Aldolase Does Not Show Enhanced Diffusion in Dynamic Light

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Aldolase does not show enhanced diffusion in dynamic light scattering experiments Yifei Zhang, Megan J Armstrong, Neda M. Bassir Kazeruni, and Henry Hess Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b04240 • Publication Date (Web): 28 Nov 2018 Downloaded from http://pubs.acs.org on December 2, 2018

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Aldolase does not show enhanced diffusion in dynamic light scattering experiments Yifei Zhang, Megan J. Armstrong, Neda M. Bassir Kazeruni, Henry Hess* Department of Biomedical Engineering, Columbia University, 351L Engineering Terrace, 1210 Amsterdam Ave., New York, NY 10027, United States

ABSTRACT：Recent experimental studies have measured a 30–80% increase of the diffusion coefficient when various enzymes, including aldolase, are catalytically active. This observation has been supported by several theoretical explanations, but other theoretical studies argue against the possibility of enhanced diffusion, and two of them ascribe the experimental observations to potential artifacts arising in fluorescence correlation spectroscopy (FCS) measurements. Here, we utilized dynamic light scattering (DLS) to measure the diffusion coefficient of aldolase in the absence and presence of its substrate. The DLS measurements have an experimental error of 3%, and do not find a statistically significant change of the aldolase diffusion coefficient even at a saturating substrate concentration. This finding lends support to the contention that photophysical artifacts may have affected the FCS measurements and challenges the idea that enzymes can be self-propelled by their catalytic activity.

KEYWORDS: Enzymes, catalysis, enhanced diffusion, DLS, nanomotors

1 ACS Paragon Plus Environment

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Energy-dependent nanoscale movement is a fascinating phenomenon in biology,1,2 chemistry,3 and engineering.4-6 Recent studies have described observations of an increase in the diffusion coefficient of individual enzymes when their substrate is made available,7-13 and some of those studies have interpreted the observations as support for the concept of “leaps” associated with each catalytic event.13 Additional support for the “enhanced diffusion” phenomenon comes from observations that the diffusion of passive tracer particles (ranging from dye molecules to microspheres) is also enhanced in the presence of active enzymes,11 from the study of the chemotactic behavior of enzymes in substrate gradients,13-15 and from the observations of enhanced diffusion by enzyme-coated16,17 and catalytic nano- or micro-spheres,18,19 organic catalysts,20 and molecular motors.21,22 Enhanced diffusion has been observed in a large range of enzymes (urease, catalase, aldolase, and others), which implies that any enzyme can in principle be considered as a molecular engine.23 However, molecular leaps over distances exceeding 10 nm conflict with the classic picture of “life at low Reynolds numbers”24 and the current picture of motor protein operation1,25 which relies on power strokes and Brownian ratcheting rather than catalysis-dependent leaps.26 Interestingly, dedicated theoretical studies have come to different conclusions in their effort to explain the experimental observations. Riedel et al. explained enhanced diffusion by a chemoacoustic effect in which an asymmetric pressure wave induced by heat released during catalytic reactions transiently pushes the enzyme. This mechanism was opposed by Golestanian27-29 and Bai et al.30 who argued that the acoustic pressure is 6–7 orders of magnitude too small to affect the locomotion of enzymes and that ballistic motion would be rapidly damped by the solvent. Golestanian proposed that global heating by exothermic reactions increases the temperature of solution, reduces the solution viscosity and thereby increases diffusivity, but


