Direct Single Molecule Imaging of Enhanced Enzyme Diffusion
aa r X i v : . [ q - b i o . S C ] N ov Direct Single Molecule Imaging of Enhanced Enzyme Diffusion
Mengqi Xu and Jennifer L. Ross
Department of Physics, University Massachusetts Amherst, MA 01003
Lyanne Valdez and Aysuman Sen
Department of Chemistry, Pennsylvania State University, State College, PA 18602 (Dated: November 22, 2018)Recent experimental results have shown that active enzymes can diffuse faster when they are in thepresence of their substrates. Fluorescence correlation spectroscopy (FCS), which relies on analyzingthe fluctuations in fluorescence intensity signal to measure the diffusion coefficient of particles, hastypically been employed in most of the prior studies. However, flaws in the FCS method, due to itshigh sensitivity to the environment, have recently been evaluated, calling the prior diffusion resultsinto question. It behooves us to adopt complementary and direct methods to measure the mobilityof enzymes in solution. Herein, we use a novel technique of direct single-molecule imaging to observethe diffusion of single enzymes. This technique is less sensitive to intensity fluctuations and gives thediffusion coefficient directly based on the trajectory of the enzymes. Our measurements recapitulatethat enzyme diffusion is enhanced in the presence of its substrate and find that the relative increasein diffusion of a single enzyme is even higher than those previously reported using FCS. We also usethis complimentary method to test if the total enzyme concentration affects the relative increase indiffusion and if enzyme oligomerization state changes during catalytic turnover. We find that thediffusion increase is independent of the total background concentration of enzyme and the catalysisof substrate does not change the oligomerization state of enzymes.
PACS numbers:
Molecular enzymes are active matter systems that useenergy to perform a variety of tasks required for the ba-sic functions of cells. Enzymatic activity is thought tobe essential to maintain cellular temperature and activemixing of the crowded and visco-elastic environment in-side cells [1, 2]. When active enzymes were bound tothe surface of micron-scale colloidal particles, they wereable to self-propel in the presence of the enzyme sub-strate [3, 4]. Thus, active enzymes can act as a source ofpropulsion to move large-scale objects in aqueous media.Recent experimental studies have demonstrated thatactive enzymes diffuse faster in the presence of theircorresponding enzymatic substrates [5–12]. These priorstudies measured the relative increase in the diffusion co-efficient, ranging from 20% to 80%, depending on the en-zyme used and the substrate concentration [5–12]. A ma-jor drawback of prior measurements is that they all usea single method: fluorescence correlation spectroscopy(FCS). In FCS, the diffusion coefficient is found by mea-suring and fitting the autocorrelation function of the fluc-tuations in fluorescence intensity signal to a diffusionmodel. Although FCS is referred to as a single-moleculetechnique, the measurement often relies on signal fromseveral particles [13]. Further, the intensity fluctuationsof fluorophores are highly sensitive to the environment inaqueous media.A recent publication evaluated possible artifacts ofFCS measurements and the subsequent effects on thediffusion measurements of enzymes [12]. They discussedthat enzymes at low concentration can dissociate intosmaller subunits. This dissociation cannot be detected by FCS, but would cause an increase of the measureddiffusion coefficient. They also described that free dyesremaining in solution can affect the measured autocorre-lation functions, which subsequently impact the determi-nation of diffusion rate. Most importantly, they demon-strated that substrate binding to enzymes can cause fluo-rescence quenching in some cases that resulted in a fasterdecay of the autocorrelation curves and thus a larger dif-fusion constant [12]. Experts agree that interpretation ofautocorrelation curves is complicated and requires mod-eling of experimental situations. Thus, it is imperativethat these results are repeated and recapitulated with adistinct experimental method. Here, we use direct singlemolecule imaging to visualize the trajectories of enzymesin solution over time and calculate their mean squareddisplacements (MSD) to determine the diffusion coeffi-cients. This method has the added value that it is trulysingle molecule and mobility increases were obvious byeye.Our single particle tracking experiments were per-formed with total internal reflection fluorescence (TIRF)microscopy (Fig. 1A) using a custom-built laser sys-tem (488 nm, 638 nm) constructed around a Nikon Ti-Emicroscope with a 60x, 1.49 TIRF objective and 2.5xmagnification prior to the EM-CCD camera (Andor).We directly observe the diffusing trajectory of each in-dividual enzyme by recording at 8 - 20 frames/s (Fig.1B,C). Enzymes are blocked from sticking to the silanizedhydrophobic