Local geometry of polypeptide chains Elements of secondary structure ( turns )

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