MINIREVIEW
Single-molecule Enzymology*
X. Sunney
Xie
and
H. Peter
Lu
From the Pacific Northwest National Laboratory, William R. Wiley
Environmental Molecular Sciences Laboratory,
Richland, Washington 99352
 |
Movies of Molecular Motions and
Chemical Reactions of Single Molecules |
Viewing a movie of an enzyme molecule made by molecular
dynamics simulation, we see incredible details of molecular motions, be
they changes of the conformation or actions during a chemical reaction.
Molecular dynamics simulations have advanced our understanding of the
dynamics of macromolecules in ways that would not be deducible from the
static crystal structures (for review see Refs. 1 and 2).
Unfortunately, these "virtual movies" do not run long enough
compared with the time scale of milliseconds to seconds in which most
enzymatic reactions take place. In recent years, rapid advances in the
patch clamp technique (for review see Ref. 3), atomic force microscopy
(4, 5), optical tweezers (6, 7), and fluorescence microscopy (for
review see Refs. 8 and 9) have permitted making single-molecule
"movies" in situ at the millisecond to second time
scale. Unlike molecular dynamics simulation, these techniques have low
time resolutions, but their single-molecule sensitivities allow probing
of slow conformational motions, which are otherwise masked in
ensemble-averaged experiments. Moreover, chemical reactions can now be
observed on a single-molecule basis. For example, enzymatic turnovers
of a few motor proteins (10-14), a nuclease (15), and a flavoenzyme (16) have been monitored optically in real time.
Our knowledge of enzyme kinetics has come primarily from experiments
conducted on large ensembles of enzyme molecules, in which
concentration changes over time are measured. In a single-molecule experiment, the concentration of the molecule being studied becomes meaningless in discussing chemical kinetics. However, this does not
negate the fundamental principles of chemical kinetics. As we shall
show, chemical kinetics can be cast in terms of single-molecule probabilities. Thinking of chemical kinetics in terms of single molecules is not only pertinent to the ever increasing single-molecule studies but is also insightful and very often more informative.
Such "single-molecule" thinking is also useful in understanding
chemistry in living cells. In a living cell, the number of enzyme
molecules in a cellular component may not be large. Under this
situation, the concentration in a small probe volume is no longer a
constant but a fluctuating quantity, as molecules react or diffuse in
and out of the probe volume. In fact, the reaction rate (and diffusion
rate) can be extracted from the analyses of concentration fluctuations
(17, 18). This approach is referred to as fluctuation correlation
spectroscopy (for review see Ref. 19) and has recently been conducted
with single-molecule sensitivity (20). A typical fluctuation
correlation spectroscopy trace, however, is averaged from a large
number of molecules diffusing one or a few at a time in and out of a
fixed probe volume. There are situations in which we need to focus on
the behavior of a single molecule. For example, DNA exists as a
"single molecule" inside a bacteria cell. The trajectory of a
DNA-enzyme complex can be tracked. In another example, a single
receptor protein at a particular spot in a membrane can be interrogated
by optical or scanning probe microscopy. Studies in a similar line have
been extensively carried out on ion channel proteins with the patch clamp technique (3).
In this minireview, we utilize our recent work on a flavoenzyme (16) to
discuss the underlying principles of single-molecule kinetics and the
information obtainable from single-molecule studies.
 |
Why Single-molecule Real-time Studies? |
What does one gain by doing single-molecule enzymatic studies? The
stochastic events of individual molecules are not observable in
conventional measurements, and the steady state concentrations of
transient intermediates are usually too low to detect. The single-molecule experiments allow direct observations of individual steps or intermediates of biochemical reactions. The trajectories of
motor proteins serve as good examples of the visualization of
individual steps (10-14). Single-molecule spectroscopy is capable of
capturing reaction intermediates.
