- Email: [email protected]
The fluctuating enzyme: a single molecule approach
Chemical Physics ELSEVIER
Chemical Physics 247 (1999) 11-22 www.elsevier.nl/locate/chemphys
The fluctuating enzyme: a single molecule approach Lars Edman, Zeno FiSldes-Papp, Stefan Wennmalm, Rudolf Rigler * Karolinska Institute, Department of Medical Biophysics, MBB, 171 77 Stockholm, Sweden Received 16 December 1998
Abstract
The excess of structural degrees of freedom in a protein enzyme opens questions about the conformational homogeneity. We studied single horseradish peroxidase enzyme turnovers by fluorescence spectroscopy. Application of a two-state dynamic model to the measured data shows exponential product dissociation kinetics, but a large distribution of rates for the enzyme to form the enzyme-product complex. The experiments show that in addition to the peroxidative cycle thermodynamic fluctuation phenomena on a wide range of time scales affect enzyme activity. © 1999 Elsevier Science B.V. All rights reserved. 1. I n ~ o d u c f i o n
Enzymes make chemical reactions faster without changing the position of the chemical equilibrium. Hence, an enzyme merely changes the time scale of a reaction process. Almost all enzymes are proteins, which because of their inherent complex structure have many structural degrees of freedom. An enzyme acts as a molecule complementary in structure to the molecular configuration that is intermediate to the reactants and the products [1], for which the enzyme lowers the activation energy required for a reaction to occur. Static protein enzyme secondary structures can be routinely determined by nuclear magnetic resonance spectroscopy (NMR) or by crystallization [2]. Much attention has been given to exploit the mechanisms of protein folding. Theory [3-6], molecular simulations [7], and experiments [8] indicate a complex
* Corresponding author. Tel.: +46-8-728-6801; Fax: +46-832-6505; E-mail: [email protected]
mechanism involving many intermediate structural forms. Dynamics of the already folded protein are less investigated, although experiments [9,10], molecular simulations [11], and theoretical studies [12-14] have proven that a broadened understanding of the connection between protein function and structural fluctuations is needed to understand the role played by thermodynamics in the case of proteins and other complex biomolecules. Since the primary structure of a protein can fold into many slightly different conformations [3-14] the free energy of the protein is rough and has many local minima [12]. The excess of conformational degrees of freedom in a protein enzyme opens questions about the conformational homogeneity in an enzyme population [3-6,9], and about the conformational variability over time of an individual enzyme. Experimental studies on carbon monoxide (CO) binding to myoglobin (Mb) indicate differences in reaction energy barriers between different Mb molecules [9]. Recent experiments involving single enzymes [15,16] indicate differences in the activity between different individual molecules.
0 3 0 1 - 0 1 0 4 / 9 9 / $ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: $ 0 3 0 1 - 0 1 0 4 ( 9 9 ) 0 0 0 9 8 - 1
L. Edman et aL / Chemical Physics 247 (1999) 11-22
12
In this article we are concerned with the enzyme horseradish peroxidase (HRP), a 44 kDa heme protein [17,18]. HRP is an effective catalyst for the decomposition of hydrogen peroxide (H20 2) in the presence of hydrogen donors [17,18]. The reaction is monitored by existing experimental methods [19] based on fluorescence spectroscopy. We used the non-fluorescent substrate (S) dihydrorhodamine 6G which after oxidation yields the highly fluorescing rhodamine 6G fluorophore (P). Hence, direct observation of the individual substrate turnover reactions is made possible by means of fluorescence microscopy if single enzymes (E) are observed. The free enzyme (E), the substrate (S), or the enzymesubstrate complex (ES) are all non-fluorescent. However, if the substrate is oxidized while still bound to the enzyme, the ES will transform into an enzymeproduct complex (EP) [13] which should be fluorescent.
2. Experiments 2.1. Horseradish peroxidase The donor hydrogen peroxide oxidoreductase, EC 1.11.1.7, from horse radish shows kinetics with the following characteristics of the conventional peroxidative cycle [20]: native (ferric, trivalent redox state) enzyme ~ Compound I (pentavalent redox state) Compound II (tetravalent redox state) ---> native enzyme (see Scheme 1). The essential prosthetic group is the ferric protoporphyrin IX. Horseradish peroxidase decomposes H202 into oxygen and water with low specificity for hydrogen donors. In order to analyze the enzyme catalysis at single molecule level we have chosen the nonfluorescent leukodye dihydrorhodamine 6G (Molecular Probes, the Netherlands) as donor substrate which is turned over into the fluorescent product rhodamine 6G. The biotinylated enzyme (Molecular Probes, the Netherlands) was dissolved in 100
H o2
S PE4+S\ Scheme 1.
+
mM potassium phosphate, pH 7.0, 100 mM NaC1, and 50% ( v / v ) glycerol (Sigma, USA, for Molecular Biology). The suspensions were stored at - 2 0 ° C for two months. Prior to use the suspensions were diluted in 100 mM potassium phosphate, pH 7.0, and kept on ice. The solutions were immediately used. As control assay for the horseradish peroxidase activity we used the established guaiacol test method. In brief, the reaction mixtures contained in a final volume of 1 ml at room temperature: 100 mM potassium phosphate, pH 7.0; 320 t-~M guaiacol (extra pure) obtained from Merck, Germany; for example approximately 0.005 U / m l diluted enzyme suspension; 120 tzM H2O 2 (puriss.) purchased from Fluka, Germany. The reaction was started by addition of H202, the concentration of which was adjusted spectrophotometrically at 240 nm. The absorbance of the reaction mixtures was monitored at 436 nm for at least 25 rain at room temperature (Pharmacia Biochrom 4060 spectrophotometer, Amersham Pharmacia Biotech, Sweden). No changes in the absorbance were found in the blank reaction without enzyme. The enzymatic activity was calculated from the linear and steepest range of the curve using the absorption coefficient e25oc 2.55 l/retool mm related to 1 mmol tetraguaiacol. We determined the specific activity of the biotinylated horseradish peroxidase to b e 46 _+ 6 guaiacol units per mg HRP (n = 8) corresponding to 34 _+ 4 tool of substrate per mol of enzyme and second. These measurements were performed at a maximum turnover rate, but not at substrate excess. One unit horseradish peroxidase oxidizes 1 ~mol of guaiacol tetramer to product in 1 rain at 25°C and pH 7.0. =
2.1.1. Preparation of immobilized horseradish peroxidase Our experimental procedure of preparing streptavidin-coated coverslips is based on the conditions published in Ref. [19]. In brief, the coverslips, 170 Izm thick, were boiled in concentrated HNO 3 (Suprapure, Merck, Germany) and then dried at 5 0 60°C in an oven. A teflon holder was cleaned and dried by rinsing in water-free ethanol, water-free acetone and finally in water-free ether. The coverslips were incubated in the teflon holder with a 10% ( v / v ) solution of 3-glycidoxypropyltrimethoxysilane (Aldrich, USA) in pure toluene (Merck, Germany)
L. Edman et al. / Chemical Physics 247 (1999) 11-22
for 24 h. After baking at 110°C for 6-8 h they were treated with 20 t~1 streptavidin solution (11 p~M streptavidin from Sigma, USA, in 0.2 M carbonate buffer, pH 9.0) at room temperature in petri dishes and stored in the same closed petri dishes under water-saturated atmosphere. The covalent bond between the epoxy group and the amine on the streptavidin was stable during storage for some time. Excess of streptavidin adsorbed at the surface was removed by shaking the coverslips in 0.5 M Tris-HC1, pH 9.0, overnight in the teflon holder. After washing with the final buffer (100 mM potassium phosphate, pH 7.0), the coverslips were ready for incubation with approx. 1 nM biotinylated horseradish peroxi-
|
Glass Silane/Streptavidin layer Biotin
t3
dase solution. The incubation was performed at 4°C for about 1 h followed by exhaustively rinsing the coverslips in 100 mM potassium phosphate, pH 7.0, to remove unbound enzyme. 2.1.2. Enzymatic reaction The peroxidative cycle can be accompanied by side reactions: the ferrous (divalent) enzyme/Compound 111 shuttle (native enzyme ~ ferrous enzyme Compound III -0 ferrous enzyme), the ferrous enzyme/oxyperoxidase shuttle (native enzyme ferrous enzyme ~ oxyperoxidase ~ native enzyme), the reaction of Compound II with H202, the reaction of the native enzyme with the superoxide
0
o
Single enzyme Product molecule Substrate molecule
Fig. 1. Principal scheme for the measurements of single enzymes. The distance from the laser intensity maximum to the coverslip surface was adjusted to 2 _+ 0.5 I~m for all measurements.
