Ensemble-function relationships to dissect mechanisms of enzyme catalysis

Abstract

Decades of structure-function studies have established our current extensive understanding of enzymes. However, traditional structural models are snapshots of broader conformational ensembles of interchanging states. We demonstrate the need for conformational ensembles to understand function, using the enzyme ketosteroid isomerase (KSI) as an example. Comparison of prior KSI cryogenic x-ray structures suggested deleterious mutational effects from a misaligned oxyanion hole catalytic residue. However, ensemble information from room-temperature x-ray crystallography, combined with functional studies, excluded this model. Ensemble-function analyses can deconvolute effects from altering the probability of occupying a state (P-effects) and changing the reactivity of each state (k-effects); our ensemble-function analyses revealed functional effects arising from weakened oxyanion hole hydrogen bonding and substrate repositioning within the active site. Ensemble-function studies will have an integral role in understanding enzymes and in meeting the future goals of a predictive understanding of enzyme catalysis and engineering new enzymes.

Fig. 1.. KSI reaction mechanism, active site, and structure-function results.

(A) KSI catalyzes double-bond isomerization of steroid substrates (shown for the substrate 5-androstene-3,17-dione) using a general acid/base D40 (which we refer to here as a general base) and an oxyanion hole composed of the side chains of Y16 and D103 (protonated). (A and B) Y16 is embedded within a hydrogen bond network with two other tyrosine residues, Y57 and Y32. The general base, oxyanion hole, and hydrogen bond network residues are colored in red, gray, and orange, respectively. Structural model 1OH0 from the Protein Data Bank (PDB) (28). (C) In Y32F/Y57F KSI (PDB 1DMN) (3) and Y57F KSI (PDB 1DMN) (3), Y16 (magenta and green, respectively) is misaligned with respect to its position in WT KSI (gray; PDB 3VSY) (35) [see table S1 and Materials and Methods for alignment root mean square deviations (RMSDs) and procedures, respectively; also see fig. S1]. The k_cat values for Y32F/Y57F and Y57F KSI are shown relative to WT [(3); also see table S2]. (D) An observed difference in traditional single conformation structures between WT and an enzyme variant can arise either because the underlying conformational ensembles of the molecules are different (case I) or because conditions trapped different states in the cryo–cooled structures from a common ensemble (case II). In case I, the gray (left) and blue (right) conformational landscapes are different, and the crystal structures have captured distinct states from each ensemble (indicated by arrows). In case II, the gray and blue conformational landscapes are the same, but the crystal structures have captured distinct states (indicated by arrows); in the traditional structure-function perspective, these structures are compared, and differences between them are correlated with functional effects potentially leading to incorrect mechanistic insights. Most generally, whenever a conclusion is based on a change in structure, then ensemble information is required.

Fig. 2.. Ensemble and functional data for Y32F/Y57F and WT KSI.

(A) Ensemble models for the fourfold effect in Y32F/Y57F variant. Left: In Y32F/Y57F KSI, Y16 are in reactive WT conformations 25% of the time and in alternative nonreactive conformations 75% of the time, whereas WT KSI is predominantly in reactive conformations (99%). Right: In Y32F/Y57F KSI, reactive WT conformations are populated by Y16 less than one-fourth of the time (1% in this schematic), and Y16 predominantly populates less reactive alternative conformations that are responsible for the observed reaction. (B) Electron density (gray mesh, contoured at 1 σ) and multiconformer modeling (magenta sticks) for the Y32F/Y57F KSI active site. (C) Overlay of the WT (gray sticks) (23) and Y32F/Y57F ensembles. (D) Superposition of the cryo–crystal structures and RT ensemble models. Left: WT RT ensemble (gray) (23) and the WT cryo-structure (PDB 3VSY) (94). Right: Y32F/Y57F ensemble (magenta) and the Y32F/Y57F cryo-structure (PDB 1DMN) (3). (E) The same rate effect is observed from ablating the general base D40 in WT (gray) and in Y32F/Y57F (magenta) for reaction of 5(10)-estrene-3,17-dione. (F) Catalytic effects in KSI variants versus changes in the hydrogen bond length with a bound TSA for KSI variants. Gray squares reproduce data from Pinney et al. (44) (R² = 0.99). The change in hydrogen bond distance for Y32F/Y57F KSI was obtained with the transition state analog dinitrophenol (44). Y32F/Y57F KSI kinetics relative to WT with the substrates 5(10)-estrene-3,17-dione (magenta triangle) and 5-androstene-3,17-dione (magenta diamond); Y32F/Y57F/D40G KSI relative to D40G with the substrate 5(10)-estrene-3,17-dione (magenta circle).

