CODE FOR VECTOR ALGEBRA DIHEDRAL ANGLE CALCULATION

I have calculated the dihedral angle (phi, psi of am amino acid in a protein) using following steps. Coordinates (X,Y,Z) of four atoms are given.

Let the four points (atoms) be a,b,c,d.

STEP 1: Calculation of vectors:

p = b - a q = c - b r = d - c

STEP 2: To find normal to the planes:

n1 = p X q n2 = q X r

(theta) = cos inverse [ (n1.n2) / n1.|n2| ]

I am getting the numerical value correct , but the sign is different. Where have I be wrong ?

[Jan]

The sign is different from what?

Answer 1

[Roger Stafford]

Your notation "(n1.n2) / n1.|n2|" is confusing. If by this you mean the dot product of n1 and n2 divided by the product of their norms, you should get the correct answer for theta. I don't see how you can possibly get the wrong sign for it since the principal values of the inverse cosine are understood to lie between 0 and pi radians and are therefore all positive.

I assume the dihedral angle you are seeking is that defined by the two half planes which contain atom a and d respectively with the line bc as their intersection. The other possible dihedral angle would be the supplement of this angle, but either angle would be positive.