Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities Chuhong Lin, Lior Sepunaru, Enno Kätelhön, and Richard G Compton J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01199 • Publication Date (Web): 11 May 2018 Downloaded from http://pubs.acs.org on May 12, 2018

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The Journal of Physical Chemistry Letters

Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities Chuhong Lin,a Lior Sepunaru,b Enno Kätelhöna and Richard G. Compton*a a

Department of Chemistry, Physical and Theoretical Chemistry Laboratory, Oxford University,

South Parks Road, Oxford OX1 3QZ, UK. b

Department of Chemistry & Biochemistry, University of California Santa Barbara, CA, USA.

*

Corresponding author, E-mail: [email protected].

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Abstract

Dynamic fluctuations of the catalytic ability of single catalase enzymes towards hydrogen peroxide decomposition are observed via the nano-impact technique. The electrochemical signals of single enzymes show that the catalytic ability of single enzymes can temporarily be much higher than expected from the classical, time-averaged Michaelis-Menten description. By combination of experimental data with a new theoretical model, we interpret the unusual enhancement of the single catalase signal and find that single catalases show large fluctuations of the catalytic ability.

Table of Content


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The electrochemistry of single nanoparticles and macromolecules is the subject of many current studies.1-3 Recent work on collision electrochemistry (the “nano-impact technique”) has reported the electrochemical observation of single enzymes and indicated the potential for exploring single enzyme catalysis.4-7 In these studies, single enzymes in solution containing a substrate on which the enzyme acts individually arrive near an electrode interface due to their Brownian motion and the chemical product of enzyme catalysis is detected by the same micro/nanoelectrode. By recording the current signal from the detector electrode, the enzyme activity is observed. In a previous work, we demonstrated theoretically that it is possible to detect a single freely-diffusing enzyme in solution via this method and that the maximum current at the electrode is determined by the enzyme activity.8 However the experimental current signals seen from catalase mediated hydrogen peroxide decomposition are hundreds or even thousands times larger than predicted using the time-averaged kinetic parameters inferred from the activity of catalase ensembles.

9-10

However, fluorescence studies of some single enzymes show that the

activities of these perform random fluctuations during the catalysis revealing a “sleep and work” feature, attributed to configurational changes of the protein structure.11-12 In the following we consider the effect of the fluctuation in catalytic activity on the electrochemical detection of single enzymes. In this work, using a simple fast-slow activity fluctuation model, the electrochemical signals of a single enzyme with varying activities are simulated. This simulation model shows results which are consistent with experimental data and allow details of single enzyme kinetics to be inferred, not only confirming the possibility of observing freely-diffusing single enzymes via the nano-impact technique but also providing a novel approach for the investigation of single enzyme kinetics.


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Figure 1. Illustration of the single enzyme detection via the nano-impact method. S and P are the substrate and product of the enzyme catalysis. X is the product of the electrolysis of P and e- is the electron transferred. Signals are only seen at the electrode when the enzyme is both catalytically active and close to the electrode.

Figure 1 illustrates schematically the system we investigate in the study of single enzyme catalysis. In particular when a microelectrode is used to detect the product generated by a free single enzyme in solution, the amount of product reacting at the electrode surface is very sensitive to the distance between the enzyme and the electrode.8 Hence a current signal “spike” can be observed when the enzyme moves to and leaves the electrode. Taking the possible fluctuation of the catalytic ability into consideration, only when the enzyme is near the electrode and stays in a catalysis-active state, can the spike be observed. Therefore, the kinetic information on the single enzyme catalysis can be inferred from the spike features, notably the size and


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frequency of the spikes observed. The details of the implementation of the model in Figure 1 are explained below and in the Supporting Information. Catalase was chosen in this work due to its fast catalytic ability. Single catalase impact experiments were conducted in a 9 pM bovine liver catalase solution with chronoamperograms recorded at a 4.9 µm radius carbon microdisc electrode. 100 mM H2O2 was added to the solution; the catalase converts H2O2 into ½O2 in solution.9 A potential of -1.0 V (vs SCE) is applied to the microdisc electrode to reduce O2 in a two-electron transfer leading to the generation of H2O2.13 The average kinetics of the catalase enzymes can be described by the classic Michaelis-Menten mechanism:

 → ES  E + S ← → E+P 

(1)

where the enzyme E binds reversibly with the substrate S to form an enzyme-substrate complex ES and the complex ES decomposes into E and the product P. The expression for the product formation rate is:

k c ∂N P = cat S ∂t K M + cS

(2)

