METHODS 19, 306 –321 (1999)
Article ID meth.1999.0858, available online at http://www.idealibrary.com on
Substrate Channeling 1
H. Olin Spivey* ,2 and Judit Ovádi†
*Department of Biochemistry and Molecular Biology, 246 NRC, Oklahoma State University, Stillwater,
Oklahoma, 74078 –3035; and †Institute of Enzymology, Biological Research Center,
Hungarian Academy of Sciences, Budapest, H-1518, P.O.B. 7, Hungary
Substrate channeling is the process in which the intermediate
produced by one enzyme is transferred to the next enzyme without complete mixing with the bulk phase. This process is equivalent to a microcompartmentation of the intermediate, although
classic diffusion occurs simultaneously to varying extents in many
of these cases. This microcompartmentation and other factors of
channeling provide many potential biological advantages. Extensive examples of channeling can be found in the cited reviews.
The choice of methods to detect and characterize substrate channeling depends extensively on the type of enzyme associations
involved, the constants of the system, and, to some extent, the
mechanism of channeling. Thus it is important to distinguish
stable, dynamic, and catalytically induced enzyme associations as
well as recognize different mechanisms of substrate channeling.
We discuss the principles, experimental details, and limitations
and precautions of five rather general methods. These use measurements of transient times, isotope dilution or enhancement,
competing reaction effects, enzyme buffering kinetics, and
transient-state kinetics. These encompass methods applicable to
studies in vitro, in situ, and in vivo. None of these methods is
applicable to all systems. They are also susceptible to artifacts
without proper attention to precautions. Transient-state kinetic
methods clearly excel in elucidating molecular mechanisms of
channeling. However, they are often not the best method for
initial detection and characterization of the process and they are
not applicable to many complex systems. Several other methods
that have been successful in indicating substrate channeling are
briefly described. © 1999 Academic Press
1
Approved for publication by the Director, Oklahoma Agricultural
Experimental Station (OAES). This research was supported in part
by NSF Grants MCB-9513613 and BIR-9512912, Oklahoma Center
for Advancement of Science and Technology (OCAST) Grant HR98061, and OAES Project OKLO-1393 to H.O.S., and grants from the
Hungarian National Science Foundation,OTKA-25291, European
Commission Grant INCO-COPERNICUS (ERBIS 15CT960307),
MKM-FKFP 158/97, and 1023/97 to J.O.
2
To whom correspondence should be addressed. Fax: (405) 7447799. E-mail: ospivey@Biochem.Okstate.Edu.
306
The term “substrate channeling” designates the coupling of two or more enzymatic reactions in which the
common intermediate (I) is transferred from the first
enzyme (E 1) to the second (E 2) without escaping into
the bulk phase. The simplest of such coupled reactions
is shown in Scheme 1. The substrate S is converted to
product P via an intermediate I. Substrate channeling
has been well documented in vitro, in situ, and in vivo,
and with enzymes from prokaryotic and eukaryotic
plants and animals [for recent reviews see (1, 2)]. The
potential advantages of substrate channeling are more
numerous than normally considered. Most of these consequences result from the microcompartmentation of
metabolites that is inherent in this mechanism. These
potential advantages include: (1) isolating intermediates from competing reactions; (2) circumventing unfavorable equilibria and kinetics imposed by bulkphase metabolite concentrations (3, 4); (3) protecting
unstable intermediates (5); (4) conserving the scarce
solvation capacity of the cell (6); (5) enhancing catalysis by avoiding unfavorable energetics of desolvating
substrates (7); (6) reducing lag transients (times to
reach steady-state response to a change in substrate
concentration upstream in a coupled reaction path) (8,
9); and (7) providing new means of metabolic regulation by modulation of enzyme associations, e.g., as
shown in (10), and increased sensitivities to regulatory
signals (11). Thus, studies of substrate channeling are
essential for a better understanding of metabolism.
Substrate channeling defined operationally as above
(intermediate transferred between enzymes without
escaping into the bulk phase) can be achieved by several different molecular factors or mechanisms. In fact,
many of the examples of substrate channeling probably
involve a combination of the basic (elementary) molecular mechanisms, some of which may not be understood or even documented at this time. Therefore, we
will avoid a strict definition of mechanisms. However,
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SUBSTRATE CHANNELING
the method of detecting and characterizing substrate
channeling for an enzyme pair or larger metabolon (12)
depends strongly on the nature of the interaction of the
enzymes and significantly on the nature by which the
intermediate is transferred. Thus, we need to recognize
and distinguish among the following processes with
which substrate channeling can occur. The best known
of these channeling processes transfers covalently attached intermediates from one subunit to another
within a stable multisubunit enzyme complex. The oxidative decarboxylation of a-keto acids by pyruvate and
a-ketoglutarate dehydrogenase complexes is an example of this general mechanism. We do not discuss methods for characterizing this type of channeling. Channeling of substrates is also now well known for the
stable ab complex tryptophan synthase, in which the
indole intermediate travels through an internal channel within the enzyme (13). The active sites are 25–30
Å apart, but connected by a molecular tunnel that
impedes the escape of indole, which otherwise could
escape from the cell since it is an uncharged molecule.
On the other hand, just the close proximity of active
sites of two enzymes can provide a substantial channeling in addition to the random diffusion path. This is
exemplified by enzymes coimmobilized (statically or
dynamically) on or in a phase separate from the bulk
aqueous phase (14). In principle proximity of active
sites might be sufficient for channeling between the
sites on soluble multifunctional enzymes, though it is
likely that local interactions are also important in retaining at least a portion of the intermediates from
escaping into the bulk phase. A specific example of
such a process is electrostatic channeling, which uses
the favorable electrostatic field between adjacent enzyme sites to constrain a significant fraction of the
intermediate within the channeling path. This occurs
although the active sites are 40 to 60 Å apart. Brownian dynamic simulations demonstrate that this is
much too far apart for channeling by random diffusion
mechanisms alone. The correlation of experimental
(15) and theoretical (16) studies has established this
mechanism especially well. Another process of channeling occurs when the active sites of two enzymes are
transiently brought into contact with each other, forming an enclosure that permits direct transfer of the
intermediate and sterically prevents its escape into the
bulk phase. We believe that NADH channeling between dehydrogenases of opposite chiral specificity for
the C-4 hydrogen of NADH is an example of this type
(17, 18). The fact that this channeling has never been
observed between enzymes of the same chiral specific-
SCHEME 1
307
ity forces one to conclude that the NADH does not
escape into the bulk phase where its rotation between
syn and anti conformations would destroy this chiral
specficity in less than a nanosecond.
An aspect of great importance in dictating the methods needed for studying substrate channeling is the
nature of interaction between the enzyme active sites.
Three classes of interactions need to be considered: (1)
static (sometimes called stable) complexes, (2) dynamic
(sometimes called transient) complexes, and (3) catalytically induced enzyme associations. In contrast to
dynamic complexes, the extent of complex formation
for static complexes is independent of the enzyme concentrations, at least in the range and conditions of
study. Least well known are what we shall call catalytically induced enzyme–macromolecule associations.
These are characterized by enzymes (E 2) that exhibit
no detectable association with their cognate enzyme
(E 1) or protein in the absence of the catalytic reaction. Nevertheless, E 2 associates with E 1 (or E 1–
intermediate complex) or a protein as an obligatory
part of its catalytic cycle. The case where E 1–
intermediate (E 1–I, e.g., E 1–NADH), forms an E 1–I–E 2
complex is equivalent to E 1–I being a substrate of E 2.
