local geometry of polypeptide chains elements of secondary structure turns
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Local geometry of polypeptide chains Elements of secondary structure ( turns ). Levels of protein structure organization. Atom symbols and numbering in amino acids. Chirality. Enantiomers.

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chirality
Chirality

Enantiomers

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

representation of geometry of molecular systems
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).
slide9

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)

slide10

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)

slide13

Dihedral (torsional) angle

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

slide18

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)

slide20

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

slide21

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).

slide22

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)

peptide bond geometry
Peptide bond geometry

Hybrid of two canonical structures

60% 40%

slide25

Peptide bond: planarity

  • The partially double character of the peptide bond results in
  • planarity of peptide groups
  • their relatively large dipole moment
slide29

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

conformations of a terminally blocked amino acid residue
Conformations of a terminally-blocked amino-acid residue

E

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

C7eq

C7ax

g and b turns
g- and b-turns

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

b-turns

types of b turns in proteins
Types of b-turns in proteins

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

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