- 2013 - 3D Structures of Biological Macromolecules Part 6: Selected Topics

1. - 2013 - 3D Structuresof Biological Macromolecules Part 6: Selected Topics (Quantum Chemistry, Molecular Dynamics, Statistical Potentials, Lattice Models) Jürgen Sühnel jsuehnel@fli-leibniz.de Leibniz Institute for Age Research, Fritz Lipmann Institute, Jena Centre for Bioinformatics Jena / Germany Supplementary Material: www.fli-leibniz.de/www_bioc/3D/

2. Quantum Chemistry

3. Quantum Chemistry

5. Quantum-chemical Calculations: Telomeric DNA

6. Quantum-chemical Calculations: Telomeric DNA

7. Quantum-chemical Calculations: Telomeric DNA

8. Quantum-chemical Calculations: Telomeric DNA

9. Molecular Dynamics

10. Simulation of Protein Folding – Molecular Dynamics AMBER GROMOS CHARMM TINKER

11. 1HGV, extended structure 1HGV, actual structure 1HGV, 61% helix, 1.928 ns 1HGV, 75% helix, 3.428 ns Molecular Dynamics Simulation Protein Capsid Of Filamentous Bacteriophage Ph75 From Thermus Thermophilus Images created using VMD (Visual Molecular Dynamics) (HUMPHREY, W., DALKE, A. and SCHULTEN, K., 1996.VMD - Visual Molecular Dynamics. Journal Molecular Graphics,14, pp33-38).

12. Molecular Dynamics Simulation amber.scripps.edu

13. Molecular Dynamics Simulation

14. Molecular Dynamics Simulation – GROMOS Package www.gromos.net

15. Molecular Dynamics Simulation – GROMOS Package

16. Molecular Dynamics Packages www.charmm.org

17. Molecular Dynamics Packages dasher.wustl.edu/ffe/

18. Visualizing and Analyzing Molecular Dynamics Simulations www.ks.uiuc.edu/Research/vmd/

19. Folding Surface for Lysozyme Dobson, Sali, Karplus, Angew. Chem. Int. Ed.1998, 37, 868.

20. Protein Folding States Dobson, Sali, Karplus, Angew. Chem. Int. Ed.1998, 37, 868.

21. Monitoring Protein Folding by Experimental Methods Dobson, Sali, Karplus, Angew. Chem. Int. Ed.1998, 37, 868.

22. Monitoring Protein Folding by Experimental Methods Paxco, Dobson, Curr. Opin. Struct. Biol.1996, 6, 630.

23. Protein Folding by Molecular Dynamics

24. Protein FoldingbyMolecular Dynamics

25. Protein FoldingbyMolecular Dynamics Villin headpiece domain (PDB code: 1vii) Actin binding site highlighted 36 amino acids

26. Protein FoldingbyMolecular Dynamics

27. Protein Folding by Molecular Dynamics

28. Protein Folding by Molecular Dynamics

29. Radius of Gyration In a globular protein the radius of gyration Rg can be predicted with reasonable accuracy from the relationship Rg(pred) = 2.2 N 0.588 where N is the number of amino acids.

30. Protein FoldingbyMolecular Dynamics

31. Protein FoldingbyMolecular Dynamics

32. Statistical Potentials A statistical potential or knowledge-based potential is an energy function derived from an analysis of known protein structures. They are mostly applied to pairwise amino acid interactions. The statistical potential assigns to each possible pair of amino acids a weight or score or energy. Statistical potentials are applied to protein structure prediction and to protein folding. Their physical interpretation is highly disputed. Nevertheless, they have been applied with great success, and do have a rigorous probabilistic justification. Thomas, Dill, J. Mol. Biol.1996, 257, 457-469

33. Statistical Potentials • Boltzmann distribution: • The Boltzmann distribution applied to a specific pair of amino acids, is given by: • where r is the distance, k is the Boltzmann constant, T is the temperature and Z is the partition function, with • The quantity F(r) is the free energy assigned to the pairwise system. Simple rearrangement results in the inverse Boltzmann formula, which expresses the free energy F(r) as a function of P(r): • To construct a so-called Potentail of Mean Force (PMF) , one then introduces a so-called reference state with a corresponding distribution QR and partition functionZR, and calculates the following free energy difference: • The reference state typically results from a hypothetical system in which the specific interactions between the amino acids are absent. The second term involving Z and ZR can be ignored, as it is a constant.

34. Statistical Potentials In practice, P(r) is estimated from the database of known protein structures, while QR(r) typically results from calculations or simulations. For example, P(r) could be the conditional probability of finding the Cβ atoms of a valine and a serine at a given distance r from each other, giving rise to the free energy difference ΔF. The total free energy difference of a protein, ΔFT, is then claimed to be the sum of all the pairwise free energies: where the sum runs over all amino acid pairs ai,aj (with i < j) and rij is their corresponding distance. It should be noted that in many studies QR does not depend on the amino acid sequence Intuitively, it is clear that a low free energy difference indicates that the set of distances in a structure is more likely in proteins than in the reference state. However, the physical meaning of these PMFs have been widely disputed since their introduction. The main issues are the interpretation of this "potential" as a true, physically valid potential of mean force, the nature of the reference state and its optimal formulation, and the validity of generalizations beyond pairwise distances.

35. Statistical Potentials wij(r) – interaction free energy ij(r) - pair density * - reference pair density at infinite separation Statistical potentials can be determined by simply counting interactions of a specific type in a dataset of experimental structures. The distance dependence may or may not be taken into account. If not, the interaction free energy is usuallycalled a contact potential. It represents an average over distances shorter than some cutoff distance rc. Thomas, Dill, J. Mol. Biol.1996, 257, 457-469

36. Lattice Folding

37. Lattice Algorithm • Red = hydrophobic, Blue = hydrophilic • If Red is near empty space E = E+1 • If Blue is near empty space E = E-1 • If Red is near another Red E = E-1 • If Blue is near another Blue E = E+0 • If Blue is near Red E = E+0