(Received for publication, January 31, 1997, and in revised form, March 12, 1997)
From the Markey Center for Molecular Genetics, Department of Microbiology and Molecular Genetics, The University of Vermont, Burlington, Vermont 05405
To investigate the relationship between RNA
folding and ribozyme catalysis, we have carried out a detailed kinetic
analysis of four structural derivatives of the hairpin ribozyme.
Optimal and suboptimal (wild-type) substrate sequences were studied in conjunction with stabilization of helix 4, which supports formation of
the catalytic core. Pre-steady-state and steady-state kinetic studies
strongly support a model in which each of the ribozyme variants
partitions between two major conformations leading to active and
inactive ribozyme· substrate complexes. Reaction rates for
cleavage, ligation, and substrate binding to both ribozyme conformations were determined. Ligation rates (3 min1) were typically 15-fold greater than cleavage
rates (0.2 min
1), demonstrating that the hairpin ribozyme
is an efficient RNA ligase. On the other hand, substrate binding is
very rapid (kon = 4 × 108
M
1 min
1), and the
ribozyme· substrate complex is very stable (KD < 25 pM; koff < 0.01 min
1).
Stabilization of helix 4 increases the proportion of RNA molecules folded into the active conformation, and enhances substrate association and ligation rates. These effects can be explained by stabilization of
the catalytic core of the ribozyme. Rigorous consideration of
conformational isomers and their intrinsic kinetic properties was
necessary for development of a kinetic scheme for the
ribozyme-catalyzed reaction.
Since the first description of a catalytically active RNA molecule (1), much effort has been focused toward elucidating the molecular mechanisms of ribozyme catalysis. Valuable information has emerged from detailed kinetic and thermodynamic analyses of intramolecular and intermolecular reactions catalyzed by several naturally occurring ribozymes, including self-splicing group I introns (2-6) and group II introns (7-9), ribonuclease P (10, 11), hammerhead ribozymes (12, 13). and hairpin ribozymes (14).
It is widely accepted that the folded structure of RNA is critical for its catalytic activity. However, few studies have addressed the problem of how differences in ribozyme folding may affect individual steps of the reaction pathway. One major complication in kinetic analysis of ribozymes results from the ability of most RNA molecules to fold into multiple conformations (15). We believe that the study of conformationally heterogeneous ribozymes is important because it represents a direct and realistic approach to the problem of RNA structure and function.
As a model to investigate the relationship between RNA structure and
kinetic behavior, we are studying the hairpin ribozyme. This ribozyme
is a relatively small RNA molecule (50 nucleotides, 17 kDa) derived
from the minus strand of the satellite RNA associated with tobacco
ringspot virus (16-18). It acts as a reversible, site-specific endoribonuclease, cleaving RNA substrates at a NpG linkage using a
transesterification mechanism to generate products containing 5-hydroxyl and 2
,3
-cyclic phosphate termini or ligating molecules with such end structures. The secondary structure of the
ribozyme· substrate complex, as well as the nucleotides and
functional groups required for catalysis, has been elucidated through
mutational studies, phylogenetic analysis, and in vitro
selection experiments (for review, see Ref. 19). The substrate
interacts with the ribozyme through two intermolecular helices, H1 and
H2 (see Fig. 1A), separated by a symmetrical loop (loop A)
composed of four nucleotides in both substrate and ribozyme. Within the
ribozyme, two intramolecular helices (H3 and H4) are separated by a
large asymmetrical loop (loop B). Nucleobases essential for catalysis are concentrated within loops A and B. Chemical modification and linker-insertion experiments have led to the hypothesis that loop A and
loop B establish tertiary interactions for the ribozyme catalytic core
to be formed, therefore implying a sharp bend between helix 2 and helix
3 (for review, see Ref. 20). This hypothesis has received further
support from experiments which demonstrated that activity can be
reconstituted following separation of the A and B domains (21).
Loop B and its flanking helices constitute an independent folding domain, as indicated by cross-linking and chemical modification studies (22, 23). Although, to a first approximation, the sequence of the helices is not relevant for ribozyme activity (24), we found that extension of helix 4 produces a significant increase in catalytic proficiency, probably through stabilizing the active tertiary structure of loop B as measured by photocross-linking (25).
To achieve a better understanding of structure-function relationships in the hairpin ribozyme system, we have carried out a detailed kinetic analysis of different structural variants of this ribozyme. First, the effect of extending helix 4 was analyzed since its length is likely to affect the stability of the flanking catalytic core. Second, hairpin ribozymes with different substrate specificity were also examined because the naturally occurring substrate is conformationally heterogeneous (26).1 Therefore, four derivatives of the hairpin ribozyme that combine these two modifications, were studied. As shown in Fig. 1, the original helix 4 was extended with three extra base pairs and a stable GUAA tetraloop, and the sequence of the substrate and ribozyme were varied to avoid substrate self-complementarity, as described in Butcher et al. (21). The four resulting hairpin ribozymes were assayed in combination with their cognate substrates. Substrate specificity will be indicated as original sequence (wt)2 or modified sequence (SV5), and the presence of an extended helix 4 will be referred to as EH4.