L. Edman et al. / Chemical Physics 247 (1999) 11-22
14
anion radical (O~-). To avoid enzymatic side reactions occurring at high substrates-to-enzyme ratios [21], but also nonenzymatic autocatalytic reaction cascades oxidizing thermally the leukodye by H202 via reactive oxygen species (O;-, OH , ROOH) [22], we performed the experiments with a minimum amount of H202 and leukodye. The generation and the recombination of free oxygen radicals were found only in cases where the free radicals had relatively long lifetimes and the steady-state concentration of the reactive oxygen species was comparatively high [23]. In systems containing no free metal ions, the
products of oxygen reduction have a low reactivity and do not constitute a significant reaction path for the autoxidation of the leukodye. Under the experimental conditions used here autoxidation was not observed in the time frame of the measurements or its rate was negligibly small at 130 nM dihydrorhodamine 6G. The biotinylated enzyme prepared as described in the Section 2.1 was studied after immobilization on a glass surface (or in solution) in 100 mM potassium phosphate buffer, pH 7.0, 1 nM up to 130 nM dihydrorhodamine 6G, at HaO 2 concentration of 120 p~M,
A I 2
B
1 4
I ~
I
%-
8
10
1 t/a:
k t/s
C 0
2
4
I
I
2
4
6
8
6
tO
n/kH!
D : t
0
0
/
8
r
I0
7 t/N
Fig. 2. Fluorescence intensity traces f r o m 10 s intervals are s h o w n for three molecules in A - C . In D, a trace f r o m a control m e a s u r e m e n t is shown. The control m e a s u r e m e n t w a s p e r f o r m e d as the single e n z y m e measurements, with the exception that no e n z y m e was b o u n d to the streptavidin surface.
15
L. Edman et al. / Chemical Physics 247 (1999) 11-22
2.2. Single molecule and FCS analysis Confocal single molecule detection [24,25] as well as imaging [26] was used for the analysis of the product formation of single surface bound HRP molecules. The streptavidinized micro-coverslide (170 Ixm thick) surface with the bound HRP molecules together with substrate in the reaction buffer was either covered with a second microslide carrying a 10 ~ m spacer (Menzel-Gl~ser, Brauschweig, Germany), or used in the 'hanging drop' regime [24,25] with controlled vapour pressure to avoid concentration effects during the enzyme catalysis. For the optical measurement a 40 × NA 0.9 objective (Neofluar, Carl Zeiss) providing a detection volume element with half axes of 0.5 ~ m and 2 ~ m was used. The measurement spot was positioned 2 _+ 0.5 Ixm underneath the microslide surface, which corresponds to the dimensions of the half axis of the volume element in the vertical direction (Fig. 1). In this position an optimal discrimination was achieved between the fluctuating single molecule signal and background reflection at the microslide surface. The measuring strategy involved a computer-controlled scum on the surface of the microscope slide until a single molecule process was observed. The observatton of a single enzyme molecule was evidenced by (i) the fact that the concentration of the applied enzyme (1 riM) was chosen so that there was much less than one molecule per observation area. (ii) Condition (i) is manifested by the fact that a scan search was needed to find spots with fluctuations (Fig. 2A-C), most spots showed an intensity trace hike the control measurement in Fig. 2D. (iii) The intensity of a single tetramethyl rhodamine molecule linked to the streptavidin surface is found to be 3.5 kHz (average of 100 molecules) [27]. For rhodamine 6G the produced counting rate is about 3.0 kHz. Hence, the intensity increases of the fluctuations in Fig. 2 A - C are in the same range as the intensities of a single rhodamine 6G molecule. Single molecule traces are recorded during multiples of 10 s or for longer times up to 300 s. Simultaneously the autocorrelation functions of the single molecule fluctuations are recorded on line and stored automatically. Details of the instrumentation have been published previously [19]. For data evalua-
tion and parameter estimation non-linear least square optimization after Marquardt was used [28]. The analysis is based on material which comprises more than 100 individual enzyme molecules.
3. Results and discussion In this section we will first present the main results of the single enzyme experiment. Then, an expression for the intensity fluctuation correlation function G(r) is made based on the kinetics Scheme 2. Thereafter, the model is fitted to the present data. The result is discussed together with an analysis of the traces. Finally, we treat the present findings in the perspective of previous studies of proteins and single molecules.
3.1. Results Under the conditions chosen the enzyme exists preferentially in its pentavalent form (Compound I) and will produce the fluorescent product by oxidation of the non-fluorescent substrate dihydrorhodamine 6G. At the same time the enzyme is reduced to its tetravalent state (Compound II). In order to complete the catalytic cycle a second substrate molecule is oxidized yielding the trivalent enzyme form which in the presence of H202 is oxidized again to the pentavalent form. Given a single HRP molecule on the surface it will turnover substrate molecules to create photons at the very spot of the enzyme molecule which are released into the volume element of detection (Fig. 1). Typical traces of the substrate turnover of single HRP molecules as well as of a control in the absence of enzyme are shown in Fig. 2. The autocorrelation functions were recorded simultaneously and are shown for the 10 s trace in Fig. 3A and 3B, as well as a trace which has been averaged up for 17 consecutive 10 s runs (Fig. 3C). In a second series of experiments, which was carried out on a hanging drop in order to be able to k 1
E
•
EP kq Scheme 2.
L. Edman et al. / Chemical Physics 247 (1999) 11-22
16
assess also the average production of the fluorescent product, FCS measurement was done by locating the volume element 10 Ixm below the surface (not shown). Here the turned over fluorescent product is measured only and the substrate concentration in - - T
1.20
r
l
T--r-'-'-
3.2. A model for the intensity fluctuation correlation function G('r )
0BS 1.15
I.I0
A 1.05
8 1.00 5. O. -5. re
-I0.
-1.
0.
1.
2.
3.
LOG(tlme [msll I
I
I
I
I
1.150
08S CALC
1.125 1.100
B
,,o
1.075
g
1 .0 5 0
(D
1.025 1.000
6.
o~
4.
8
2. 0.
re -4.
I
I
I
I
I
-1.
0.
1.
2.
3.
I
I
kOG(tlme [msl) I
I
ig.0
I
OBS
18.5
J C 8
terms of molecular numbers per volume element of detection can be determined. We have recorded the autocorrelation functions of 10 s and 300 s traces from single enzyme molecules for two substrate concentrations (65 nM and 5 riM, see Fig. 4).
18.0
"
In order to perform an analysis of the intensity fluctuation correlation from a single enzyme a spectroscopic model is proposed (Scheme 2). The choice of a two-state transition model is a consequence of the experimental conditions; one state is fluorescent (EP), the other is not (E). The EP state describes the situation when the enzyme is bound to a product molecule and hence can be monitored by fluorescence microscopy. The E state hence represents all other states of the enzyme. The transition rate k 1 to the EP state may be distributed due to existence of many processes leading to the EP. We will, however, assume that the life time of the EP complex is well defined so that the rate k 1 is not distributed. Even though more complex models as compared to the model in Scheme 2 could be used, we prefer to study the present data via a model that does not restrict the analysis to a particular set of physical a n d / o r biochemical states. The present situation implies an enzyme that 'produces' fluorescence molecules and also experiences an intermediate EP complex form before product release. Here, we will not consider correlation between EP and P since the diffusion of the product molecules through the detection volume is fast (100 txs range) as compared to the processes under study. Hence, in the present experiments the only photon source accounted for fluorescence intensity fluctuation correlation is the EP complex. Since the E and
17.5
17.0
2.
i
Ili
i.
0. -2.
I -1.
I O.
I 1.
LOG(tlme [ms])
I 2.
I 3.
Fig. 3. A single enzyme measured in the coverslip set-up at a substrate concentration of 130 nM. Fluorescence intensity correlation curves are shown for the molecule measured for two different 10 s periods (A,B). In C, data representing a 170 s data acquisition from 17 superimposed 10 s correlation curves for the same molecule are shown. The molecule is represented in Table 1 as molecule no. 3. The model fit is shown as a straight line through the measurement data.