NP is the number of products formed, t is the reaction time (s), is the average turnover number (s-1), cS is the concentration of substrate (mM) and KM is the Michaelis-Menten constant (mM). When there is sufficient substrate in the solution and cS >> KM, the product formation rate is only determined by , which is the condition in our experiments. If we assume that each single catalase has the same catalytic ability as the ensemble behaviour, the maximum current of a single catalse detected by the electrode should be hence e0 ≈ 1.2x10-13 A,6 where e0 =


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1.6x10-19 C is the charge carried by one electron and = 7.4x105 s-1 for a catalase ensemble. However, as described below, it is found experimentally that the observed spike current can be much larger than the theoretical value. The catalysis of single catalases does not follow the average behaviour of catalase ensembles, suggesting that fluctuating enzyme catalysis needs to be taken into consideration. To simulate the fluctuation of the single enzyme catalysis, we propose a simplified activity switching model. Only two possible enzyme states, the active E and the inactive E’, are taken into consideration:

Active state:

kactive E + Substrate  → E + Product

Inactive state: E ' + Substrate ≠ E ' + Product

(3)

The switch between the active and inactive states E and E’ and described as: k

f  → E' E ← 

(4)

kb

where kf and kb are the forward and backward rate constants of the activity switch. In the simulation, we assume that the probability of a single enzyme being active is P and the minimum time when the enzyme remains in one state before the next possible switch is ∆tswitch. The parameters P and ∆tswitch reflect the above first-order kinetic model Eqn.(4) and are defined as:

P = k b ( kf + k b )

∆tswitch = ( kf + k b )

(5)

−1

(6)


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P and ∆tswitch hence represent the fluctuation kinetics and are key parameters in the following model. P reflects the extent of the fluctuation on catalytic ability while ∆tswitch reflects the timescale of the activity fluctuation. It is assumed that the switch between two states is not infinitely fast and the single enzyme keeps at one state for at least a time of ∆tswitch. In the simulation, the state of the enzyme is determined arbitrarily based on the probability P after each timestep ∆tswitch. We assume that the time-averaged behavior of a single enzyme is identical with that of the enzyme ensemble. Thus, the turnover number in the active state is kactive = /P and the maximum current corresponding to a single enzyme becomes kactivee0 = e0/P, which increases 1/P fold compared to that expected from pure Michaelis-Menten kinetics. Note that the active turnover number is only observable when 1) the timescale required to reach the preceding  → ES in Eqn.(1) is shorter than ∆tswitch; 2) the enzyme activity does not equilibrium E + S ← 

exceed diffusion limitation. For catalase, the reaction rate for the preceding steady-state step was reported to be ultrafast14 and the mass transport limit for a single catalase in 100 mM H2O2 solution is 6.75x109 s-1.6 Therefore, the value of kactive considered in the simulation is limited and 1/P cannot exceed 104. Figure 2 shows two examples of single enzyme catalysis as measured experimentally (Figures 2a and 2b) and as simulated (Figures 2c and 2d). The currents are all normalized by e0 to illustrate the deviation of the single enzyme catalysis from their average prediction. In Figure 2, each experimental chronoamperogram is measured independently and each simulated one is calculated with different fluctuation kinetics. In the simulation model, the enzyme fluctuation kinetics is represented by a pair of P and ∆tswitch. The experimental data is background subtracted and normalized by -e0 for comparison with the averaged catalytic ability of catalase ensembles (Original data is shown in Figure S3 of the Supporting Information). The


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experimental spike currents show hundreds- or even thousands-fold enhancement compared to the average behavior of enzyme ensembles. The simulations in Figures 2c and 2d suggest that the dynamic fluctuation of the enzyme catalysis can lead to such significant increase of the spike current. Note that in contrast to the simulation results, due to the limitations imposed by equipment noise, experimental signals smaller than 1 pA cannot be recognized (using 4 KHz bandwidth). Thus, only enzymes with a heavily fluctuating catalytic ability (kactive needs to be at least 100 times higher than the average, see Figure S2 in Supporting Information) can be observed via the electrochemical method.

Figure 2. (a), (b) Experimental single catalase signals from two independent measurements; (c), (d) Simulated single enzyme signals evaluated for two different fluctuation kinetics, where (c) P = 0.01, ∆tswitch = 1.0 ms; (d) P = 0.0005, ∆tswitch = 0.1 ms. In the simulation, the diffusion coefficient of O2 is DO2 = 1.96*10-9 m2 s-1;15 the electrode radius rel = 5.0 µm; kcat = 7.4*105s-1.10 The current in both experiment and simulation is not the original current but normalized by e0.


