The heat released during catalytic turnover enhances the
diffusion of an enzyme
Clement Riedel
1
, Ronen Gabizon
1
, Christian A. M. Wilson
1,2
, Kambiz Hamadani
1,†
,
Konstantinos Tsekouras
3
, Susan Marqusee
1,4
, Steve Pressé
3,5
, and Carlos
Bustamante
1,4,6,7,8,9
1
California Institute for Quantitative Biosciences, QB3, University of California, Berkeley,
California 94720, USA
2
Departamento de Bioquímica y Biología Molecular, Facultad de Ciencias Químicas y
Farmacéuticas, Universidad de Chile, 1058 Santiago, Chile
3
Department of Physics, Indiana University-Purdue University Indianapolis (IUPUI), Indiana
46202, USA
4
Department of Molecular and Cell Biology, University of California, Berkeley, California 94720,
USA
5
Department of Cellular and Integrative Physiology, Indiana University School of Medicine,
Indiana 46202, USA
6
Jason L. Choy Laboratory of Single-Molecule Biophysics and Department of Physics, University
of California, Berkeley, California 94720, USA
7
Department of Chemistry, University of California, Berkeley, California 94720, USA
8
Howard Hughes Medical Institute, University of California, Berkeley, California 94720, USA
9
Kavli Energy Nano Sciences Institute, University of California, Berkeley and Lawrence Berkeley
National Laboratory, California 94720, USA
Abstract
Recent studies have shown that the diffusivity of enzymes increases in a substrate-dependent
manner during catalysis
1,2
. Although this observation has been reported and characterized for
©2015 Macmillan Publishers Limited. All rights reserved
Reprints and permissions information is available at www.nature.com/reprints
Correspondence and requests for materials should be addressed to: S.P (stevenpresse@gmail.com) or C.B.
(carlosjbustamante@gmail.com).
2
Present address: Department of Chemistry and Biochemistry, California State University San Marcos, California 92078, USA.
Supplementary Information is available in the online version of the paper.
Author Contributions C.R. performed fluorescence correlation spectroscopy (FCS) measurements, assisted in most experiments and
was the primary writer of the manuscript. R.G. and C.A.M.W. ran most bulk biochemistry experiments; K.H. built the FCS setup and
assisted in the FCS experiments; S.M. gave direction to the project. S.P. supervised the research and S.P. and K.T. developed the
theory. Finally C.B. conceived the project, and supervised all of the research. All authors participated in the writing and editing of the
manuscript.
The authors declare no competing financial interests.
Readers are welcome to comment on the online version of the paper.
HHS Public Access
Author manuscript
Nature. Author manuscript; available in PMC 2015 March 17.
Published in final edited form as:
Nature. 2015 January 8; 517(7533): 227–230. doi:10.1038/nature14043.
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several different systems
3–10
, the precise origin of this phenomenon is unknown. Calorimetric
methods are often used to determine enthalpies from enzyme-catalysed reactions and can therefore
provide important insight into their reaction mechanisms
11,12
. The ensemble averages involved in
traditional bulk calorimetry cannot probe the transient effects that the energy exchanged in a
reaction may have on the catalyst. Here we obtain single-molecule fluorescence correlation
spectroscopy data and analyse them within the framework of a stochastic theory to demonstrate a
mechanistic link between the enhanced diffusion of a single enzyme molecule and the heat
released in the reaction. We propose that the heat released during catalysis generates an
asymmetric pressure wave that results in a differential stress at the protein–solvent interface that
transiently displaces the centre-of-mass of the enzyme (chemoacoustic effect). This novel
perspective on how enzymes respond to the energy released during catalysis suggests a possible
effect of the heat of reaction on the structural integrity and internal degrees of freedom of the
enzyme.
Externally induced temperature spikes—through the use of laser pulses, for example—can
have dramatic effects on enzyme catalysis and protein conformations
13
. Thus, pyramine and
green fluorescent protein have been shown to blink with characteristic frequencies when
excited with a laser. Some authors
14,15
have related this blinking to local temperature and
pH changes. Yet, no equivalent effect has been attributed to the heat exchanged in an
enzyme-catalysed reaction despite the fact that some enzymes, like catalase, release enough
heat to unfold a protein
16
.
Fluorescence correlation spectroscopy (FCS) results obtained in experiments similar to those
presented here
1,2
have demonstrated that the diffusion coefficient (D) of urease increases in
the presence of its substrate
1
. These authors explored various potential mechanisms that
might account for this enhanced diffusion, including global temperature increase of the
solution, charged product induced electrophoresis, and pH changes around the enzyme
immediately following catalysis. Recently, the same group has shown that the diffusion
coefficient of catalase, which mediates the conversion of hydrogen peroxide into water and
oxygen, also increases in a substrate-dependent manner
2
, ruling out charge or pH as a
general explanation. They have also ruled out global or local temperature changes of the
solution to explain the enhanced enzyme diffusion phenomenon
1
. More recently, these
authors have proposed that the enzyme diffusion coefficient increase arises from chemo-
tactic behaviour in which the enzyme preferentially diffuses towards higher substrate
gradients, although they provided no mechanism by which this may occur
2
.
