Resolution of Submillisecond Kinetics of Multiple Reaction Pathways for Lactate Dehydrogenase

Abstract

Enzymes are known to exhibit conformational flexibility. An important consequence of this flexibility is that the same enzyme reaction can occur via multiple reaction pathways on a reaction landscape. A model enzyme for the study of reaction landscapes is lactate dehydrogenase. We have previously used temperature-jump (T-jump) methods to demonstrate that the reaction landscape of lactate dehydrogenase branches at multiple points creating pathways with varied reactivity. A limitation of this previous work is that the T-jump method makes only small perturbations to equilibrium and may not report conclusively on all steps in a reaction. Therefore, interpreting T-jump results of lactate dehydrogenase kinetics has required extensive computational modeling work. Rapid mixing methods offer a complementary approach that can access large perturbations from equilibrium; however, traditional enzyme mixing methods like stopped-flow do not allow for the observation of fast protein dynamics. In this report, we apply a microfluidic rapid mixing device with a mixing time of <100 μs that allows us to study these fast dynamics and the catalytic redox step of the enzyme reaction. Additionally, we report UV absorbance and emission T-jump results with improved signal-to-noise ratio at fast times. The combination of mixing and T-jump results yields an unprecedented view of lactate dehydrogenase enzymology, confirming the timescale of substrate-induced conformational change and presence of multiple reaction pathways.

Introduction

Enzymes, like all proteins, are dynamic molecules whose structures are in constant flux due to the search for thermal equilibrium with the surrounding environment. Consequently, enzymatic reactions are not well described by a classic single-barrier reaction coordinate; they are instead better illustrated by a multidimensional reaction landscape (1, 2, 3). The multitude of available protein conformations exist on the landscape as minima separated by low barriers representing small-scale atomic level motions or vibrations, by high barriers representing large-scale protein domain rearrangements, or anything in-between (4, 5). A multitude of enzymatic reaction pathways are also available on the landscape connecting the various minima. This idea has been explored theoretically in various enzymes (6, 7, 8, 9), and studied experimentally by single-molecule experiments that reveal enzyme populations with various reaction rates (10, 11), and by vibrational spectroscopy of reactive substates (12, 13, 14). We have previously studied the reactivity of coexistent reaction pathways in the model enzyme lactate dehydrogenase, and we return to this model system here to expand our investigation (15).

Lactate dehydrogenase (LDH) is an oxidoreductase enzyme that catalyzes the reduction of pyruvate to lactate aided by a NADH cofactor. There are multiple variants of LDH within the same organism, such as heart, muscle, and sperm, with different reactivities. We studied porcine heart LDH, which exists as a homotetramer (16, 17), as a model for enzyme dynamics and catalysis because it has been previously well studied and contains a significant structural change produced by the binding of substrate or substrate analog (16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27). This structural change is characterized by the closing of a small loop section of the enzyme, located on the surface, over the active site. The loop closure brings a catalytically relevant arginine (Arg-109) into position to stabilize the reduction site carbonyl on the substrate pyruvate (see Fig. 1). The loop closure event has been studied previously, both theoretically and experimentally, to show that the loop can close into a variety of substates (13, 15, 25, 28, 29, 30, 31, 32, 33). Closure also appears to occur on a range of timescales, from submillisecond to millisecond times (26, 34, 35, 36). We have previously examined these conformational substates by temperature-jump (T-jump) spectroscopy to show that they exhibit varied reactivity (15). Recent theoretical studies on LDH have reinforced the connections between conformational and reactive heterogeneity by developing an atomistic view of the system (37). The kinetic relationship between the conformational and reactive dimensions of the LDH mechanism still need to be resolved. Kinetics methods based on mixing would allow for this relationship to be determined; however, conventional biophysical mixing methods like stopped-flow do not have the time-resolution to observe these fast conformational changes. Mixing methods with better time resolution needed to be developed and applied (38).

Figure 1.

Structure of the pig heart LDH active site (PDB:5LDH). Most of the protein is colored gray as a cartoon diagram or hidden for clarity. Key active site residues are highlighted as stick structures in other colors with their bonding interactions highlighted as black dashed lines. These interactions include Arg-109 on the mobile loop (green) and Arg-171 and His-195 (orange). The crystallized S-Lac-NAD⁺ substrate-cofactor analog has been colored to represent the NAD⁺ cofactor segment in cyan and the lactate segment in magenta; to emphasize each component, the bond between the cofactor and substrate mimic segments is not displayed. Image created with PyMOL (www.pymol.org) (38). To see this figure in color, go online.

In this study, we apply a microfluidic fast mixing device that has a mixing time, <100 μs, significantly shorter than traditional stopped-flow methods (39). We introduce this device to study the kinetic properties of LDH to understand the complicated dynamics within the Michaelis complex and as a proof of principle for its application to other enzyme systems more broadly. This device allows us to study the reaction on a timescale relevant to the conformational change in a straightforward manner. By studying the reaction with a variety of intrinsic fluorescent probes, tryptophan emission, NADH emission, and fluorescence resonance energy transfer (FRET) from tryptophan to NADH, we are able to clearly interpret the resultant transients. Our results define the rate of both the substrate and substrate analog-induced conformational change in LDH and on-enzyme hydride transfer. We are also able to relate these results to T-jump relaxation spectroscopy of the same system using NADH emission and absorbance as probes. This complementary approach also measures submillisecond events but can pick up events not observed by mixing studies. The combination of these approaches yields, to our knowledge, new certainty on the mechanism of lactate dehydrogenase. Our work indicates that a full characterization of a complex reaction mechanism, like the mechanism of LDH, requires multiple methods and probes.