coverglass by adding Pluroinc F127 block-copolymer (see Supplemental Information). The lifetimeof the fluorescence is extended by adding glucose oxidaseand catalase as an oxygen scavenging system, which isexactly the same for all experiments. TIRF microscopycan only image the first 300 nm distance from the cov-erglass (Fig. 1A), so all experiments included the ad-dition of methylcellulose to crowd the enzyme close tothe surface. Trajectories of enzymes were analyzed byan ImageJ/FIJI plugin ParticleTracker 2D/3D [14](Fig.1D). The diffusion coefficient, D in m /s , was determinedfrom the slope of the MSD plot according to the Brow-nian motion equation in 2D: (cid:10) (∆ r ) (cid:11) = 4 Dτ , where τ isthe lagtime in s . The enzyme we used was urease fromJack Bean (TCI Chemicals), a fast, highly exothermicenzyme, that breaks down its substrate, urea, into am-monia and carbon dioxide. Urease is a hexamer which wefluorescently labeled one fluorophore per monomer with acommercially available dye labeling kit (Thermo Fisher).In agreement with prior work, we find that urease dis-plays enhanced diffusion in the presence of its substrateurea. The change in motility was visible directly fromtrajectories and the MSD plots (Fig. 1B-D). For our as-says, we measured over 100 single particle trajectories foreach experimental condition to obtain statistically signif-icant data. Diffusion data displayed a lognormal distri-bution that could be plotted and fit with a Gaussian afterlog-transformation (Fig. 2A). The mean of the Gaussianfits was then transformed back and used as the generaldiffusion coefficient for each case (see Supplemental In-formation for fits).Interestingly, we find that the relative increase of thediffusion coefficient in our single molecule experiments issignificantly higher than those previously reported usingFCS methods [6, 9]. For the highest concentration ofurea we tested (100 mM ), we found a ∼ ∼
30% increase [6, 9]. Con-trol experiments performed with green fluorescent pro-tein and inhibited urease that cannot interact with ureaboth show a slight decrease in diffusion coefficient in thegroup with the presence of urea (Supplemental Informa-tion, Figs. S1-3). These controls demonstrate that theenhanced diffusion of urease is not due to the presenceof urea in solution, but rather to the interaction betweenurea and urease.We calculate and plot the relative increase in the diffu-sion coefficient as a function of urea concentration (Fig.2B), which displays a typical hyperbolic dependence ofthe form: ( D − D ) /D = A × [ urea ][ urea ]+ K , where D isthe measured diffusion coefficient, D is the diffusion co-efficient in the absence of substrate, A is an amplitude,[ urea ] is the urea substrate concentration, and K is a rateconstant. We find that the best fit has K = 21 ± µM (see Supplemental Information for fit parameters). The K D for urea binding to urease was reported as 250 µM [15], and the K M was reported as 3 mM [16]. Compar-ing our results to these two rate constants, we find that A. Single molecule imaging T I R F e v ane sc en t w a v e laser illuminationPluronic F-127 ureasemethylcellulose D. Mean Squared Displacement t = 0 s μ m B. Time series of single molecule mobility M S D ( μ m ) MSD( τ ) = 4D τ i. 0 urea, buffer onlyii. 1 mM ureaC. Time color overlayi. 0 urea ii. 1 mM urea μ m μ m Lag Time (s)
FIG. 1. A) Experimental setup for single particle imaging ofurease using TIRF imaging of fluorescent urease in a cham-ber with Pluronic F127 coating the surface and a crowdingagent, methylcellulose. B) Example trajectories of a singleurease enzyme over time. i) without urea, and ii) with ureaat 1 mM . Scale bar 5 µm . C) Example 2D trajectories dis-played over time as collapsed images with rainbow scale rep-resenting time as given in the time color bar over 111 frameswith 0.08 s between frames for urease i) without urea, andii) with 1 mM urea. Scale bar 5 µm . D) Calculated meansquared displacement (MSD) plot of the trajectories and fitwith a linear equation to determine the diffusion coefficient, D , for urease without urea (red circles) and with 1 mM urea(blue squares). Error bars represent the standard error of themean. our data is more similar to the binding coefficient, K D , in-stead of the reaction turn-over rate, K M . Several theoret-ical models have suggested that substrate binding couldchange the size or flexibility of enzymes, driving the dif-ference in the diffusion coefficient [10, 17], but no modelhas predicted such a large shift in the diffusion coefficientas we measure here.Prior works have noticed a correlation between the dif-fusion coefficient increase and the heat released duringenzymatic turnover [9]. Assuming the enzyme size doesnot change during the turnover, in order for the diffu-sion coefficient to increase by a factor of 3, as we observe(Fig. 2B), the temperature would need to increase by55 K locally. This increase was estimated by using the U r ea C on c en t r a t i on ( mM ) ( D - D ) / D .
