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

Levels of protein structure organization

Atom symbols and numbering in amino acids

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

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).

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)

Internal coordinate system i dij aijk bijkl 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)

Bond length

Bond (valence) angle

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

Improper dihedral (torsional) angle

Bond length calculation zj zi xi yi xj xj

Bond angle calculation j aijk i k

Dihedral angle calculation bijkl k j l

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)

Need to bring the coordinates to the global coordinate system

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

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).

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)

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

Electronic structure of peptide bond

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

Side chain conformations: the c angles

Dihedrals with which to describe polypeptide geometry side chain main chain

Peptide group: cis-trans isomerization Skan z wykresem energii

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

Side chain conformations

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

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

The Ramachandran map

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

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

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

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

Older classification