Here we performed a series of experiments and carried out a number of crucial controls to
show that when enzymes catalyse reactions, the heat released in the process is responsible
for accelerating the protein’s centre-of-mass, giving rise to the enhanced diffusion
coefficient observed by FCS. We present a stochastic theory that predicts the linear
dependence observed between the diffusion coefficient (measured by FCS) and the reaction
rate V (measured by bulk enzymatic assays), and demonstrate that the coefficient of
proportionality depends linearly on the enthalpy released by a single chemical reaction.
We studied four enzymes: catalase, urease, alkaline phosphatase and triose phosphate
isomerase (TIM) (see Supplementary Information for more details on the enzymes). The
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rates of reaction catalysed by these enzymes and normalized by theenzyme concentration,
were determined as a function of the substrate concentrations, V([S]), using bulk enzymatic
assays (Extended Data Fig. 1). All enzymes followed Michaelis–Menten kinetics with k
cat
and K
M
values in agreement with those previously reported in the literature
17–20
(Table 1).
FCS experiments of the fluorescently labelled enzymes were carried out in parallel to bulk
assays to generate fluorescence intensity correlation functions, G(
τ
), as a function of
substrate concentrations and initial velocities using previously described protocols for
monitoring each enzymatic activity
12,13
. These correlation functions were fit by the normal
diffusion of a single species in a dilute solution to obtain the diffusion time (
τ
D
) and
molecular occupancy of the labelled molecules within the confocal volume of observation
21
(see Methods). Measurements were performed at a protein concentration of 1 nM for all
enzymes. The FCS curves are shown in Fig. 1. The diffusion coefficient D can be calculated
from the diffusion time
τ
D
using the radius, r, of the illuminated circular area crossed by the
molecules according to: D =r
2
/4
τ
D
. The radius r was determined to be 500 nm by
monitoring the diffusion of a free dye with a known diffusion coefficient through the
illuminated area. Using the bulk assays to relate the substrate concentration to the enzyme’s
specific activity, we find a linear dependence between the normalized relative increase in
diffusion coefficient, (D − D
0
)/D
0
, and the reaction rate for the enzyme systems (Fig. 2a–d).
To confirm that the observed increase in diffusion coefficient is a result of the chemical
reaction itself and not simply due to the binding or unbinding of the substrate, we performed
control experiments with catalase using its non-competitive reversible inhibitor, sodium
azide. FCS measurements were repeated for catalase in the presence of 5 mM sodium azide
and a high concentration of substrate (25 mM hydrogen peroxide). Under these conditions,
the enzyme is known to associate with and dissociate from the substrate without forming
any product
17
. In the presence of inhibitor, we observe no increase in the diffusion
coefficient relative to the measurements performed in the absence of substrate, indicating
that the enhanced diffusion of catalase depends on the enzymatic reaction taking place and
not just on the association or dissociation of the substrate to the enzyme.
To rule out other potential indirect effects on the apparent diffusion coefficient of the
labelled diffusing enzymes (such as convective flows owing to oxygen bubbling, as in the
case of catalase), we carried out experiments in which non-labelled, catalytically active
catalase, in the presence of its substrate, was mixed with fluorescently labelled urease in the
absence of its substrate. Increased diffusion of the labelled urease molecules was observed
only under conditions when the concentration of hydrogen peroxide was greater than 100
mM and catalase concentration was above 5 nM. These results show that, below these
concentrations, neither oxygen bubbling, nor global heating of the solution owing to the heat
released by other molecules in the reaction, are responsible for the enhanced diffusion of
enzymes observed in the presence of their substrate. Accordingly, all the results analysed
here were obtained below these concentrations to ensure that only first-order, direct effects
were being monitored (see Extended Data Fig. 3 for more details). Local heating of the
solvent around the enzyme following a turnover event can also be eliminated because
assuming the reaction heat is moved into a 1 nm thick spherical shell surrounding catalase,
which we assume to be a 4 nm radius spherical molecule, and using water’s heat capacity,
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the local temperature of this shell would only increase by 0.15 K (see Supplementary
Information).
Catalase, urease and alkaline phosphatase, which exhibit enhanced diffusion in the presence
of their substrate (Fig. 2a–c), catalyse chemical reactions that are strongly exothermic
(above 40 kJ mol
−1
). Thus, we wondered whether the effect of the heat of the reaction on the
enzyme itself could be responsible for the increased in diffusion coefficient observed upon
catalysis. To test this idea we performed a negative control with triose phosphate isomerase
(TIM). If the heat of the reaction is responsible for the increase in the diffusion coefficient
observed, it follows that no such effect should be seen if the reaction is not exothermic or if
it is only slightly so. TIM catalyses the reversible interconversion of the triose phosphate
isomers dihydroxyacetone phosphate and D-glyceraldehyde 3-phosphate. The enthalpy of
this reaction is small (−3 kJ mol
−1
; ref. 22). Consistent with the hypothesis formulated here,
FCS experiments with TIM and diffusion coefficient analysis revealed no enhancement in
the diffusion of the enzyme in the presence of its substrate throughout the range of substrate
concentrations studied here (0 to 1.2 mM of D-glyceraldehyde 3-phosphate corresponding to
reaction rates ranging from 0 to ~6,000 s
−1
) (Fig. 2d). Table 1 summarizes thermodynamic
and kinetic parameters of each enzyme investigated.
