1. Local geometry of polypeptide chains Elements of secondary structure (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
Cartesian coordinates
describe absolute geometry of a system,
versatile with MD/minimizing energy,
need a molecular graphics program to visualize.
Internal coordinates
describe local geometry of an atom wrt a selected reference frame,
with some experience, local geometry can be imagined without a molecular graphics software,
might cause problems when doing MD/minimizing energy (curvilinear space).

9. Cartesian coordinate systemz
Atom x (Å) y (Å) z (Å)
C(1)
O(2)
H(3)
H(4)
H(5)
H(6)
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 dij aijk bijkl j k l
C(1)
O(2) *
H(3) * *
H(4) * * *
H(5) * * *
H(6) * * *
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 calculationzj zi xi yi xj xj

16. Bond angle calculationj
aijk i k

17. Dihedral angle calculation
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 pi-1 qi+2 qi+2 wi+1 qi+1 wi+1 i+1 i+1 di+1 di+1 i i wi

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, (1970)

23. Hybrid of two canonical structures
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

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
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, (1994)

38. Older classification