Materials and Methods

Materials

NADH, pyruvate, and oxamate were purchased from Sigma-Aldrich (St. Louis, MO). Pig heart LDH was purchased from EMD Millipore (Billerica, MA). The buffer used for all studies was 50 mM sodium phosphate and 100 mM NaCl at a pH of 7.1. The lyophilized LDH from EMD Millipore was prepared by buffer exchange, as per manufacturer’s instructions, in a 10-kDa, 4-mL Amicon Ultra-4 Centrifugal filter (also available from EMD Millipore). The concentrations of LDH (40) and NADH (16) were confirmed spectrophotometrically using extinction coefficients of 50,040 cm⁻¹ M⁻¹ at 280 nm and 6220 cm⁻¹ M⁻¹ at 340 nm, respectively. The concentration of the protein is reported here as the concentration of active sites. Solutions of pyruvate and oxamate were prepared each day by weighing out the respective sodium salt and dissolving into a precise volume of buffer using a volumetric flask. LDH solutions were kept refrigerated for no more than a week after preparation. NADH, pyruvate, and oxamate solutions were prepared fresh daily.

Equilibrium fluorescence

All equilibrium fluorescence measurements were performed on a HORIBA (Edison, NJ) Dual-FL charge-coupled device (CCD) Array Fluorimeter with a 1.16 nm resolution, with fixed 5 nm slits, and a CCD gain setting of “Medium”. For the 280 nm excitation experiments, a 0.10 s integration time was used, and for the 340 nm excitation experiments a 3.0 s integration time was used. The reported spectra are an average of three scans. The cuvette used for these studies was a 0.100-mm short path-length demountable cell (Starna Cells, Atascadero, CA). The cuvette was placed in a custom-designed cuvette base that held the cuvette at an ∼30° angle. This configuration allowed for larger sample concentrations, like in the flow experiments, but without significant inner filter effects or incident reflection onto the detector. The data were exported and analyzed with the software Igor Pro 5.00 (WaveMetrics, Lake Oswego, OR). To mimic the flow conditions, the samples initially contained 200 μM LDH and 300 μM NADH and either no additional substrate or substrate analog, 1000 μM pyruvate, or 1000 μM oxamate. Upon mixing enzyme, cofactor (NADH), and pyruvate, this system became a chemically competent reaction and would mainly contain enzyme, oxidized cofactor (NAD⁺), and the reaction product lactate, because these conditions strongly favor the production of NAD⁺ and lactate. The emission of a 100 μM NADH sample under the same conditions was also taken as a reference for the mixing experiments because this is approximately equivalent to the excess cofactor available during the mixing experiments (enzyme concentration 200 μM, cofactor concentration 300 μM) that contributes excess fluorescence signal during those studies. Experiments were carried out at room temperature, ∼22°C.

Microfluidic fast mixing

The construction and characterization of the fast mixer used in this study has been detailed elsewhere (39), but briefly it is constructed of two concentric cylindrical fused silica capillaries initially containing distinct solutions. The inner capillary is heated and pulled to a conical tip on one end before use. The inner capillary (initially 90 μm outer diameter, 20 μm inner diameter) ends in a tip (∼7.4 μm in diameter) part of the way down the outer capillary (350 μm outer diameter, 200 μm inner diameter). After the inner capillary solution exits this tip, the solution in the outer capillary hydrodynamically focuses it into a thin jet. The two solutions, the inner-sample stream and the outer-sheath stream, mix by diffusion. In this experiment we flowed a solution of 200 μM LDH and 300 μM NADH in the inner stream and, where applicable, a 1 mM solution of substrate or substrate analog in the outer stream. We chose to flow the substrate or substrate analog in the outer solution because of its small size and therefore faster diffusion time. The mixing time of the substrate or substrate analog with the inner solution is ∼100 μs. As the diffusion time of the protein is slow, the concentration of protein remained relatively constant in the inner solution for several milliseconds. Eventually, at much longer times, the protein would significantly diffuse throughout the entire capillary and have an effective lower concentration. However, on our experimental timescale, the mixing time is limited by diffusion of the substrate or substrate analog into the center stream.

Fluorescence images of the reaction flow in the mixer were collected with an Olympus (Center Valley, PA) IX81 microscope system. For direct tryptophan emission and FRET emission studies, the source of fluorescence excitation light was the frequency tripled output from a Coherent (Santa Clara, CA) Mira Ti:Sapphire laser pumped by a Coherent Verdi-V12. The mode-locked output produces 150 fs pulses at 82 MHz centered around 850 nm and the tripled output is at 283 nm. For direct NADH excitation studies, the light source was a CrystaLaser (Reno, NV) Q-Switched 351-nm diode-pumped laser run at a 1000 Hz repetition rate. Excitation light was directed through an appropriate short-pass filter from IDEX Optics and Photonics (Albuquerque, NM) then through a 40× UV focusing objective from Thorlabs (Newton, NJ). Emission is collected through the same objective and reflected off the short-pass filter through an appropriate band-pass filter (also from IDEX Optics and Photonics), depending on the optical probe, and collected as an image on a Hamamatsu (Bridgewater, NJ) C9100-14 ImageM-1k EM-CCD camera. Images were collected with various exposure times to maximize the signal, but typical exposure times were 20 s for direct excitation of tryptophan, 5 s for direct excitation of NADH, and 3 s for FRET studies with a gain setting of 1 and an intensification setting of 255. The CCD array was actively cooled to −57°C. Experiments were carried out at room temperature, ∼22°C, because this version of the flow system does not allow for well-controlled temperature handling. Performing data collection at room temperature allowed for the most accurate description of the experimental temperature.

