1. Coupling of SCC-DFTB, Generalized Born and Hydrophobic Models in Description of Hydration Free Energies Bogdan Lesyng Interdyscyplinary Centre for Mathematical and Computational Modelling and Faculty of Physics, University of Warsaw (http://www.icm.edu.pl/~lesyng) and European Centre of Excellence for Multiscale Biomolecular Modelling, Bioinformatics and Applications (http://www.icm.edu.pl/mamba) AMM-IV Leicester, 18-21/08/2004

2. Dynamics, classical and/or quantum one in the real molecular environment Sequences at the protein & nucleic acids levels 3D & electronic structure Function Metabolic pathways & signalling Sub-cellular structures & processes Cell(s), structure(s) & functions 1 RPDFCLEPPY 10 11 TGPCKARIIR 20 21 YFYNAKAGLC 30 31 QTFVYGGCRA 40 41 KRNNFKSAED 50 51 CMRTCGGA 58

3. In our organisms we have ~ 10 3 protein kinases and phosphatases which phosphorylate/ dephosphorylate other proteins activating or disactivating them. These are controllers of most of methabolic pathways.

4. A Protein Kinase Molecule with ATP (catalytic domain)

5. Designing inhibitors Every two years we organize international conferences on ”Inhibitors of Protein Kinases”, and workshops on „Mechanisms on Phosphorylation Processes” The next one: June 26-30, 2005 Warsaw http://www.icm.edu.pl/ ipk2005/ Ref. To Piotr Setny’s poster

6. Classes of Models Microscopic models Mesoscopic models

8. R” : H, R’ : H, OH X : H, OH, NH 2 Y : H, OH, NH 2 W.R.Rudnicki et al., Acta Biochim. Polon., 47, 1-9(2000)

10. . Motivation for multiscale modelling Structure formation mechanisms -> molecular recognition processes, –M.H.V. van Regenmortel, Molecular Recognition in the Post-reductionist Era, J.Mol.Recogn., 12, 1-2(1999) –J.Antosiewicz, E. Błachut-Okrasińska, T. Grycuk and B. Lesyng, A Correlation Between Protonation Equilibria in Biomolecular Systems and their Shapes: Studies using a Poisson-Boltzmann model., in GAKUTO International Series, Mathematical Science and Applications. Kenmochi, N., editor, vol. 14, 11- 17, Tokyo, GAKKOTOSHO CO, pp.11-17, 2000. Quantum forces in complex biomolecular systems. –P. Bala, P. Grochowski, B. Lesyng, J. McCammon, Quantum Mechanical Simulation Methods for Studying Biological System, in: Quantum-Classical Molecular Dynamics. Models and Applications, Springer-Verlag, 119-156 (1995) –Grochowski, B. Lesyng, Extended Hellmann-Feynman Forces, Canonical Representations, and Exponential Propagators in the Mixed Quantum-Classical Molecular Dynamics, J.Chem.Phys, 119, 11541-11555(2003) To understand structure & function of complex biomolecular systems.

11. 11 Protonation equilibria in proteins M. Wojciechowski, T. Grycuk, J. Antosiewicz, B.lesyng Prediction of Secondary Ionization of the Phosphate Group in Phosphotyrosine Peptides, Biophys.J, 84, 750-756 (2003)

12. Active site (quantum subsystem) Classical molecular scaffold (real molecular environment) Solvent (real thermal bath) Interacting quantum and classical subsytsems. Enzymes, special case of much more general problem.

13. Microscopic generators of the potential energy function AVB – (quantum) AVB/GROMOS - (quantum-classical) SCC-DFTB - (quantum) SCC-DFTB/GROMOS - (quantum-classical) SCC-DFTB/CHARMM - (quantum -classical).... Dynamics MD (classical) QD (quantum) QCMD (quantum-classical).... Mesoscopic potential energy functions Poisson-Boltzmann (PB) Generalized Born (GB)....