We know of seven well-documented systems involving
either an E 1–I–E 2 or enzyme–protein complex during
the catalytic reaction, where, in each case, all attempts
to demonstrate an E 1–E 2, an E 1–I–E 2, or a protein–E 2
complex in the absence of the catalytic reaction have
failed (5, and references therein, 19). The last two of
these seven cases are the acyl-CoA dehydrogenase (a
flavoprotein) with the electron tranferring flavoprotein
(D. K. Srivastava, personal communication) and several dehydrogenases that channel NADH efficiently,
but do not associate at any level of NADH (H. O. Spivey
et al., unpublished results). All seven of these systems
involve enzymes of very different nature. For many if
not all of these seven cases, saturation of the kinetic
response falls within the micromolar range. An equilibrium complex with this dissociation constant would
be nearly completely associated with 1 mg/ml of enzymes and would be very easy to detect by many physical methods. Such catalytically induced enzyme associations are very similar to binding of the second
substrate to an enzyme following a compulsory ordered
two-substrate mechanism. That is, no association of
the second substrate to the enzyme is detectable in the
absence of the reaction. Also the equilibrium dissociation constant has little affect on the K m of the first
substrate in a ping–pong mechanism, in sharp contrast
to an ordered mechanism (20, p. 143). Knowing these
facts should make the catalytically induced enzyme
associations easier to accept. We have chosen the word
“induced” (associations) rather than “enhanced” to emphasize the fact that enzyme associations in the absence of the catalytic reaction are not experimentally
308
SPIVEY AND OVÁDI
detectable. However, the word induced is not meant to
preclude small (as yet undetected) extents of association that become greatly enhanced in the catalytic reaction. Thus catalytically induced associations may be
considered an extreme example of enzyme associations
that are detectable in the absence of the catalytic reaction. This alerts us to the very likely possibility that
a catalytic reaction may well alter the extents of the
associations between enzymes known to be in dynamic
equilibrium, a fact of considerable importance in testing for substrate channeling as we will see.
In summary, several different general mechanisms
are involved in substrate channeling—first in the manner by which the enzymes interact with each other and
second in the mechanisms providing the channeling
once the enzymes associate. In addition, the fraction of
the reaction flux going by the channeled path is virtually 100% for some of the channeling processes, but
significantly less for others. The latter are called “leaky
channels.”
It is important to know these different processes
since the choice of methods for detecting and characterizing substrate channeling depend to a considerable
extent on the types of processes involved. The success
of a method also depends heavily on the kinetic and
equilibrium constants of the enzymes and the conditions of the experiments. Therefore, the best method is
very dependent on the system under study; there is no
single best method for all systems. Also there are optimal conditions for use of each method, which most
often depend on the system constants. We discuss five,
more or less general methods in detail: transient-time
analysis, isotope dilution or enhancement, competing
reaction, enzyme buffering, and, more briefly,
transient-state kinetics. A few other methods are mentioned at the end. The relative length of these sections
is dictated by how many details were considered important to mention and does not reflect the relative
value of a method.
under the following conditions or approximations
thereto: (1) the reactions are irreversible, (2) the rate of
the first reaction is constant over the period recorded,
(3) the steady-state concentration of the intermediate
[I] ss ! K m2, the K m of the coupling enzyme E 2, and (4)
the amount of intermediate bound to the coupling enzyme [E 2–I] is a small fraction of the total intermediate
concentration ([I] t 5 [I] 1 [E 2–I]). With these conditions, the rate constant k of the transient phase is the
apparent first order rate constant of E 2, i.e.,
k ; 1/ t 5 k 2 @E2 #/K m2 5 V 2 /K m2,
[3]
where t is the lag-time for product formation, K m2 and
V 2 are the Michaelis constant and limiting velocity of
E 2, respectively, and k 2 is the k cat of E 2. The steadystate equations corresponding to Eqs. [1] and [2] are,
therefore,
@P# ss 5 v 1 ~t 2 t !
and
@I# ss 5 v 1 t 5 v 1 K m2/V 2 ,
@4#
which shows that the line representing the steadystate part of the progress curve has intercepts of t and
2[I] ss on the time and [P] axes, respectively (22) (Fig.
1). Equation [3] shows that 1/t is linear with [E 2] for
nonassociating enzymes. Physically, the lag time for
reactions catalyzed by unassociated enzymes is the
time for [I] to increase to 1/e of [I] ss. The rate of the
second reaction will increase during the transient state
until [I] 5 [I] ss. The first two conditions (irreversible
reactions and constant v 1 ) are often well approximated
(especially in vitro) by limiting the record to the initial
velocity periods of E 1 and E 2, using sufficiently high
substrate conditions and using high [E 2] to minimize
the reverse reaction of E 1. However, E 1 enzymes with
very unfavorable equilibria fail condition 1 and need
special treatment (23) as discussed below. Condition 3
METHODS
Transient-Time Analysis
Principles
For the coupled reactions of Scheme 1, where the
first reaction proceeds with constant velocity v 1 , the
“progress curves,” i.e., time course of formation of P
and I, can be represented by (21)
P~t! 5 v 1 t 2
@I# 5
v1
~1 2 e 2kt !,
k
v1
~1 2 e 2kt !,
k
[1]
[2]
FIG. 1. Transient in coupled enzymatic reactions. Product P versus
time showing transient time t 5 10 s and steady-state concentration
of I, [I] ss 5 5 mM.
SUBSTRATE CHANNELING
(“first-order kinetics”) can also frequently be achieved
by using sufficiently high [E 2]. Condition 4 (avoiding
significant fractions of enzyme-bound I) can often be
achieved in vitro, but is frequently not valid in vivo.
Also, increasing [E 2] to improve conditions 1 and 3 can
create a violation of condition 4 ([I] ' [I] t) as well as
raise some practical problems discussed under Other
Limitations and Precautions below. Fortunately, even
without meeting the above conditions, appropriately
modified equations exist for predicting correct transient times. Analytical expressions exist for most of
these more complex conditions. However, the most general cases require numerical integration of the model
kinetic and conservation equations.
Lack of first-order kinetics is easily accommodated if
V 2 . v 1 (8, 24), giving
t 5 K m2/~V 2 2 v 1 !
[5]
@I# ss 5 v 1 K m2/~V 2 2 v 1 !.
[6]
and
Easterby shows that for V 2 /v 1 . 2, the first-order
kinetic approximation is adequate, but rapidly loses
accuracy at lower ratios (8). By focusing on the intermediate rather than the enzyme, Easterby’s expressions are simpler and valid for more complex conditions (8, 25). This formulation also offers the
advantages that integration of rate laws is often not
required, and the transient times can be associated
with separate physical processes. This approach also
provides instructive insights into some general principles. For example, the overall transient time of a sequence of several reactions is the sum of the transient
times for each step. These steps include: (a) the transient time to reach the steady state in enzyme forms
(free and substrate/product forms of each enzyme), (b)
the sum of transient times for each intermediate concentration [I j], and (c) transient time for “feedback” on
the pathway (25). The last step allows for variation in
the rate of v 1 and includes reversal of the first reaction.
The transient times of enzyme forms are typically a
few milliseconds or less, whereas transient times of [I j]
for most of the applications we discuss in this section
are several seconds. Thus for this section, we can ignore the transient times in enzyme forms. The independent extensions of the transition-time analysis of
Elcock et al. (16) are referenced here and are discussed
further under Experimental Details. Neither Easterby
nor Elcock et al. have provided explicit solutions to two
additional conditions that are sometimes encountered
although Easterby’s general formulations are applicable. The first is the condition where significant fractions of I are bound to E 2 (the enzyme usually in excess
over E 1). Several authors have provided solutions to
309
this condition [see references in (23)]. The second condition that is sometimes encountered is one where the
first enzyme in the sequence has a very unfavorable
equilibrium—the overall reaction proceeds extensively
only because of the still more favorable DG of the
second enzyme reaction. Yang and Schulz (23) found
that their system required this consideration and they
provided equations for a two-enzyme sequence to deal
with this condition as well as all other conditions 1– 4
enumerated above. Though analytic solutions exist for
certain limited conditions, the general solution requires numerical integration.
