Polarization and dehydration effects in protein- membrane association, To Be Submitted, 2004 n W.Xin and A.H. Juffer, A BEM formulation of biomolecular interaction, To Be Submitted, 2004 n C.M. Shepherd, H.J. Vogel and A.H. Juffer, Monte Carlo and molecular dynamics studies of peptide-bilayer binding, in: High Performance Computing Systems and Applications 2000 (Nikitas J. Dimpoulos and Kin F. Li, Eds.), Kluwer Academic Publishers (Dordrechts, The Netherlands), Chapter 29, 447-464, 2002. n C.M. Shepherd, K.A. Schaus, H.J. Vogel and A.H. Juffer, A Molecular Dynamics Study of Peptide-Bilayer Adsorption. Biophys. J. 80, 579-596, 2001. n A.H. Juffer, C.M. Shepherd and H.J. Vogel, Protein-membrane electrostatic interactions: Application of the Lekner summation technique. J. Chem. Phys. 114, 1892-1905, 2001. n A.H. Juffer, J. de Vlieg and P. Argos, Adsorption of Proteins onto Charged Surfaces: A Monte Carlo Approach with Explicit Ions. J. Comput. Chem., 17, 1783-1803, 1996.

3. Background n Interactions between lipid molecules and proteins crucial role in regulation biological function. n Membrane proteins: u Integral proteins: e.g. photosynthetic reaction center: F Fully embedded into membrane u Peripheral proteins: e.g. phospholipase C-  1: F Only weakly bound to surface, separable by change in pH or ionic strength

4. Background n Understanding the physics of protein-lipid interactions leads to deeper insight Equilibrium constant ↕ Standard free energy THERMODYNAMICS, NOT MECHANISM

5. Modeling protein-membrane binding lipid bilayers sandostatin

6. Free energy of binding Non-polar hydrophobic effect (expulsion of non-polar compounds from water Direct electrostatic interaction between basic residues and anionic lipids. Conformational Change. Difference in dielectric properties between water and hydrocarbon region (mutual polarization effects). Changes in motional degrees of freedom. Changes inside membrane.

7. Coulomb interaction r ij ++ Long-ranged: beyond dimension of protein

8. How to calculate it? Assume periodicity along x, y-direction q Image LyLy LxLx LyLy

9. The Lekner Summation Conditionally converging sum Fast absolutely converging sum

10. Four surface charges: potential

11. Four surface charges: field

12. Ions next to flat surface carrying a negative surface charge density. Accumulation of Na +. Depletion of Cl -. Electric moment pointing towards flat surface. Symmetry along x- and y-axis but not along z-axis. z-axis

13. Ion densities near POPC

14. Ion densities near POPG

15. Free energy of adsorption Change in free energy in moving protein from bulk solution at z=-  to A point z=z 0 near the surface: Thermodynamic integration

16. Electrostatic force acting on Sandostatin POPC

17. Force acting on Sandostatin, MD POPC

18. Movie The first 2 ns of a 6 ns MD simulation. Biophys. J. 80, 579-596, 2001.

19. Electrostatic force acting on Sandostatin POPG

20. Two solutes A, B immersed in polarizable solvent S q Q Solvent A B approximation cavity

21. Two polarisable objects

22. Future improvements n Inclusion of internal (`essential’) degrees of freedom. n Dynamical simulations n Stochastic modeling of proteins n Effects of pH.

23. Acknowledgements n Weidong Xin n Craig Shepherd n Heritage Foundation n Human frontiers n MRC n Biocenter n Academy of Finland.