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Math Help - Molecular geomatry Problem !

  1. #1
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    Molecular geomatry Problem !

    Hi,

    I am an undergraduate in the field of Biology. I am dealing with proteins and wish to calculate the dihedral angles. The problem is as follows-

    Given the coordinates of 4 atoms how can we calculate the dihedral or torsion angle between the planes defined by atom 123 and 234 ?
    Now there are two components, first, magnitude of the dihedral angle and second, sign +/- as dihedral angle varies from -180 degree to +180 degree.
    How can we calculate both magnitude and the sign of the dihedral angle ? I have to implement the solution in a computer program.

    The second program is vice-versa of the first one. Given all the internal coordinates i.e. all bond lengths, bond angles and the dihedral angle how can we find the x,y,z coordinates of the fourth atom? If not given we can assume the coordinates of first atom to be 0,0,0.

    Please tell the solution. Thanks in anticipation.

    -Param
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  2. #2
    MHF Contributor
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    The don't give you a clue? That's a tough row to hoe.

    Given three points in 3space, a plane isn't too bad. Subtract two pairs of points to produce two vectors in the plane, then find the cross product to to product the vector normal to the plane.

    (Coordinates of 2) less (Coordinates of 1) = Plane Vector 1
    (Coordinates of 3) less (Coordinates of 1) = Plane Vector 2
    (Plan Vector 1)x(Plan Vector 2) = Normal Vector 1

    Do that with the other set of three points and you now have two normal vectors.

    These can be used to calculate the angle between the planes.

    Unfortunate Note: It is common practice for other fields of study to use their own language and not the mathematical language. You may be more acquainted with the idea than the terminology. Don't be discouraged if you haven't a clue what I am talking about. It's just a language barrier. Once we overcome that, you'll see it.
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