Fig. 3.. KSI oxyanion hole catalytic model.

During the KSI reaction, the amount of negative charge on the substrate carbonyl increases and this negative charge accumulation is stabilized by hydrogen bonds (reflected in the size of the red δ−). Analogously, hydrogen bonds become stronger as the charge density on the hydrogen bond donating hydrogen increases (reflected in the size of the blue δ+) (45, 52, 53, 96). Thus, WT (grey, A), Y32F/Y57F (magenta, B), and Y57F (green, C) have decreasing hydrogen charge densities, respectively, and provide lesser extent of transition state stabilization (hydrogen bond strength is depicted by the size of the dots representing the hydrogen bonds). In all cases, hydrogen bonds shorten and strengthen in the transition state (indicated with thicker doted lines in the TS compared to GS), but the shortening and strengthening in the TS decreases in the following order: WT, Y32F/Y57F, Y57F.

Fig. 4.. Ensemble and functional data for Y57F and WT KSI.

(A) Ensemble models for the 9-fold effect in Y57F KSI. Left: in Y57F KSI, Y16 samples reactive WT conformations ~10% of the time, while spending ~90% of the time in alternative, non-reactive conformations. Right: in Y57F KSI, reactive Y16 WT conformations are not sufficiently populated, which instead reacts (less efficiently) from its alternative conformation(s). (B) Representative electron density (gray mesh) and multiconformer models for the KSI Y57F apo (top, green sticks) and Y57F (D40N) TSA-bound (bottom, orange sticks) active site. Also shown are stick model (pink) and electron density (gray mesh) of the bound TSA. D40N was present to mimic the protonated general base and increase TSA affinity (67, 95). Electron density contoured at 1 σ. (C) KSI ensemble overlays, color-coded as noted in figure; WT from (23) and Y57F ensembles from this study. (D) Y57F KSI cryo–crystal structure (PDB 1DMM) (3) and RT ensemble overlays. (E) Catalytic effects in KSI variants versus changes in the hydrogen bond length from Fig. 2A (gray symbols), now including Y32F/Y57F data points. Y57F KSI kinetics with the substrate 5-androstene-3,17-dione relative to WT (green triangle), Y57F kinetics relative to WT with the substrate 5(10)-estrene-3,17-dione (green diamond), and Y57F/D40G relative to D40G (green circle) with the substrate 5(10)-estrene-3,17-dione. (F) Different rate effects from ablating the general base D40 in WT (gray) and in Y57F (green) for reaction of the substrate 5(10)-estrene-3,17-dione (table S2). (G) KSI reaction with the steroid substrates 5-androstene-3,17-dione (left) and 5(10)-estrene-3,17-dione (right). The shuffled proton is red.

Fig. 5.. Catalysis from an ensemble perspective.

(A) Enzymes form a set of states specified by energy wells on a free energy landscape, with dimensionality defined by the thousands of degrees of freedom from each rotatable bond of each residue, depicted here schematically in a single dimension. (B) An example ensemble of near-energy substates in which state 1 (brown) and state 2 (blue) lie within the lowest-energy basin (“native-state basin”). These substates have different intrinsic reactivities, reflecting different barrier heights along their individual reaction coordinates (see Fig. 6). (C) Mathematically, the observed rate constant of the WT (k_obs^WT) with substrate S is the probability-weighted (occupancy-weighted) sum of the intrinsic rate constants of each microscopic substate. Here, we show a simplified example with two states; this example can be generalized across all states with sufficient occupancy and reactivity to contribute appreciably to the observed reaction rate: $k_{\text{obs}}={\sum }_i{P}_i\times k_i$, where P is the probability of occupying state i and k is the rate of reacting from that state. Modified from (97).

Fig. 6.. The effects of functional (k-effects) and occupancy changes (P-effects) to reactivity from an enzyme ensemble.

In all panels, the k-axis is the reaction coordinate, the P-axis is the conformational coordinate, here simplified to two conformational states, and the Z axis is free energy. Profiles for enzyme variants are in gray and light green, and the green profiles (with ≠) represent the preferred reaction path; the corresponding WT profiles are in black and dark green. (A) A simplified ensemble reaction coordinate for a WT enzyme that reacts preferentially from the most active and most probable state (green). A less reactive and less probable state is also depicted (black). (B) Depiction of a k-effect, which increases the barrier to reaction uniformly in both states and reactions, occur via the most populated state (≠; green). (C) Depiction of a P-effect that changes the occupancy of states, but not the most reactive conformation. Reduced reactivity results from decreased occupancy of the more-reactive state. (D) Depiction of a P-effect that results in the enzyme reacting from a more probable but less reactive conformation (≠; green).