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.


S3
Purification of PaHBDH. All purification procedures were performed at 4 °C and all chromatographic steps employed an AKTA Start FPLC system (GE Lifesciences). Cells were thawed on ice for 20 min before being resuspended in buffer A [50 mM HEPES (pH 7.5)] containing 0.2 mg mL −1 lysozyme, 0.05 mg mL −1 DNase I, and half a tablet of EDTA-free protease inhibitor cocktail, disrupted in a high-pressure cell disruptor (Constant Systems), and centrifuged at 48000 g for 30 min to remove cell debris. Buffer A containing 1.5 M (NH4)2SO4 was added dropwise to the supernatant, which was stirred for 30 min and centrifuged at 48000 g for 30 min to remove the precipitate. The supernatant was dialysed against 3  2 L of buffer A, filtered through a 0.45-μm membrane and loaded onto a HiTrap Q FF column (GE Healthcare), pre-equilibrated with buffer A. The column was washed with 15 column volumes (CV) of 5% buffer B [50 mM HEPES, 2 M NaCl (pH 7.5)], and the adsorbed proteins were eluted with 20 CV of a linear gradient from 5 to 20% buffer B. Fractions containing the desired protein were pooled and dialyzed against 3  2 L of buffer C [50 mM HEPES (pH 6.5)], filtered through a 0.45-μm membrane and loaded onto a HiTrap Blue HP column (GE Healthcare) preequilibrated with buffer C. The flow through was collected and loaded onto a HiTrap Q HP column (GE Healthcare) pre-equilibrated with buffer C. The column was washed with 20 CV of 5% buffer D [50 mM HEPES, 500 mM NaCl (pH 6.5)], and the adsorbed proteins were eluted with 20 CV of 31% buffer D. Fractions containing the desired protein were pooled and dialyzed against 2  2 L of buffer E [50 mM HEPES, 1.5 M (NH4)2SO4 (pH 6.5)], filtered through a 0.45-μm membrane and loaded onto a HiTrap Phenyl Sepharose column (GE Healthcare) pre-equilibrated with buffer E. The column was washed with 10 CV of 25% buffer A, and the adsorbed proteins were eluted with a linear gradient from 25 to 53% buffer A. Fractions were analysed by sodium dodecyl sulphate−polyacrylamide gel electrophoresis (SDS−PAGE) (NuPAGE Bis-Tris 4−12% Precast gels, Thermo Fisher Scientific), pooled, concentrated using 10000-molecular-weight-cut-off (MWCO) ultrafiltration membranes (Millipore), dialyzed against 2  2 L of 20 mM HEPES (pH 8.0), aliquoted, and stored at 80 °C. The concentration was determined spectrophotometrically (NanoDrop) at 280 nm using the theoretical extinction coefficient (ε280) of 16960 M −1 cm −1 . The molecular mass was determined by electrospray ionization mass spectrometry (ESI-MS).

S4
Purification of AbHBDH. All purification procedures were performed at 4 °C and all chromatographic steps employed an AKTA Start FPLC system (GE Lifesciences). Cells were allowed to thaw on ice for 20 min before being resuspended in buffer A [50 mM HEPES, 300 mM NaCl, 10 mM imidazole, (pH 8.0)] containing 0.2 mg mL −1 lysozyme, 0.05 mg mL −1 DNase I, and half a tablet of EDTA-free Cømplete protease inhibitor cocktail, disrupted in a high-pressure cell disruptor Thermal denaturation curves were recorded over a temperature range from 25 -93 °C with 1 °C min -1 increments. Control curves lacking enzyme were subtracted from curves containing enzyme. All measurements were carried out in triplicate.