Perhaps less obviously, single-molecule experiments allow determination
of static and dynamic disorder. Seemingly identical copies of
biomolecules often have non-identical properties. Static disorder is
the stationary heterogeneity of a property within a large ensemble of
molecules. Dynamic disorder (21) is the time-dependent
fluctuation of the property of an individual molecule. Distributions of
molecular properties of an ensemble are usually broad because of both
static and dynamic disorder. The distribution is difficult to determine
by ensemble-averaged measurements. Furthermore, ensemble-averaged
measurements cannot distinguish between static and dynamic disorders.
A recent single-molecule enzymatic assay by Xue and Yeung (22) has
revealed static disorder in enzymatic turnover rates of genetically
identical and electrophoretically pure enzyme molecules. In a capillary
tube containing a solution of highly diluted enzyme molecules (lactate
dehydrogenase) and concentrated substrate molecules (lactate and
NAD+), each enzyme molecule produced a discrete zone of
thousands of NADH molecules after 1 h of incubation. The zones
were then eluted by capillary electrophoresis and monitored by natural
fluorescence of NADH. The enzyme molecules had a broad and asymmetrical
distribution of activity, which was otherwise masked by
ensemble-averaged measurements. The heterogeneity was found to be
static at the hour time scale because the same enzyme molecule produces
the same zone intensity after another incubation period. The
microscopic origin of the static disorder observed is an interesting
subject that deserves future research. Using a similar approach, Craig
et al. (23) have studied single alkaline phosphatase
molecules and found an even broader, multipeak distribution of
activities. The static disorder in this system was attributed to
glycosylation and other post-translational modifications, which produce
non-identical copies of enzyme in this system.
Such experiments are capable of determining static disorder but not
dynamic disorder. Dynamic disorder in enzymatic turnover rates has been
observed by real time single-molecule experiments, as is discussed
below. With the separation of static and dynamic disorders, relations
between the dynamics and functions of enzyme molecules can be better
interrogated with single-molecule real-time measurements.
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Viewing Single-molecule Enzymatic Reactions by Fluorescence |
Consider the example of cholesterol oxidase, a 53-kDa flavoprotein
that catalyzes the oxidation of cholesterol by oxygen (Fig. 1). The active site of the enzyme
(E) involves a FAD, which is naturally fluorescent in its
oxidized form but not in its reduced form. The FAD is reduced by a
cholesterol molecule to FADH2 and is then oxidized by
molecular oxygen. As shown in Fig. 1, fluorescence turns on and off as
the redox state of the FAD toggles between the oxidized and reduced
states. Each on-off cycle corresponds to an enzymatic turnover. The
turnover trajectory contains detailed information about the chemical
dynamics.

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Fig. 1.
Enzymatic cycle of cholesterol
oxidase and real-time observation of enzymatic turnovers of a single
cholesterol oxidase molecule. Each on-off cycle in the emission
intensity trajectory corresponds to an enzymatic turnover.
ct, count; ch, channel.
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|
The single-molecule fluorescence measurements are carried out with an
inverted fluorescence microscope, as described elsewhere (16, 24, 30).
It is desirable to study immobilized molecules to avoid the
complications of the diffusion process. The samples are thin films of
agarose gel of 99% water. The single-enzyme molecules are confined in
the gel with no noticeable translational diffusion. In contrast, small
substrate molecules still diffuse freely. Though confined in the
polymer matrix, the enzyme molecules freely rotate within the gel,
which was evidenced by a polarization modulation experiment, as
previously described (25, 26). This means that the enzyme molecules do
not bind to the polymer matrix. Control experiments were done to ensure
that the conventional enzymatic assays gave the same results in gel and
in solution. Polyacrylamide gel, which has a smaller pore size, has
also been used to confine proteins, such as green fluorescence proteins (GFP)1 (27).