Data was recorded over several days with fresh solutions of substrate, substrate analog, cofactor, and enzyme prepared each day. On a given day, multiple data images (usually five) were collected for each set of conditions. The reagent solutions are flowing continuously; therefore, each image is representative of a different mixture of samples. Each image is analogous to a shot from a stopped-flow experiment. The images from one day were averaged together. The fluorescent transients from each day were generated as discussed below, and the different transients were averaged together to get the final transients presented here. The error values reported in this article are the uncertainty values from the fitting procedures performed on the final averaged transients.

Images collected from the CCD camera were exported as TIFF images into Igor Pro (WaveMetrics). We used Igor Pro’s built-in image processing routines to obtain the fluorescence at each pixel along the flow path. The pixel number is then converted to time using the pixel-to-time calibration methods we have previously reported (39). Time zero in these experiments is taken to be the point where mixing is initiated at the end of the inner capillary. A control fluorescence profile was generated by flowing just buffer in the outer capillary and the same LDH⋅NADH solution in the inner capillary, to compensate for fluctuations in the fluorescence intensity due to changes in pixel response and excitation laser profile. The signals were first dark corrected and then the substrate or substrate analog-mixing fluorescence profiles were divided by the buffer-mixing fluorescence profiles to generate a background-corrected fluorescence profile. These profiles are therefore normalized to the buffer-mixing transients (i.e., normalized to one at early time), and the y axis of the data given below reports on the degree of change in the substrate or substrate analog-mixing experiments from the buffer-mixing controls.

Troubleshooting protein solution flow

One reality of flowing protein solutions in small capillary systems is a propensity for clogging. While doing the work reported here, that was our experience as well. We were eventually successful in performing the experiments described herein with multiple repetitions, but it is worth noting the difficulties we encountered. It was very common for the inner capillary tip to become irreparably clogged with protein aggregates during data collection. We attempted to avoid this problem by several methods. We tried various methods of protein purification, both centrifugal filtration and dialysis, to minimize impurities or aggregates. We surveyed various buffer systems (e.g., phosphate based, TRIS based, borate based). We used both stainless steel and titanium based in-line filters (0.5 μm porosity; IDEX Optics and Photonics) to clean up the sample just before injection. Finally, we tried coating the inside of the inner capillaries to reduce reactive silanol or siloxane groups as these have been purported to cause protein adsorption in capillary electrophoresis (41, 42). We tried using both a Poly(L-lysine)-g-Poly(ethylene glycol) coating (43) and a Poly(ethylene glycol)-modified silane coating (44). In summary, we found that none of these approaches led to a significant decrease in inner capillary occlusion. However, we did find that simply cutting the inner capillary tip decreased the frequency of clogging compared to high-temperature pulling of the tip. This result implies that the high-temperature pulling process results in a tip surface that is more reactive (see our previous work for more details on this process (39)). Further work to optimize the pulling process to be nonreactive or to establish an effective coating method would probably make this technique more efficient. As is, we were only able to use this technique to study LDH because of the low cost of sample and mixer construction, which allowed us to replace the mixer and sample whenever the system clogged.

Laser-induced T-jump

The laser-induced T-jump experimental setup that can raise the temperature within a small volume of sample in ∼20 ns has been described in Zhadin et al. (32). To study the LDH-catalyzed reaction, we first allow the system to come to equilibrium at some initial temperature. The sample temperature is rapidly changed (T-jump), and the relaxation kinetics of the system is probed by optical absorption or fluorescence emission as the system reestablishes at its new higher temperature. The sample is heated in the irradiated spot of 1–1.5 mm diameter by 8°C in the experiments presented herein. The necessary IR emission is generated by Raman shifting the fundamental (1064 nm) of a Powerlite 7010 Q-switched Nd:YAG laser (Continuum, Santa Clara, CA). The Raman shifter cell, model 101 PAL-RC (Light Age, Somerset, NJ), has a 1-m path length and is filled with deuterium gas at 650 psi. Both forward and back-scattered beams from the Raman shifter are directed toward the sample from two sides to obtain a more uniform longitudinal heating pattern. Polarization of the forward beam is rotated by 90° to avoid Bragg grating formation inside the sample. The sample temperature after the jump is monitored over time by probing changes in water IR absorption at 1460 nm.

To monitor UV-Vis absorption changes in the sample, a collimated and sharply (∼0.5 mm) focused beam of light from a Photomax arc lamp source (Oriel Instruments, Stratford, CT) with a 75 W Xe lamp is passed through the heated spot of the sample, and then directed to a monochromator (model 270 M; Instruments SA, Edison, NJ) with a H6780-03 photomultiplier tube module (Hamamatsu). The light incident on the sample is prefiltered with a wide band optical filter. When fluorescence detection is used, the fluorescence is excited by an Innova 200 Ar-ion laser (Coherent) emitting a group of lines near 360 nm (351.1 and 363.8 nm). The excitation beam is focused on the sample in a spot of ∼0.3 mm diameter, in the center of the IR-heated spot. The fluorescence emission is collected at an ∼50° angle. This light, after passing through a three-lens spatial filter with a narrow band interference filter in the parallel part of the beam, is detected by a R4220P photomultiplier tube (Hamamatsu). To select NADH fluorescence, we used a 450 nm narrow-band filter with the bandwidth of 40 nm full width at half-maximum. The signal from the photomultiplier tube, after a lab-made trans-impedance preamplifier with 3 ns response time, is sent to a CS82G digitizing PCI board (Gage Applied, Lachine, QC Canada) for data acquisition at 1 GS/s sampling rate. For the computer control of the setup, a lab-made program is used written in LabVIEW (National Instruments, Austin, TX). For both the absorbance and fluorescence T-jump experiments presented herein, the system’s initial conditions were 0.4 mN LDH (moles of active sites), 0.4 mM NAD⁺, and 5 mM lactate (total initial concentrations). The T-jump raised the temperature of the sample from 14 to 22°C for the data shown in Fig. 6. The NADH absorbance T-jump data shown in Fig. 7 had a temperature change from 24 to 32°C to more closely match the conditions of the infrared data (15). The T-jump kinetic response from pure buffer, measured in a special series of experiments, was subtracted from all absorption kinetics.