L. Edmanet al./ ChemicalPhysics247 (1999) 11-22 hence the EP are immobilized, molecular diffusion does not need to be considered for the enzyme. Denote the excitation light intensity profile by I(x). The probability that an excitation photon is accepted by the EP located at position x 0 so that it makes a transition to the excited fluorescent state is o-. Define the probability that the EP leaves the exited state by the release of a photon as q. Finally, the probability that an emitted photon is detected is s. In the present experimental set-up,
x~+y~
17
where a is a constant > 0. However, for values k 1 > Q and Q >> k_ s
EP(t) = b e x p [ - ( k l t )
~] +c
where b and c are constants > 0 and 0
(1)
where I 0 is the maximum intensity in the centre of the laser beam, w 0 and P0 are the distances from the optical axis and the focal plane, respectively. In Eq. (2), EP(t)dt is the probability that a photon is detected in the time interval [~',T + dt] given that a photon was registered at time 0. For the present case using the state transition model in Scheme 2, EP(t) will be given by the solution of the system
Hence, for this choice of p(ks), EP(t) will have a stretched exponential appearance for small times t << l / k _ 1. For larger times t EP(t) becomes more and more single exponential and will finally converge exactly to Eq. (6). The normalized intensity fluctuation correlation function calculated for an individual immobilized enzyme molecule will then to the first order be equal to G(~') = 1 + a e x p ( - k _ s T ) + bexp[-(kd-) ~] +c.
k I
_k t
,
meaning that at time 0, the system in Scheme 2 was in state EP. The solution for EP in Eqs. (2) and (3) is k_s EP(t) = --exp[-(k~ k s -t-k_ s
+ k_l)t]
ks + k 1+ k~"
(4)
If k I is distributed with distribution function p(k 1) due to existence of a manifold of processes leading to the EP state, but k_ 1 is not distributed we obtain P(kl)
k 1 +k-----~
--S
de s.
(5)
For values k I < R and R << k 1, EP(t) as given by Eq. (5) is still dominated by a single exponential, EP(t) = a exp( - k_ 1t),
Other choices besides the stretched exponential of the distribution function p(k 1) can also be studied. However, we chose the stretched exponential due to its simplicity, and because of its wide use both in experimental evaluation of biological macromolecules [29] supported by theoretical studies on the origin the distribution [30]. A single stretched exponential can include a broad distribution of reaction rates, the exponential is 'stretched' over several orders of magnitude dependent on the stretch parameter/3. If diffusion of the free product should be accounted for, Eq. (8) is expanded to G(~') = 1 +
( xo+yoz )2 2
N+e
,1 } -~" ki k - - --1---~_l
(9)
(2)
with initial condition
EP(t) =
(8)
4
l ( x , y , z ) = I 0 ( e w°~ "e °~),
dt
(7)
(6)
xle
w~ .e
2 2 2(x0+y0)
w0~
2
24 .e
o~ { a e x p ( - k _ l ~ - )
18
L. Edman et al./ Chemical Physics 247 (1999) 11-22
where N is the average n u m b e r of diffusing molecules in the v o l u m e e l e m e n t [31], and % is the characteristic diffusion time of the fluorophore [31]. For the experiments were the sandwich set-up is used Eq. (9) is applicable. However, for the case of the h a n g i n g droplet set-up, diffusion of the free product c a n n o t be neglected, and hence Eq. (10) should be used.
l N
+ 1+--]
1+
'/'D
(10) --
--
Z0
A
I
'FD
i 2
, 4
I
i 6
I
I
i 8
I
, 10
I
I
tz'S
I
OBS 1D
1.15
IO
S~b ~J
I.I0
-o
B
¢. e~
1.05
o
¢,/1 ,-.,i
o,,.i
~m
0. -2.
0.
1.
2.
3.
4.
5.
LOGCtlme [ms]) Fig. 4. Single enzymes measured with the substrate applied as a hanging droplet. Fluorescence intensity correlation curves are shown for two molecules (A,B and C,D, respectively) measured for 10 s (A,C) and 300 s (B,D). The substrate concentrations were 65 nM (A,B) and 5 nM (C,D). The parameter values for the model fit is shown in Table 1 for molecule no. 4 and no. 5, respectively.
19
L. Edman et al. / Chemical Physics 247 (1999) 11-22
C 7 0
2
1 6
4
I
I
T 8
I
T
10
1 t/s
I
/
1.08 "o 4~
S
-1
OBS
h
1.07
(b
co
1.06
"0
D
1.05 C_ V) e~
o
1.04 1.03 2, 1. O.
rv
-1. "2°
O.
-1.
1.
2.
LOG(tlme [ms]) Fig. 4 (continued).
3.3. Evaluation of the data with the model G(~-) The model Eq. (8) was applied to the data obtained from the FCS measurements on the single enzymes (Figs. 3 and 4). However, in order to verify the assumption that k i is not distributed, a stretched parameter was used for both exponentials in the evaluations of the experimental data. This additional stretch parameter is shown in Table 1 as y together with the other parameters. The additional stretch
parameter is close to 1 for all 300 s measurements; the only exception is the 5 nM substrate concentration measurement. As the substrate concentration is lowered, the spectrum of fluctuation rates that can be visible is restricted. In terms of our model Eq. (8), this is shown as a change in p ( k 1) towards lower values of k 1. Hence we interpret the lower value y = 0.53 as an influence of a spectral shift in p(k 1) due to the low substrate concentration. Fits with the models Eqs. (9) and (10) where y is fixed to 1.0
L. Edman et al, / Chemical Physics 247 (1999) 11-22
20 Table 1
Rate parametersfor the substrate turnovers into products by HRP molecules measured for different times and at different substrate concentrationsa
k_ 1
Molecule
Time
[S]
no.
(s)
(nM) (s- 1)
i 1 2 3 1 4 5
10 10 70 100 170 300 300
130 130 130 130 130 65 5
5 4 10 10 11 21 41
y
k1
¢1
a/ b
0.66 0.45 0.26 0.29 0.16 0.20 0.10
0.26 1.7 0.33 0.54 0.96 1.4 0.4
(s- l) 1.2 2.1 0.83 0.91 0.80 0.74 0.53
860 510 2200 4100 920 380 850
a The relative mean uncertainties for the parameters were: 50% for kl, t9, a / b , and 20% for k_ 1, %
show insignificant differences in the X2-distributed residuals as compared to fits with y set free to vary for all data except the 5 nM case. We conclude that the assumption made in Section 3.2 regarding k 1 is valid for reasonably higher substrate concentrations. Measurement data acquisition intervals between 10 s and 300 s were used (Table 1). Data are presented from experiments using a coverslip sandwich (Fig. 3) as well as mono-coverslip with the substrate solution applied as a hanging droplet at the enzyme area (Fig. 4). The data fit the model of Eq. (8) very well (parameter values are not shown but are similar to those in Table 1 except that 3' is fixed to 1.0). The rate k I is almost exponential with values ranging from 4 to 41 s - 1 for the molecules in Table 1. The other rate, k I is varying in the range 380-4100 s -1 with a stretch parameter /3 in the interval 0.10-0.29 for all measurements except the 10 s intervals, where /3 is larger (0.45 and 0.66). Other models including additional exponential functions have also been used without improving the X Z-values. Also, single exponential models with p(kl) centred at one single rate failed to fit the observed data from single enzymes.
3.4. Fluctuations in the traces Each trace shown in Fig. 2, except the control trace shown in Fig. 2D, show a pattern where the fluorescence intensity is interrupted by periods of higher mean intensity. The fluorescence is fluctuating in a time scale clearly visible in the 10 s traces
where the bin size is ~ 20 ms; there are periods lasting from less than 20 ms up to almost 1 s that are characterized by an intensity above the average. It becomes clear from the above analysis with the two-state transition model that small values of k~ are not visible in G(~-), only those values for which k 1 is in the same time range or larger than k_ ~ are visible in the fluorescence intensity correlation G(z). However, in the fluorescence intensity traces (Fig. 2) low values of k 1 are clearly seen as fluctuation between periods with two fluorescence intensity levels. Obviously, the transition rate to the EP state is fluctuating over a wider range of time scales than what can be observed only by an evaluation of the single enzyme data by FCS using model Eqs. (9) and (10). However, the value of the stretch parameter/3 is less than 0.3 for all measurements were the enzyme has been measured more than 10 s. A stretch parameter of 0.3 will make the exponential being 'stretched' over three orders of magnitude. Hence, the low values of /3 indicate that the k s rate is distributed over more than three orders of magnitude.