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considering the relatively short measurement time (~30 s) and low enzyme concentration (~1 nM), the temperature increase is also too small to result in a diffusivity enhancement of 30– 80%.28 Mikhailov and Kapral suggested that conformation fluctuations of enzymes during catalysis can cause collective hydrodynamic effects which manifest as enhanced diffusion constants.31 However, simulations showed that increases in the diffusion constant on the order of 30% require enzyme concentrations five orders of magnitude greater than those in the above cited experiments (1–10 nM).32 Notably, Bai and Wolynes concluded that the observed enhanced diffusion in fluorescence correlation spectroscopy (FCS) experiments, which represent the majority of the experimental studies, may be an artifact of fluorescence quenching.30 The concern regarding the interpretation of FCS data has been echoed by Günther et al., who outlined common sources of artifacts in FCS measurements.33 Dynamic light scattering (DLS) – a standard tool in polymer science – is similar to FCS in that it relies on the measurement of light intensity fluctuations to determine diffusion constants. In contrast to FCS, the detected light does not originate from a fluorophore attached to the molecule of interest, but is light scattered by the molecule itself. While FCS spectra are typically acquired at nanomolar concentrations where only a few fluorescently labeled molecules occupy the excitation volume (~1 fL),34 DLS measurements require micromolar concentrations of the molecule of interest and larger scattering volumes (~1 nL, estimated from a beam width of 50 μm and a scattering angel at 173o) due to the small scattering cross section of an individual macromolecule.35,36 Here, we measured the diffusion coefficients of aldolase, the enzyme at the center of the controversy, in the absence and presence of its substrate by DLS rather than FCS. DLS allows us to directly assess the diffusion behavior of a larger ensemble of proteins (1 nL of a 1 μM solution


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for DLS versus 1 fL of a 1 nM solution for FCS) without encountering problems such as enzyme deactivation during labeling, fluorescence quenching, and dissociation of the multimeric protein at low concentration. We experimentally show that DLS is accurate enough to detect a 30% increase in the diffusion coefficient of enzymes with a diameter of 10 nm. However, we did not detect enhanced diffusion of aldolase in saturating substrate concentrations. This result challenges the notion that a slower (compared with those whose turnover numbers is ~104 s-1) and endothermic enzyme can act as an active swimmer, and lends support to the previous reports raising concerns regarding the accuracy of FCS measurements.

Figure 1. Michaelis-Menten kinetics of aldolase. The error bars on the data points indicate the s.d. from three replicates. Rabbit muscle aldolase is a class I aldolase that catalyzes the reversible cleavage of fructose1,6-bisphosphate (FBP) into the products dihydroxyacetone phosphate (DHAP) and glyceraldehyde 3-phosphate (G3P). The activity of aldolase can be measured by coupling it with a α-glycerophosphate dehydrogenase/triosephosphate isomerase (α-GDH-TPI) mixture, where the G3P is isomerized to DHAP, and then the two-equivalent DHAP is reduced by GDH in the presence of NADH. The turnover number of our batch of aldolase is determined to be 32.3 ± 0.3


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s-1 (Figure 1), which is identical to its nominal activity (12 U/mg protein correspond to 31.6 s-1 assuming that the protein is pure aldolase (Figure S1) and the molecular weight is 158 kD). This activity is six times higher than the one quoted by Illien et al.10 The Michaelis-Menten constant of aldolase is determined to be 10.4 ± 0.5 μM (mean ± standard deviation), in good agreement with the measurement by Zhao et al.14 We carried out DLS experiments on a Malvern Nano-ZS zetasizer with an enzyme concentration of 2 μM in HEPES buffer (50 mM Na-HEPES, 100 mM NaCl, pH 7.4). The dynamic viscosity of the buffer was measured to be 0.997 ± 0.004 cP at 25 oC (Table S1). For aldolase, the dissociation constant for the tetramer–monomer equilibrium is below 10−27 M3 and that for the tetramer–dimer equilibrium is on the order of 10−12 M,37 therefore, native aldolase is an extremely stable homotetramer due to the tight interaction at subunit interfaces, and its dissociation is negligible in a micromolar concentration range. The determined hydrodynamic diameter of aldolase is 10.6 ± 0.3 nm, corresponding to a diffusion coefficient of 41.3 ± 1.1 μm2 s–1. This result agrees with the FCS measurements by Illien et al. and Zhao et al. (42.6 ± 1.0 μm2 s–1).10,14 We then tested the sensitivity of DLS measurements to the existence of a fraction of protein that diffuses 20% to 30% faster than aldolase in an aldolase solution. Based on the Stokes– Einstein equation, a protein with a diameter of 8.2 to 8.8 nm is suitable to produce this effect. For globular proteins, the molecular weight can be estimated from the hydrodynamic radius RH through an empirical formula, Mw = (1.68 RH / 1 nm)2.34 kDa, given by Nobbmann.38 Therefore, yeast hexokinase (HK) with a molecular weight of 104 kD for its native dimer is selected as a model protein in this test. The measured average diameter of hexokinase is 8.2 ± 0.2 nm, corresponding to a 30% greater diffusion coefficient (53.9 ± 1.4 μm2 s–1) relative to aldolase