We strongly recommend numerical integration of the
model equations whenever there is any doubt about the
validity of simpler expressions. An attractive alternative to integrating the quite complex equations of Yang
et al. (23, 26) is to use one of the several simulation
programs. The easiest of these allows the user to specify the reactions in normal chemical symbols. An editor
program translates these reactions into the corresponding differential and algebraic equations and integrates them with user-specified initial conditions
(27–30). The Gepasi program offers the advantage that
either enzyme kinetic rate laws or rate equations using
chemical rate constants can be specified. Enzyme kinetic constants are often known when chemical rate
constants are not, and rate equations with enzyme
kinetic constants are much more quickly integrated
numerically. Equations with enzyme kinetic constants
require that steady states of the enzyme forms are
established, but these are established within a few
milliseconds and are guaranteed to last subsequently
throughout the enzyme-catalyzed reactions whenever
substrate and intermediate concentrations are much
greater than the enzyme concentrations. However,
even more general simulation programs can be used. It
is easy to learn to write the model equations, which are
simply the minimum number of differential equations,
each representing the rate law for a reactant plus all
the possible conservation of mass equations (this keeps
the number of differential equations to a minimum).
The set of equations is complete when each variable on
the right-hand side of the equations is defined on the
left-hand side by another equation.
Experimental Details
Stable Enzyme Complexes
If all the intermediate is transferred directly from E 1
to E 2 in an E 1–I–E 2 complex (transient or stable), the
transient time will be zero except for the very fast
transient times for enzyme forms (usually less than a
few milliseconds). However, within a multienzyme
complex some of the intermediate, after dissociating
from E 1, may remain in an internal pool that is not
mixed with the bulk phase while the remainder of I
escapes into the bulk phase (“leaky channeling”). To
310
SPIVEY AND OVÁDI
visualize this, one may consider two sequential enzymes that are coimmobilized at high surface density
on a membrane. These are often dynamic rather than
static complexes in reality, but may be considered stable for the purpose of this illustration. This coimmobilization situation approaches that studied by Goldman
and Katchalski (31) and experimentally by Gondo (14,
32). Another example of leaky channeling is electrostatically controlled channeling between associated enzymes (16). With these partial channeling conditions,
the experimental transient times will often be less
than those of the unassociated enzymes or enzymes
without any channeling, but it will not be zero. Ovádi et
al. (33) first developed equations for such leaky channeling using the approximation of first-order kinetic
response of E 2. Easterby (34) developed equations
without this assumption. His analyses demonstrate
that the transient time will not be reduced by channeling if: (a) the second enzyme obeys the kinetics of a
rapid-equilibrium steady-state mechanism or (b) the
coupling enzyme concentration is comparable to its K m
or higher. In other cases, a reduction in transient times
is predicted. Elcock et al. (16) also developed equations
for transient times beyond the “first-order kinetic” condition. Their treatment is based on the probability p c
that the intermediate, after release from E 1, is channeled without mixing with the bulk phase, and related
probabilities for kinetic events. Their analyses also
consider the effects of competitive inhibitors of E 2 and
competing reactions (e.g., by E 3) on the transient times.
The resulting equations were used to analyze the experimental data from two independent coupled enzyme
systems, a natural bifunctional enzyme (35) and a genetically fused enzyme pair (15). Unassociated enzyme
pairs were used for reference data sets for both (unassociated enzyme forms for the first study were from a
different microbial system in which these enzymes exist as individual monofunctional forms).
To use transient times to conclude that substrate
channeling is occurring, one must know the kinetic
parameters of the associated enzymes, since complex
formation can alter these constants from those of the
unassociated enzymes. In static complexes where the
extent of complex formation is independent of enzyme
concentrations, the kinetic parameters of each enzyme
can often be determined by addition of only the cosubstrate for the enzyme being characterized. An experimental transient time smaller than predicted by the
kinetic parameters of the individual enzymes in the
complex is then good evidence of channeling. In addition the extent of channeling a (“channeling efficiency”)
can be calculated from these data from all three formulations (16, 33, 34). With an independent method of
determining a, e.g., by isotope dilution (see below), the
“channeling advantage” b (ratio of internal to external
[I]) may also be calculated (34). Analysis is even more
definitive if the concentration of the intermediate as
well as the product can be measured. These methods
have been applied with success to several bifunctional
or fusion enzymes (15, 35–37).
Dynamic Enzyme Complexes
Dynamic enzyme complexes present a more difficult
problem for prediction of transient times if the changes
in enzyme association alter the kinetic constants.
Equations and several different approaches have been
developed for this case assuming first-order kinetic
behavior of the enzymes and assuming that the catalytic reaction does not alter the extent of enzyme associations (33, 38 – 40). In these cases, the apparent firstorder rate constants, V 2 /K m2, were determined for E 2 in
the presence of E 1 at the same concentration as used
for measurements of t. This was expected to prevent
changes in enzyme associations between these two
measurements and any resulting changes in kinetic
constants. In addition, Salerno et al. (39) used the
dependence of t on [E 2] to include the enzyme associations in their model, and the strategy of increasing [E 2]
and [E 1] in constant ratio to maintain [I] ss constant.
However, the significant number of catalytically enhanced (virtually induced) enzyme associations now
known (see introduction) raises questions about the
assumption that use of the same enzyme concentrations during measurement of the apparent first-order
rate constant and the t of the coupled reactions guarantees the same extent of enzyme association. Although the E 2 reaction is present in both measurements, the E 1 reaction is present only during
measurement of t. This E 1 reaction might alter the
extent of enzyme association from that in its absence.
This concern can be dismissed if different extents of
enzyme association cause smaller changes in the kinetic constants than required to explain the differences
in t from that of the nonchanneling reference case. The
maximum effects on kinetic constants can be established by saturating E 1 with E 2 (the enzyme normally
in molar excess). Also it is conceivable that physical
data, e.g., light scattering, could be obtained to test the
assumption of changes in enzyme association during
the E 2 and E 1 reactions relative to associations with
the E 2 reaction alone.
Catalytically Induced Enzyme Associations
If anomalous (nonclassic) transient times are obtained for catalytically induced enzyme associations,
this may be due to substrate channeling, but there are
two alternative mechanisms that need to be excluded
before this conclusion is rigorous. In one of these, the
“association model,” it is proposed that the catalytically
induced association changes the enzyme kinetic constants sufficiently to give the greatly shortened t. However, the magnitude of the decreased t and the enzyme
SUBSTRATE CHANNELING
concentration dependence makes this alternative implausible in some cases. For example, Rudolph and
Stubbe (5) found that changing the ratio of E 1 and E 2
gave results that required different kinetic constants
for these different progress curves; i.e., the “association
model” alone doesn’t fit the data. They also found that
it would take a nearly 100-fold lower K m of E 2 in the
E 1–E 2 complex relative to the free E 2 to explain the
experimental t by a classic diffusion coupling mechanism. Such large changes in the enzyme kinetic constants on complex formation are not likely. Although
binding of the protein a-lactalbumin to galactosyl
transferase reduces the K m for glucose 700-fold (19),
this is a case of the protein complex generating an
enzymatic activity that is scarcely present at all in the
absence of the protein. It seems unlikely, however that
two enzymes that are separately efficient (typically low
K m values) would associate to give still 100-fold lower
K m values. Also in the case of NADH channeling, increasing free E 1 at constant E 1–NADH actually inhibits the E 2 reaction (17, 41), which is opposite the
hypothesis that an E 1–E 2 complex is more efficient
(lower K m).
The second mechanism for producing anomalous kinetics of coupled reactions that we need to exclude
before concluding that substrate channeling exists is
what we call the “reactive intermediate” model. This
requires no E 1–E 2 associations. It proposes that the
intermediate released from E 1 exists initially in a pure
highly reactive isomeric form of I for a short lifetime (a
few microseconds), which is, however, sufficiently long
for this reactive form to diffuse from E 1 to E 2 and be
converted to product. This “reactive” form of I has a
much higher k cat and/or lower K m than the predominant equilibrium form of I that exists in exogenous
samples of I. Isomer equilibrium is established long
before I is used from exogenous sources. Such a model
was proposed for the apparent anomalous kinetics (low
t) of the coupled aspartate aminotransferase (E 1) and
malate dehydrogenase (E 2) reactions (42). No E 1–E 2
association could be found between these enzymes at
equilibrium (absence of the catalytic reactions). Since
catalytically induced enzyme associations were not
considered then, the authors proposed this reactive
intermediate model as the only other reasonable mechanism for the apparent anomalous t value. Reinvestigation of this system failed to find the experimental
anomalies (43), but this is a second potential nonchanneling mechanism that has to be considered and excluded before channeling can be accepted. Fortunately,
additional data can be persuasive evidence against this
reactive intermediate model. For example, this model
still predicts the same type of v-versus-[I] curve as with
exogenous intermediate I (usually a Michaelis–Menten
curve) although with different K m and V. In the case of
putative NADH channeling, such a model does not fit
311
the experimental velocity versus [E 1–NADH] data. Independent of this fact, the K m required by the reactive
intermediate model (about 100-fold lower than for free
NADH) seems unrealistic for a substrate that already
has a low K m relative to other good substrates.