01 0 . B. -13 -12 μ M urea1 mM urea100 mM urea
Log (D) P D F A. -14 -13 -13 -13 -13 -13 -13 -13
92 pM urease40 nM urease
Urea ( m M) D i ff u s i on C oe ff i c i en t ( m / s ) p = 0.568N.S.p = 0.499N.S. p = 0.004 C. ii. Low urease concentration:
92 pM labeled i. High urease concentration:
40 nM unlabeled + 92 pM labeled μ m3 μ m iii. labeled unlabeled FIG. 2. A) Representative probability distribution histograms of log-transformed diffusion data at different urea concentrations0 (red region, N = 141), 10 µM (green region, N = 97), 1 mM (blue region, N=178), 100 mM (purple region, N = 203).Gaussian fit lines 0 (red line), 10 µM (green line), 1 mM (blue line), 100 mM (purple line). Fit parameters can be found in thesupplemental information. B) The normalized relative increase in diffusion coefficient ( D − D ) /D , plotted as a function ofthe urea concentration. Inset shows the same data plotted on a logarithmic scale. Error bars are determined from the standardderivations σ of the Gaussian distribution fits from part (A). The fit equation is a hyperbolic function with a amplitude andcharacteristic concentration, K ; fit parameters given in supplemental information. C) i) Cartoon of 40 nM urease with averagespacing between molecules of 400 nm . ii) Cartoon of 90 pM urease with average spacing between molecules of 3 µm . iii)Median diffusion coefficients of urease without urea in high urease concentration (40 nM , dark gray bars, N = 31) and lowurease concentration (90 pM , light gray bars, N = 30) and with 1 mM urea in high urease concentration (40 nM , dark graybars, N = 35) and low urease concentration (90 pM , light gray bars, N = 36). Error bars are determined from the standardderivations σ of their Gaussian distribution fits. Stokes-Einstein relation: D = k B T πηa , in which the viscos-ity, η in P a · s , is also considered as a function of tem-perature: η ( T ) = 2 . × − × . / ( T − for water[18] in our calculation (see Supplemental Information fordetails). Using a rough estimation method as describedpreviously [9], the maximum temperature increase withina 1 nm water shell around the enzyme would be 0 . K for urease, which is too small to account for the factor of3 increase in diffusion we observed.We also estimate the temperature increase around asingle enzyme using the solution to the heat diffusionequation with a instantaneous point source. Since theconcentration of enzyme was set to be extremely low( ∼ pM ), each single enzyme is modeled as an in-stantaneous point source of heat during each enzymaticturnover. Thus, we have:∆ T ( r, t ) = ∆ Qρc (4 πκt ) / exp (cid:2) − r κt (cid:3) , (1)where ∆ Q = 25 k B T is the heat released from a singlecatalytic reaction. The background material is waterwith specific heat capacity c = 4 . J/ ( K · g ), density ρ = 1 g/cm , and thermal diffusivity κ ≃ − m /s . Weestimated the temperature increase during one catalyticturnover, with t = t c = 1 /k cat ≃ − s for urease atsaturating urea concentrations and used a distance com-parable to enzyme size with r = 2 nm . We found thetemperature shift would be minuscule, ∆ T ∼ − K ,so it seems unlikely that heating the local environmentalone could cause such a large increase in the diffusioncoefficient. Another model suggested that enhanced diffusioncould arise from heating the entire chamber due to manyenzymes in solution [19]. Using their model, with theparameters of our experiments, we estimated that thetemperature increase in the whole chamber would be∆ T total ∼ − K (see Supplemental Information for in-formation on this estimate), which is still too small toaccount for the large increase in diffusion coefficients.In the above estimations, the enzymes each act as inde-pendent sources of heat or activity. Two recent modelshave taken collective effects of many enzymes into ac-count. One is a collective heating model [19] and anotheris a collective hydrodynamics model [20]. Both of thesemodels predict that the diffusion rate increase will de-pend linearly on the total concentration of the enzymesin solution.To test the predictions of these collective models, werepeat our experiments at two different total enzyme con-centrations, 40 nM and 90 pM (Fig. 2C). For bothgroups, we keep the concentration of labeled enzyme con-stant at single molecule level (90 pM ). The average spac-ing between enzymes depends on their concentrations insolution, which we estimate to be ∼ nm for 40 nM and ∼ µm for 90 pM (Fig. 2Ci-ii). We compared thediffusion coefficients for different concentration groups inthe absence of urea or with 1 mM urea (saturating con-centration Fig. 2B). We find no difference in the diffusionconstants between 40 nM and 90 pM concentrations foreither the buffer case or urea case (Fig. 2Ciii). Althoughthe proportional relationship with total enzyme concen-tration was not observed in our experiments, it is possiblethat collective phenomena would come into play at