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(Figure 2). This result is in good agreement with the reported values (RH = 4.3 nm and diffusion coefficient of 56.4 μm2 s–1 for its native dimer).39 We then mixed the aldolase and hexokinase with various molar ratios at a fixed total protein concentration of 2 μM. Since the sizes of these two proteins are too close to be distinguished by the DLS method, the autocorrelation function will be fitted by the instrument software with a single Gaussian distribution in the protein size range (1 to 1000 nm, see Figure S2). Figure 2 shows that the increase in the molar fraction of hexokinase gradually increases the measured average diffusion coefficients. The dependence is not linear because a larger protein scatters disproportionally more light than a small one, and thus contributes disproportionally to the averaged diffusion coefficient determined here. DLS is not sensitive to the presence of 10% HK, but it can detect the presence of 25% of HK in the aldolase solution, which corresponds to an increase in the average diffusion coefficient of only 6%.

Figure 2. The average diffusion coefficients and hydrodynamic diameters of the mixtures of aldolase and hexokinase (HK). The errors bars represent the s.d. from six replicates. A pairsample t-test was conducted to test the significant differences. NS means not significant. We then measured the diffusion coefficients of aldolase in the presence of its substrate FBP. The DLS measurements were carried out with 2 μM aldolase in 20 mM or 50 mM substrate FBP, in which condition the aldolase runs at its maximum velocity (we measured 32.6 ± 0.6 s-1 in 20


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mM FBP and 33.4 ± 0.5 s-1 in 50 mM FBP). The aldolase-catalyzed conversion of FBP to G3P and DHAP is a reversible reaction with an equilibrium constant of 8×10-5 M at 30 oC and pH 7.40 Within about one minute, the reaction will approach an equilibrium state in which aldolase catalyzes the forward reaction (cleavage) and reverse reaction (condensation) at the same rates. The actual cleavage rate at equilibrium has been assessed via isotope exchange experiments. Rose et al.41 determined the exchange rate of the

32

P labeled FBP into G3P to be 51% of the

maximum forward reaction rate for an equilibrium mixture of FBP (0.1 mM) and DHAP (0.092 mM) and G3P (0.092 mM) at pH 7. At higher concentrations of substrates, the reaction velocity will be an even higher fraction of the maximum velocity of aldolase. We estimate from the reported kinetic parameters that aldolase at equilibrium catalyzes the forward reaction at a rate of 80% of its maximum velocity in our reaction system (see Supporting Information, Table S2 for the detailed discussion). Since the reverse reaction should also propel the enzyme based on the principle of microscopic reversibility,42 the overall rate of propulsion events in equilibrium is similar to or even higher than the one at the maximal reaction rate. The addition of 20 mM and 50 mM FBP in HEPES buffer increases the solution viscosity from 0.997 ± 0.004 cP to 1.020 ± 0.003 cP and 1.052 ± 0.003 cP, respectively (Table S1). Figure 3a shows that the average diameter of aldolase in the substrate solutions was exactly the same as that in buffer (10.5 ± 0.3 nm in 20 mM FBP and 10.6 ± 0.3 nm in 50 mM FBP, see also Figure S3 and Table S2). The corresponding diffusion coefficients are 40.9 ± 1.2 μm2 s–1 in 20 mM FBP and 39.4 ± 1.0 μm2 s–1 in 50 mM FBP. The slight decrease in the diffusion coefficients is mainly due to the increased viscosity of the solutions (Figure 3b and Table S1). In conclusion, we do not find any enhancement in diffusivity of aldolase in the presence of FBP.


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Figure 3. The average hydrodynamic diameters (a) and diffusion coefficients (b) of aldolase in the absence and presence of 20 mM and 50 mM FBP. Errors bars represent the s.d. from at least six replicates. A pair-sample t-test was conducted to test the significance. NS means not significant. As the aldolase catalyzed cleavage of FBP is an endothermic reaction, there may be a concern that the decrease in temperature during the reaction slows down the diffusion of aldolase. Given a reaction enthalpy of at most +60 kJ/mol,10,40 even if the reaction completely converts 50 mM FBP, it can only lead to a temperature decrease of 0.7 oC. Since the sample was placed in a temperature-controlled cell holder, the temperature change should be less than that and therefore unable to cause a significant decrease in the diffusivity of the enzymes.