In summary, transient-time analysis is a quite rigorous test of substrate channeling for stable enzyme
complexes. However, dynamic and catalytically induced enzyme association systems present difficulties
that make transient-time analysis less rigorous. Nevertheless, even for these systems, transient-time data
can in some cases provide very persuasive indication of
channeling when supported by additional data and
complementary methods.
Other Limitations and Precautions
In addition to the limitations discussed above, some
systems will have kinetic constants and system constraints that make it impractical to use transient time
analysis. This was the case for our study of oxaloacetate channeling in polyethylene glycol-induced solidstate complexes of malate dehydrogenase and citrate
synthase (44). Also the time resolution of measurements is limited by the signal amplitude resolution
(sensitivity) of the detector (43). For example, despite
the 2-ms time resolution of the stopped-flow instrument, in one study the time resolution for the reaction
was only 50 ms. This is the result of the fact that very
little product is formed during the early part of a transient. Thus longer times are required to reach detectable levels of product formation for longer transient
times. Increasing [E 1] improves the time resolution,
but raises v 1 and [I] ss of Eq. [4]. If [I] ss approaches K m2,
the first-order approximation is lost, but more seriously, eventually v 1 will exceed V 2 whereupon no
steady state in I will be achieved. Under first-order
rate conditions, the increase in [I] ss can be avoided by
increasing E 1 and E 2 in constant ratio. However, increasing [E 2] decreases the experimental t, requiring
higher time resolution than before to record it. Higher
resolution is provided by the increased [E 1], but by no
more than enough to cancel the effect of increased [E 2].
Thus, the inadequate time resolution originally encountered remains.
Another precaution to be aware of is that graphical
measurements of transient times will almost invariably underestimate the true transient time since v 1 is
only asymptotically approached by monitoring P. This
error increases greatly as the transient times increase
relative to the recorded times. Since the recorded time
needs to be limited to prevent product inhibition, etc.,
this can cause serious errors for the longer transient
times. Thus to use progress curves to obtain transient
times t, it is far better to obtain v 1 as a best-fit parameter from nonlinear regression analysis than to visually assume its value. The equation to use is either Eq.
[1] or its more complex forms depending on the condi-
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SPIVEY AND OVÁDI
tions of the experiments. Nonlinear least-squares analyses can even be done with the numerically integrated
equations for the more complex conditions [e.g.,
(28, 30)].
Isotope Dilution or Enrichment
Principles
The isotope dilution/enrichment method is the most
traditional way to test for substrate channeling. In a
sense, this method is a direct test for channeling since
the lack of dilution by the bulk phase of the endogenously generated intermediate I is the operational
definition of channeling. Scheme 2 illustrates isotope
dilution where for simplicity we consider irreversible
reactions. An isotopically labeled precursor S* in a
sequential path of reactions is added (usually concomitantly) with a large concentration of unlabeled intermediate I that is called the “exogenously” added I.
After an appropriate reaction time, one quenches the
reactions and isolates a product P. This may be the
immediate product of I or one of the products several
reaction steps downstream. We will assume nonbranched reactions downstream for simplicity although branched paths can also be dealt with in principle. If the catalytic reactions producing and acting on
I are coupled only by classic diffusion of I through the
bulk phase between these two enzymes, the labeled
(“endogenously produced”) I* will be diluted by the pool
of unlabeled I at concentration [I], and the specific
radioactivity of P will be reduced relative to that of S*.
As illustrated below, the extent of dilution in this case
of classically coupled reactions is predictable as a minimum extent if [I*] SS is measured or is reliably predicted. Significantly less dilution of the specific radioactivity than the minimum dilution via the classic
diffusion path is evidence of channeling, i.e., is evidence for the absence of equilibration of endogenously
generated I* with exogenously added I. In perfect channeling the ratio of specific radioactivities of P* to S* is
1, but it is less than 1 for leaky channeling (channeling
efficiencies a less than 1). The same type of information
is obtained if the initial substrate is unlabeled and the
intermediate is labeled. In this case isotope incorporation would be expected by any nonchanneled path.
Experimental Methods
The most widely used and generally applicable approach is equally rigorous with all three types of enzyme associations since it does not need to know the
SCHEME 2
kinetic parameters of the enzymes involved. That is
not to say that the isotope method will work well with
all systems. Limitations are discussed below. The procedure used by Lyle et al. (37) to evaluate channeling in
the bifunctional enzyme ATP sulfurylase and adenosine 5’-phosphosulfate kinase illustrates the approach.
The production of P* is measured during a fixed period
for a range of initial concentrations [I 0] of I. From this
curve, the [I 0] that reduces the relative specific radioactivity of P*/S* to 50% of that of S* is obtained. In
their system, this concentration of exogenous I was
60-fold higher than the endogenously generated [I*] ss.
However, the channeling efficiency would be still
higher since during the transient phase of [I*], its
concentration would be lower than that at its steady
state. Therefore, they repeated the experiments, but
withheld the exogenous I for a fixed time interval.
Enormously higher concentrations of [I 0] were required
to give significantly reduced specific radioactivities in
P*. The first of these experiments gives a lower limit to
the channeling efficiency, which in this case is very
high. Specifically for this example, it allows one to say
that less than one in 60 molecules escapes the channeling path. If the enzyme kinetic constants and dissociation constant for E 2–I were known, a more quantitative value could be obtained by numerically
integrating the model equations using one of the simulation programs described in the section on transient
time analysis. These equations would allow for: (1) [I]
to be in excess of first-order concentrations; (2) a significant fraction of [I*] binding to E 2; and (3) significant
reversal of the E 1 and E 2 reactions. However, this more
demanding analysis would probably be justified only
when the channeling efficiency was so low as to be in
question.
Orosz and Ovádi (40) devised a quantitative approach to isotope dilution valid when [I] 1 [I*] are low
relative to K m2 (the K m of E 2) and the reactions are
irreversible. For the classic, nonchanneling system the
specific radioactivity of the product would then be
SRAp :
@P*#
@P*# 1 @P#
5
v 1 t 2 ~v 1 /k! ~1 2 e 2kt !
,
v 1 t 2 ~v 1 /k! ~1 2 e 2kt ! 1 @I0#~1 2 e 2kt !
[7]
where [I 0] is the initial concentration of the exogenously added I, k 5 V 2 /K m2 and v 2 5 k([I] 1 [I*]).
Specific radioactivities significantly larger than predicted by this equation would be evidence of channeling of I between the enzymes. The ratio of specific
radioactivities of product to substrate, r 5 SRA P/SRA S,
would be 1 for perfect channeling and the lower value
predicted by Eq. [7] for nonchanneling. However, the
first-order kinetic requirement greatly limits the max-
SUBSTRATE CHANNELING
imum [I] that can be used to assess channeling, which
in turn limits the dilution possible and makes the
changes in r small between the channeled and nonchanneled systems. Isotope enrichment experiments
might provide larger changes in r. Another problem
with this method, unlike the method of Lyle et al. (37),
is that it requires knowledge of the kinetic constants
K m2 and V 2 . While this is not a problem for static
enzyme complexes, it is a problem for dynamic associations and is most likely impractical for catalytically
induced enzyme associations for reasons discussed under the transient-time analysis.
