Bogdan Lesyng Interdyscyplinary Centre for Mathematical and Computational Modelling

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

3. In our organisms we have ~ 103 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, OH X : H, OH, NH2 Y : H, OH, NH2 R” : H, 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. Grycukand 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. Protonation equilibria in proteins M. Wojciechowski, T. Grycuk, J. Antosiewicz, B.lesyng Prediction of Secondary Ionization of the PhosphateGroup in Phosphotyrosine Peptides,Biophys.J, 84, 750-756(2003)

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

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

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: total electron density 1-electron orbitals 1-electron Hamiltonian (Kohn-Sham equation)

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

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 net charges of free atoms

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

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

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

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: which involves Meyers bond order: and the correction function which is taken to be a second order polynomial with coefficients depending on the atom types:

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

28. ”GB” – Generalized Born Ak- van der Waals surface area of atom k gk- 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. Coulomb Field appr. (I) Kirkwood Model (II) (III) M.Feig, W.Im, C.L.Brooks, J.Chem.Phys.,120,903-911(2004) (IV)

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

33. Ratio of the GB solvation enery to the Kirkwood solvation energy (zooming) ein/eex case IV

34. The optimal value of the exponent

35. Corrections to the ionic strength 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.

37. SASA A2 CHARMM SASA A2Fit 1 SASA A2CHARMM SASA A2 Fit 2

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

41. Acknowledgements PhD students: Jarek Kalinowski Michał Wojciechowski Piot Kmieć Magda Gruziel Collaboration: Dr. T. Frauenheim SCC-DFTB Dr. M. Elstner Dr. D. Truhlar CM3-charges Dr. J. Thompson Minnesota Solvation Data Base Dr. C. Cramer Studies supported by ”European CoE for Multiscale Biomolecular Modelling, Bioinformatics and Applications”.