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Illien et al. suggested that rapid conformational fluctuations of aldolase between a free state and a bound state as the underlying origin of the enhanced diffusion.10 The hypothesis is that the binding of substrate would reduce the effective hydrodynamic radius of the enzymes. In our experiments, substrate molecules at a saturating concentration fill all available enzyme binding sites and create the largest possible enhanced diffusion effect. However, we still did not find any detectable difference in the hydrodynamic radius of aldolase. Given that we have the highest activity of aldolase among the relevant studies, and the ability of DLS measurements to detect the presence of only 25% of proteins with a 30% increased diffusion constant, we believe that the binding of substrate does not lead to conformational changes which are large enough to cause a significant increase in diffusivity of aldolase. There must be other factors responsible for the observed enhanced diffusion of enzymes in FCS experiments. As discussed by Günther et al., the dissociation of multimeric enzymes could be a source of enhanced diffusion.33 It should be carefully considered in FCS measurements due to the ultralow concentrations (pM to nM) of the enzyme. Even for aldolase with extremely low dissociation constants, if the experiment is performed with 1 nM aldolase, the equilibrium mixture will consist of 0.75 nM tetramer, 0.03 nM dimer and 0.93 nM monomer. Dissociation will be even more extensive for enzymes with weaker interactions between their subunits. For instance, yeast hexokinase is a dimer with a moderate dissociation constant of 10-6 to 10-7 M at pH 6.5 and pH 8.0,43,44 and the presence of its substrates glucose or Mg-ATP could promote its dissociation.43 In this study, we found that the diffusion coefficient of hexokinase at 2 μM concentration was 53.8 ± 1.4 μm2 s–1, suggesting that the major species in the solution is its dimer.39 However, in an FCS experiment it was measured to be ~70 µm2 s−1,14 indicating that the hexokinase had almost completely dissociated into monomers (the diffusion coefficient for a hexokinase subunit is


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about 74.6 μm2 s–1)39. Moreover, the degree of dissociation may still be increasing during the experiment after dilution, or increasing due to absorption of enzymes to the vessel wall (see Figure S5). Therefore, substrate-induced dissociation could be partially responsible for the observed enhanced diffusion of hexokinase. Other factors that could affect the accuracy of FCS measurement, such as fluorescent quenching and blinking, a poor quality of the autocorrelation functions and the existence of free fluorophores should also be carefully considered in the determination of diffusion coefficients of enzymes.33 In summary, the measurement of the diffusion coefficient and hydrodynamic radius of aldolase as it is catalytically active is accessible to a standard DLS measurement, because the low turnover rate of aldolase prevents an exhaustion of the substrate even at the micromolar enzyme concentrations required by DLS. Neither an enhancement in diffusivity nor a shrinking in hydrodynamic diameter were observed even at a saturating substrate concentration. This lends experimental support to the concerns of Bai and Wolynes30 and Günther et al.33 regarding the possibility of artefacts in FCS experiments, and emphasizes the need to confirm the enhanced diffusion effect by multiple complementary experimental approaches.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] ORCID Yifei Zhang: 0000-0002-0014-611X Henry Hess: 0000-0002-5617-606X


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Author Contributions Y.Z. and H.H. conceived and designed the research. Y.Z. performed experiments. All authors discussed the results and contributed to editing the manuscript. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT We gratefully thank Dr. Luis Avila from the Department of Chemistry at Columbia for his assistance in the measurement of refractive index. This work was supported by the Defense Threat Reduction Agency under award number HDTRA 1-14-1-0051. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publication website at DOI:XXXXXXX. Details about the experimental methods, viscosity and refractive index measurements, representative DLS results, analysis of the enzymatic kinetics at equilibrium, concentrationdependent dissociation of aldolase. (PDF) REFERENCES 1

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Nano Letters

For TOC only

ACS Paragon Plus Environment

Aldolase Does Not Show Enhanced Diffusion in Dynamic Light

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