Linear Eyring Plots Conceal a Change in the Rate-Limiting Step in an Enzyme Reaction.

The temperature dependence of psychrophilic and mesophilic ( R)-3-hydroxybutyrate dehydrogenase steady-state rates yields nonlinear and linear Eyring plots, respectively. Solvent viscosity effects and multiple- and single-turnover pre-steady-state kinetics demonstrate that while product release is rate-limiting at high temperatures for the psychrophilic enzyme, either interconversion between enzyme-substrate and enzyme-product complexes or a step prior to it limits the rate at low temperatures. Unexpectedly, a similar change in the rate-limiting step is observed with the mesophilic enzyme, where a step prior to chemistry becomes rate-limiting at low temperatures. This observation may have implications for past and future interpretations of temperature-rate profiles.

Temperature–rate profiles are powerful tools for gaining insight into thermodynamic activation parameters of chemical reactions.[1] In enzyme-catalyzed reactions, analysis of the temperature-dependent behavior of rate constants is widely used to uncover catalytic properties among psychrophilic, mesophilic, and thermophilic enzymes[2] and to probe protein dynamics and hydrogen tunneling[3] and even allosteric regulation.[4,5] Plotting ln(k/T) versus 1/T (Eyring plot) often results in a straight line, and fitting data to eq yields the activation enthalpy and entropy, assuming they are constant over the temperature range and recrossing is negligible.[1,6,7] However, nonlinear Eyring plots have been reported,[8] and a recent and elegant hypothesis for interpreting them invokes a role for activation heat capacity in enzyme catalysis upon fitting data to eq .[9,10] In eqs and 2, k is the rate constant; kB, h, and R are the Boltzmann, Planck, and gas constants, respectively; ΔH⧧ and ΔS⧧ are the activation enthalpy and entropy, respectively; T is the temperature; T0 is a reference temperature; ΔH⧧ and ΔS⧧ are ΔH⧧ and ΔS⧧ at T0, respectively; and ΔC⧧ is the activation heat capacity.

Nonlinear Eyring plots without protein denaturation could also arise from a switch in the rate-limiting step at a given temperature, which must be tested.[2,8] Conversely, linear Eyring plots are often assumed to reflect the same rate-limiting step at all temperatures.[2,6,9,11,12] Here we show that linear Eyring plots may accommodate a change in the rate-limiting step.

We cloned and expressed the bacterial (R)-3-hydroxybutyrate dehydrogenase (HBDH)-encoding gene from mesophilic Acinetobacter baumannii(13) and from psychrophilic Psychrobacter arcticus(14) and purified the recombinant mesophilic (AbHBDH) and psychrophilic (PaHBDH) enzymes (Figure S1). HBDH (EC 1.1.1.30) catalyzes the NADH-dependent reduction of acetoacetate to (R)-3-hydroxybutyrate, with 3-oxovalerate being an alternative substrate turned over more slowly by the enzyme (Scheme S1).[15]

HBDH is part of the short-chain dehydrogenase/reductase (SDR) superfamily, one of the largest known protein groups.[16] SDR proteins share a low level of sequence identity but highly conserved three-dimensional architecture and catalytic residues.[17] HBDH has applications in asymmetric synthesis of precursors of pharmaceuticals and monomeric constituents of biodegradable polyhydroxyalkanoates.[18,19]

We measured saturation curves for AbHBDH and PaHBDH at various temperatures (283–330 K for AbHBDH and 283–318 K for PaHBDH) (Figure S2 and Tables S1–S4). Differential scanning fluorimetry demonstrated no denaturation occurs in this temperature range (Figure S3 and Table S5). Apparent steady-state catalytic constants (kcat) were used to construct Eyring plots for each enzyme (Figure ). Fitting all data with both eqs and 2 resulted in best-fit lines that are linear for AbHBDH but nonlinear for PaHBDH. Accordingly, a significant negative ΔC⧧ is predicted for the psychrophilic enzyme but not for the mesophilic one (Table S6).

Figure 1

Eyring plots for PaHBDH and AbHBDH with acetoacetate and 3-oxovalerate as substrates.