Figure 6.

Absorption (A) and fluorescence (B) T-jump kinetics of the reaction system: 0.4 mN LDH, 0.4 mM NAD⁺, and 5 mM lactate (total initial concentrations) to a final temperature of 22°C. Transients are also shown where C2-d-lactate was used to measure the primary kinetic isotope effect. After irradiation with the 20 ns laser pulse induces the T-jump, the temperature in the sample remains constant until the millisecond time range; the temperature decays to ambient with a 30 ms half-time. Hence the lifetimes of any observed kinetics may contain a strong cooling component past 10 ms. Double-exponential fits between 1 μs and 10 ms are shown in the plots as black lines, and their fit rates are given in the legend. The ragged features in (A) below 1 μs are artifacts, due to cavitation effects. To see this figure in color, go online.

Figure 7.

Comparison of the T-jump absorption kinetics of the LDH reaction system when probed by the infrared absorbance of the C-2 pyruvate carbonyl stretch at 1685 cm⁻¹ and when probed by the NADH absorbance at 340 nm. The infrared data is from http://pubs.acs.org/doi/abs/10.1021/jp5050546 (15), reproduced by permission. The UV data is under the same conditions as Fig. 6, except the T-jump is from 24 to 32°C to more closely match the infrared conditions. The bumps near 5 μs are artifacts due to cavitation effects. To see this figure in color, go online.

Results and Discussion

The goal of this study is to characterize the search for reactive conformations in LDH by measuring the kinetic properties of the LDH Michaelis complex. The system has been thoroughly investigated on the millisecond timescale. However, only recently has it been feasible to study the submillisecond events. These are crucial for LDH (and many if not most other enzymes) because they set up all that follows, i.e., reactive conformations that determine the rate of catalysis form on this timescale (15). We introduce here a system based on microfluidics, mixing LDH⋅NADH with either the native substrate pyruvate or its nonreactive analog, oxamate. The time resolution of this instrument of ∼100 μs is ∼20 times better than conventional stopped-flow instruments. In addition, we examine the system with a laser-induced T-jump relaxation spectrometer measuring NADH optical emission and absorption that has a resolution of ∼50 ns. Mixing and relaxation approaches yield different views of the kinetics. In part this is because a mixing experiment starts the reaction far from equilibrium, whereas a relaxation experiment involves a small perturbation of the reaction equilibrium. Also, the final equilibrium state reached by the two approaches is usually quite different. Finally, the observed kinetics in a relaxation experiment report on both fast and slow interconversions, regardless of their ordering. So, for example, in a system like that shown in Scheme 1 the fast step is not obscured by the rate-limiting slow step in the relaxation approach; both steps can be observed. In contrast, if the reaction had been initiated from left to right in a mixing experiment, only the rate-determining slow step would be observed.

$$\dots \mathrm{A}\stackrel{\text{slow}}{\rightleftharpoons }\mathrm{B}\stackrel{\text{fast}}{\rightleftharpoons }\mathrm{C}\dots$$ Scheme 1

The sequence of steps is sometimes difficult to disentangle within either approach alone. However, the sequence of steps can often be determined by combining the results from the mixing study with those of the relaxation approach. This situation applies to LDH because it is believed that there is a slow conformational rearrangement before hydride transfer (26, 32). In such a case, states A, B, and C in Scheme 1 would represent LDH⋅NADH⋅pyruvate, LDH^∗⋅NADH⋅pyruvate (^∗ = reactive state), and LDH⋅NAD⁺⋅lactate, respectively. Thus, we utilize both fast mixing and temperature-jump to study LDH comprehensively.

Equilibrium fluorescence

The catalytically competent LDH system has three intrinsic fluorescence probes: direct tryptophan emission (excitation at 280 nm, emission at 350 nm), direct NADH emission (excitation at 340 nm, emission at 445 nm), and FRET from tryptophan to NADH emission (excitation at 280 nm, emission at 445 nm). In the fluorescence fast mixing experiments below, we use all three of these probes to investigate the mixing of LDH⋅NADH with both the catalytically competent substrate pyruvate and the noncompetent substrate analog oxamate. As a guide to interpreting the fast mixing experiments, we obtained the equilibrium fluorescence spectra of various LDH⋅NADH complexes.

Fig. 2 shows the equilibrium emission spectra from NADH in solution, in the LDH⋅NADH binary complex, and in the LDH⋅NADH⋅oxamate ternary complex. The equilibrium conditions approximate the final conditions expected for the mixing reactions. As expected, the NADH emission spectrum increases for the binary complex (due to a more hydrophobic environment) compared to water. Somewhat unexpectedly, the NADH emission is heavily quenched in the ternary complex of oxamate. There is experimental evidence that this is due to the formation of the active site, in which ionic groups interact with the substrate or substrate analog to change the electronic structure of the dihydronicotinamide group (45). In our own work (46), we find that bound oxamate (and pyruvate) acts as an electron acceptor in the quenching of fluorescence of NADH. Efficient quenching in LDH complexes requires that oxamate or pyruvate form a salt bridge with Arg-171 and hydrogen bonds with His-195. Thr-246 and Asn-140 also perturb the fluorescence. Hence, we can employ this as a structural tool because the quenched emission is the result of the formation of the active site.

Figure 2.

