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 polypeptidechainsElements of secondarystructure (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

  • 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).


  • 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

    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)


    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

    i

    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

    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


    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)


    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

    c1

    c2

    c3

    c1=0


    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

    E

    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


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