Enhancing computational enzyme design by a maximum entropy strategy

Abstract

Although computational enzyme design is of great importance, the advances utilizing physics-based approaches have been slow, and further progress is urgently needed. One promising direction is using machine learning, but such strategies have not been established as effective tools for predicting the catalytic power of enzymes. Here, we show that the statistical energy inferred from homologous sequences with the maximum entropy (MaxEnt) principle significantly correlates with enzyme catalysis and stability at the active site region and the more distant region, respectively. This finding decodes enzyme architecture and offers a connection between enzyme evolution and the physical chemistry of enzyme catalysis, and it deepens our understanding of the stability-activity trade-off hypothesis for enzymes. Overall, the strong correlations found here provide a powerful way of guiding enzyme design.

Keywords: catalysis; enzyme design; evolution; maximum entropy.

Fig. 1.

The MaxEnt model for enzyme sequences connects enzyme evolution and function. (A and B) The enzyme accelerates chemical reaction by lowering the activation energy using mainly the residues in the catalytic center. Haloalkane dehalogenase (PDB ID code 2dhc) is used as an example to illustrate enzyme catalysis and the reaction mechanism. (A) The residues within a distance of 7.0 Å from the substrate are highlighted. (B) The scheme of the substitution nucleophilic (S_N2) step is illustrated using the substrate of 1,2-dichloroethane. (C) The MaxEnt model connects enzyme evolution to the physical chemistry of enzyme catalysis. A pairwise MaxEnt model is learned from the MSA, and each protein sequence ($\mathit{S}$) is associated with statistical energy ($E_{\text{MaxEnt}}$) following the Boltzmann distribution. We found that decreasing the statistical energy significantly correlates with increasing enzyme efficiency and stability in the catalytic center and enzyme surface, respectively.

Fig. 2.

The MaxEnt model for enzyme sequences correlates with enzyme efficiency at the catalytic center. (A and B) Haloalkane dehalogenase. (C and D) Chorismate mutase. (E and F) Alcohol dehydrogenase. (A, C, and E) Substrates and mutated residues in the dataset are shown in red and blue, respectively; only one unit of the dimeric chorismate mutase and the tetrameric alcohol dehydrogenase is highlighted. For alcohol dehydrogenase, the cofactor NADP⁺ and catalytic triad are colored in red because of the absence of substrate. PDB ID codes used in rendering the structures are (A) 2dhc, (C) 1ecm, and (E) 6tq5. Substrates are (A) 1,2-dichloroethane, (C) chorismate, and (E) cyclohexanol. (B, D, and F) Correlations between $E_{\text{MaxEnt}}$ and experimental catalytic power. The least-squares regression line is plotted for each enzyme; the WT enzyme has a zero value of $E_{\text{MaxEnt}}$.