Equilibrium fluorescence of LDH⋅NADH complexes. The complexes are LDH⋅NADH with no substrate or substrate analog (black); LDH⋅NAD⁺⋅lactate (blue) produced by mixing LDH⋅NADH and pyruvate; LDH⋅NADH⋅oxamate (red); and a reference NADH solution (green, dashed). (A) Spectra excited at 280 nm showing tryptophan emission centered around 350 nm and FRET from tryptophan to NADH centered around 445 nm. (B) Spectra excited at 340 nm showing NADH emission centered around 445 nm. To see this figure in color, go online.

When equimolar pyruvate is added to a solution of LDH⋅NADH, we expect the enzymatic reduction of pyruvate to lactate to go to near completion because the lactate side has a much lower Gibbs free energy. In contrast, the mixing studies in this report do not reduce all the pyruvate present because it is present in large excess and there is a limited amount of NADH present. The reduction of pyruvate by LDH is most clearly observed in Fig. 2 B where we see the emission of NADH from direct excitation disappear almost entirely. Upon oxidation of NADH to NAD⁺ on the enzyme, NADH loses its 340-nm absorbance band. Similarly, we observe in Fig. 2 A that upon mixing pyruvate with LDH⋅NADH, the FRET band at 445 nm also disappears almost entirely for the same reason. As a consequence of this loss of FRET from the excited tryptophan to the NADH, we also observe a significant increase of the tryptophan emission.

Oxamate is a nonreactive analog to pyruvate; hence, in contrast to the chemical turnover that occurs with the addition of pyruvate to LDH⋅NADH, no catalytic turnover occurs with the addition of oxamate to the enzyme binary complex. However, without oxidation of NADH from enzyme turnover there are still significant changes to the emission spectra of LDH⋅NADH upon binding of oxamate. The addition of oxamate to the binary complex induces enzyme conformational changes that, in turn, effect the cofactor orientation and hence its fluorescence, as has been discussed above.

The enzyme conformational change that alters the cofactor and active site when either the substrate or substrate analog binds to the enzyme is observed spectroscopically in three ways. First, the emission from direct excitation of NADH is decreased by almost 85% and the emission wavelength red-shifts by a few nanometers. Second, due to quenching of the NADH acceptor emission there is also at least an 85% decrease in FRET intensity. Third, the signal from direct tryptophan emission is also slightly decreased. Because we know the NADH emission, which is the acceptor in the tryptophan-NADH FRET pair, is decreased, there are two likely explanations for the decrease in tryptophan emission. First, there could be increased FRET efficiency in the ternary enzyme complex, which decreases tryptophan emission without a corresponding increase in NADH emission due to acceptor quenching. Second, it is possible that the substrate or substrate analog-binding-induced conformational changes of the enzyme may be causing some of the tryptophans not involved in energy transfer to NADH to be exposed to a more quenching environment like a nearby histidine or solution. Discerning which of these mechanisms is most correct is not trivial because each LDH monomer contains six tryptophans, and it is believed that only two to three of these residues are significantly involved in FRET (47). The origin of this signal change is not key to our work, but it is useful to note that tryptophan emission is decreased upon substrate or substrate analog binding.

In summary, the equilibrium fluorescence spectra presented in Fig. 2 indicate that there are very significant changes to the emission spectra of LDH⋅NADH upon mixing with pyruvate or oxamate. Furthermore, because there is a difference in both the magnitude and direction of these changes depending on whether oxamate or pyruvate is introduced, we can use this information to sort out which changes in the fluorescence mixing experiments presented below are due to substrate or substrate analog binding, and which are due to chemical turnover by comparing the results of mixing pyruvate or oxamate with LDH⋅NADH.

Microfluidic fast mixing

The results of probing the fast mixing of LDH⋅NADH with pyruvate by tryptophan emission are markedly different than those obtained by fast mixing with oxamate (Fig. 3). The most obvious difference in the two transients shown in Fig. 3 is the opposite sign of their signal change. The pyruvate-mixing transient shows a significant increase in tryptophan emission whereas the oxamate transient shows a slight decrease in tryptophan emission. This result is consistent with the equilibrium fluorescence data presented above. The obvious assignment for the kinetic event observed in the pyruvate transient is chemical turnover. Not only does the tryptophan emission increase as expected, see above, but we do not see a commensurate change in the oxamate signal where chemical turnover does not occur. The kinetic event fits to a single exponential curve with a rate of 330 ± 10 s⁻¹. Two relevant rates for comparison are k_cat and k_hydride. k_cat has been reported as 245 s⁻¹ and is believed to be primarily determined by slow structural rearrangements within the Michaelis complex (13, 35). k_hydride reports on the specific rate of reaction for the hydride transfer process and has been reported as 637 s⁻¹. The primary kinetic isotope effect (KIE) is low, 1.9, so the value of this rate coefficient is clearly a mixture of the chemistry step coupled with protein conformational changes and therefore underestimates the actual rate of hydride transfer (32). We have already explained how the increase in the tryptophan emission could be due to the redox (hydride transfer) step of the reaction or a conformational change; therefore, it is reasonable that the observed rate is in between these two rates from the literature. The exponential fit to the oxamate data is shown to help the reader see the difference in the timescales of the observed changes, but should not be taken as accurate because the fit yields a decay time (10 ms) substantially outside the data collection window (4.5 ms). By comparison of the oxamate and pyruvate mixing data, we can conclude that a (major, see below) chemistry step occurs with a rate of 330 s⁻¹.

Figure 3.

Tryptophan-probed mixing transient of LDH⋅NADH and pyruvate or oxamate. The data are presented as the normalized fluorescence intensity of tryptophan emission (excitation: 280 nm, emission: 340 nm). Single-exponential fits to the data are shown and their fit rates are listed in the legend. The fit shown for the oxamate data is shown to emphasize the difference in the traces, but should not be taken as an accurate fit because the fit lifetime is outside the observation window. To see this figure in color, go online.