Studies in Situ
In situ systems are especially valuable since they
retain much of the complexities of the cell including
membranes, cytoskeletal components, and locally high
enzyme concentrations. Dilute cell suspensions provide
sufficiently slow kinetics to allow valuable experimental procedures despite the high physiological enzyme
concentrations. Isotope dilution and enrichment tests
are especially good for tests of channeling in situ since
they do not require knowledge of the kinetic properties
of the enzymes involved. Few other channeling tests
are known for these conditions, though some notable
exceptions have worked on occasion (45, 46). However,
experimental complexities and the precautions required for these radioisotope studies are generally considerably greater than for studies in vitro. In most
cases, the cells have to be made permeable to the initial
substrate and/or the intermediate. A large number of
permeabilizing agents have been used (47–50). Most of
these are what we call macropermeabilizing agents,
which produce membrane holes larger than the macromolecules within the cell. Surprisingly, loss of enzymes is sufficiently slow in many of these cases to
permit the studies desired, which in itself indicates the
binding of these enzymes to each other or structural
components in the cell. However, a long retention of
enzymes is definitely not always found. Fortunately, a
small loss of enzymes will not necessarily preclude
evidence of channeling, since loss of enzymes would be
expected to decrease channeling giving false negative indications. In contrast to macropermeabilizing
agents, a-toxin (also known as a-hemolysin), from
Staphylococcus aureus, forms a cylindrical heptamer of
subunits across the cell plasma membrane with an
inner pore 1–2 nm in diameter (51, 52). Molecules
smaller than approximately 1000 Da can pass through
this pore; however, trypan blue should be excluded
(53), contrary to earlier reports. Permeability to trypan
blue is thought to result from lytic components contaminating the a-toxin preparation. Commercial preparations of a-toxin are frequently heavily contaminated
and have been extremely expensive although this toxin
can be easily and safely purified in normal biochemistry laboratories (53). For successful tests of channeling,
313
e.g., by isotope dilution, it is essential that the intermediate have as rapid an access to the same intracellular compartment as the initial substrate. Otherwise,
a false-positive indication of channeling can result
from lack of the intermediate at the site of metabolism
of the substrate. ATP and hexose phosphates were
reported to pass freely through a-toxin pores. However,
recent studies in progress from several laboratories
find that these substrates pass poorly or not at all
through these pores. Permeability depends on the cells
(54), permeabilizing conditions, and possibly the substrain of S. aureus Woods 46 that is used. These questions on substrate permeability are now under active
investigation by a collaboration of laboratories. In addition, the conditions for permeabilization need to be
optimized for each cell type for virtually all of the cell
permeabilizing methods.
Numerous references can be cited for substrate channeling studies with permeabilized cells (55–58). To our
knowledge, the most thorough and fullest description
of the necessary controls are those of Cohen and coworkers (55) indicating channeling in most of the steps
of the urea cycle [see (59) for recent review]. Results of
these studies were subsequently fortified with electron
microscopic methods demonstrating colocalization of
some of the enzymes and their mRNAs (60, 61). Due to
variability in cell preparations from experiment to experiment, many of the control experiments must be
done with every experiment.
Other Limitations and Precautions
Numerous practical problems and some limitations
need to be understood for successful applications of
isotope methods for studies of substrate channeling.
The time of quenching of the reaction can be very
important, since utilization of exogenous I is proceeding during the reactions. This can be especially important in obtaining definitive values of r when low concentrations of I are used and for studies in situ, where
further metabolism of products may complicate the
analyses. Isotopically labeled biochemicals are frequently expensive and often not commercially available, requiring one to make them from a labeled precursor. The resulting compounds are not always
sufficiently stable for the desired studies. The quenching and subsequent isolation of the product free from
isotope contamination have to be guaranteed. This contamination can also come from breakdown of any unstable S* or intermediates—not just the parent compounds. Strong acids or bases are commonly used to
quench enzymatic reactions and these promote many
decompositions that may contaminate the isolated
product. Errors from these sources are especially serious when: (1) the quantity of product is a small fraction
of the original substrate (the usual case to maintain a
constant velocity) and (2) the quantitative differences
in isotope dilutions predicted for different mechanisms
314
SPIVEY AND OVÁDI
are small. Thus small decompositions that are not normally thought of can contaminate or alter the radioactivity of the isolated product seriously in these experiments. In some cases, quenching by milder conditions,
e.g., with excess EDTA or liquid N 2, can circumvent
this problem. CO 2 release from the product is often
used to determine specific radioactivities. Despite the
long history of such measurements, we have found
surprisingly large errors in such determinations due to
nonenzymatic decarboxylations and poor retention of
CO 2 in the common scintillation cocktails. Recommendations to minimize these are provided by Lehoux et al.
(62).
Coupled reactions that regenerate the substrate or
cofactor, e.g., coupled dehydrogenases or kinases regenerating NAD or ATP, present increased problems
since product and substrate are the same and hence
cannot be distinguished. In principle, the nonchanneled path will dilute the specific radioactivity of the
substrate (product) from its original value, but since
the amount of initial substrate is usually in large excess over the regenerated substrate, changes in r will
usually be too small for practical use. Isotope enhancement experiments would circumvent this problem to a
significant extent, but would still lead to smaller
changes in r than in nonregenerating reactions since
the unlabeled substrate will dilute the radioactivity of
the intermediate that is converted to product/
substrate. This does illustrate the relative advantages
of the dilution versus enhancement approaches for certain systems. It is more accurate to compare a small
radioactivity against a near-zero background level
than to compare radioactivities of similar magnitude.
In addition, the labeled intermediate may be more
stable or less expensive than the labeled substrate.
Isotope dilution experiments have been used to test
the “reactive intermediate” model of anomalous kinetics of coupled enzymes. However, the equations proposed to test this model have been disputed (43). It is
questionable whether an adequate isotope dilution experiment could be devised to test for this mechanism of
coupled reactions. However, independent data can exclude this mechanism or provide supporting evidence
for it as discussed under Transient-Time Analysis and
under Enzyme Buffering Method sections.
Competing Reaction Method
Principles and Experimental Details
Competing reactions for the intermediate I can provide a very useful indication or test of channeling. This
competition can be provided by enzymatic (E 3) or nonenzymatic reactions. One should use a large excess
activity of E 3 (or fast nonenzymatic reaction) relative to
E 2 to provide a robust test. One assumes or experimentally verifies that E 3 remains in the bulk phase, i.e., it
does not bind to the E 1–E 2 complex (but see comments
below). The advantages of the test are its experimental
simplicity and range of systems to which it is applicable. Like the isotope dilution/enhancement method, it
does not require knowledge of any kinetic constants,
hence it is applicable in principle to all types of associating systems. It also may be considered a direct test
of substrate channeling in the sense that it detects the
presence or absence of the intermediate in the bulk
phase.
We found the competing reaction method especially
helpful in demonstrating channeling of oxaloacetate
between malate dehydrogenase and citrate synthase in
solid-state suspensions of the polyethylene glycol
(PEG) induced enzyme complex (44). The experimental
difficulties in preparing and maintaining the solidstate enzymes complexes and in mixing such viscous
(PEG) solutions make alternative approaches much
more difficult if practical at all with this system. This
illustrates the dictum that no one method is best for all
systems. Subsequently Srere and co-workers have used
the competing reaction method with the same E 3 as
well as an alternative competing enzyme reaction to
test for channeling of oxaloacetate in genetically fused
complexes of these enzymes (15, 63).
These authors (63) found that increasing [E 3] did not
decrease the observed reaction rate (v 2 ) linearly; a
decreasing effect at higher [E 3] was found instead. This
was initially puzzling, since we had observed essentially complete trapping of oxaloacetate in the solidstate complex of these enzymes (44). However, a simple
treatment reveals that the velocity of the competing
reaction v 3 } =[E 3] and thus dv 3 /d[E 3 ] } 1/ =[E 3 ],
which is qualitatively consistent with the data of Lindbladh et al. The more quantitative model of Elcock et
al. (16) also reproduces these data (63). Our ability to
virtually abolish the v 2 reaction is most likely due to
the nearly 10-fold higher ratio of E 3 activity to that of
E 2 in our study (44). With the fused enzyme complex,
Lindbladh et al. (63) and Shatalin et al. (15) were also
able to apply the transient time method. Competing
reactions should decrease transient times. This is most
easily understood by realizing that any and all reactions that increase utilization of I will lower [I] ss and
hence shorten the time it takes to reach this level via
the v 1 reaction. The model equations of Elcock et al.
demonstrate this effect more quantitatively (16). It is
unclear then why Srere et al. (15, 63) found no changes
in the transient times in the presence of the competing
reaction.
