Exploring Protein Structure Organization: A Guide to Molecular Geometry

1. Local geometry of polypeptidechainsElements of secondarystructure (turns)

2. Levels of protein structure organization

6. Atom symbols and numbering in amino acids

7. Chirality Enantiomers Phenomenological manifestation of chiraliy: optical dichroism (rotation of the plane of polarized light).

8. Representation of geometry of molecular systems • Cartesiancoordinates • describeabsolute geometry of a system, • versatilewith MD/minimizing energy, • need a moleculargraphics program to visualize. • Internalcoordinates • describelocal geometry of an atom wrt a selectedreferenceframe, • withsomeexperience, local geometry can be imaginedwithout a moleculargraphics software, • mightcauseproblemswhendoing MD/minimizing energy (curvilinearspace).

9. Cartesian coordinate system z Atom x (Å) y (Å) z (Å) C(1) 0.000000 0.000000 0.000000 O(2) 0.000000 0.000000 1.400000 H(3) 1.026719 0.000000 -0.363000 H(4) -0.513360 -0.889165 -0.363000 H(5) -0.513360 0.889165 -0.363000 H(6) 0.447834 0.775672 1.716667 zH(6) H(6) O(2) H(4) C(1) yH(6) xH(6) x H(5) y H(3)

10. Internal coordinate system i dijaijkbijkl j k l C(1) O(2) 1.40000 * 1 H(3) 1.08900 * 109.47100 * 1 2 H(4) 1.08900 * 109.47100 * 120.00000 * 1 2 3 H(5) 1.08900 * 109.47100 * -120.00000 * 1 2 3 H(6) 0.95000 * 109.47100 * 180.00000 * 2 1 5 H(6) O(2) H(4) C(1) H(5) H(3)

11. Bond length

12. Bond (valence) angle

13. Dihedral (torsional) angle The C-O-H plane is rotated counterclockwise about the C-O bond from the H-C-O plane.

14. Improper dihedral (torsional) angle

15. Bond length calculation zj zi xi yi xj xj

16. Bond angle calculation j aijk i k

17. Dihedral angle calculation i bijkl k j l

18. Calculation of Cartesian coordinates in a local reference frame from internal coordinates H(5) z H(6) d26 C(1) a426 H(3) b3426 O(2) y x H(4)

19. Need to bring the coordinates to the global coordinate system

20. Polymer chains qi+2 qi+2 wi+1 wi+1 qi+1 i+1 i+1 di+1 di+1 i i wi pi-1 di ai wi-1 wi-1 qi-1 qi-1 i-1 i-1 di-1 di-1 qi i-2 i-2

21. For regular polymers (when there are „blocks” inside such as in the right picture, pi is a full translation vector and TiRi is a full transformation matrix).

22. Ring closure 3 4 q3 w4 2 d2 n-3 1 a21n d1n a1 n n-1 wn n n-2 dn qn n-1 N. Go and H.A. Scheraga, Macromolecules, 3, 178-187 (1970)

23. Peptide bond geometry Hybrid of two canonical structures 60% 40%

24. Electronic structure of peptide bond

25. Peptide bond: planarity • The partially double character of the peptide bond results in • planarity of peptide groups • their relatively large dipole moment

26. Side chain conformations: the c angles c1 c2 c3 c1=0

27. Dihedrals with which to describe polypeptide geometry side chain main chain

28. Peptide group: cis-trans isomerization Skan z wykresem energii

29. Because of peptide group planarity, main chain conformation is effectively defined by the f and y angles.

30. Side chain conformations

31. The dihedral angles with which to describe the geometry of disulfide bridges

32. Some andpairs are not allowed due to steric overlap (e.g, ==0o)

33. The Ramachandran map

34. Conformations of a terminally-blocked amino-acid residue E Zimmerman, Pottle, Nemethy, Scheraga, Macromolecules, 10, 1-9 (1977) C7eq C7ax

35. Energy minima of therminally-blocked alanine with the ECEPP/2 force field

36. g- and b-turns g-turn (fi+1=-79o, yi+1=69o) b-turns

37. Types of b-turns in proteins Hutchinson and Thornton, Protein Sci., 3, 2207-2216 (1994)

38. Older classification