3.5. The fluctuating enzyme The combined analysis by FCS and the traces gives a total picture of the present findings. Clearly, there is a concentration dependent contribution to p(kl). The finding of an exponential dissociation rate for the enzyme-product complex is in line with previous measurements done for the individual A T P - A D P turnovers in myosin, where the single fluorescing ADP-myosin complex showed an exponential dissociation rate [32]. The k I rate on the other hand is widely distributed ranging over several orders of magnitude. Hence, there exists a manifold of rates to the EP state. The analysis suggests two obvious processes. First, the peroxidative cycle including the substrate binding to the enzyme, and the transition of the ES to an EP, is a process dependent on substrate concentration. Secondly, as was discussed above, the enzyme fluctuates in its catalytic activity over time ranging from ms to several s. Fast fluctuations of the EP [14] leading to spectroscopic fluctuations may also contribute. Rates for the catalytic step determined for the present enzyme by stopped flow measurements
L Edman et al./Chemical Physics 247 (1999) 11-22
[33,34] are in the same time range as the rates given for k_l in Table 1. A consequence of our analysis showing exponential kinetics for k_~ is that the off-rates for Compound I and II [33,34] are very similar. From the evaluations shown in Fig. 3A and B it is evident that a single enzyme molecule changes its character between different 10 s measurement intervals. Our data indicate that the enzyme fluctuates in activity over a wide range of time scales. However, measurements done over longer times with a given substrate concentration show rather similar values in the evaluation parameters for different enzyme molecules (Table 1, molecules 1, 2 and 3). The data therefore indicate that the difference in mean enzymatic activity as observed for different enzymes is only dependent on the observation time, ile. the observed enzymes obey the ergodic assumption. This is an interesting indication as compared to studies on conformational fluctuations in single DNA molecules where the non-ergodicity in the time scales observed is rather pronounced [19,35-38]. Previous experiments on single enzymes show differences in the activity for different molecules when measured over a very long time period as compared to one enzymatic cycle [15,16]. Here, we observe the enzyme at all time scales, thereby revealing enzymatic activity fluctuations for a single enzyme mtolecule. In a very recent paper oxidationreduction fluctuations are observed for single cholesterol oxidase molecules [39]. The lifetime of the oxidized state is distributed between different enzymes. Also, some molecules show a positive dependency on the lifetimes of consecutive oxidized states. The authors attribute the latter phenomenon to conformational fluctuations of the enzyme in a time scale of about 1 s. The measurements in [39] are indirect in the sense that the product is never observed; the oxidation of the prosthetic group is the observable. In the present single enzyme experiment, the product is directly observed as the enzyme-product complex is formed. Nevertheless, we see similarities between the present result and the result presented in [39]; static and dynamic disorder is observed for both enzymes. However, in the present experiment it is possible to resolve two processes; the peroxidative cycle and the activity fluctuations. Also, we note that for the present experiment the
21
static and the dynamic disorder are two viewpoints of the same phenomenon, i.e. dynamic disorder implies static disorder and vice versa. The analysis presented here does not reveal detailed information about the involved biochemical processes, but still gives information about the enzyme. The finding that the enzyme activity is fluctuating implies the necessity to enlarge the description of how the enzyme works. Fig. 5 gives a total model summary of the present experiments. The model has two dimensions: (a) The biochemical dimension where the catalysis of the substrate takes place. (b) The physical thermodynamic dimension where, in terms of Franenfelder's energy landscape [40], the conformational substrates (CS) of the enzyme are shown. The protein does not have a unique structure, and does not reach a unique conformation after folding, but one of a very large number of slightly different conformations [29]. Transitions between CS occur on a wide range of time scales, the system is
H202 S PF~+S\
+
r~
la ,,=
F$'-
Fg+'.
Zg÷
;?
LT
;T
. .
l l
l
[.. : sC p
s p-'5
Biochemistry Fig. 5. Grand scheme describing the total model description for the experiments. It has a biochemical dimension (horizontal) and a thermodynamic dimension (vertical) and is a consequence of the present experiment and analysis.
22
L. Edman et a L / Chemical Physics 247 (1999) 11-22
ergodic but the time scale for a single enzyme to experience all CS is large. For some states the activity is high, implying fast substrate turnovers. Other states make the enzyme not active, so the substrate turnover rate is zero. Hence, the present experiment and analysis show that conformational changes on a large number of time scales generated by thermodynamic fluctuations affect enzyme activity.
Acknowledgements
We thank Ebba Hagman and Britt Larson for excellent laboratory assistance, Lennart Wallerman for expert workshop assistance, and Anders Ehrenberg for stimulating discussions. This work was supported in part by grants from the Swedish Science Research Council as well as the Swedish National Board for Technical Development.
References [1] L. Pauling, Nature 161 (1948) 707. [2] G.E. Schulz, R.H. Schirmer, Principles of Protein Structure, Springer, New York, 1979. [3] P.G. Wolynes, J.N. Onuchic, D. Thintmalai, Science 267 (1995) 1619. [4] J.N. Onnchic, P.G. Wolynes, Z. Luthey-Schulten, N.D. Socci, Proc. Natl. Acad. Sci. USA 92 (1995) 3626. [5] K.A. Dill, K.M. Fiebig, H.S. Chart, Proc. Natl. Acad. Sci. USA 90 (1993) 1942. [6] P.E. Leopold, M. Montal, J.N. Onuchic, Proc. Natl. Acad. Sci. USA 89 (1992) 8721. [7] E.M. Boczko, C.L. Brooks III, Science 269 (1995) 393. [8] T. Pascher, J.P. Chesick, J.R. Winkler, H.B. Gray, Science 271 (1996) 1558, and references therein. [9] R.H. Austin, K.W. Beeson, L. Eisenstein, H. Franelffelder, I.C. Gunsalns, Biochemistry 14 (1975) 5355. [10] N. Alberding, S.S. Chart, L. Eistenstein, H. Frauenfelder, D. Good, I.C. Gunsalus, T.M. Nordlund, M.F. Perutz, A.H. Reynolds, L.B. Sorensen, Biochemistry 17 (1978) 43. [11] H. Gmbmiiller, P. Tavan, J. Chem. Plays. 101 (1994) 5047.
[12] J.D. Bryngelson, P.G. Wolynes, J. Phys. Chem. 93 (1989) 6902. [13] C. Careri, in: B. Korsunoglu, S.L. Mintz, S.M. Windmayer (Eds.), Quant. Stat. Mech. Nat. Sci., Plenum, New York, 1974, p. 15. [14] G. Careri, P. Fasella, E. Gratton, Crit. Rev. Biochem. 3 (1975) 141. [15] Q. Xue, E. Yeung, Nature 373 (1995) 681. [16] D.B. Craig, E. Arriaga, J.C. Wong, H. Lu, N.J. Dovichi, Anal. Chem. News Feat. 39A (1998). [17] R. Willst~itter, A. Pollinger, A. Liebigs Ann. 430 (1923) 269. [18] H. Theorell, A. ~d~esson, Ark. Kemi Min. Geol. 16A (8) (1943). [19] S. Wennmalm, L. Edman, R. Rigler, Proc. Natl. Acad. Sci. USA 94 (1997) 10641. [20] W.D. Hewson, L.P. Hager, Peroxidases, Catalases, and Chloroperoxidase, in: D. Dolphin (Ed.), The Porphyrins, Vol. VIII, Academic Press, New York, 1979, pp. 295-332. [21] J.N. Rodriguez-Lopez, A.T. Smith, R.N.F. Thomeley, J. Biol. Chem. 272 (1997) 389. [22] Z. FNdes-Papp, G. Gerber, R. Sttisser, G. Schneider, J. Prakt. Chem. 333 (1991) 293. [23] Z. FNdes-Papp, Gen. Physiol. Biophys. 11 (1992) 3. [24] R. Rigler, U. Mets, SPIE Laser Spectrosc. Biomol. 1921 (1992) 239. [25] (). Mets, R. Rigler, J. Fluoresc. 4 (1994) 259. [26] J. Dapprich, U. Mets, W. Simm, M. Eigen, R. Rigler, Exp. Tech. Phys. 46 (1995) 259. [27] S. Wennmalm, R. Rigler, J. Phys. Chem., in press. [28] D. Marquardt, J. Soc. Ind. Appl. Math. 11 (1963) 431. [29] H. Frauenfelder, in: K.L. Ngai (Ed.), Glasses and Glass Formers, Material Research Society, 1997. [30] M.F. Shlesinger, Ann. Rev. Phys. Chem. 39 (1988) 269. [31] E. Elson, D. Magde, Biopolymers 13 (1974) 1. [32] T. Funatsu, Y. Harada, M. Tokunaga, K. Salto, T. Yanagida, Nature (London) 374, 555. [33] B. Chance, J. Biol. Chem. 151 (1943) 553. [34] B. Chance, Arch. Biochem. 22 (1949) 224. [35] L. Edman, 1~. Mets, R. Rigler, Exp. Tech. Phys. 41 (1995) 157. [36] L. Edman, U. Mets, R. Rigler, Proc. Natl. Acad. Sci. USA 93 (1996) 6710. [37] L. Edman, S. Wennmalm, F. Tamsen, R. Rigler, Chem. Phys. Lett. 292 (1998) 15. [38] S. Wennmalm, L. Edman, R. Rigler, Chem. Phys., submitted for publication. [39] H.P. Lu, L. Xun, X.S. Xie, Science 282 (1998) 1877. [40] H. Franenfelder, S.G. Sligar, P.G. Wolynes, Science 254 (1991) 1598.
