From Crystallography of Biomolecules to More Detailed Understanding of their Structure and Function Bogdan Lesyng ICM and Faculty of Physics, University of Warsaw ( and European Centre of Excellence for Multiscale Biomolecular Modelling, Bioinformatics and Applications ( Łódź, 4/10/2004

Chapter 4.5, page 72

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

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

Fields are equally important as structures !

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 TGPCKARIIR YFYNAKAGLC QTFVYGGCRA KRNNFKSAED CMRTCGGA 58

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

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

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

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.

. 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 ,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, , Tokyo, GAKKOTOSHO CO, pp.11-17, M. Wojciechowski, T. Grycuk, J. Antosiewicz, B.Lesyng, Prediction of Secondary Ionization of the Phosphate Group in Phosphotyrosine Peptides, Biophys.J, 84, (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, (1995) –Grochowski, B. Lesyng, Extended Hellmann-Feynman Forces, Canonical Representations, and Exponential Propagators in the Mixed Quantum-Classical Molecular Dynamics, J.Chem.Phys, 119, (2003)

14 Protonation equilibria in proteins

Protonation equilibria - microstates

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

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

The microstate energy

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, (1994) phosphotyrosine

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

Open and close forms of PKA

Typical results for phosphorylated proteins moleculepredictionexperimental phopsphotyrosine tetrapeptide dodecapeptide phospholipase C-  phosphoserine tetrapeptide phosphoglucomutase <4 phosphothreonine tetrapeptide 36.1

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.

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

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.

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)....

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