On the basis of these observations, we propose that the increase in diffusion coefficient of
the enzyme upon catalysis has its origin in an effect similar to that observed in photoacoustic
spectroscopy. Here a vibrationally excited protein relaxes by dissipating its energy into the
solvent through acoustic waves that are generated from the transient expansion and
recompression of the protein immediately following excitation that can be detected by a
microphone
23
. Likewise, we propose that an enzyme expands, albeit asymmetrically,
following the release of the heat of reaction (a process we call ‘chemoacoustic effect’). The
asymmetry is due to the location of the catalytic site with respect to the enzyme’s centre-of-
mass, as is the case in urease, catalase and alkaline phosphatase. The asymmetric pressure
wave—following a catalytic event—should result in differential stress at the protein–solvent
interface. The solvent’s response is twofold: it dissipates energy through an acoustic wave
and, more importantly, pushes back on the enzyme as dictated by Newton’s third law,
transiently displacing its centre-of-mass. In the Supplementary Material we compute an
upper bound on the pressure exerted by the expanding protein on the solvent (about 500 pN
nm
−2
).
To validate this interpretation, we performed experiments in which we directly excited the
catalase haem group using a laser line at 402 nm (the Soret band of catalase is centred at 405
nm (ref. 24) and this transition possesses a fluorescence quantum yield Q <10
−5
)
25
. In these
experiments we sought to determine if the heat released upon radiationless de-excitation of
the enzyme could also lead to an increased diffusion coefficient of the catalyst. Indeed, an
increase of about 50% in the diffusion coefficient of the enzyme in the range of power
between 0 and 1 mW was observed in these experiments (Extended Data Fig. 4), indicating
that the local heat released by the haem in its transition from the excited to the ground state
also generates a centre-of-mass motion of the enzyme (see Supplementary Discussion).
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A stochastic model (detailed in the Supplementary Information and Extended Data Figs 6, 7
and 8) describes the enhanced diffusion upon catalysis in terms of the heat released by the
chemical reaction. In this model, we assume that enzymes transiently diffuse more quickly
—with diffusion coefficient D
1
—for some short period of time, δt, following a chemical
reaction. Otherwise, the enzyme displays its diffusion coefficient in the absence of substrate,
D
0
. The net diffusion coefficient in the presence of substrate, D, is therefore the ensemble
average over both subpopulations with the probability of observing an enhanced diffusion
proportional to V, the reaction rate. We then relate the enhanced diffusion coefficient, D
1
, to
the amount of heat, Q, evolved by an enzymatic reaction. To do so, we assume that the
kinetic energy of the enzyme’s centre-of-mass immediately following a reaction is
proportional to some fraction
γ
of Q. From this simple model, we obtain the following
expression
which shows a diffusion coefficient enhancement linear in V and Q, where m is the mass of
the enzyme, δt =m/
ζ
is the relaxation timescale associated with the enzyme displacement
following an enzymatic turnover, and
ζ
is an effective friction coefficient for the enzyme
(see Supplementary Materials).
The parameter
α
describes the proportionality between the diffusion coefficient and the rate
of the reaction.
α
itself depends on
γ
, the proportion of catalytic heat contributing to the
enhanced translation of the centre-of-mass of the enzyme. As the protein’s structure may
dictate the precise mechanism by which enzymes dissipate catalytic heat, there is no simple
correlation between the enhanced diffusion quantified by α and the enthalpy of the chemical
reaction (see Table 1). For instance, the active sites of urease (two nickel atoms, see
Extended Data Fig. 5a) are situated at the protein–solvent interface. By contrast, the haem
sites of catalase (Extended Data Fig. 5b) are buried deep inside a highly conserved structure
situated more than 20 Å from the nearest molecular surface
26
. Accordingly, the heat
released during catalysis may partition differently between the centre-of-mass and the
internal degrees of freedom in these two proteins. In fact, time-resolved crystallography
coupled with single-crystal microspectroscopy has been used to measure the correlation of
electronic transitions with structural transitions during catalysis in catalase from Proteus
mirabilis. This study indicates that the catalytic event is accompanied by small structural
changes of the enzyme
27
. It is possible that for catalase, part of the heat released during the
chemical reaction is either absorbed by changes in the enzyme’s conformation and/or
dissipated through the protein’s internal degrees of freedom, reducing its effect on the
displacement of its centre-of-mass. Future simulations and experiments with different
systems may shed light on the structural basis for energy dissipation and the partitioning of
the heat of the reaction between the centre-of-mass and the internal degrees of freedom of
the enzyme.
Here we considered catalytic reactions by globular proteins with freely diffusing substrates.
However, many processive molecular machines (for example DNA polymerases, RNA
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