Chemical Physics 247 (1999) 11-22 www.elsevier.nl/locate/chemphys
The fluctuating enzyme: a single molecule approach Lars Edman, Zeno FiSldes-Papp, Stefan Wennmalm, Rudolf Rigler * Karolinska Institute, Department of Medical Biophysics, MBB, 171 77 Stockholm, Sweden Received 16 December 1998
Abstract
The excess of structural degrees of freedom in a protein enzyme opens questions about the conformational homogeneity. We studied single horseradish peroxidase enzyme turnovers by fluorescence spectroscopy. Application of a two-state dynamic model to the measured data shows exponential product dissociation kinetics, but a large distribution of rates for the enzyme to form the enzyme-product complex. The experiments show that in addition to the peroxidative cycle thermodynamic fluctuation phenomena on a wide range of time scales affect enzyme activity. © 1999 Elsevier Science B.V. All rights reserved. 1. I n ~ o d u c f i o n
Enzymes make chemical reactions faster without changing the position of the chemical equilibrium. Hence, an enzyme merely changes the time scale of a reaction process. Almost all enzymes are proteins, which because of their inherent complex structure have many structural degrees of freedom. An enzyme acts as a molecule complementary in structure to the molecular configuration that is intermediate to the reactants and the products [1], for which the enzyme lowers the activation energy required for a reaction to occur. Static protein enzyme secondary structures can be routinely determined by nuclear magnetic resonance spectroscopy (NMR) or by crystallization [2]. Much attention has been given to exploit the mechanisms of protein folding. Theory [3-6], molecular simulations [7], and experiments [8] indicate a complex
* Corresponding author. Tel.: +46-8-728-6801; Fax: +46-832-6505; E-mail: [email protected]
mechanism involving many intermediate structural forms. Dynamics of the already folded protein are less investigated, although experiments [9,10], molecular simulations [11], and theoretical studies [12-14] have proven that a broadened understanding of the connection between protein function and structural fluctuations is needed to understand the role played by thermodynamics in the case of proteins and other complex biomolecules. Since the primary structure of a protein can fold into many slightly different conformations [3-14] the free energy of the protein is rough and has many local minima [12]. The excess of conformational degrees of freedom in a protein enzyme opens questions about the conformational homogeneity in an enzyme population [3-6,9], and about the conformational variability over time of an individual enzyme. Experimental studies on carbon monoxide (CO) binding to myoglobin (Mb) indicate differences in reaction energy barriers between different Mb molecules [9]. Recent experiments involving single enzymes [15,16] indicate differences in the activity between different individual molecules.
0 3 0 1 - 0 1 0 4 / 9 9 / $ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: $ 0 3 0 1 - 0 1 0 4 ( 9 9 ) 0 0 0 9 8 - 1
L. Edman et aL / Chemical Physics 247 (1999) 11-22
12
In this article we are concerned with the enzyme horseradish peroxidase (HRP), a 44 kDa heme protein [17,18]. HRP is an effective catalyst for the decomposition of hydrogen peroxide (H20 2) in the presence of hydrogen donors [17,18]. The reaction is monitored by existing experimental methods [19] based on fluorescence spectroscopy. We used the non-fluorescent substrate (S) dihydrorhodamine 6G which after oxidation yields the highly fluorescing rhodamine 6G fluorophore (P). Hence, direct observation of the individual substrate turnover reactions is made possible by means of fluorescence microscopy if single enzymes (E) are observed. The free enzyme (E), the substrate (S), or the enzymesubstrate complex (ES) are all non-fluorescent. However, if the substrate is oxidized while still bound to the enzyme, the ES will transform into an enzymeproduct complex (EP) [13] which should be fluorescent.
2. Experiments 2.1. Horseradish peroxidase The donor hydrogen peroxide oxidoreductase, EC 1.11.1.7, from horse radish shows kinetics with the following characteristics of the conventional peroxidative cycle [20]: native (ferric, trivalent redox state) enzyme ~ Compound I (pentavalent redox state) Compound II (tetravalent redox state) ---> native enzyme (see Scheme 1). The essential prosthetic group is the ferric protoporphyrin IX. Horseradish peroxidase decomposes H202 into oxygen and water with low specificity for hydrogen donors. In order to analyze the enzyme catalysis at single molecule level we have chosen the nonfluorescent leukodye dihydrorhodamine 6G (Molecular Probes, the Netherlands) as donor substrate which is turned over into the fluorescent product rhodamine 6G. The biotinylated enzyme (Molecular Probes, the Netherlands) was dissolved in 100
H o2
S PE4+S\ Scheme 1.
+
mM potassium phosphate, pH 7.0, 100 mM NaC1, and 50% ( v / v ) glycerol (Sigma, USA, for Molecular Biology). The suspensions were stored at - 2 0 ° C for two months. Prior to use the suspensions were diluted in 100 mM potassium phosphate, pH 7.0, and kept on ice. The solutions were immediately used. As control assay for the horseradish peroxidase activity we used the established guaiacol test method. In brief, the reaction mixtures contained in a final volume of 1 ml at room temperature: 100 mM potassium phosphate, pH 7.0; 320 t-~M guaiacol (extra pure) obtained from Merck, Germany; for example approximately 0.005 U / m l diluted enzyme suspension; 120 tzM H2O 2 (puriss.) purchased from Fluka, Germany. The reaction was started by addition of H202, the concentration of which was adjusted spectrophotometrically at 240 nm. The absorbance of the reaction mixtures was monitored at 436 nm for at least 25 rain at room temperature (Pharmacia Biochrom 4060 spectrophotometer, Amersham Pharmacia Biotech, Sweden). No changes in the absorbance were found in the blank reaction without enzyme. The enzymatic activity was calculated from the linear and steepest range of the curve using the absorption coefficient e25oc 2.55 l/retool mm related to 1 mmol tetraguaiacol. We determined the specific activity of the biotinylated horseradish peroxidase to b e 46 _+ 6 guaiacol units per mg HRP (n = 8) corresponding to 34 _+ 4 tool of substrate per mol of enzyme and second. These measurements were performed at a maximum turnover rate, but not at substrate excess. One unit horseradish peroxidase oxidizes 1 ~mol of guaiacol tetramer to product in 1 rain at 25°C and pH 7.0. =
2.1.1. Preparation of immobilized horseradish peroxidase Our experimental procedure of preparing streptavidin-coated coverslips is based on the conditions published in Ref. [19]. In brief, the coverslips, 170 Izm thick, were boiled in concentrated HNO 3 (Suprapure, Merck, Germany) and then dried at 5 0 60°C in an oven. A teflon holder was cleaned and dried by rinsing in water-free ethanol, water-free acetone and finally in water-free ether. The coverslips were incubated in the teflon holder with a 10% ( v / v ) solution of 3-glycidoxypropyltrimethoxysilane (Aldrich, USA) in pure toluene (Merck, Germany)
L. Edman et al. / Chemical Physics 247 (1999) 11-22
for 24 h. After baking at 110°C for 6-8 h they were treated with 20 t~1 streptavidin solution (11 p~M streptavidin from Sigma, USA, in 0.2 M carbonate buffer, pH 9.0) at room temperature in petri dishes and stored in the same closed petri dishes under water-saturated atmosphere. The covalent bond between the epoxy group and the amine on the streptavidin was stable during storage for some time. Excess of streptavidin adsorbed at the surface was removed by shaking the coverslips in 0.5 M Tris-HC1, pH 9.0, overnight in the teflon holder. After washing with the final buffer (100 mM potassium phosphate, pH 7.0), the coverslips were ready for incubation with approx. 1 nM biotinylated horseradish peroxi-
|
Glass Silane/Streptavidin layer Biotin
t3
dase solution. The incubation was performed at 4°C for about 1 h followed by exhaustively rinsing the coverslips in 100 mM potassium phosphate, pH 7.0, to remove unbound enzyme. 2.1.2. Enzymatic reaction The peroxidative cycle can be accompanied by side reactions: the ferrous (divalent) enzyme/Compound 111 shuttle (native enzyme ~ ferrous enzyme Compound III -0 ferrous enzyme), the ferrous enzyme/oxyperoxidase shuttle (native enzyme ferrous enzyme ~ oxyperoxidase ~ native enzyme), the reaction of Compound II with H202, the reaction of the native enzyme with the superoxide
0
o
Single enzyme Product molecule Substrate molecule
Fig. 1. Principal scheme for the measurements of single enzymes. The distance from the laser intensity maximum to the coverslip surface was adjusted to 2 _+ 0.5 I~m for all measurements.
