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From Crystallography of Biomolecules to More Detailed Understanding of their Structure and Function Bogdan Lesyng ICM 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) Łódź, 4/10/2004

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Chapter 4.5, page 72

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W.Saenger & K.H.Sheit, J.Mol.Biol., 50, 153-169(1970) B.Lesyng & W.Saenger, Z.Naturforsch. C, 36, 956-960(1981) Crystallized from water Crystallized from butyric acid !

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Structures in the crystalline state can be interpreted in terms of packing forces, properties of hydrogen bonds, a kind of consensus between the intramolecular energy and the intermolecular interaction energy, etc. B.Lesyng, G.A.Jeffrey, H.A.Maluszynska, A Model for the Hydrogen-bond-length Probability Distributions in the Crystal Structures of Small-molecule Components of the Nucleic Acids, Acta Crystallog., B44, 193-8(1988) However, this problem can also be seen in a different, more abstract way, namely as minimization of the free energy of a selected molecular system in its real molecular environment – in this particular case this is the environment formed by surrounding molecules with imposed constraints resulting from the symmetry. Towards generalization of experimentally observed structural changes

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Fields are equally important as structures !

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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

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Determination of biomolecular structures X-ray and neutron diffraction data NMR Molecular quantum mechanics. Minimization of the B.-O. energy Homology analysis and structure prediction ”Ab intio” methods Minimization of the MM-energy or free energy Experimental and ”data-mining” approaches

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Towards global minimum of the free energy (Gibbs & Boltzmann – equilibrium properties, Kramers & Eyring - kinetics)

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Homology analysis and structure prediction. Making use of molecular evolution concepts and Darwinian-type approach.

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Optimal sequence alignment, followed by a 3D structure alignment, results in prediction of a correct, 3D-hierarchical biomolecular structure. ”Optimal” – consistent with current evolutionary concepts. Wrong sequence alignment typically results in a wrong structure.

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. Multiscale modelling methods, the approach to refine structures and to understend functioning of complex biomolecular systems and processes Virtual titration -J. Antosiewicz, E. Błachut-Okrasińska, T. Grycuk, J. Briggs, S. Włodek, B. Lesyng, J.A. McCammon, Prediction of pKas of Titratable Residues in Proteins Using a Poisson-Boltzman Model of the Solute-Solvent System, in “Computational Molecular Dynamics: Challenges, Methods, Ideas”, Lecture Notes in Computational Science and Engineering, vol. 4, Eds. P.Deuflhard et al, Springer-Verlag, Berlin, Heidelberg, pp. 176-196,1999 –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. -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) Quantum forces and dynamics in complex biomolecular systems. –P. Bala, P. Grochowski, B. Lesyng, J.A. 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)

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14 Protonation equilibria in proteins

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Protonation equilibria - microstates

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The model group – a reference state This difference assumed to be purely electrostatic

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Ensamble -role of a reference state (”model group”)

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The microstate energy

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Phosphotyrosine in phospholipase C- SH2 domain of phospholipase C- 1 (pdb: 2PLE) S.M.Pascal,A.U.Singer,G.Gish,T.Yamazki S.E.Shoelson, T.Pawson, L.E.Kay, J.D.Forman-Kay, Nuclear Magnetic Resonance Structure Of An Sh2 2ple Domain Of Phospholipase C-Gamma1 Complexed With A High Affinity Binding Peptide, Cell, 77,461-472(1994) phosphotyrosine

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phosphoglucomutase (pdb: 3PMG) W.J.Ray, Junior, Y.Liu, S.Baranidharan, Structure of Rabbit Muscle Phosphoglucomutase at 2.4 Angstroms Resolution. Use of Freezing Point Depressant and Reduced Temperature to Enhance Diffractivity, to be published phosphoserine Phosphoserine in phosphoglucomutase

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Open and close forms of PKA

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Typical results for phosphorylated proteins moleculepredictionexperimental phopsphotyrosine tetrapeptide 15.365.9 dodecapeptide5.666.1 phospholipase C- 1 3.714.0 phosphoserine tetrapeptide 25.76.1 phosphoglucomutase <4 phosphothreonine tetrapeptide 36.1

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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.

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Quantum-classical dynamics in simulations of enzymatic processes (phospholipase A 2 – a case study)

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Acknowledgements PhD students: Marta Hallay Jarek Kalinowski Piotr Kmieć Magda Gruziel Michał Wojciechowski Łukasz Walewski Franek Rakowski Janek Iwaszkiewicz Coworkers: Prof. J.Antosiewicz Prof. P.Bała Dr. P.Grochowski Collaboration: Prof. J.A.McCammon Prof. W.Saenger Prof. D.Truhlar Studies are supported by ”European CoE for Multiscale Biomolecular Modelling, Bioinformatics and Applications” and Polish State Committee for Scientific Research.

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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)....

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

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