Local frustration around enzyme active sites

Abstract

Conflicting biological goals often meet in the specification of protein sequences for structure and function. Overall, strong energetic conflicts are minimized in folded native states according to the principle of minimal frustration, so that a sequence can spontaneously fold, but local violations of this principle open up the possibility to encode the complex energy landscapes that are required for active biological functions. We survey the local energetic frustration patterns of all protein enzymes with known structures and experimentally annotated catalytic residues. In agreement with previous hypotheses, the catalytic sites themselves are often highly frustrated regardless of the protein oligomeric state, overall topology, and enzymatic class. At the same time a secondary shell of more weakly frustrated interactions surrounds the catalytic site itself. We evaluate the conservation of these energetic signatures in various family members of major enzyme classes, showing that local frustration is evolutionarily more conserved than the primary structure itself.

Keywords: bioinformatics; catalytic sites; evolution; local frustration; protein enzymes.

Fig. 1.

Local frustration patterns in enzymes. (A) Examples of frustration patterns in various enzymes. The backbones of the proteins are shown as gray cartoons, minimally frustrated contacts are depicted with green lines, and highly frustrated interactions with red lines. Neutral interactions were omitted to help visualization. The alpha carbons (C$\alpha$) of catalytic sites are marked with yellow spheres. (B) Pair distribution functions, $g\left(r\right)$, between the C$\alpha$ of the annotated catalytic residues and the center of mass of the contacts, divided by local frustration class, for the monomeric enzymes, homodimers, and all of the dataset. Green, minimally frustrated contacts; red, highly frustrated contacts; gray, neutral contacts; black, all contacts. g(r) plots were adjusted in their axis ranges to enhance visualizations; however, in all cases g(r) values were normalized such that g(20) = 1.

Fig. 2.

(A and B) Local frustration patterns of EC classes for (A) monomers and (B) homodimers. The ratio of the $g\left(r\right)$ value for each type of contact (green, minimally frustrated; red, highly frustrated; gray, neutral) and the total $g\left(r\right)$ involving all interaction functions is shown. The first shell is defined from 0.5 Å to 1.5 Å with respect to the catalytic residue positions, and the second shell is defined from 2 Å to 3.5 Å.

Fig. 3.

Local frustration and topology. (A and B) Local frustration patterns of CATH classes for (A) monomers and (B) homodimers. The ratio of the $g\left(r\right)$ value for each type of contact (green, minimally frustrated contacts; red, highly frustrated contacts; gray, neutral contacts) and all interactions is shown. The first shell is defined from 0.5 Å to 1.5 Å with respect to the catalytic residue positions, and the second shell is defined from 2 Å to 3.5 Å. (C) Frustration patterns in enzyme pairs that share a high structural similarity but catalyze different reactions. (D) Frustration patterns in enzyme pairs that catalyze similar reactions but are structurally different. The backbones of the proteins are shown as gray ribbons, minimally frustrated contacts are depicted with green lines, and highly frustrated interactions with red lines. Neutral interactions were omitted to help visualization. The C$\alpha$s of the catalytic residues are marked with yellow spheres.

Fig. 4.

Conservation of local frustration and sequence identity for $\beta$-lactamases class A family. (A) FrstIC based on the single-residue level frustration index. Green, minimally frustrated contacts; red, highly frustrated contacts; gray, neutral contacts. Black circles show the values of the SeqIC. (B) $\beta$-Lactamase structure: in green and red, residues with FrstIC values greater than 0.5, minimally frustrated and highly frustrated, respectively. (C) Catalytic residues at the active site. (D) Mutational frustration at the catalytic site. Red lines correspond to highly frustrated interactions of the catalytic residues (in yellow) among themselves and with nearby residues in the structure.

Fig. 5.

Conservation of local frustration and sequence for the aldolases family. (A) FrstIC based on the single-residue level frustration index. Green, minimally frustrated contacts; red, highly frustrated contacts; gray, neutral contacts. Black circles show the values of the SeqIC. (B) Aldolase structure: in green and red, residues with FrstIC values greater than 0.5, minimally frustrated and highly frustrated, respectively. (C) Catalytic residues at the active site. (D) Frustration index at the contact level. Red lines correspond to highly frustrated interactions of the catalytic residues (in yellow) among themselves and with nearby residues in the structure.