L. Edman et al. / Chemical Physics 247 (1999) 11-22
14
anion radical (O~-). To avoid enzymatic side reactions occurring at high substrates-to-enzyme ratios [21], but also nonenzymatic autocatalytic reaction cascades oxidizing thermally the leukodye by H202 via reactive oxygen species (O;-, OH , ROOH) [22], we performed the experiments with a minimum amount of H202 and leukodye. The generation and the recombination of free oxygen radicals were found only in cases where the free radicals had relatively long lifetimes and the steady-state concentration of the reactive oxygen species was comparatively high [23]. In systems containing no free metal ions, the
products of oxygen reduction have a low reactivity and do not constitute a significant reaction path for the autoxidation of the leukodye. Under the experimental conditions used here autoxidation was not observed in the time frame of the measurements or its rate was negligibly small at 130 nM dihydrorhodamine 6G. The biotinylated enzyme prepared as described in the Section 2.1 was studied after immobilization on a glass surface (or in solution) in 100 mM potassium phosphate buffer, pH 7.0, 1 nM up to 130 nM dihydrorhodamine 6G, at HaO 2 concentration of 120 p~M,
A I 2
B
1 4
I ~
I
%-
8
10
1 t/a:
k t/s
C 0
2
4
I
I
2
4
6
8
6
tO
n/kH!
D : t
0
0
/
8
r
I0
7 t/N
Fig. 2. Fluorescence intensity traces f r o m 10 s intervals are s h o w n for three molecules in A - C . In D, a trace f r o m a control m e a s u r e m e n t is shown. The control m e a s u r e m e n t w a s p e r f o r m e d as the single e n z y m e measurements, with the exception that no e n z y m e was b o u n d to the streptavidin surface.
15
L. Edman et al. / Chemical Physics 247 (1999) 11-22
2.2. Single molecule and FCS analysis Confocal single molecule detection [24,25] as well as imaging [26] was used for the analysis of the product formation of single surface bound HRP molecules. The streptavidinized micro-coverslide (170 Ixm thick) surface with the bound HRP molecules together with substrate in the reaction buffer was either covered with a second microslide carrying a 10 ~ m spacer (Menzel-Gl~ser, Brauschweig, Germany), or used in the 'hanging drop' regime [24,25] with controlled vapour pressure to avoid concentration effects during the enzyme catalysis. For the optical measurement a 40 × NA 0.9 objective (Neofluar, Carl Zeiss) providing a detection volume element with half axes of 0.5 ~ m and 2 ~ m was used. The measurement spot was positioned 2 _+ 0.5 Ixm underneath the microslide surface, which corresponds to the dimensions of the half axis of the volume element in the vertical direction (Fig. 1). In this position an optimal discrimination was achieved between the fluctuating single molecule signal and background reflection at the microslide surface. The measuring strategy involved a computer-controlled scum on the surface of the microscope slide until a single molecule process was observed. The observatton of a single enzyme molecule was evidenced by (i) the fact that the concentration of the applied enzyme (1 riM) was chosen so that there was much less than one molecule per observation area. (ii) Condition (i) is manifested by the fact that a scan search was needed to find spots with fluctuations (Fig. 2A-C), most spots showed an intensity trace hike the control measurement in Fig. 2D. (iii) The intensity of a single tetramethyl rhodamine molecule linked to the streptavidin surface is found to be 3.5 kHz (average of 100 molecules) [27]. For rhodamine 6G the produced counting rate is about 3.0 kHz. Hence, the intensity increases of the fluctuations in Fig. 2 A - C are in the same range as the intensities of a single rhodamine 6G molecule. Single molecule traces are recorded during multiples of 10 s or for longer times up to 300 s. Simultaneously the autocorrelation functions of the single molecule fluctuations are recorded on line and stored automatically. Details of the instrumentation have been published previously [19]. For data evalua-
tion and parameter estimation non-linear least square optimization after Marquardt was used [28]. The analysis is based on material which comprises more than 100 individual enzyme molecules.
3. Results and discussion In this section we will first present the main results of the single enzyme experiment. Then, an expression for the intensity fluctuation correlation function G(r) is made based on the kinetics Scheme 2. Thereafter, the model is fitted to the present data. The result is discussed together with an analysis of the traces. Finally, we treat the present findings in the perspective of previous studies of proteins and single molecules.
3.1. Results Under the conditions chosen the enzyme exists preferentially in its pentavalent form (Compound I) and will produce the fluorescent product by oxidation of the non-fluorescent substrate dihydrorhodamine 6G. At the same time the enzyme is reduced to its tetravalent state (Compound II). In order to complete the catalytic cycle a second substrate molecule is oxidized yielding the trivalent enzyme form which in the presence of H202 is oxidized again to the pentavalent form. Given a single HRP molecule on the surface it will turnover substrate molecules to create photons at the very spot of the enzyme molecule which are released into the volume element of detection (Fig. 1). Typical traces of the substrate turnover of single HRP molecules as well as of a control in the absence of enzyme are shown in Fig. 2. The autocorrelation functions were recorded simultaneously and are shown for the 10 s trace in Fig. 3A and 3B, as well as a trace which has been averaged up for 17 consecutive 10 s runs (Fig. 3C). In a second series of experiments, which was carried out on a hanging drop in order to be able to k 1
E
•
EP kq Scheme 2.
L. Edman et al. / Chemical Physics 247 (1999) 11-22
16
assess also the average production of the fluorescent product, FCS measurement was done by locating the volume element 10 Ixm below the surface (not shown). Here the turned over fluorescent product is measured only and the substrate concentration in - - T
1.20
r
l
T--r-'-'-
3.2. A model for the intensity fluctuation correlation function G('r )
0BS 1.15
I.I0
A 1.05
8 1.00 5. O. -5. re
-I0.
-1.
0.
1.
2.
3.
LOG(tlme [msll I
I
I
I
I
1.150
08S CALC
1.125 1.100
B
,,o
1.075
g
1 .0 5 0
(D
1.025 1.000
6.
o~
4.
8
2. 0.
re -4.
I
I
I
I
I
-1.
0.
1.
2.
3.
I
I
kOG(tlme [msl) I
I
ig.0
I
OBS
18.5
J C 8
terms of molecular numbers per volume element of detection can be determined. We have recorded the autocorrelation functions of 10 s and 300 s traces from single enzyme molecules for two substrate concentrations (65 nM and 5 riM, see Fig. 4).
18.0
"
In order to perform an analysis of the intensity fluctuation correlation from a single enzyme a spectroscopic model is proposed (Scheme 2). The choice of a two-state transition model is a consequence of the experimental conditions; one state is fluorescent (EP), the other is not (E). The EP state describes the situation when the enzyme is bound to a product molecule and hence can be monitored by fluorescence microscopy. The E state hence represents all other states of the enzyme. The transition rate k 1 to the EP state may be distributed due to existence of many processes leading to the EP. We will, however, assume that the life time of the EP complex is well defined so that the rate k 1 is not distributed. Even though more complex models as compared to the model in Scheme 2 could be used, we prefer to study the present data via a model that does not restrict the analysis to a particular set of physical a n d / o r biochemical states. The present situation implies an enzyme that 'produces' fluorescence molecules and also experiences an intermediate EP complex form before product release. Here, we will not consider correlation between EP and P since the diffusion of the product molecules through the detection volume is fast (100 txs range) as compared to the processes under study. Hence, in the present experiments the only photon source accounted for fluorescence intensity fluctuation correlation is the EP complex. Since the E and
17.5
17.0
2.
i
Ili
i.
0. -2.
I -1.
I O.
I 1.
LOG(tlme [ms])
I 2.
I 3.
Fig. 3. A single enzyme measured in the coverslip set-up at a substrate concentration of 130 nM. Fluorescence intensity correlation curves are shown for the molecule measured for two different 10 s periods (A,B). In C, data representing a 170 s data acquisition from 17 superimposed 10 s correlation curves for the same molecule are shown. The molecule is represented in Table 1 as molecule no. 3. The model fit is shown as a straight line through the measurement data.
