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

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Local geometry of polypeptide chains elements of secondary structure turns

Local geometry of polypeptidechainsElements of secondarystructure (turns)


Levels of protein structure organization

Levels of protein structure organization


Atom symbols and numbering in amino acids

Atom symbols and numbering in amino acids


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).


  • Local geometry of polypeptide chains elements of secondary structure turns

    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)


    Local geometry of polypeptide chains elements of secondary structure turns

    Internal coordinate system

    idijaijkbijkl 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)


    Local geometry of polypeptide chains elements of secondary structure turns

    Bond length


    Local geometry of polypeptide chains elements of secondary structure turns

    Bond (valence) angle


    Local geometry of polypeptide chains elements of secondary structure turns

    Dihedral (torsional) angle

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


    Local geometry of polypeptide chains elements of secondary structure turns

    Improper dihedral (torsional) angle


    Local geometry of polypeptide chains elements of secondary structure turns

    Bond length calculation

    zj

    zi

    xi

    yi

    xj

    xj


    Local geometry of polypeptide chains elements of secondary structure turns

    Bond angle calculation

    j

    aijk

    i

    k


    Local geometry of polypeptide chains elements of secondary structure turns

    Dihedral angle calculation

    i

    bijkl

    k

    j

    l


    Local geometry of polypeptide chains elements of secondary structure turns

    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)


    Local geometry of polypeptide chains elements of secondary structure turns

    Need to bring the coordinates to the global coordinate system


    Local geometry of polypeptide chains elements of secondary structure turns

    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


    Local geometry of polypeptide chains elements of secondary structure turns

    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).


    Local geometry of polypeptide chains elements of secondary structure turns

    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%


    Local geometry of polypeptide chains elements of secondary structure turns

    Electronic structure of peptide bond


    Local geometry of polypeptide chains elements of secondary structure turns

    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

    Side chain conformations: the c angles

    c1

    c2

    c3

    c1=0


    Dihedrals with which to describe polypeptide geometry

    Dihedrals with which to describe polypeptide geometry

    side chain

    main chain


    Local geometry of polypeptide chains elements of secondary structure turns

    Peptide group: cis-trans isomerization

    Skan z wykresem energii


    Local geometry of polypeptide chains elements of secondary structure turns

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


    Side chain conformations

    Side chain conformations


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

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


    Some and pairs are not allowed due to steric overlap e g 0 o

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


    The ramachandran map

    The Ramachandran map


    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


    Energy minima of therminally blocked alanine with the ecepp 2 force field

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


    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)


    Older classification

    Older classification


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