A negative ΔC⧧ for kcat could suggest a decrease in the number of vibrational modes as the Michaelis complex progresses toward the transition state.[9,11,12,20] However, enzymatic rates often contain contributions from several steps, and a negative ΔC⧧ can report on vibrational modes associated with chemical[10,20] and physical steps.[2]

To test if diffusional steps limit the steady-state rate in PaHBDH and AbHBDH reactions at 298 K, we determined solvent viscosity effects by measuring saturation curves at different concentrations of glycerol (Figure S4 and Tables S7–S10), and plots of kcat ratios versus relative viscosity[21] are shown in Figure . Fitting data to eq S5 yielded slopes of 0.43 ± 0.04 and 0.36 ± 0.02 for PaHBDH and AbHBDH, respectively, indicating product release is significantly rate-limiting with acetoacetate as the substrate.[21,22] With 3-oxovalerate as the substrate, slopes decrease to 0.25 ± 0.02 for PaHBDH, consistent with only a modest product release contribution to the rate-limiting step, and −0.16 ± 0.02 for AbHBDH, showing no contribution from diffusional steps to kcat. Diffusional steps from substrate binding do not limit reaction rates for either enzyme (Figure S4), and 5% PEG-8000 as a macroviscogen had no effect on saturation curves (Figure S5), pointing to the effects of glycerol resulting from an increase in solvent microviscosity.[21,23]

Figure 2

Solvent viscosity effects on kcat for PaHBDH and AbHBDH with acetoacetate and 3-oxovalerate as substrates. Lines are fits of data to eq S5.

The solvent viscosity effects on kcat suggest that the curvatures in the Eyring plots and the consequent negative ΔC⧧ calculated for PaHBDH may report on distinct steps when acetoacetate and 3-oxovalerate are used as substrates. To probe further the nature of the rate-limiting step for this enzyme, we employed multiple-turnover pre-steady-state kinetics to characterize the approach to the steady state[24] at 283, 298, and 318 K (Figure A). No burst in substrate consumption is observed with 3-oxovalerate as the substrate. These results support the conclusion from solvent viscosity effects at 298 K that kcat is not limited by the product release rate with 3-oxovalerate as the substrate.

Figure 3

Rapid kinetics for PaHBDH with acetoacetate and 3-oxovalerate as substrates. (A) Multiple-turnover pre-steady-state kinetics. Black lines are fits of data to eq S3. (B) Single-turnover pre-steady-state kinetics. Black lines are fits of data to eq S4.

When acetoacetate is used as the substrate, even though a burst in substrate depletion at 298 and 318 K cannot be directly observed, it can be inferred[25] (Figure A). The concentration of co-substrate NADH at time zero in the presence of PaHBDH and acetoacetate is significantly offset from its value in the control without acetoacetate (Figure S6), suggesting at least one turnover has happened within the 0.9 ms dead time of the stopped-flow spectrophotometer. This suggests a step after chemistry, likely product release, is rate-limiting at 298 and 318 K, in agreement with the significant solvent viscosity effect on kcat at 298 K. At 283 K, however, there is no burst (Figure A and Figure S6), indicating a change in the rate-limiting step at low temperatures.

The hypotheses regarding rate-limiting steps in the PaHBDH reaction at different temperatures were tested further by single-turnover pre-steady-state kinetics at 283 and 298 K with NADH as the limiting reagent. PaHBDH single-turnover rate constants (kSTO) were independent of enzyme concentration (Figure B), demonstrating NADH is saturated with PaHBDH and kSTO is unimolecular.[24] With 3-oxovalerate, kSTO and kcat values are similar at the same temperatures (Table S11). Along with the absence of a pre-steady-state burst and a negligible solvent viscosity effect on kcat with this substrate, this result indicates that interconversion between PaHBDH-NADH-3-oxovalerate and PaHBDH-NAD+-3-hydroxyvalerate is rate-limiting. With acetoacetate as the substrate, if the hypothesis emerging from multiple-turnover pre-steady-state kinetics and solvent viscosity effects holds, kSTO should be measurable at 283 K but should not be possible to monitor at 298 K as it takes place within the dead time of the instrument. This is exactly what is observed (Figure B and Table S11), with kSTO being too fast to be detected at 298 K although NADH is consumed. At 283 K, kSTO is 2.2-fold higher than kcat, which, combined with the absence of a burst, indicates a step prior to acetoacetate reduction is rate-limiting at this temperature.