L. Edmanet al./ ChemicalPhysics247 (1999) 11-22 hence the EP are immobilized, molecular diffusion does not need to be considered for the enzyme. Denote the excitation light intensity profile by I(x). The probability that an excitation photon is accepted by the EP located at position x 0 so that it makes a transition to the excited fluorescent state is o-. Define the probability that the EP leaves the exited state by the release of a photon as q. Finally, the probability that an emitted photon is detected is s. In the present experimental set-up,
x~+y~
17
where a is a constant > 0. However, for values k 1 > Q and Q >> k_ s
EP(t) = b e x p [ - ( k l t )
~] +c
where b and c are constants > 0 and 0
(1)
where I 0 is the maximum intensity in the centre of the laser beam, w 0 and P0 are the distances from the optical axis and the focal plane, respectively. In Eq. (2), EP(t)dt is the probability that a photon is detected in the time interval [~',T + dt] given that a photon was registered at time 0. For the present case using the state transition model in Scheme 2, EP(t) will be given by the solution of the system
Hence, for this choice of p(ks), EP(t) will have a stretched exponential appearance for small times t << l / k _ 1. For larger times t EP(t) becomes more and more single exponential and will finally converge exactly to Eq. (6). The normalized intensity fluctuation correlation function calculated for an individual immobilized enzyme molecule will then to the first order be equal to G(~') = 1 + a e x p ( - k _ s T ) + bexp[-(kd-) ~] +c.
k I
_k t
,
meaning that at time 0, the system in Scheme 2 was in state EP. The solution for EP in Eqs. (2) and (3) is k_s EP(t) = --exp[-(k~ k s -t-k_ s
+ k_l)t]
ks + k 1+ k~"
(4)
If k I is distributed with distribution function p(k 1) due to existence of a manifold of processes leading to the EP state, but k_ 1 is not distributed we obtain P(kl)
k 1 +k-----~
--S
de s.
(5)
For values k I < R and R << k 1, EP(t) as given by Eq. (5) is still dominated by a single exponential, EP(t) = a exp( - k_ 1t),
Other choices besides the stretched exponential of the distribution function p(k 1) can also be studied. However, we chose the stretched exponential due to its simplicity, and because of its wide use both in experimental evaluation of biological macromolecules [29] supported by theoretical studies on the origin the distribution [30]. A single stretched exponential can include a broad distribution of reaction rates, the exponential is 'stretched' over several orders of magnitude dependent on the stretch parameter/3. If diffusion of the free product should be accounted for, Eq. (8) is expanded to G(~') = 1 +
( xo+yoz )2 2
N+e
,1 } -~" ki k - - --1---~_l
(9)
(2)
with initial condition
EP(t) =
(8)
4
l ( x , y , z ) = I 0 ( e w°~ "e °~),
dt
(7)
(6)
xle
w~ .e
2 2 2(x0+y0)
w0~
2
24 .e
o~ { a e x p ( - k _ l ~ - )
18
L. Edman et al./ Chemical Physics 247 (1999) 11-22
where N is the average n u m b e r of diffusing molecules in the v o l u m e e l e m e n t [31], and % is the characteristic diffusion time of the fluorophore [31]. For the experiments were the sandwich set-up is used Eq. (9) is applicable. However, for the case of the h a n g i n g droplet set-up, diffusion of the free product c a n n o t be neglected, and hence Eq. (10) should be used.
l N
+ 1+--]
1+
'/'D
(10) --
--
Z0
A
I
'FD
i 2
, 4
I
i 6
I
I
i 8
I
, 10
I
I
tz'S
I
OBS 1D
1.15
IO
S~b ~J
I.I0
-o
B
¢. e~
1.05
o
¢,/1 ,-.,i
o,,.i
~m
0. -2.
0.
1.
2.
3.
4.
5.
LOGCtlme [ms]) Fig. 4. Single enzymes measured with the substrate applied as a hanging droplet. Fluorescence intensity correlation curves are shown for two molecules (A,B and C,D, respectively) measured for 10 s (A,C) and 300 s (B,D). The substrate concentrations were 65 nM (A,B) and 5 nM (C,D). The parameter values for the model fit is shown in Table 1 for molecule no. 4 and no. 5, respectively.
19
L. Edman et al. / Chemical Physics 247 (1999) 11-22
C 7 0
2
1 6
4
I
I
T 8
I
T
10
1 t/s
I
/
1.08 "o 4~
S
-1
OBS
h
1.07
(b
co
1.06
"0
D
1.05 C_ V) e~
o
1.04 1.03 2, 1. O.
rv
-1. "2°
O.
-1.
1.
2.
LOG(tlme [ms]) Fig. 4 (continued).
3.3. Evaluation of the data with the model G(~-) The model Eq. (8) was applied to the data obtained from the FCS measurements on the single enzymes (Figs. 3 and 4). However, in order to verify the assumption that k i is not distributed, a stretched parameter was used for both exponentials in the evaluations of the experimental data. This additional stretch parameter is shown in Table 1 as y together with the other parameters. The additional stretch
parameter is close to 1 for all 300 s measurements; the only exception is the 5 nM substrate concentration measurement. As the substrate concentration is lowered, the spectrum of fluctuation rates that can be visible is restricted. In terms of our model Eq. (8), this is shown as a change in p ( k 1) towards lower values of k 1. Hence we interpret the lower value y = 0.53 as an influence of a spectral shift in p(k 1) due to the low substrate concentration. Fits with the models Eqs. (9) and (10) where y is fixed to 1.0
L. Edman et al, / Chemical Physics 247 (1999) 11-22
20 Table 1
Rate parametersfor the substrate turnovers into products by HRP molecules measured for different times and at different substrate concentrationsa
k_ 1
Molecule
Time
[S]
no.
(s)
(nM) (s- 1)
i 1 2 3 1 4 5
10 10 70 100 170 300 300
130 130 130 130 130 65 5
5 4 10 10 11 21 41
y
k1
¢1
a/ b
0.66 0.45 0.26 0.29 0.16 0.20 0.10
0.26 1.7 0.33 0.54 0.96 1.4 0.4
(s- l) 1.2 2.1 0.83 0.91 0.80 0.74 0.53
860 510 2200 4100 920 380 850
a The relative mean uncertainties for the parameters were: 50% for kl, t9, a / b , and 20% for k_ 1, %
show insignificant differences in the X2-distributed residuals as compared to fits with y set free to vary for all data except the 5 nM case. We conclude that the assumption made in Section 3.2 regarding k 1 is valid for reasonably higher substrate concentrations. Measurement data acquisition intervals between 10 s and 300 s were used (Table 1). Data are presented from experiments using a coverslip sandwich (Fig. 3) as well as mono-coverslip with the substrate solution applied as a hanging droplet at the enzyme area (Fig. 4). The data fit the model of Eq. (8) very well (parameter values are not shown but are similar to those in Table 1 except that 3' is fixed to 1.0). The rate k I is almost exponential with values ranging from 4 to 41 s - 1 for the molecules in Table 1. The other rate, k I is varying in the range 380-4100 s -1 with a stretch parameter /3 in the interval 0.10-0.29 for all measurements except the 10 s intervals, where /3 is larger (0.45 and 0.66). Other models including additional exponential functions have also been used without improving the X Z-values. Also, single exponential models with p(kl) centred at one single rate failed to fit the observed data from single enzymes.
3.4. Fluctuations in the traces Each trace shown in Fig. 2, except the control trace shown in Fig. 2D, show a pattern where the fluorescence intensity is interrupted by periods of higher mean intensity. The fluorescence is fluctuating in a time scale clearly visible in the 10 s traces
where the bin size is ~ 20 ms; there are periods lasting from less than 20 ms up to almost 1 s that are characterized by an intensity above the average. It becomes clear from the above analysis with the two-state transition model that small values of k~ are not visible in G(~-), only those values for which k 1 is in the same time range or larger than k_ ~ are visible in the fluorescence intensity correlation G(z). However, in the fluorescence intensity traces (Fig. 2) low values of k 1 are clearly seen as fluctuation between periods with two fluorescence intensity levels. Obviously, the transition rate to the EP state is fluctuating over a wider range of time scales than what can be observed only by an evaluation of the single enzyme data by FCS using model Eqs. (9) and (10). However, the value of the stretch parameter/3 is less than 0.3 for all measurements were the enzyme has been measured more than 10 s. A stretch parameter of 0.3 will make the exponential being 'stretched' over three orders of magnitude. Hence, the low values of /3 indicate that the k s rate is distributed over more than three orders of magnitude.
