Quantitative Symmetry in Structure−Activity Correlations:  The Near <i>C</i>₂ 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 C2 symmetric structure. We extended to C2 symmetry our findings that quantitative chirality is a useful, predictive parameter in enzymatic structure−activity correlations (J. Am. Chem. Soc. 1998, 120, 6152−6159). We provide a quantitative assessment of this deviation, the degree of C2-ness, S(C2), 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(C2) 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 C2 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 C2 symmetry on the bound inhibitor, rendering it more C2 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 C2 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 C2 symmetry change: a global symmetry-well for this protein, has been identified.