Limitations and Precautions
Binding of E 3 to the E 1–E 2 complex or either of its
components may decrease the activity of E 3, even eliminating it, but since a large excess of E 3 relative to E 1
and E 2 is used, it is hard to see how this would give a
false-positive indication of channeling. Binding of E 3
could either decrease channeling or possibly enhance
315
SUBSTRATE CHANNELING
binding of E 1 to E 2, causing a more complex result.
Several examples of such cooperative ternary complexes are known, e.g., (64, 65). If this led to increased
channeling between E 1 and E 2, this would be an important result though the correct understanding of the
observed channeling would require knowing that it
was induced by E 3. Appropriate binding data should
elucidate this mechanism and use of an alternative
competing reaction may be helpful as well. If binding of
E 3 to the complex decreased channeling a falsenegative indication could result. In summary, only a
possibly false-negative conclusion concerning channeling should result from the competing reaction method
if adequate control experiments are made. Reasons for
the failure to observe the expected effect of a competing
reaction on the transient times (63) remain unclear at
this time, but would appear to reside in the experimental method rather than the theory.
Enzyme Buffering Method
Principles
The enzyme buffering method is especially helpful
for some systems, but is limited to those where the K d
of E 1–I is not more than the K m of E 2, as explained
below. The advantages of this method are best exemplified for NADH dehydrogenases where the channeling of NADH is being tested. Therefore, we discuss it in
terms of NADH, though it is applicable to some other
systems as well. Since the K d of E 1–NAD is usually
about 100-fold higher than that of E 1–NADH (66), this
method is not practical for testing channeling of NAD
in most cases. NADPH channeling has been reported
for two different enzyme pairs (67, 68) we know of
without a thorough search.
NADH channeling presents two special problems. It
is an example of an intermediate that is regenerated by
E 2 into its original form (NAD). This makes it difficult
to apply the methods discussed above. Second, our
recent studies to be published elsewhere show that
these systems are among the catalytically induced association type; i.e., no association of the two enzymes
can be detected in the absence of the catalytic reaction.
Thus the test preferred by some of directly measuring
the rates of NADH transfer from E 1 to E 2 in the absence of the reaction (69, 70) is not applicable. The
enzyme buffering method has been criticized by these
authors, but we believe these criticisms are very inaccurate. However, the enzyme buffering method is not a
good choice of a channeling test for systems without
the special properties of these dehydrogenases (low K d
of E 1–I and regeneration of the substrate), and improved methods are needed even for these dehydrogenases for reasons discussed under Further Precautions, Limitations, and Alternative Approaches.
The question the enzyme buffering method addresses is equivalent to asking if an E 2 enzyme can use
the E 1-bound form (subscript b in text and Scheme 3) of
the common intermediate (NADH in our example) in
addition to the free form (subscript f). The obvious
approach is to replace NADH f with NADH b. This is not
entirely possible since these forms are in equilibrium.
However, the dissociation constant K d of E 1–NADH is
usually about 1 mM, so with excess E 1 it is possible to
reduce [NADH] f to a value well below its K m for E 2
(K m2f in Scheme 3). The larger arrow on the left of
Scheme 3 indicates that for this binding equilibrium,
NADH is normally more than 99% in its E 1-bound
form. Thus, the expected (“classic”) velocity, v cl0 5 V 2f/
(1 1 K m2f/[NADH] f), of the E 2 reaction in the presence
of high [E 1] can often be reduced to a fraction of the V 2f,
the limiting velocity of E 2 for free NADH. Instead the
experimental velocity, v exp, is frequently found to be
many times v cl0 (3, 17), which is the maximum velocity
the reaction could have assuming that E 2 could use
only NADH f. The experimental criterion of anomalous
kinetics is thus R [ v exp/v cl0. An R value significantly
greater than 1 is, therefore, incompatible with the classic mechanism. The most reasonable explanation is
that E 2 can use the only other form of NADH that is
present in the solution, namely, E 1-bound NADH,
which is also the vastly predominant form. The alternative, nonchanneling mechanisms (“enzyme association” and “reactive intermediate” models) discussed
under Transient-Time Analysis for such anomalous
kinetics do not appear compatible with the data. However, the data do fit the kinetics of a channeling model
very well as will be described elsewhere. Thus we consider the R criterion to be a good indication of NADH
channeling when R @ 1. NADH channeling has been
found only for enzymes of opposite chiral specificity (A
or B) for the C-4 hydrogen on the nicotinamide of
NADH (18). Thus control experiments using E 1 or E 2
paired with enzymes of the same chiral specificity (3,
17) have demonstrated that the average R is within
11% of 1.00. Thus, the R values of 4 or more found for
several enzyme pairs of opposite chirality (3, 17, 41)
are 40-fold or more above the reasonable experimental
errors.
SCHEME 3
316
SPIVEY AND OVÁDI
E 1 is not catalyzing any reaction since its cosubstrate
is missing. E 1 is simply buffering NADH to a low
[NADH] f, hence the name “enzyme buffering test.” In
summary, the velocity of E 2 with its cosubstrate is
examined in the absence of E 1 and again in the presence of substrate levels of E 1. Data without E 1 give
accurate values of K m2f and V 2f and data with varying
[E 1] give v exp. v cl0 is calculable for each v exp data point
using the K m2f, V 2f, and K d determined in previous
experiments. Normal assay concentrations (nanomolar
level) of E 2 are used that are typically 10 3- to 10 4-fold
more dilute than [E 1]. Thus the dissociation equilibrium of E 1–NADH is not altered by the presence of E 2.
Also, the lifetime for equilibration of the E 1–NADH
dissociation is a few milliseconds so that this dissociation equilibrium is maintained throughout the steadystate reaction of E 2. Kinetic measurements in the absence of E 1 are almost always well described by the
Michaelis–Menten equation, but any other function,
e.g., an empirical power series, would serve the purpose equally well. Sigmoidal kinetics, e.g., offer no
problem. That is, no kinetic model need be assumed.
Experimental Details
Typically the kinetic experiments with E 1-buffered
NADH are done in two ways: (1) by varying total concentrations of E 1 and NADH, but at constant ratio of
[E 1] t/[NADH] t, where subscript t means total, and (2)
with constant [NADH] t, but varying [E 1] t (all in excess
of [NADH] t). The former provides plots closely approximating the hyperbolic Michaelis–Menten curves representing the E 2 activity with E 1–NADH substrate
[see, e.g., (17)]. The latter strategy virtually always
gives higher R values in the limit of high [E 1], but the
data will not give the usual Michaelis–Menten or
double-reciprocal plots. However, combination of both
sets of data can be analyzed by nonlinear least-squares
methods to obtain all the information contained in the
graphical procedures and more.
There are primarily only three experimental constants that are needed for this test: K m2f, V 2f, and K d of
E 1–NADH. In principle, the molar absorptivity of the
E 1-bound rather than free NADH should be used in the
calculation. However, the difference between the absorptivities of free and bound NADH are rarely significant relative to other sources of error although we still
prefer to measure the absorptivity of E 1-bound NADH.
The kinetic constants (K m2f and V 2f), of E 2 for the free
NADH are obtained in the usual manner in the absence of E 1. For most dehydrogenases, these constants
can be determined with considerable accuracy, e.g.,
10% relative standard deviation, since oxidations of
NADH are very favorable; i.e., large changes in absorbance occur within the initial velocity portion of the
data. The dissociation constant K d can be determined
with similar accuracy only with careful attention to
correct procedures, which we discuss next.
