Quantitative symmetry in structure-activity correlations:: The near C2 symmetry of inhibitor/HIV protease complexes

We studied the way in which the binding of inhibitors of human immunodeficiency virus (HIV) protease causes the protein to deviate from its original C-2 symmetric structure. We extended to C-2 symmetry our findings that quantitative chirality is a useful, predictive parameter in enzymatic structure-activity correlations (J. Am. Chem. Sec. 1998, 120, 6152-6159). We provide a quantitative assessment of this deviation, the degree of C-2-ness, S(C-2), by employing the continuous symmetry measures methodology. The data analyzed was for a group of 13 inhibitor/protease complexes, for which the structures and the binding energies are known. S(C-2) was determined for the inhibitors before and after binding, for each pair of amino acids of the protein, and for the whole protein complexes. We were able to track the spreading of the C-2 distortion throughout the protein to various zones. Maps of iso-symmetry value proved to be a powerful descriptive tool for protein structure-deviation visualization. The main findings are the following: (i) For most inhibitors, the active site imposes its C-2 symmetry On the bound inhibitor, rendering it more C-2 symmetric than its free form and confirming the picture of enzymes as mechanical devices. (ii) The binding energy of the inhibitors correlates with this imposed C-2 symmetry change: the smaller the symmetry change, the better the inhibition. (iii) Analysis of the enzyme's mutant strain V82A (raised against the inhibitors) shows that it has "learned" to cope better with an inhibitor by "following" this symmetry/binding energy correlation. (iv) Symmetry deviations occur in the protein upon binding at remote zones from the active site. Despite variations in the details of these deviations for the different HIV protease/inhibitor complexes, the protein as a whole responds to the various inhibitors with a very similar C-2 symmetry change: a global symmetry-well for this protein, has been identified.