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The Geometry of Biomolecular Solvation 1. Hydrophobicity

The Geometry of Biomolecular Solvation 1. Hydrophobicity. Patrice Koehl Computer Science and Genome Center http://www.cs.ucdavis.edu/~koehl/. The Importance of Shape. Sequence. KKAVINGEQIRSISDLHQTLKK WELALPEYYGENLDALWDCLTG VEYPLVLEWRQFEQSKQLTENG AESVLQVFREAKAEGCDITI. Structure. Function.

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The Geometry of Biomolecular Solvation 1. Hydrophobicity

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  1. The Geometry of Biomolecular Solvation1. Hydrophobicity Patrice Koehl Computer Science and Genome Center http://www.cs.ucdavis.edu/~koehl/

  2. The Importance of Shape Sequence KKAVINGEQIRSISDLHQTLKK WELALPEYYGENLDALWDCLTG VEYPLVLEWRQFEQSKQLTENG AESVLQVFREAKAEGCDITI Structure Function ligand

  3. Enzyme – Substrate Binding Substrate (ligand) Enzyme (receptor) + Induced Fit

  4. Co-factors may induce the fit: allostery Ligand Receptor Ligand binds Co-factors bind Co-factors induce conformational Change: allostery

  5. Biomolecular Solvation Stability of Protein Structures Geometric Measures of Protein Structures Applications Accessibility Binding sites

  6. Biomolecular Solvation Stability of Protein Structures Geometric Measures of Protein Structures Applications Accessibility Binding sites

  7. Energy of a Protein Bonded Interactions (chemistry) Bonds, Angles, Dihedral angles Non Bonded Interactions (“local” information) van der Waals interactions, Electrostatics Solvent (environment)Most difficult

  8. SolventExplicit or Implicit ?

  9. Potential of mean force A protein in solution occupies a conformation X with probability: X: coordinates of the atoms of the protein Y: coordinates of the atoms of the solvent The potential energy U can be decomposed as: UP(X): protein-protein interactions US(X): solvent-solvent interactions UPS(X,Y): protein-solvent interactions

  10. Potential of mean force We study the protein’s behavior, not the solvent: PP(X) is expressed as a function of X only through the definition: WT(X) is called thepotential of mean force.

  11. Potential of mean force The potential of mean force can be re-written as: Wsol(X) accounts implicitly and exactly for the effect of the solvent on the protein. Implicit solvent models are designed to provide an accurate and fast estimate of W(X).

  12. Solvation Free Energy Wsol + + Wnp

  13. The SA model Surface area potential Eisenberg and McLachlan, (1986) Nature, 319, 199-203

  14. Surface area potentialsWhich surface? Accessible surface Molecular Surface

  15. Hydrophobic potential:Surface Area, or Volume? Surface effect (Adapted from Lum, Chandler, Weeks, J. Phys. Chem. B, 1999, 103, 4570.) Volume effect “Radius of the molecule” For proteins and other large bio-molecules, use surface

  16. Biomolecular Solvation Stability of Protein Structures Geometric Measures of Protein Structures Applications Accessibility Binding sites

  17. Representations of Biomolecules Space-filling Model Cartoon

  18. Computing the Surface Areaand Volume of a Union of Balls

  19. Computing the Surface Areaand Volume of a Union of Balls Power Diagram:

  20. Computing the Surface Areaand Volume of a Union of Balls Decomposition of the Space-filling diagram

  21. Computing the Surface Areaand Volume of a Union of Balls bi ri si Volume Surface Area

  22. Computing the Surface Areaand Volume of a Union of Balls The weighted Delaunay triangulation is the dual of the power diagram

  23. Computing the Surface Areaand Volume of a Union of Balls The dual complex K is the dual of the decomposition of the space-filling diagram

  24. Computing the Surface Areaand Volume of a Protein K complex Pocket Protein Delaunay Complex http://www.cs.ucdavis.edu/koehl/ProShape/

  25. Computing the Surface Areaand Volume of RNA K complex P4-P6 domain Group I intron Delaunay Complex Pocket

  26. Biomolecular Solvation Stability of Protein Structures Geometric Measures of Protein Structures Applications Accessibility Binding sites

  27. Experimental measures of accessibilities Hydroxyl radical footprinting: H5’’ H3’ H1’ H2’ H5’ H4’ HO2’

  28. Footprinting count /Ribose H accessibility Residue number

  29. BINDING POCKETS IN 16S RIBOSOMAL RNA Hygromycin B PDB structure: 1HZN

  30. BINDING POCKETS IN 16S RIBOSOMAL RNA 8 Å Probe Size 1.4 Å

  31. BINDING POCKETS IN 16S RIBOSOMAL RNA

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