CS6: Hydrophobic Bonding

1. CS6: Hydrophobic Bonding Tessellation and Likelihood

2. Goals • Review “knowledge-based potentials”; what constitutes a legitimate database of known structures? • Resolution • Homologs • What is a side-chain rotamer library? • What situations require hydrogen atoms? • How well does inverted structure prediction work? • Define Delaunay tessellation • Why use different methods to determine neighbors • Why not use mean distance criteria • When is it legitimate to use side chain centroid? • What is SNAPP analysis all about? • MUSE: what about mutants that alter the structure?

3. Hydrophobicity is proportional to accessible surface area

4. The earliest rotamer library database

5. Antecedents of Butterfoss, Richardson, Hermans To interpret X-ray maps, it is better to use mean values for the dihedral angles, than to try to fit the electron density! cf. Engh & Huber (1991) Acta Cryst. A47:392-

6. Toward Tertiary Templates

7. Successive filters on satisfactory sequences

8. Each question is still unanswered!

9. What can 4-body potentials bring to the table?

10. Voronoi Tessellationfills space with irregularly shaped polytopes containing points that lie closer to the central point than to any other points in the set. - J.L. Finney, F.M. Richards Delaunay Tessellationpartitions space into simplices with an equal number of vertices (triangles in 2D, tetrahedra in 3D). Nearest neighborsare unambiguously defined in sets of three (in 2D) and in sets of four (in 3D). R. Singh, I. Vaisman, A. Tropsha, Medicinal Chemistry, UNC 2D Voronoi/Delaunay Tessellation

11. L122 M136 I108 L139 Compositions of the tetrahedra can be scored by their frequency in known protein structures. SNAPP: Simplicial Neighborhood Analysisof Protein Packing- Stephen Cammer, Alex Tropsha Non-bonded, packing interactions between amino acids in proteins can be decomposed into elementary tertiary motifs by tessellation and identification of the Delaunay tetrahedra. ILLM occurs 18.5 times more frequently in proteins than is expected.

12. L L M M L L I L L L122 M L M M136 I I108 L L139 M M L L I I L I L I Four-body potentials integrate many context-dependent interactions

13. 2 R = 0.93 y = -0.0965x - 0.1406 5 0 -5 -10 -15 -20 4 S I =1 Likelihood and thermodynamic properties become highly correlated in 4-body potentials Score vs. (Hydrophobicities) for [ACILMNQSTV] S 2 1.5 SNAPP 1 0.5 (Hydrophobicities), kcal/mol -0.5 -1

14. 4 3 A V L 2 LLLL I FLLL { Log Likelihood AILV • Almost exclusively nonpolar • Steepest slope • Highest signal:noise ILLM 1 ILMV 0 -1 0 2000 4000 6000 8000 10000 Quadruplet compositions Tetrahedra with four hydrophobic amino acids encode the most information

15. Virtual mutagenesis:http://mmlsun4.pha.unc.edu/3dworkbench.html L68A lowers the CI2 SNAPP score by -2.4 log-likelihood units, DDGunfold) = -3.84 Kcal/mole

16. Four-body SNAPP potentials correlate with D(DGunfold)

17. Degrees of freedom: sidechains

18. What did we learn about 1o, 2o, 3o structure? • 1. Cs4: PDB database affords modest, but robust correlations between specific amino acids and the Ramachandran angles for different secondary structures (Munoz & Serrano). • 2. Cs5: As the quality of X-ray crystal structures gets better, the dihedral angles approach more closely to canonical rotamers (Rotamer libraries - Ponder & Richards) and their distributions match closely to those derived theoretically from QMMM calculations (Butterfoss, Hermans). • 3. Cs6: SNAPP scoring captures much of the coarse-grained detail in hydrophobic cores. It also turns out that as the quality of X-ray crystal structures improves for a given protein during refinement, so does the total SNAPP score! => Packing improves! • 4. From a former case study: As the quality of X-ray crystal structures improves, so does the fraction of possible hydrogen bonds that is actually realized (approaching 90% for amide nitrogen and 95% for carbonyl oxygen atoms. => Very few polar groups are buried without H-bonding partners.