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

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Local geometry of polypeptidechainsElements of secondarystructure (turns)

Chirality

Enantiomers

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

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).

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)

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)

The C-O-H plane is rotated counterclockwise about the C-O bond from the H-C-O plane.

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)

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).

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)

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

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.

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

Some andpairs are not allowed due to steric overlap (e.g, ==0o)

Conformations of a terminally-blocked amino-acid residue

E

Zimmerman, Pottle, Nemethy, Scheraga, Macromolecules, 10, 1-9 (1977)

C7eq

C7ax

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

Types of b-turns in proteins

Hutchinson and Thornton, Protein Sci., 3, 2207-2216 (1994)

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