3.5. The fluctuating enzyme The combined analysis by FCS and the traces gives a total picture of the present findings. Clearly, there is a concentration dependent contribution to p(kl). The finding of an exponential dissociation rate for the enzyme-product complex is in line with previous measurements done for the individual A T P - A D P turnovers in myosin, where the single fluorescing ADP-myosin complex showed an exponential dissociation rate [32]. The k I rate on the other hand is widely distributed ranging over several orders of magnitude. Hence, there exists a manifold of rates to the EP state. The analysis suggests two obvious processes. First, the peroxidative cycle including the substrate binding to the enzyme, and the transition of the ES to an EP, is a process dependent on substrate concentration. Secondly, as was discussed above, the enzyme fluctuates in its catalytic activity over time ranging from ms to several s. Fast fluctuations of the EP [14] leading to spectroscopic fluctuations may also contribute. Rates for the catalytic step determined for the present enzyme by stopped flow measurements
L Edman et al./Chemical Physics 247 (1999) 11-22
[33,34] are in the same time range as the rates given for k_l in Table 1. A consequence of our analysis showing exponential kinetics for k_~ is that the off-rates for Compound I and II [33,34] are very similar. From the evaluations shown in Fig. 3A and B it is evident that a single enzyme molecule changes its character between different 10 s measurement intervals. Our data indicate that the enzyme fluctuates in activity over a wide range of time scales. However, measurements done over longer times with a given substrate concentration show rather similar values in the evaluation parameters for different enzyme molecules (Table 1, molecules 1, 2 and 3). The data therefore indicate that the difference in mean enzymatic activity as observed for different enzymes is only dependent on the observation time, ile. the observed enzymes obey the ergodic assumption. This is an interesting indication as compared to studies on conformational fluctuations in single DNA molecules where the non-ergodicity in the time scales observed is rather pronounced [19,35-38]. Previous experiments on single enzymes show differences in the activity for different molecules when measured over a very long time period as compared to one enzymatic cycle [15,16]. Here, we observe the enzyme at all time scales, thereby revealing enzymatic activity fluctuations for a single enzyme mtolecule. In a very recent paper oxidationreduction fluctuations are observed for single cholesterol oxidase molecules [39]. The lifetime of the oxidized state is distributed between different enzymes. Also, some molecules show a positive dependency on the lifetimes of consecutive oxidized states. The authors attribute the latter phenomenon to conformational fluctuations of the enzyme in a time scale of about 1 s. The measurements in [39] are indirect in the sense that the product is never observed; the oxidation of the prosthetic group is the observable. In the present single enzyme experiment, the product is directly observed as the enzyme-product complex is formed. Nevertheless, we see similarities between the present result and the result presented in [39]; static and dynamic disorder is observed for both enzymes. However, in the present experiment it is possible to resolve two processes; the peroxidative cycle and the activity fluctuations. Also, we note that for the present experiment the
21
static and the dynamic disorder are two viewpoints of the same phenomenon, i.e. dynamic disorder implies static disorder and vice versa. The analysis presented here does not reveal detailed information about the involved biochemical processes, but still gives information about the enzyme. The finding that the enzyme activity is fluctuating implies the necessity to enlarge the description of how the enzyme works. Fig. 5 gives a total model summary of the present experiments. The model has two dimensions: (a) The biochemical dimension where the catalysis of the substrate takes place. (b) The physical thermodynamic dimension where, in terms of Franenfelder's energy landscape [40], the conformational substrates (CS) of the enzyme are shown. The protein does not have a unique structure, and does not reach a unique conformation after folding, but one of a very large number of slightly different conformations [29]. Transitions between CS occur on a wide range of time scales, the system is
H202 S PF~+S\
+
r~
la ,,=
F$'-
Fg+'.
Zg÷
;?
LT
;T
. .
l l
l
[.. : sC p
s p-'5
Biochemistry Fig. 5. Grand scheme describing the total model description for the experiments. It has a biochemical dimension (horizontal) and a thermodynamic dimension (vertical) and is a consequence of the present experiment and analysis.
22
L. Edman et a L / Chemical Physics 247 (1999) 11-22
ergodic but the time scale for a single enzyme to experience all CS is large. For some states the activity is high, implying fast substrate turnovers. Other states make the enzyme not active, so the substrate turnover rate is zero. Hence, the present experiment and analysis show that conformational changes on a large number of time scales generated by thermodynamic fluctuations affect enzyme activity.
Acknowledgements
We thank Ebba Hagman and Britt Larson for excellent laboratory assistance, Lennart Wallerman for expert workshop assistance, and Anders Ehrenberg for stimulating discussions. This work was supported in part by grants from the Swedish Science Research Council as well as the Swedish National Board for Technical Development.
References [1] L. Pauling, Nature 161 (1948) 707. [2] G.E. Schulz, R.H. Schirmer, Principles of Protein Structure, Springer, New York, 1979. [3] P.G. Wolynes, J.N. Onuchic, D. Thintmalai, Science 267 (1995) 1619. [4] J.N. Onnchic, P.G. Wolynes, Z. Luthey-Schulten, N.D. Socci, Proc. Natl. Acad. Sci. USA 92 (1995) 3626. [5] K.A. Dill, K.M. Fiebig, H.S. Chart, Proc. Natl. Acad. Sci. USA 90 (1993) 1942. [6] P.E. Leopold, M. Montal, J.N. Onuchic, Proc. Natl. Acad. Sci. USA 89 (1992) 8721. [7] E.M. Boczko, C.L. Brooks III, Science 269 (1995) 393. [8] T. Pascher, J.P. Chesick, J.R. Winkler, H.B. Gray, Science 271 (1996) 1558, and references therein. [9] R.H. Austin, K.W. Beeson, L. Eisenstein, H. Franelffelder, I.C. Gunsalns, Biochemistry 14 (1975) 5355. [10] N. Alberding, S.S. Chart, L. Eistenstein, H. Frauenfelder, D. Good, I.C. Gunsalus, T.M. Nordlund, M.F. Perutz, A.H. Reynolds, L.B. Sorensen, Biochemistry 17 (1978) 43. [11] H. Gmbmiiller, P. Tavan, J. Chem. Plays. 101 (1994) 5047.
[12] J.D. Bryngelson, P.G. Wolynes, J. Phys. Chem. 93 (1989) 6902. [13] C. Careri, in: B. Korsunoglu, S.L. Mintz, S.M. Windmayer (Eds.), Quant. Stat. Mech. Nat. Sci., Plenum, New York, 1974, p. 15. [14] G. Careri, P. Fasella, E. Gratton, Crit. Rev. Biochem. 3 (1975) 141. [15] Q. Xue, E. Yeung, Nature 373 (1995) 681. [16] D.B. Craig, E. Arriaga, J.C. Wong, H. Lu, N.J. Dovichi, Anal. Chem. News Feat. 39A (1998). [17] R. Willst~itter, A. Pollinger, A. Liebigs Ann. 430 (1923) 269. [18] H. Theorell, A. ~d~esson, Ark. Kemi Min. Geol. 16A (8) (1943). [19] S. Wennmalm, L. Edman, R. Rigler, Proc. Natl. Acad. Sci. USA 94 (1997) 10641. [20] W.D. Hewson, L.P. Hager, Peroxidases, Catalases, and Chloroperoxidase, in: D. Dolphin (Ed.), The Porphyrins, Vol. VIII, Academic Press, New York, 1979, pp. 295-332. [21] J.N. Rodriguez-Lopez, A.T. Smith, R.N.F. Thomeley, J. Biol. Chem. 272 (1997) 389. [22] Z. FNdes-Papp, G. Gerber, R. Sttisser, G. Schneider, J. Prakt. Chem. 333 (1991) 293. [23] Z. FNdes-Papp, Gen. Physiol. Biophys. 11 (1992) 3. [24] R. Rigler, U. Mets, SPIE Laser Spectrosc. Biomol. 1921 (1992) 239. [25] (). Mets, R. Rigler, J. Fluoresc. 4 (1994) 259. [26] J. Dapprich, U. Mets, W. Simm, M. Eigen, R. Rigler, Exp. Tech. Phys. 46 (1995) 259. [27] S. Wennmalm, R. Rigler, J. Phys. Chem., in press. [28] D. Marquardt, J. Soc. Ind. Appl. Math. 11 (1963) 431. [29] H. Frauenfelder, in: K.L. Ngai (Ed.), Glasses and Glass Formers, Material Research Society, 1997. [30] M.F. Shlesinger, Ann. Rev. Phys. Chem. 39 (1988) 269. [31] E. Elson, D. Magde, Biopolymers 13 (1974) 1. [32] T. Funatsu, Y. Harada, M. Tokunaga, K. Salto, T. Yanagida, Nature (London) 374, 555. [33] B. Chance, J. Biol. Chem. 151 (1943) 553. [34] B. Chance, Arch. Biochem. 22 (1949) 224. [35] L. Edman, 1~. Mets, R. Rigler, Exp. Tech. Phys. 41 (1995) 157. [36] L. Edman, U. Mets, R. Rigler, Proc. Natl. Acad. Sci. USA 93 (1996) 6710. [37] L. Edman, S. Wennmalm, F. Tamsen, R. Rigler, Chem. Phys. Lett. 292 (1998) 15. [38] S. Wennmalm, L. Edman, R. Rigler, Chem. Phys., submitted for publication. [39] H.P. Lu, L. Xun, X.S. Xie, Science 282 (1998) 1877. [40] H. Franenfelder, S.G. Sligar, P.G. Wolynes, Science 254 (1991) 1598.