The turnover trajectories contain detailed dynamic information, which
is extractable from statistical analyses. Good statistical analyses
require long trajectories. The lengths of the trajectories are limited
by photobleaching through photochemistry on the excited state (8). We
observed a better photostability for the FAD chromophore in protein
than for dye molecules, most likely because of the protection by the
protein. Trajectories with more than 500 turnovers and 2 × 106 detected photons (detection efficiency, 10%) have been
recorded. Similar photostability has been seen for other natural
fluorophores, such as those in GFP (27). In the case of GFP, emission
of a single molecule blinks off because of photoinduced chemical
reactions. We did not observe such photoinduced blinking of cholesterol
oxidase. We have also done control experiments to make sure that
repetitive excitation/de-excitation does not perturb the enzymatic reactions.
 |
Chemical Kinetics in Terms of a Single Molecule |
Many two-substrate enzymes, such as cholesterol oxidase, follow
the ping-pong mechanism for the two-substrate binding processes, obeying the Michaelis-Menten mechanism (28).
|
(Eq. 1)
|
|
(Eq. 2)
|
The most obvious feature of the turnover trajectory in Fig. 1 is
its stochastic nature. The emission on-times and off-times correspond
to the "waiting time" for the reductive and oxidative reactions,
respectively. The simplest analysis of the trajectory is the
distribution of the on- or off-times. We limit our discussion below to
the on-time distributions although similar analyses can be done for
off-times as well.
First, take a simple case in which k2 is
rate-limiting. This situation can be created with a slowly reacting
substrate (derivative of cholesterol) and a high concentration of the
substrate. The FAD reduction reaction follows a simple kinetic
scheme.
|
(Eq. 3)
|
For this scheme, the probability density of the on-time,
, for
a single-molecule turnover trajectory is an exponential function, pon(
) = k2
exp(
k2
), with the average of the on-times
being 1/k2, the time constant of the
exponential. The exponential function follows from the fact that
Equation 3 is a Poisson process. One caveat is that this does not mean
that zero on-time has the highest probability;
pon(
) is the probability density, whereas the
probability for the on-time to be between
and 
is given by
pon(
)
, with the integrated area under
pon(
) being unity.
A simple example of a Poisson process is the case of a telephone being
turned on and off. The Poisson process corresponds to a situation in
which all phone calls are independent. This results in an exponential
probability density distribution of the lengths of the calls
(on-times). In such an analogy, our real-time experiment determines the
on-time distribution of a single phone, Yeung's experiment (22)
determines the average on-time of a single phone, and an
ensemble-averaged measurement gives the average on-time of all the
phones in the world.
Fig. 2A shows the histogram of
on-times derived from a trajectory with a cholesterol derivative of 2 mM concentration, which was fitted with a single
exponential. The inset of Fig. 2A shows the
distribution of k2 among 33 molecules examined,
reflecting the large static disorder for the activation step. However,
we did not observe static disorder for k1,
k'1, and k'2.

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Fig. 2.
A, histogram of the on-times in a
single-molecule turnover trajectory taken with a derivative of
cholesterol (see Fig. 3C, inset) at 2 mM
concentration (k2 being rate-limiting). The
solid line is a single exponential fit with
k2 = 3.9 ± 0.5 s 1. The
inset shows the distribution of k2
derived from 33 molecules in the same sample. B, histogram
of the on-times in a single-molecule turnover trajectory taken with
cholesterol at 2 mM concentration. The solid
line is the convolution of two exponentials with time
constants k1 = 33 ± 6 s 1 and
k2 = 17 ± 2 s 1.
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|
The on-time histogram (or probability density) takes a more complex
form when k2 is not rate-limiting. Assuming that
k
1 = 0 in Equation 1, the probability density
of the on-times is expected to be the convolution of the two
exponential functions (time constants of 1/k1
and 1/k2) with an exponential rise (the faster
one of k1 and k2) and an
exponential decay (the slower one of k1 and
k2) (16). Fig. 2B shows an on-time
histogram for an enzyme molecule with 2 mM cholesterol,
with the solid line being the convolution of two
exponentials. The time lag in the histogram arises from the fact that
there is an intermediate, E-FAD·S. There is no
E-FADH2 generated until the intermediate emerges. In the telephone analogy, this corresponds to the caller having to wait for an operator to connect. If there is more than one
fluorescent intermediate, the on-times are expected to have a narrower
distribution. This is discussed in detail in Ref. 29.