Fig. 4 shows the results of observing the mixing reaction by FRET from the tryptophan to the NADH. In contrast to the tryptophan transients displayed in Fig. 3, there is more similarity in the FRET transients. Both the pyruvate and oxamate FRET transients show a decrease in overall signal of approximately the same amount. When these transients are fit to exponential functions, the oxamate data fits to a faster decay rate of 2060 ± 10 s⁻¹, whereas the slower rate from the pyruvate data fits to a decay rate of 1620 ± 10 s⁻¹. The oxamate transient is well fit to a single exponential function whereas a double exponential function is required to fit the pyruvate transient. The faster decay rate of the double exponential fit was 17,400 ± 800 s⁻¹, which is approximately equal to the rate expected for pyruvate binding of 15,000 s⁻¹ under our conditions (32). In contrast, the rate constant for oxamate binding is twice as fast at this temperature and is therefore difficult to distinguish from the mixing time (27). Furthermore, our data normalization process effectively removes fluorescence changes due to processes within the mixing time (the burst phase; Materials and Methods). The combination of these two effects, faster oxamate binding and overlap with the mixing timescale, explains why we only need a single exponential function to fit the oxamate data well.

Figure 4.

FRET-probed mixing transient of LDH⋅NADH and pyruvate or oxamate. The data are presented as the normalized fluorescence intensity of FRET emission, tryptophan to NADH (excitation: 280 nm, emission: 460 nm). Exponential fits to the data are shown; see text. To see this figure in color, go online.

We assign the major phase of the FRET decays shown in Fig. 4 to a conformational change induced by substrate or substrate analog-binding. As has been discussed in the literature, it was previously observed that motions of the mobile loop on LDH closing down over the active site (and involving motions of the protein atoms outside the active site) after the substrate or substrate analog binds and before chemistry occur with millisecond and submillisecond rates (26, 28). The observed rates of 2060 and 1620 s⁻¹ are much slower than the rate of substrate or substrate analog binding. Furthermore, the tryptophan transients shown in Fig. 3 allow us to determine the rate of the chemistry step under these experimental conditions to be much slower than the FRET decay rates. Therefore, because the observed rate is in between substrate or substrate analog-binding and the chemistry step, and we know the loop motion should affect the acceptor emission of the FRET pair (27), we can confidently assign the FRET decay to the loop motion in the enzyme. Previous T-jump studies agree with our finding that the rate of the loop motion is faster in the oxamate-bound complex as opposed to the pyruvate-bound complex (27, 32, 48).

The final spectroscopic probe we used to investigate these mixing reactions was direct excitation of the NADH cofactor. The results of these experiments are shown in Fig. 5. The mixing transients probed by direct excitation of NADH are more similar to the FRET transients than the tryptophan transients. We again see similarity between the oxamate-mixing and pyruvate-mixing transients because both signals decrease by about the same amount. A key difference between the NADH probed data sets, however, is that the oxamate transient (red trace) levels off on the millisecond timescale, whereas the pyruvate transient (blue trace) exhibits a sharp decrease on this timescale. This difference is significant and the fits provide further insight on its origin. The oxamate NADH transient is again well fit by a single exponential curve. The decay rate of 1870 ± 20 s⁻¹ is similar enough (<10% different) to the FRET decay rate of 2060 s⁻¹ that, within the error of the experiment, the two transients are likely reporting on the same event. The pyruvate NADH data can also be fit to a single exponential curve. The decay rate of this fit is ∼1100 ± 10 s⁻¹. Unlike with the case of the oxamate data, the pyruvate NADH decay rate is not very close to the pyruvate FRET data (>30% different). A reasonable explanation for this discrepancy is that we would expect the NADH emission to report on more than just the loop motion. The oxidation of NADH during the chemistry step should also be visible here. We have shown the chemistry step to occur on the 330 s⁻¹ timescale and the loop motion to occur on the 1600 s⁻¹ timescale. These two events are close enough in timescale that they cannot be treated as independent reaction events. Instead, we can fit the data as a series of dependent consecutive unimolecular transformations to test this hypothesis (49). An explanation and derivation of the mathematical model used to perform this fit is given in the Supporting Material.

Figure 5.

NADH-probed mixing transient of LDH⋅NADH and pyruvate or oxamate. The data are presented as the normalized fluorescence intensity of NADH emission (excitation: 355 nm, emission: 460 nm). Fits to the data are shown and their representative fit rates are listed in the legend. See the text for a discussion of the fitting functions used. To see this figure in color, go online.

If we fit the pyruvate NADH mixing data to Eq. S8, the root mean square deviation (RMSD) of the fit improves by ∼3% compared to the single exponential fit. The decay rates are 1400 ± 40 s⁻¹ and 150 ± 20 s⁻¹. These rates, particularly the slower one, are smaller than expected. Furthermore, some of the other fit constants, like y₀ = −0.012, are nonsensible. Based on how we have normalized the data, we expect to see a positive signal baseline due to the excess NADH in solution. The nonlinear least squares fitting process likely fails due to the small amplitude of the slow phase and because there is a limited amount of time in the millisecond region of the observation window through which to fit the slow phase. A more reliable approach to this fitting task is to hold the decay rate of the second phase to the rate of the slow phase from the tryptophan transient data of 330 s⁻¹. When the fit is repeated under these conditions, the RMSD of the fit is within 2% of the original single exponential fit. The similarity in the RMSD values indicates that the fits are equally valid on a statistical basis; however, the results of the latest fit make more sense chemically. The fast phase is fit to a decay rate of 1970 s⁻¹ while the slow phase is held to 330 s⁻¹. The y₀ is fit to 0.028, a more physically reasonable final fluorescence level than the previous negative value for y₀ noted above. Finally, the spectroscopic constant relating the fluorescence intensity of state A to state B is fit to a value of 0.38. This number is very close to the value 0.30 predicted by scaling the data in Fig. 2 to the appropriate concentrations and integrating the intensity of the emission band by the parameters of the bandpass filter used to observe the NADH emission on the detector. We have already assumed in this analysis that there is a slow rate related to chemistry. We can assign the faster decay rate by observing the similarity of this rate to that of the FRET pyruvate transient, meaning that it is likely due to the loop motion. Therefore, the NADH pyruvate mixing transient data are well fit to a sequence of coupled consecutive steps (Scheme S2 in the Supporting Materials and Methods), specifically loop closure followed by the hydride transfer.

