Quantitative comparison of catalytic mechanisms and overall reactions in convergently evolved enzymes: implications for classification of enzyme function

Abstract

Functionally analogous enzymes are those that catalyze similar reactions on similar substrates but do not share common ancestry, providing a window on the different structural strategies nature has used to evolve required catalysts. Identification and use of this information to improve reaction classification and computational annotation of enzymes newly discovered in the genome projects would benefit from systematic determination of reaction similarities. Here, we quantified similarity in bond changes for overall reactions and catalytic mechanisms for 95 pairs of functionally analogous enzymes (non-homologous enzymes with identical first three numbers of their EC codes) from the MACiE database. Similarity of overall reactions was computed by comparing the sets of bond changes in the transformations from substrates to products. For similarity of mechanisms, sets of bond changes occurring in each mechanistic step were compared; these similarities were then used to guide global and local alignments of mechanistic steps. Using this metric, only 44% of pairs of functionally analogous enzymes in the dataset had significantly similar overall reactions. For these enzymes, convergence to the same mechanism occurred in 33% of cases, with most pairs having at least one identical mechanistic step. Using our metric, overall reaction similarity serves as an upper bound for mechanistic similarity in functional analogs. For example, the four carbon-oxygen lyases acting on phosphates (EC 4.2.3) show neither significant overall reaction similarity nor significant mechanistic similarity. By contrast, the three carboxylic-ester hydrolases (EC 3.1.1) catalyze overall reactions with identical bond changes and have converged to almost identical mechanisms. The large proportion of enzyme pairs that do not show significant overall reaction similarity (56%) suggests that at least for the functionally analogous enzymes studied here, more stringent criteria could be used to refine definitions of EC sub-subclasses for improved discrimination in their classification of enzyme reactions. The results also indicate that mechanistic convergence of reaction steps is widespread, suggesting that quantitative measurement of mechanistic similarity can inform approaches for functional annotation.

Figure 1. Quantification of overall reaction and mechanistic similarity.

The reactions catalyzed by alkaline phosphatase (MACiE M0044, EC 3.1.3.1, PDB 1alk) –, and protein-tyrosine-phosphatase (MACiE M0047, EC 3.1.3.48, PDB 1ytw) – are used as examples. Each reaction in MACiE is described as an overall transformation (A) and as a sequence of mechanistic steps (B). For measuring reaction similarity, each overall reaction and mechanistic step is represented as the set of bond changes occurring in the transformation from substrates to products, with c: bond cleaved, d: bond decreased in order, f: bond formed, and i: bond increased in order. Similarity between sets of bond changes is computed using Tanimoto coefficients (Tc). (A) Overall similarity is computed as the Tanimoto coefficient between the set of bond changes occurring in the transformation of substrates to products of the reactions. (B) Mechanistic similarity is computed from a global alignment of the mechanistic steps. First, Tanimoto coefficients between all possible pairs of steps are stored in a similarity matrix, and then the maximum-match pathway is obtained using the Needleman-Wunsch algorithm. To obtain the mechanistic similarity a new Tanimoto coefficient is computed using the number of steps in each reaction and the Needleman-Wunsch alignment score as inputs (see Methods).

Figure 2. Overall reaction similarity.

(A) Distribution of overall similarity scores for pairs of reactions in the background dataset (Background) and for the functionally analogous pairs in the dataset (Dataset). (B) F-measures and significance levels for all possible similarity scores. Selected overall similarity scores are shown within the plot, including the cutoff for similarity where the F-measure is maximized (0.8750), and the cutoff at the 5% significance level (0.5833). (C) ROC curves for the overall similarity scores of pairs of reactions in the dataset assessed against those in the background (Dataset vs. Background, AUC = 0.88), for an ideal classification method with no false positives and no false negatives (Ideal, AUC = 1.00), and for a non-discriminating classification method (Random, AUC = 0.50). Selected overall reaction similarity scores are shown within the curves.

Figure 3. Mechanistic similarity.

(A) Distribution of mechanistic similarity scores for pairs of reactions in the background dataset (Background), for all functionally analogous pairs in the dataset (Dataset), and for functionally analogous pairs with high overall reaction similarity (Filtered Dataset). (B) F-measures for the dataset and filtered dataset, and significance levels at all possible mechanistic similarity scores. Selected scores are shown within the plot, including the cutoff for similarity where the F-measure is maximized (0.3793), and the cutoff at the 5% significance level (0.2537). (C) ROC curves for the mechanistic similarity scores of pairs of reactions in the dataset assessed against those in the background (Dataset vs. Background, AUC = 0.76), for pairs in the filtered dataset assessed against those in the background (Filtered Dataset vs. Background, AUC = 0.81), for an ideal classification method with no false positives and false negatives (Ideal, AUC = 1.00), and for a non-discriminating classification method (Random, AUC = 0.50). Selected mechanistic similarity scores are shown within the curves.

Figure 4. Mechanistic vs. overall reaction similarity.

All 95 pairs in the dataset of functional analogs and 3570 pairs in the background dataset are included. Sizes of shapes are not proportional to the number of pairs they contain.

Figure 5. Venn diagram showing combinations of similarity of overall reaction and mechanism, and identical mechanistic steps for pairs of enzymes in the dataset.

Sizes of shapes are not proportional to the number of pairs they contain.