 |
What Is the New Information? |
So far, the analyses of on-time distributions illustrate at the
single-molecule level the validity of chemical kinetics, in particular,
the Michaelis-Menten mechanism (Equation 1). What new information can
we obtain from the trajectory analyses? Chemical kinetics holds for
Markovian processes, implying that an enzyme molecule undergoing a
turnover exhibits no memory of its preceding turnovers. Dynamic
disorder is beyond the scope of chemical kinetics. Fig. 2 does not have
a good enough signal-to-noise ratio to reveal multiexponential decay
because of dynamic disorder. Furthermore, being a scrambled histogram,
Fig. 2 is not sensitive to memory effects. What we need is a way to
examine how a particular turnover turn is affected by its previous turnovers.
We evaluated the conditional probability,
p(X,Y), for a pair of on-times
(X and Y) separated by a certain number of
turnovers. Fig. 3, A and
B, shows the two-dimensional histograms of a pair of
on-times adjacent to each other and those separated by 10 turnovers, respectively. In the absence of dynamic disorder,
p(X,Y) should be independent of the
separation of turnovers. However, Fig. 3A and Fig.
3B are clearly different. For the separation of 10 turnovers (Fig. 3B), the loss of memory leads to
p(X,Y) = p(X)p(Y), where p(X) and p(Y) are the same
as in Fig. 3A. For pairs of adjacent on-times (Fig.
3A), there is a diagonal feature, indicating that a short
on-time tends to be followed by another short on-time, and a long
on-time tends to be followed by another long on-time. This means that
an enzymatic turnover is not independent of its previous turnovers. The
memory effect arises from a slowly varying rate
(k2). Coming back to the telephone analogy, this
corresponds to the average lengths of phone calls varying over the
course of a day.

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Fig. 3.
A, two-dimensional histogram of pairs of
on-times (X, Y) adjacent to each other. The
scales of X and Y are from 0 to 1 s. The diagonal
feature indicates a memory effect. B, two-dimensional
histogram of pairs of on-times separated by 10 turnovers. The on-times
that are 10 turnovers apart become independent as the memory is lost.
C, autocorrelation function of the on-times for a turnover
trajectory, r(m) = < (0) (m)>/< 2>, where
m is the index number of the turnovers and
 (m) = (m) < >. The fact that
r(m) is not a spike at m = 0 indicates dynamic disorder. The time constant of the decay gives the
time scale of the k2 fluctuation. The
inset shows the structure of the substrate used, which is a
derivative of cholesterol.
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|
Although the two-dimensional conditional probability plot provides a
clear visual illustration, it needs to be constructed of a large number
of turnovers of many molecules. A more practical and quantitative way
to evaluate the dynamic disorder is the autocorrelation function of the
on-times, r(m) = <
(0)
(m)>/<
2>, where
m is an index number for the turnovers in a trajectory and

(m) =
(m)
<
> and where the
bracket denotes the average along the trajectory. The physical meaning
of r(m) is as follows. In the absence of dynamic
disorder, r(0) = 1 and r(m) = 0 (m > 0). In the presence of dynamic disorder,
r(m) decays, with the initial (m = 1) amplitude reflecting the variance of k2 and
the decay time yielding the time scale of the k2
fluctuation. Fig. 3C shows the r(m)
derived from a single-molecule trajectory, with the decay constant
being 1.6 ± 0.5 turnovers.
We attribute the dynamic disorder behavior to a slow fluctuation of
protein conformation, which was independently observed by spontaneous
spectral fluctuation of FAD (16, 30) on the same time scale of
k2 fluctuation. Slow conformational fluctuations on a similar time scale have been observed on other systems with single-molecule experiments (4, 31-34). The simplest model we proposed
involved (at least) two slowly converting conformational states
(E and E').