14. atomic charges many-electron wave function representing i-th valence structure Approximate Valence Bond (AVB) Method See: Trylska et al., IJQC 82, 86, 2001) and references cited positions of the nuclei Hamiltonian matrix in basis of valence structures electronic ground state energy

15. SCC-DFTB Method (Self Consistent Charge Density Functional Based Tight Binding Method, SCC DFTB, Frauenheim et al. Phys Stat. Sol. 217, 41, 2000) basic DFT concepts: 1-electron orbitals total electron density 1-electron Hamiltonian (Kohn-Sham equation)

16. Total energy for arbitrary electronic density has minimum at  0 (  0 ) and  0, resulting from Kohn-Sham eq. (ground state) el. kinetic. en., el.-nuclei interaction, el.-el. Exchange and twice el.-el. electrostatic interaction n-n inter., XC non-local corr. and minus el.-el. electrostatic int. (R)

17. TB approach: expansion of the energy functional around the ground state density of the ground state second and higher order expansion terms (SCC version)

18. TBDFT approximations densities at free atoms atom pair potentials current atomic net charges of free atoms

19. + LCAO approximation atomic orbitals Mulliken charges combination coefficients (c)

20. Condition for the ground state Hamiltonian matrix overlap matrix:  TBDFT equations:

21. J.Li, T.Zhu, C.Cramer, D.Truhlar, J. Phys. Chem. A, 102, 1821(1998) New generation of charges capable reproducing electrostatic properties, in particular molecular dipole moments.

22. CM3/SCC-DFTB charges J.A. Kalinowski, B.Lesyng, J.D. Thompson, Ch.J. Cramer, D.G. Truhlar, Class IV Charge Model for the Self-Consistent Charge Density-Functional Tight-Binding Method, J. Phys. Chem. A 2004, 108, 2545-2549

23. CM3 charges are defined with the following mapping: and the correction function which is taken to be a second order polynomial with coefficients depending on the atom types: which involves Meyers bond order:

27. Microscopic (quantum) description of intermolecular interactions : Mesoscopic description of intermolecular interactions (free energies) Electrostatic Poisson-Boltzmann energy Interaction potentials See eg. E.Gallicchio and R.M.Levy, J.Comput. Chem.,25,479-499(2004)

28. ” GB ” – Generalized Born A k - van der Waals surface area of atom k  k - surface tension parameter assigned to atom k First papers on Born models: M.Born, Z.Phys., 1,45(1920) R.Constanciel and R.Contreas, Theor.Chim.Acta, 65,111(1984) W.C.Still, A.Tempczyk,R.C.Hawlely,T.Hendrikson, J.Am.Chem.Soc.,112,6127(1990) D.Bashford, D.Case, Annu.Rev.Phys.Chem., 51,129(2000)

31. M.Feig, W.Im, C.L.Brooks, J.Chem.Phys.,120,903-911(2004) (I) (II) (III) (IV) Coulomb Field appr. Kirkwood Model

32. Ratio of the GB solvation enery to the Kirkwood solvation energy

34. (zooming) case IV  in /  ex

35. The optimal value of the exponent

36. Conventional Born, D.Bashford & D.Case, Annu.Rev. Phys.Chem.,51,129-152(2000) Srinivasan et al.,Theor.Chem.Acc., 101,426-434(1999) M.Wojciechowski & B.Lesyng, Submitted to J.Phys.Chem. Corrections to the ionic strength

38. SASA A 2 CHARMM SASA A 2 CHARMM SASA A 2 Fit 1 SASA A 2 Fit 2

40. Following Gallicchio & Levy J.Comput.Chem.,25,479-499(2004) Fitting the nonpolar solvation energy with the cavity and VdW components (preliminary)

42. Acknowledgements PhD students: Jarek Kalinowski Michał Wojciechowski Piot Kmieć Magda Gruziel Collaboration: Dr. T. FrauenheimSCC-DFTB Dr. M. Elstner Dr. D. TruhlarCM3-charges Dr. J. ThompsonMinnesota Solvation Data Base Dr. C. Cramer Studies supported by ”European CoE for Multiscale Biomolecular Modelling, Bioinformatics and Applications”.