A novel protein fingerprint

Mihaly Mezei

Mihaly.Mezei@mssm.edu

  Protein Engineering, 16, 713-715 (2003)  

Theory

For a protein of n residues its fingerprint is defined by up to three of n x n binary matrices. The primary fingerprint matrix FP0 whose elements are defined by the angles (fo in the figure below) that the line connecting the carbonyl carbons of residue i and j forms with the C=O bond's direction on residue i:

FP0ij= sign {[r(Oi)-r(Ci)] . [r(Cj)-r(Ci)]},

Since the C=O directions essentially alternate by 180o in sheets, FP0 will be dominated by alternating white and black bars in such regions. On the other hand, the C=O directions are essentially parallel in helices, resulting in black equilateral right angle triangles located above the diagonal.

      

The secondary fingerprint matrices FP1 and FP2 are defined to allow the differentiation between parallel and antipararllel sheets, and between different packing of helices, respectively. FP1 is defined by the angle between the line connecting the carbonyl carbons of residue i and j and the line connecting the C and N atoms of residue i:

FP1ij= sign {[r(Ni)-r(Ci)] . [r(Cj)-r(Ci)]}.

while FP2 is defined by the angle between the line connecting the carbonyl carbons of residue i and j and the normal to the plane formed by the C and O atoms of residue i and the N of residue i+1:

FP2ij= sign {[r(Ni+1)-r(Ci)]x [r(Oi)-r(Ci)] . [r(Cj)-r(Ci)]}.

The information in FP1 encodes the direction the backbone path takes. Generally, FP0 contains the most information and in several cases it can serve in itself to characterize the fold. Combining two maps results in a matrix whose elements can take four values.

Examples

The examples below show that the minima (as a function of the alignment of a motif with a protein containig that motif) in the fingerprint fit tracks the minima in the RMSD. Note that 50% difference in fingerprint maps corresponds to random aligment.

3-helix bundle

PDZ domain

      

Checking for false positives

In the eaxmple below, the two four-helix bundle proteins difer only in the orientation of a single helix. The resulting fingerprints have obviously different pattern.


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Last modified: 11/29/02 (MM)