The dynamic disorder of k2 for the
Michaelis-Menten mechanism (Equation 2) can be accounted for by the
more complicated kinetics scheme (Scheme 1) with time-independent rates
k21 and k22. A simulation of r(m) based on this kinetic scheme, assuming
that kE/kE' = 1 and
k21/k22 = 5, matches the
observed
r(m).2
In summary, although the Michaelis-Menten mechanism provides a good
description for the averaged behaviors of many molecules and for the
averaged behaviors of many turnovers of a single molecule, it does not
provide an accurate picture of the real-time behavior of a single
molecule. On a single molecule basis, the rate for the activation step
is fluctuating, and this is a not a small effect!
 |
Open Questions |
The influence of conformational dynamics on protein functions has
been a subject of extensive studies (36-43). Our observations have
revealed the slow conformational motions that influence the enzymatic
functions. However, we still need to understand the microscopic origin
of the slow conformational change of cholesterol oxidase, which has a
relatively large activation barrier between the two conformational
states. Although the two-state model suffices to account for the
fluctuation of k2 and the spectral mean in our
initial study, there can be more than two conformational states, or
even a continuous distribution of conformational states, each with a
distinctly different k2. Our observations
confirm that conformational transitions take place among metastable
states in the energy landscape (44). Simulations based on the two-state model and the continuous-state (45, 46) model give a similar r(m).2 Further experiments are needed
to probe the distribution of conformational states, the distribution of
rates, and their correlation.
The physiological relevance of the phenomenon is of particular
interest. Similar slow conformational changes have been inferred from
other monomeric enzyme systems, which were believed to be associated
with physiological enzymatic regulation (47-49). Interestingly, an
ensemble-averaged enzymatic measurement of cholesterol oxides has
revealed a sigmoid dependence of the enzymatic rate on the substrate
concentration (50). Our simulation showed that the proposed mechanism
in Scheme 1 might account for this sigmoidal behavior. The implication
of this finding on the behavior of the monomeric enzyme is intriguing.
Not assumed in Scheme 1 is the possibility of conformational changes
induced by substrate binding and/or the redox reactions, which can
either lead to new conformational states or shift the equilibrium
between the existing conformational states (47-49). Conformational
changes associated with the "induced fit" have been illustrated
(51). At this point, our single-molecule experiments have not yet
detected the induced conformational changes. A study of
cross-correlations between simultaneous spectral and turnover trajectories is under way to investigate this possibility.
 |
In the Future |
Thinking of chemical kinetics in terms of single molecules is
becoming a necessity as new tools of microscopy allow investigations of
the dynamics of individual molecules. We have shown that statistical analyses of turnover trajectories of single-enzyme molecules can unequivocally reveal detailed mechanistic information hidden in ensemble-averaged measurements. The analyses described here will be
generally useful for other enzymatic systems. New single-molecule, in vitro enzymatic assays will be developed. Biochemical
reactions, such as gene expression (35) and cell signaling, can be
observed under physiological conditions. Single-molecule real-time
enzymology will allow investigation of molecular and cellular dynamics
at a level of great detail.
 |
ACKNOWLEDGEMENTS |
We thank Luying Xun and Greg Schenter for
fruitful collaborations, and Carey Johnson for critical reading of the manuscript.
 |
FOOTNOTES |
*
This minireview will be reprinted
in the 1999 Minireview Compendium, which
will be available in December, 1999. This is the third article of four in the
"Biochemistry at the Single-molecule Level Minireview Series." This
work was supported by the Chemical Sciences Division of the Office of
Basic Energy Sciences and the Office of Biological and Environmental
Research within the Office of Science of the United States Department
of Energy (DOE). Pacific Northwest National Laboratory is operated for
DOE by Battelle Memorial Institute.
To whom correspondence should be addressed: Dept. of Chemistry and
Chemical Biology, Harvard University, 12 Oxford St., Cambridge, MA
02138. Tel.: 617-496-9925; Fax: 617-495-1792; E-mail:
xie{at}chemistry.harvard.edu.
2
G. Schenter, H. P. Lu, and X. S. Xie,
manuscript in preparation.
 |
ABBREVIATIONS |
The abbreviation used is:
GFP, green
fluorescence proteins.
 |
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