S7
Pre-steady-state kinetics. All reactions were carried out in 100 mM HEPES (pH 7.0) by monitoring the decrease of NADH at 340 nm (283 K, 298 K and 318 K) or 370 nm (328 K) in an Applied Photophysics SX-20 stopped-flow spectrofluorimeter outfitted with a xenon lamp, a 5-L mixing cell (0.5-cm path length and 0.9-ms dead-time) and a circulating water bath for temperature control.
Multiple-turnover rates were measured at saturating concentrations of both substrates. For temperature. In all cases, the enzyme concentration was at least 10-fold higher than the NADH concentration, and pseudo-first order approximation was assumed.
Kinetic and thermal denaturation data analysis. Kinetic data were analysed by the nonlinear regression function of SigmaPlot 14 (SPSS Inc.). Data points and error bars in graphs represent mean ± standard error, and kinetic and equilibrium constants are presented as mean ± fitting error. Substrate saturation curves were fitted to eq S1 where v is the initial rate, ET is total enzyme concentration, S is the concentration of the varying substrate, kcat is the steady-state turnover number, and KM is the DSF thermal denaturation data were fitted to eq S2, where FU is fraction unfolded, T is the temperature in K, Tm is the melting temperature, c is the slope of the transition region, and LL and UL are folded and unfolded baselines, respectively. 2 Pre-steady-state multiple-and single-turnover data were fitted to eqs S3 and S4, respectively, where [NADH]t is the concentration of NADH at time t, [NADH]t0 is the NADH concentration at time zero, [NADH]∞ is the NADH concentration as time approaches infinity, A0 is the amplitude change, t is the reaction time, v is the initial velocity, and kSTO is the single-turnover rate constant. [ Solvent viscosity effects on kcat were fitted to eq S5, where kcat 0 and kcat  are kcat in the presence and absence of glycerol, respectively, rel is the relative viscosity of the solution, and m is the slope. S10 Figure S2. Substrate saturation curves for AbHBDH and PaHBDH over several temperatures.
Temperature ranges are 283 K -330 K for AbHBDH reactions, and 283 K -318 K for PaHBDH reactions. Data are mean ± SE from at least duplicate measurements, and lines are data fitting to eq S1. Figure S3. Thermal denaturation curves from DSF for AbHBDH and PaHBDH in the absence and presence of ligands. Black lines represent the data fitting to eq S2. S11 Figure S4. Solvent viscosity studies with AbHBDH (left) and PaHBDH (right) in 0% glycerol (blue), 18% glycerol (pink) and 27% glycerol (cyan). The scatter plots are substrate saturation curves where data represent mean ± SE from at least duplicate measurements, and lines are data fitting to eq S1. The bar plots show the effect of glycerol on the second-order rate constants and represent value ± fitting error obtained upon substrate saturation data fitting to eq S1. S12 Figure S5. Solvent macroviscosity studies for acetoacetate reduction catalysed by PaHBDH (left) and AbHBDH (right) in 0% PEG-8000 (blue) and 5% PEG-8000 (pink). The scatter plots are substrate saturation curves where data represent mean ± SE from at least duplicate measurements, and lines are data fitting to eq S1. The bar plots show the effect of PEG-8000 on steady-state rate constants and represent value ± fitting error obtained upon substrate saturation data fitting to eq S1. S13 Figure S7. Eyring plot for PaHBDH-catalysed reduction of acetoacetate in the temperature range of 283 K -308 K. Data represent mean ± SE of at least duplicate measurements, and line is data fitting to eq 1.
Simulated Eyring plots for microscopic and macroscopic rate constants. To illustrate the kinetic complexity underlying both linear and nonlinear Eyring plots for macroscopic rate constants, and the caution that must be wielded when attempting to interpret them in terms of specific steps in an enzyme reaction, Eyring plots were simulated ( Figure S8) for two hypothetical microscopic rate constants (k3 and k5) and the resulting macroscopic rate constant (kcat) for a simple two-step mechanism (Scheme S2).

Scheme S2.
A hypothetical two-step mechanism for an enzyme reaction.
In Scheme S2, k3 is the microscopic rate constant for the chemical step, and k5 is the microscopic rate constant for product release from the enzyme. ES, EP, E and P are the enzyme-substrate complex, enzyme-product complex, free enzyme, and free product, respectively. Since the macroscopic rate constant of interest is kcat, the mechanism starts with the substrate-saturated enzyme.
= 3 5 3 + 5 eq S6 S14 To generate the simulated Eyring plots, arbitrary values of k3 and k5 were chosen so that plots of ln (k/T) vs 1/T (283 K -318 K) would be linear. These linear plots were made to intercept one another to reflect a change in rate-limiting step from k3 at low temperatures to k5 at high temperatures. From the values of k3 and k5, kcat values were calculated using eq S6, and plotted as ln (k/T) vs 1/T. Eyring plots for k3 and k5 were fitted to eq 1, while Eyring plots for kcat were fitted to both eqs 1 and 2. Figure S8. Simulated linear Eyring plots for microscopic rate constants k3 and k5, and the resulting Eyring plot for kcat. The ratio of slopes of Eyring plots for k3 and k5 increases from left to right.
For this simple two-step mechanism, a ratio of slopes of Eyring plots for k3 and k5 (which is a ratio of the H ‡ for each step) of 2.5, where a clear change in rate-limiting step from k3 at low temperatures to k5 at high temperatures takes place, still produces a linear Eyring plot for kcat whose fitting to eqs 1 and 2 are virtually indistinguishable ( Figure S8, left). A deviation from linearity in the kcat Eyring plot only becomes noticeable once the ratio of slopes of Eyring plots for k3 and k5 reaches 2.6 ( Figure S8, middle), and can be clearly seen when that ratio increases to 2.7 ( Figure S8, right).
Obviously this would become more complex if the mechanism involved more steps. Therefore, when generating temperature-rate profiles of kcat, one should not probe the reaction for a temperaturedependent change in rate-limiting step only when a nonlinear Eyring plot is obtained.