To drive home the importance of fast mixing methods to study enzyme kinetics, Fig. S1 compares the results from probing NADH emission mixing LDH⋅NADH with oxamate using microfluidic fast mixing (Fig. 5) and conventional stopped flow. While a remnant of the 1870 s⁻¹ transient seen in Fig. 5 is observed by stopped flow, it is not resolved.

We observed the reaction kinetics of mixing pyruvate or substrate with LDH⋅NADH by utilizing the intrinsic fluorescence signals of the reaction system. While following this reaction by changes in NADH absorbance would additionally allow for a direct measurement of enzyme activity, such an approach is technically very challenging due to the small path length, and therefore poor signal-to-noise ratio, of the microfluidic device. Furthermore, previous studies of LDH employing both absorbance and fluorescence spectroscopies have demonstrated the utility of NADH fluorescence to report on both chemical turnover and conformational changes (32). Our comparisons here among fluorescence-probed microfluidic mixing, fluorescence-probed T-jump, and absorbance-probed T-jump reaffirm the utility of both absorbance and fluorescence to study LDH.

Rapid T-jump kinetics

Kinetic studies based on relaxation approaches take a system at equilibrium, rapidly change some parameter that controls the equilibrium, here temperature, and watch the system relax to the new equilibrium point. We have worked out the equilibrium conditions for the interconversion of LDH⋅NADH⋅pyruvate to LDH⋅NAD⁺⋅lactate as a function of the concentrations of LDH, NAD⁺, and lactate (32). High concentrations (approximately millimolar) of the three species with excess lactate yields an equilibrium of approximately equal amounts of the ternary complexes on the pyruvate and lactate sides of the reaction. The protein LDH consists of four independent subunits. Here, the initial concentrations of 0.4 mN (this refers to the molar concentration of subunits of the tetrameric protein), 0.4 mM NAD⁺, and 5 mM lactate, were used (see previous studies of this system (31, 32)).

The NADH emission and absorption kinetics of the LDH⋅NADH⋅pyruvate system (in equilibrium with LDH⋅NAD⁺⋅lactate) in response to a ∼8°C T-jump were taken at a variety of temperatures. Fig. 6 shows emission and absorption results for a final temperature of 22°C, which can be directly compared to the rapid flow results presented above. The graphs shows data from 100 ns to 20 ms. The temperature in the sample remains quite constant after irradiation with the 20-ns pulsed light inducing the T-jump until the millisecond time range; the temperature decays within the observation cell by heat diffusion to ambient with a 30-ms half-time. The profile of the cooling has been determined and the transient curves presented in Fig. 6 have been corrected. Nevertheless, the lifetimes of any observed kinetics contain a cooling component past 30 ms, as is clear from the data sets. The emission data of Fig. 6 agrees well with previous results (32). The absorption results extend the reliable time range of the results in Zhadin et al. (32) from ∼0.5 ms to ∼30 ms. Cavitation effects limit the early timescale signal resolution in these experiments to 1 μs; therefore, the reliable time range of the results is from 1 μs to ∼30 ms.

As can be seen in Fig. S2, there is negligible change in the NADH absorption spectrum of the ternary LDH⋅NADH⋅pyruvate complex as a function of temperature, just a small change in the amplitude. This is expected because although there are small changes to the NADH absorption spectrum for the ternary and binary complexes compared to NADH in solution, the concentrations of the reactants is very high so that there is little binary and free NADH in the sample. Hence, the decrease in absorption shown in Fig. S2 and in the transient kinetics of Fig. 6 is from on-enzyme chemistry converting some of the LDH⋅NADH⋅pyruvate species within the reaction mixture to LDH⋅NAD⁺⋅lactate.

Our previous studies employed optical NADH absorption and emission as probes of kinetic changes in structure, and were analyzed with a minimal kinetic model: binding followed by loop closure leading to chemistry (32). Subsequent studies have shown that this model was too simple. IR spectroscopy has found the LDH⋅NADH⋅pyruvate Michaelis complex is composed of a set of conformational substates each with a varying propensity toward on-enzyme chemistry (13, 15). These subsequent kinetic investigations based on laser-induced T-jump IR relaxation spectrometry have shown substantial kinetic complexity within the ternary complex (15). These results are in full agreement with the kinetic complexity revealed by the IR T-jump studies indicating that multiple reaction pathways are needed to explain the data.