Determination of K d and Related Precautions
One of the precautions needed is to ensure that the
enzyme is free of bound nucleotides, which can extensively alter enzyme kinetics as well as the NADH binding equilibrium (71). Treatment of the enzyme stock
with activated charcoal (Norit SA3 formerly Norit A)
has frequently been used to remove bound nucleotides,
but Prabhakar et al. (71) claim that their Norit needs
further washing to be maximally effective. Ionexchange (72) or dye-affinity chromatography is preferred by some investigators for removing bound nucleotides. These chromatographic methods provide
greater recovery of enzymes and may reduce some denaturing effects of charcoal treatment for some enzymes. The absorbance ratio A 280 /A 260 measured before
and after treatment is useful to more quickly ascertain
the extent of nucleotide binding in future work. Some
enzymes have negligible bound nucleotide while others, e.g., mammalian glyceralde-3-phosphate dehydrogenase (GAPD), are normally saturated with bound
nucleotide. Apo-GAPD is considerably less stable than
the holo-form and hence needs to be used for the K d
measurements as soon as possible after preparation.
Even then, a fast method of determining K d is often
necessary to prevent enzyme denaturation and excessive destruction of NADH through the frequent NADH
oxidase activity associated with E 1 preparations. The
NADH oxidase problem and ways to reduce it are discussed below.
K d has been most frequently determined by fluorescence titrations with E 1 using changes in either NADH
or protein fluorescence that accompany the binding of
NADH to E 1. This is a fast method permitting titration
of a starting enzyme concentration within about 2 min.
Stability can also be enhanced by starting titrations
with maximum concentrations of NADH and diluting
the enzyme and NADH solution successively. Data
with several E 1 concentrations are desired. It is best to
use nonlinear least-squares fitting to obtain best-fit
values of both the binding capacity n (moles of NADH
binding sites per mole of protein subunits) as well as
K d. Transforming the binding equation to a linear form
is not good practice, except for visual inspection, although this practice is entrenched by historical tradition. Transformation to linear form requires a subjective estimate of the signal for enzyme-bound NADH
that introduces potentially large systematic errors; it
distorts the distribution of random errors, and often
mixes the predominant errors into both the dependent
and independent variables. Therefore, for the final
analysis a nonlinear fit to the normally rectangular
hyperbolic binding model is best. The computer program should be capable of giving reliable estimates of
the uncertainty in both the n and K d parameters from
random errors in the data. Data missing these error
estimates are highly questionable. The consequences of
SUBSTRATE CHANNELING
systematic errors should be considered as well since
these can be the predominant source of error and extremely large, e.g., 10 or more times larger than the
true K d. This most often happens with data that are
confined to near-“stoichiometric” binding, the condition
where [E 1] and [NADH] are so high relative to their
dissociation constant that almost all of the added limiting component is bound. This is understandable
when it is realized that a significant fraction of the
limiting component must be free to provide a measure
of the strength of binding; otherwise only the maximum capacity (n) of binding is measured. Still another
deficiency is that many researchers have calculated K d
with the assumption that all the protein binding sites
are competent for binding, i.e., binding site concentrations 5 n[E 1], where [E 1] is the subunit concentration.
In fact we almost always find the experimental binding
capacities to be about 0.6 to 0.7 of the binding site
concentrations (calculated from the protein concentrations) for commercial enzymes. The same enzymes purified in our laboratory give n values of 1 within 5%
experimental errors, showing that these low binding
capacities are not due to our experimental errors. Good
channeling can be found with both commercial and
purified enzyme preparations, but higher weight concentrations of E 1 giving equivalent NADH binding site
concentrations are needed for commercial enzymes to
give binding equivalent to that of enzymes with n 5 1.
Neglecting this deficiency in binding capacity can give
false-positive results. Another potential problem is the
presence of cooperative binding of NADH. Surprisingly, the binding isotherms have all been free of this
complication in our experience as well as in other published studies, even for enzymes with well-known cooperative binding properties. This is probably because
the titration range used covers the binding to predominantly one step in the total ligation range. One needs
to be sure that this is the same step that is functioning
in the subsequent channeling measurements. Kinetic
measurements with a control, NADH acceptor enzyme
of the same chiral specificity as E 1 can provide this
assurance as described below.
The high [E 1] used (10 3–10 5 times higher than normal assay concentrations of enzymes) requires unusually high purity of E 1 with respect to E 2 activity and
NADH oxidase activity. Fortunately the presence of
these spurious activities are easily detected as described below, if they are considered. Usually there will
be NADH oxidation in the presence of E 1, even in the
absence of any substrates (“NADH oxidase” activity).
Often this can be reduced to sufficiently low levels with
purification steps, but not always. In fact this activity
is intrinsic to some enzymes, e.g., the lipoamide dehydrogenase component of a-keto-dehydrogenases. This
NADH oxidase activity will preclude all but fast methods for K d determinations unless compensated for by
317
NADH regenerating components. Regeneration systems are limited by the normally very unfavorable
equilibrium for NAD reduction, but we have found a
very good regenerating system that will be described
elsewhere. We expect this to greatly improve the accuracy of K d measurements for these systems.
Kinetics with E 1 Present
To reduce the expense of the high [E 1] used, we use
black wall microcuvettes and a solution volume of only
150 ml. Standard spectrophotometers can be adapted
easily for these solutions by adding 2-mm-wide horizontal slits to the cell holders. The loss in signal/noise
ratios is rarely significant with this reduced light
power. E 1 and the components of the reaction mixture
are added in sequence to observe changes from each
component. E 1 with NADH alone checks for the level of
NADH oxidase, and the subsequent addition of the
cosubstrate of E 2 checks for the E 2 activity (intrinsic or
contaminating) in the E 1 sample. The sum of these
represent the background reaction rate. An NADH regenerating system cannot be used for these measurements. Thus, if the background rate is more than 50%
of the final rate with E 2 present, it is best to increase
the latter rate by using higher [E 2]. This may require
using rapid kinetic methods to permit recording the
faster rates. However, [E 2] (NADH binding site concentrations) should not be increased to more than 0.1 of
[E 1] to prevent distortion of the E 1–NADH equilibrium.
We typically use 50 mM [NADH] t and from 200 to 480
mM E 1 binding site concentrations. This assures us
that we can get good initial velocities and low [NADH] f.
To save on scarce or expensive E 1, it is quite likely that
these concentrations can be lowered significantly even
with absorption detection and certainly with the
higher sensitivity of fluorescence detection. The higher
detection sensitivity allows one to stay within the initial velocity range of signal change with the lower
NADH concentrations associated with lower [E 1]. However, the essential requirement of this test is to lower
the [NADH] f well below K m2f, which requires a high
[E 1] t. Many experiments have been done with far too
little [E 1] t to achieve this condition, which gives inconclusive results. In practice, it is nearly impossible to
obtain a significant test if the K d is larger than the
K m2f, even if the predominant flux is through the channeling path, a fact persuasively demonstrated by computer simulations. Yet several authors claim conclusive evidence against channeling with such inadequate
experiments (70, 73, 74). Therefore, conditions should
be chosen to make K d as low as possible and K m2f as
high as possible. Proper choice of pH can make major
improvements in meeting this criterion. In principle,
addition of competitive inhibitors of E 2 should raise
K m2f, although we have not been successful in the few
attempts we have made with this approach.
318
SPIVEY AND OVÁDI
Data Interpretations
The R value is all that is needed to demonstrate the
anomalous kinetics of many A–B and B–A dehydrogenase pairs. As described above, the most reasonable
interpretation of R significantly greater than 1 is that
NADH is directly transferred from one dehydrogenase
to another. However, simple kinetic models allow one
to calculate the fraction of the reaction flux going
through the channel or the classic path (channeling
efficiency a as defined above). Data from both strategies (fixed [E 1] t/[NADH] t and fixed [NADH] t) can be
combined for nonlinear regression to the model equation. The calculated a values are not sensitive to details of the model. The reason is that the ratio of
[NADH] b/[NADH] f is extremely large in well-designed
experiments. Also with respect to the ratio of NADH
binding sites to NADH t, these experiments are far
more physiological than the conventional steady-state
enzyme kinetic studies (3, 75). This can also be claimed
for many enzyme–substrate systems other than dehydrogenases.