muchhigher, non-physiological concentrations of enzymes. Re-gardless, these collective models cannot explain the 3-foldincrease in diffusion that we observe in our experiments.As described above, diffusion coefficients can also besignificantly altered due to the dissociation of enzymecomplexes at the low concentrations used in FCS stud-ies [12]. Suppose an enzyme with radius R undergoes achange in size, δR , during its interaction with the sub-strate, and the liquid viscosity remains the same. Fromthe Stokes-Einstein equation, the relative change in dif-fusion can be written as∆ DD = 11 + δRR TT − . (2)A positive change in ∆ D requires a negative change in δR , as expected. We can then estimate the required sizechange of urease in our experiments needed to account fora 3-fold increase in diffusion. For our experiments, ∆ DD ∼ TT ≃ δR ≃ − R , corresponding to a 67% loss of radius.Considering the possibility that enzyme multimers mightdissociate at low concentration, the large increase in ourdiffusion measurements would most likely be due to thedissociation of urease hexamers to smaller oligomers afterinteracting with urea.Although, this dissociation process cannot be detectedby FCS, it can be directly monitored using our singlemolecule imaging method. To directly test the oligomer-ization state of the urease multimers, we perform sin-gle molecule photobleaching experiments that reveal thenumber of urease monomers within each fluorescent com-plex [21, 22]. Each urease monomer is covalently labeledwith one fluorophore, and there are reported to be 6monomers per urease complex. We first mix the labeledurease hexamers with urea at 0 or 1 mM concentrationallowing them to react and then affix them to the cov-erglass. Binding to the glass stabilizes their state andmakes the local laser illumination and z-height constantfor the entire measurement. We use TIRF microscopy toimage the enzymes without oxygen scavenging enzymes,so that the fluorophores photobleach over time (Fig. 3A).We count the number of photobleaching steps for eachcomplex, which corresponds to the number of monomersin each complex, and create a histogram of the numberof bleaching events (Fig. 3B). Urease complexes neverdisplay more than 6 bleach steps, indicating that the hex-amer is the largest oligomerization state. We find thattwo or three monomers per complex is the most com-mon state for both 0 and 1 mM urea conditions. If thedissociation really occurred due to the presence of urea,we would expect to see a large shift in the distributionof the 1 mM urea group to lower numbers of bleachingsteps. However, we find no difference between these twodistributions according to the Kolmogorov-Smirnov sta-tistical test ( p = 1 . I(t)Running Average I(t) I n t en s i t y ( A U ) ( x ) Time (s)
A. Example Intensity Traces B. Photobleaching Probability P r obab ili t y D i s t r i bu t i on F un c t i on FIG. 3. A) Two examples of the intensity of fluorescent ure-ase complexes photobleaching over time, showing a one-stepbleach (top) and a three step bleach (bottom). B) The distri-butions of photobleaching steps directly report the number offluorescent urease monomers in each complex in the presenceof 0 urea (dark gray bars, N = 100) and 1 mM urea (lightgray bars, N = 100). diffusion we observed cannot be caused by changes inthe oliomerization state. This result also demonstratesanother strength of the direct imaging technique we em-ploy over FCS measurements.In conclusion, we used a distinct method to measurethe diffusion of enzymes to test if the enhanced diffu-sion previously reported was genuine or an artifact ofthe fluorescence correlation spectroscopy technique. Ex-citingly, we have verified that the enhanced diffusion ofurease occurs on a truly single molecule level. We alsoobserve a higher increase in diffusion rates, by a factorof three, in comparison with the ∼
30% increase mea-sured with FCS. We find our large increase in diffusionis difficult to account for based on any current physicalmodels based on heat or collective interactions. Finally,the single molecule imaging techniques are able to di-rectly measure the oligomerization state of the enzymes,excluding the possibility that the enhancement in diffu-sion we observe is caused by the dissociation of enzymemultimers. We expect the direct imaging technqiue willbe a powerful, complementary method to test the pre-dictions of future models of the mechanism behind theenhanced diffusion of enzymes.
Acknowledgements
MX was partially supported byNSF MRSEC DMR-1420382 to Seth Fraden (Bran-deis University) and UMass Faculty Research Grant toJLR. JLR was partially supported by DoD ARO MURI67455-CH-MUR to S. Thayumanavan. We want tothank Ramin Golestanian for helpful feedback about ourmanuscript. [1] M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R.Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C.
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