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To quantify the influence of the enzyme dynamic fluctuation via chronoamperograms, we first explore computationally how the features in the current signal are dependent on the catalysis fluctuation. Two features, the spike frequency and the average spike current, are investigated. Based on Eqn.(5) and (6), for the same enzyme-electrode system, the frequency follows:

Frequency ∝

P (1 − P ) ∆tswitch

(7)

Details of the derivation of Eqn.(7) can be found in the Supporting Information. Figure 3 shows the simulated variation of the spike frequency and the average current for different (P, ∆tswitch). Figure 3a and 3b are the results simulated for various fluctuation extents P and a constant switching timescale ∆tswitch = 0.1 ms; Figures 3c and 3d are simulated for a series of ∆tswitch of P = 0.01. The simulated results for the frequency in Figure 3a and 3c show the same trends as predicted by Eqn.(7). Figure 3b displays the variation of the average current with the fluctuation extent P. As the maximum current of a spike signal is kcate0/P, the average current of Figure 3b is also proportional to 1/P. However, in Figure 3d, it is found that the average current is not only affected by P but also determined by ∆tswitch. The current first increases with ∆tswitch, indicating that larger signals tend to be observed for the enzymes with slower switches. This is because if the enzyme quickly switches between the active and inactive states in solution, the product diffusing to the electrode will not generate clear, discrete current signals but only lead to large background current noise. Therefore, for the same fluctuation extent, only at relatively long switching timescales, can a significant increment of the single enzyme signal be observed. However, as the maximum spike current is limited by P, when ∆tswitch continues rising, the


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average current does not increase infinitely but tends to become constant, as shown in Figure 3d for ∆tswitch > 1 ms.

Figure 3. Simulated variation of the spike frequency and the average spike current for different fluctuation kinetics (P, ∆tswitch), where P is the extent of the fluctuation and ∆tswitch refers to the timescale of the switch between two enzyme states. (a), (b) Variation of the frequency and the average current as a function of P; (c), (d) Variation of the frequency and the average current as a function of ∆tswitch. In (a) and (b), ∆tswitch =0.1 ms; in (c) and (d), P = 0.01. Other simulation parameters are the same as in the experiment (see text).

Following the simulations in Figure 3, the spike frequency and the average current can be calculated for a series of chronoamperograms recorded in experiments. The comparison between the simulated results and the experimental data is shown in Figure 4. Each point in Figure 4


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represents one single enzyme with certain fluctuation kinetics: the black points are the experimental data; the blue points are the simulation results as shown in Figure 3a and 3b; the yellow points are those in Figure 3c and 3d; the red points are simulations in the absence of dynamic fluctuation. The blue dashed line indicates the region where the current signal is controlled by the enzyme switching rate as discussed in Figure 3; while the yellow dashed line shows an example of the region where the current is limited by the fluctuation extent (here P = 0.01 is taken as the example).

Figure 4. Classification of single enzyme activities based on the spike frequency and the average spike height. Each point represents the behavior of one single enzyme with a certain fluctuation kinetics. Blue and yellow points correspond to the simulation data of various P and various ∆tswitch as shown in Figure 3. Black points correspond to the experiment results (see text). The red point is simulated for the absence of dynamic fluctuation.


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In Figure 4, the experimental data (black solid circles) deviates from the average behaviour of catalase ensembles (the red open circle), indicating that the single enzyme catalysis progresses at a different turnover speed from the average measurement. The experimental data, which represent different single catalases, are discrete rather than clustered together. Since each point in Figure 4 represents a different kind of fluctuation kinetics, it implies that the catalase catalytic ability has certain heterogeneity at the single-enzyme level or alternatively that each single catalase has more than one “active” state. The experimental data shows a strong correlation between the frequency and the average current. The correlation in the experiment matches well with the blue dashed line predicted in the simulation. Under the assumptions of our theoretical model, it indicates that single catalases can undergo large fluctuation of the catalytic ability and the switch between the active and inactive states of these single catalases is fast. Note that although the experimental data fits well with the fluctuation model, the model at this stage qualitatively explains the phenomenon in the experiment. In conclusion, we have shown that the single enzyme electrochemical measurements can be used to study the catalytic kinetics of a free diffusing single enzyme with high turnover numbers. The dynamic fluctuation of single catalase activities has been both observed via the nano-impact technique and to behave as predicted by our theoretical model.

Supporting Information for Publication Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities

Acknowledgement The research is sponsored by funding from the European Research Council under the European Union Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. [320403]


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Electrochemistry of Single Enzymes: Fluctuations of Catalase Activities

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