Further Precautions, Limitations, and Alternative
Approaches
During the enzyme buffering measurements, such
high [E 1] are used that NADH binding is virtually
“stoichiometric.” However, most physical methods for
determining K d, including fluorescence, require at
least a substantial fraction of the data to be obtained at
much lower [E 1] as explained above. This raises the
question whether changes in the quarternary structure
of E 1 occur between these different concentrations,
giving an erroneous K d for the channeling measurements. For example, mammalian glyceraldeyhyde-3phosphate dehydrogenase undergoes concentrationdependent dissociation in this enzyme concentration
range. For this and other reasons, we currently prefer
to determine K d by pairing the E 1 with an enzyme E 3 of
the same chiral specificity. The K m and V of this E 3 are
established, which then allows one to calculate
[NADH] f from the velocities of the E 3 reaction by rearrangement of the Michaelis–Menten equation. This approach allows one to use precisely the same [E 1] values
for determination of [NADH] f as used in the subsequent channeling tests. The resulting data can then be
used directly (with a small amount of interpolation of
smoothed data if desired) or K d values can be calculated, but it is the calculated [NADH] f that is used in
the calculation of R. Commercial A- and B-type enzymes are adequate for these measurements with E 1 in
our experience. However, this approach does assume
that there is no NADH channeling between enzymes of
the same chiral specificity. We have obtained dissociation constants by this method that are quite close to
published values when available. However, due to the
assumption involved, careful studies should also use
independently determined K d values. We also test the
effect of the presence of the cosubstrate of E 2 on K d,
although we have not found such effects so far. All
other components of the buffer that are to be used in
the subsequent NADH channeling test are also
present.
A serious limitation of the enzyme buffering method
is that, contrary to early impressions, almost all dehydrogenases have a maximum in the experimental R
values. These maxima are dictated by the ratios of
enzyme kinetic and equilibrium (K d) constants that are
unrelated to the fraction of channeling. Our combined
experimental and simulation studies indicate that
many A–B dehydrogenases have high NADH channeling even when their R values are close to 1. Thus, the
enzyme buffering method provides a robust test when
the R criterion is significantly larger than 1, but the
test is insensitive in being unable to detect channeling
when the kinetic and equilibrium constants are unfavorable. In this regard, it is important to realize that v cl0
is very much higher than the actual velocity going
through the free diffusion path if E 1–NADH is a good
substrate. This is because the latter substrate is so
predominant that little E 2 is left for free NADH to bind
to. However, this NADH channeling cannot be presumed to be present, so we have to use the very much
higher v cl0 value for the initial test, even if E 1–NADH is
a good substrate.
Virtues of the enzyme buffering test are its simplicity, speed, presence of good controls for the NADH
system, and robustness when R @ 1. Very high R
values demonstrating NADH channeling have been
found between enzymes from the same or widely different species (3, 17; and our more recent unpublished
studies). Nevertheless, cases exist where R values for
an enzyme pair are '1 unless these enzymes are from
different species. It does not seem reasonable that
channeling would exist in the latter case and be absent
between the enzymes of the same species. Further
support of this view comes from: (1) knowing that R
values are constrained for reasons unrelated to channeling ability and (2) computer simulations of model
equations and parameters based on real data. Therefore, improved tests of NADH channeling are needed,
even if they are more complex. We are exploring such
possibilities, focusing initially on fluorescence polarization measurements on E 2 during the catalytic cycle.
Transient-State Kinetics of Enzyme Forms (Fast Kinetics)
Rapid kinetic measurements with substrate level enzyme concentrations, e.g., 10 mM to several hundred
micromolar, can in principle directly detect enzyme
forms and their transitions during the reaction mechanism. Thus, fast kinetic measurements are capable of
providing more insight into molecular mechanisms
than steady-state methods, which can normally detect
only transitory enzyme forms capable of addition or
SUBSTRATE CHANNELING
release of substrates or products. When detectable
spectral changes occur during transitions of enzyme
forms, continuous monitoring of such transitions in
time is possible. Furthermore, time-resolved wavelength spectra are now possible, e.g., 300- to 500-nm
spectra every few milliseconds, and provide the most
insight in these circumstances. When spectral changes
are not observable, rapid quenching of the reactions is
often possible, providing fast kinetic data for a wider
range of applications. There are practical problems
that often limit the number of elementary steps that
can be determined, but fast kinetic methods can provide unique insights into enzymatic mechanisms. Recent microcapillary mixing devices made by microfabrication techniques have achieved 110-ms (76) and less
than 10-ms (77) mixing times. These provide valuable
practical advances extending kinetic studies to faster
elementary processes than previously possible and offering large economy of reagents.
Good reviews of transient-state methods have been
published by Johnson (78, 79), among others. However,
we mention below several practical limitations of and
precautions with these methods that are not discussed
in the cited reviews. Impressive examples of spectral
studies of substrate channeling are those of Dunn and
co-workers (13). When rapid quench methods are used,
it is often assumed that all elementary steps of the
reaction sequence are quenched as rapidly as the overall production of product. This is not a safe assumption.
For example, it has been shown by spectroscopic monitoring that reactions of important intermediates proceed considerably longer than the quenching of the
overall reaction (13). This oversight from rapid quenching data alone caused erroneous conclusions concerning the basic mechanism of the reaction. Without such
independent methods to test for these more slowlyquenched steps, it is not clear how such artifacts can be
detected with quench flow kinetic methods. It is also
necessary to ensure that the quenching conditions do
not decompose the reaction intermediates that are being characterized. Another precaution is to realize that
most simulated fits are not unique solutions. Therefore, overlapping and independent data are critical in
reducing the number of alternative fits. A recent study
is illustrative of chemical quench methods (80, 81).
Despite the value of transient-state kinetics for providing details of the molecular mechanisms, they are
not in general the methods of choice for initial detection and characterization of channeling. Furthermore,
their applications appear limited to highly purified
systems, which excludes, e.g., studies of channeling in
situ.
Other Channeling Tests
A variety of other methods have been used to indicate substrate channeling. Especially intriguing are
those indicating channeling in vivo. In one method,
319
asymmetrically labeled substrate is added, which is
transformed through symmetrical intermediates, yet
asymmetrically labeled products are found (45). Another method used 31P NMR magnetization transfer
measurements to indicate the channeling of ATP between the pyruvate and creatine kinases in free solution, much like the NADH channeling discussed above
(82). Unfortunately, the method is not currently practical for isotopes other than 31P due to either lack of
sensitivity or insufficient changes in chemical shifts. A
rather common indication of channeling is the finding
that precursors are used considerably faster or exclusively in preference to intermediates in a path producing the product (57, 83, 84). Another study found that
[ 13C]acetoacetyl-CoA was incorporated into hydroxymethylglutaryl-CoA without mixing with the acetate
pool (85). A novel approach using inhibitors indicated
in vivo channeling of substrates for b-carotene biosynthesis (46). Still another study used the fact that 13Clabeled intermediates did not escape from permeabilized vascular smooth muscle as evidence that
channeling occurs in the glycolytic path of these cells
(86). The value of computer modeling, especially when
correlated with experimental work, has been demonstrated by the elegant studies of Elcock et al. (16). The
prevalence and potential significance of substrate
channeling should motivate the development of improved methods.
ACKNOWLEDGMENTS
We thank John S. Easterby, Adrian H. Elcock, Michael F. Dunn,
Eric A. Lehoux, and Leonard A. Fahien for their helpful discussion
and recommendations on this manuscript.
Note added in proof. Further literature search revealed that a
heteroprotein complex can be observed between galactosyltransferase and a-lactalbumin in the presence of the first three of the four
substrates: Mn 21, UPD-galactose, and a-lactalbumin and the product
UDP. [Brew, K., and Powell, J. T. (1976) Fed. Proceedings 35, 1892–
1898), i.e., glucose need not be present. Thus, Ref. (19) in our review
is not an example of a heteroprotein complex that is observable only
during the catalytic reaction. However, it remains an example of the
special conditions and conformation of the proteins required for this
complex formation. Table 6 in this reference by Brew and Powell
contains a typographical error. The K d’s summarized should be mM
rather than mM units as both practical considerations and an original manuscript of one of the authors indicate.
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