The absorption results in Fig. 6 show double exponential behavior, with rates of 401 and 3980 s^–1 of decreasing amplitude in response to the T-jump, consistent with conversion to the lactate side of the ternary complex equilibrium. Our previous studies, which only discerned the slow component, calculated an enthalpy difference of ΔH = 1.6 kcal/mol between LDH⋅NADH⋅pyruvate and LDH⋅NAD⁺⋅lactate (32). These results show that there are at least two channels of on-enzyme chemistry: one, the main channel, occurring on the millisecond timescale; and the other, a minor channel, at submillisecond times. Our studies following on-enzyme pyruvate-lactate chemical inner conversion employing IR probes, specifically the concentration of substates identified by the frequency of the C = O stretch of the pyruvate keto group, found that the substates undergo conversion on submillisecond times with varying rates depending on the frequency of the C = O group (15). We were unable to observe any transients on the millisecond times in those studies because the cooling time in our T-jump IR cells was on the order of 1 ms. Fig. 7 shows an overlay of these optical absorption results and the IR kinetics taken at 1685 cm⁻¹. The agreement on the submillisecond timescale is quite good between the NADH absorbance transient and the 1685 cm⁻¹ IR transient from those experiments. Other keto IR frequencies of the C = O stretch arising from other conformational substates in the LDH⋅NADH⋅pyruvate Michaelis complex were evident in the IR kinetics studies (most notable 1679 cm⁻¹). These were generally somewhat faster than 1685 cm⁻¹ and are not clearly seen in the NADH absorbance data, perhaps because of the limited signal-to-noise ratio.

As mentioned above, the NADH emission kinetics such as those shown in Fig. 6 were analyzed previously by a simple kinetic model. The slow phase (367 s⁻¹ for this data set) was associated with the chemical event. The rate is quite close to values of k_cat and the decreasing value of the NADH emission is quite consistent with a loss of absorption of bound NADH to form bound NAD⁺ as the temperature is increased (see Fig. 6; Fig. S2); this assignment is also consistent with the results of the flow studies above (see Figs. 3 and 5). We have shown previously that the primary KIE of the slow phase is between 1.2 and 1.8, and our work (Fig. 6) shows a similarly low value of 2–2.6 depending on method (32). These KIE values are consistent with the primary KIE of LDH from other organisms (32, 50, 51). If the hydride transfer step of the reaction were completely rate-limiting, then we would expect a primary KIE of six to seven (52). Because the slow phase observed in the T-jump studies indicates a much lower KIE effect, we can conclude that the hydride transfer step is not very rate limiting and must be significantly coupled to a slower step. Previous cryogenic stopped-flow studies have identified at least two conformational changes that are important to LDH catalysis: a faster loop closure step and a potentially rate-limiting slower conformational change from an inactive to active form (26). The 300–400 s⁻¹ slow phase that we observe with both T-jump probes and rapid mixing is consistent with the interpretation that the chemistry is rate limited by this slow change to an active form.

The relatively sizable increase in NADH emission in the T-jump results, occurring with a rate of 2193 s⁻¹, can arise from two possible physical events. For the concentration of the species here and the known bimolecular binding rates (31), one can calculate that the bimolecular binding of pyruvate to LDH⋅NADH lies in this range. We originally assigned this feature to this binding event. The relative emission of the binary complex compared to the ternary complex is large (Fig. 1) and a rise in temperature favors the formation of the binary complex. The problem with this assignment is that the relative proportion of the binary complex given the high concentrations of the various species is small, and signal size in relaxation studies is a function of relative concentrations. Hence, this assignment seems very doubtful. Our recent IR static and kinetic studies show conclusively that the LDH⋅NADH⋅pyruvate species consists of a number of interconverting conformational substates (13, 15); hence, it would be expected that the unimolecular substate interconversions should be included in any kinetic model. In our analysis of the T-jump IR experiments, the model we used required the conformational substates to return to the encounter complex and go through a conformational change to convert to a different conformational substate. Our modeling work predicted that the rate of this conformational change would vary for each substate, but that the majority population would perform this conformational change with at a rate of 3000 s⁻¹, which is similar to the 2193 s⁻¹ transient in Fig. 6 (15). Moreover, the results from rapid flow mixing above (Fig. 5) support molecular events on the same timescale and direction.

Conclusions

Clearly, mixing studies are important to the study of enzymes. Just as clearly, as shown by this study, mixing approaches with better than 1 ms resolution are crucial. The microfluidic approach presented and developed here has good resolution, ∼20 times better that stopped flow, and consumes relatively little protein. Our mixing studies allowed us to conclusively show that the architecture of the active site, including closed conformations of LDH⋅NADH⋅pyruvate (or oxamate), is formed on the submillisecond timescale and allowed us to resolve the rate constant for the conformational change at more physiologically relevant conditions than previous studies.

In agreement with past results, we find that there are two parallel pathways for chemistry, a millisecond (∼300 s⁻¹) path that is concomitant with observed k_cat, and a submillisecond path (∼3980 s⁻¹). Two parallel reaction pathways were observed in a stopped-flow study of LDH at cryogenic temperatures (26). The reaction was conducted at −16°C with 30% dimethyl sulfoxide to slow it down to a point that was easily resolvable by stopped-flow. The authors note that as they increased the temperature or decreased the concentration of dimethyl sulfoxide, the reaction kinetics collapse into a single pathway, the slower of their two pathways. The two pathways are clearly observed in our above T-jump relaxation study of the change in absorbance of NADH in LDH⋅NADH⋅pyruvate under more physiological conditions. The flow results yield the 330 s⁻¹ kinetic event but the 3980 s⁻¹ kinetics are not observed. This may be because this channel has small amplitude. But we think it more likely that it is obscured by a preceding slow structural change. The flow results show that the active site is largely organized at a rate of ∼1970 s⁻¹. This is the time it takes for substrate to reach the active site and some aspects of loop closure to occur; further protein conformational changes are almost certainly rate limiting to the fast chemical event. This conclusion agrees with the kinetic model developed for our T-jump IR studies, having a loop closure that precedes the fast chemical event. The study here confirms this order of events.

Author Contributions

M.J.R., R.B.D., and R.C. designed research. M.J.R. performed research and analyzed data. M.J.R., R.B.D., and R.C. wrote the manuscript.

Editor: Elizabeth Rhoades.