Whereas there is precedent for a change in the rate-limiting step in nonlinear Eyring plots of enzyme reactions,[26]PaHBDH Eyring plots are linear in the range of 283–308 K (Figure S7), and the switch in the rate-limiting step occurs between 283 and 298 K. This indicates a temperature-dependent shift in the rate-limiting step giving rise to a linear Eyring plot.

To assess whether this unusual behavior is displayed by the mesophilic enzyme, we carried out rapid kinetics experiments with AbHBDH, whose Eyring plots are linear throughout the experimental temperature range. Remarkably, multiple-turnover pre-steady-state kinetics at 283, 298, and 328 K (Figure A) show a change in the rate-limiting step with both substrates. A burst in substrate consumption at 298 and 328 K with acetoacetate and at 328 K with 3-oxovalerate is too fast to be directly observed but is clearly inferred[25] from the offset in NADH concentration at time zero in the presence and absence of acetoacetate or 3-oxovalerate (Figure S6), indicating the first turnover occurs within the dead time of the stopped-flow spectrophotometer. Conversely, there is no burst at 283 K with either substrate or at 298 K with 3-oxovalerate (Figure A and Figure S6). The results at 298 K are in strict agreement with the conclusions drawn from solvent viscosity effects for both substrates.

Figure 4

Rapid kinetics for AbHBDH with acetoacetate and 3-oxovalerate as substrates. (A) Multiple-turnover pre-steady-state kinetics. Black lines are fits of data to eq S3. (B) Single-turnover pre-steady-state kinetics. Black lines are fits of data to eq S4.

As with PaHBDH, we performed single-turnover pre-steady-state kinetics experiments at 283 and 298 K, with NADH as the limiting reagent, to examine further the hypothesis of a change in the rate-limiting step in AbHBDH catalysis at different temperatures. AbHBDH kSTO values were independent of enzyme concentration (Figure B), demonstrating NADH is saturated with AbHBDH and kSTO is unimolecular. The kSTO for acetoacetate reduction can be measured at 283 K, but it is too fast to be monitored at 298 K, even though NADH is consumed. This is in accordance with the results from rapid kinetics under multiple-turnover conditions. The kSTO for 3-oxovalerate reduction can be measured at 283 and 298 K, as predicted by the absence of a burst at these temperatures. The affinity between AbHBDH and its substrates decreases severely at high temperatures, which prevented single-turnover experiments at 328 K (the enzyme could not be concentrated enough to ensure sufficient binding to NADH). Combined, these results demonstrate a shift in the rate-limiting step between 283 and 298 K for AbHBDH-catalyzed reduction of acetoacetate and between 298 and 328 K for reduction of 3-oxovalerate despite linear Eyring plots with both substrates.

The kSTOs for AbHBDH-catalyzed reduction of 3-oxovalerate are 10- and 7-fold higher than kcat at 283 and 298 K, respectively, and the kSTO for acetoacetate reduction at 283 K is 8-fold higher than the corresponding kcat (Table S12). Therefore, unlike the PaHBDH reaction, a step preceding chemistry limits the AbHBDH reaction rate with 3-oxovalerate at 283 and 298 K and with acetoacetate at 283 K. Distinct rate-limiting steps between enzyme orthologues have been reported for other members of the SDR superfamily.[27,28]

Temperature–rate profiles are invaluable for the investigation of enzymatic mechanisms, encompassing probing quantum mechanical tunneling,[3] enzyme dynamics,[10,12] allostery,[4,5] and calculation of thermodynamic parameters of activation.[6,9−12] They are also instrumental for studying the evolution of modern enzymes from primitive catalysts that arose in a hot Earth.[2,29,30]

A temperature-dependent change in the rate-limiting step could produce a linear Eyring plot for kcat if the ratio of Eyring plot slopes for the microscopic rate constant(s) determining each step is relatively small. This scenario is demonstrated (Supporting Information) from simulated data (Figure S8) for a hypothetical two-step mechanism (Scheme S2) and may explain the results with AbHBDH. This highlights the importance of confirming whether the same rate-limiting step holds throughout the experimental temperature range before further interpretation of both nonlinear and linear Eyring plots of macroscopic rate constants.