This comparative analysis has provided new data on the relationship between RNA folding and catalysis by detecting two inherent conformational states of the hairpin ribozyme and interpreting the resulting biphasic kinetics in terms of individual rate constants. These results provide important insights into folding of the hairpin ribozyme and illustrate how structural diversity can be reflected in kinetic behavior. We expect that our results will also be useful for the rational design of new ribozymes with more homogeneous folding and improved catalytic efficiency.
DNA templates for ribozyme
transcription and ribozyme substrates (see Fig. 1) were synthesized on
an Applied Biosystems 392 DNA/RNA synthesizer using standard DNA and
RNA phosphoramidite chemistry. The sequence of the DNA
oligonucleotide complementary to the wt RNA substrate was
5-CCAAACAGGACTGTCGGTTG-3
. Ribozymes were synthesized by
transcribing partially duplex synthetic DNA templates with T7 RNA
polymerase, basically as described (27). All DNA and RNA molecules were
purified by polyacrylamide gel electrophoresis as described (25). In
addition, RNA products of solid-phase synthesis were purified by
reversed-phase high pressure liquid chromatography. RNA substrates were
5
-end-labeled with [
-32P]ATP and T4 polynucleotide
kinase. For RNA ligations in cis, ribozymes were internally
labeled with [
-32P]CTP during transcription.
All reactions were carried out in a reaction buffer containing 50 mM Tris-HCl, pH 7.5, and 12 mM MgCl2 at 25 °C. Ribozyme and substrate RNAs were preincubated separately for 10 min at 37 °C in reaction buffer. Complete denaturation of ribozymes was avoided to prevent formation of ribozyme dimers (23). The solutions were then allowed to equilibrate for 10 min at 25 °C. Reactions were initiated by mixing equal volumes of solutions containing the ribozyme and substrate. Aliquots of the reaction (10 µl) were removed and quenched with an equal volume of loading buffer (15 mM EDTA, 97% formamide). Samples were analyzed in 20% (cleavage and trans-ligation assays) or 6% (cis-ligation assays) polyacrylamide-urea (7 M) gel electrophoresis. Radioactive bands were quantified using a Bio-Rad GS-525 radioimaging system.
Cleavage Activity Under Single-turnover ConditionsCleavage
reactions were carried out with 200 nM ribozyme and less
than 1 nM 5-32P-substrate, unless otherwise
indicated. No change either in the rate or in the extent of cleavage
was observed at higher ribozyme concentrations, indicating that 200 nM ribozyme is saturating (data not shown). The fraction of
substrate cleaved was plotted versus time and fitted to
single- or double-exponential equations. The single-exponential
equation was,
![]() |
(Eq. 1) |
![]() |
(Eq. 2) |
Cleavage reactions were carried out with 1-10 nM substrate and 0.1 nM ribozyme. Reactions were incubated at different times to obtain initial velocities for each substrate concentration. In some cases, higher substrate concentrations (1 µM) were used to evaluate the linearity of the product formation velocity at long reaction times (up to 5 h). Kinetic parameters were obtained by fitting the data to the Michaelis-Menten equation,
![]() |
(Eq. 3) |
For reactions in cis,
ligation assays utilize self-cleaving molecules in which the 5-end of
the substrate is tethered through a short linker (five consecutive
cytidines) to the 3
-end of the ribozyme (28). These molecules were
obtained by transcription from synthetic DNA templates in the presence
of [
-32P]CTP. RNA self-cleavage takes place during
transcription, and the larger product (ribozyme tethered to the 5
cleavage product containing a 2
,3
-cyclic phosphate) was gel-purified
as described (25). The 3
cleavage product was obtained by solid-phase
synthesis. Ligation reactions were carried out with 10 nM
internally labeled ribozymes (ribozyme-5
cleavage product) and 10 µM 3
cleavage product. Neither the rate nor the extent
of ligation was changed by increasing the concentration of the 3
cleavage product, indicating that 10 µM is enough to
achieve saturation (data not shown). The fraction of ribozyme ligated
was plotted versus time and fitted to the single-exponential
equation shown above (Equation 1). The final extent of ligation was
typically between 0.5 and 0.7. The equation parameters were fitted by
means of nonlinear regression analysis as described above. Experimental
and fitting errors were as described for the cleavage reaction.
The 5 cleavage product with a
2
,3
-cyclic phosphate was obtained from a preparative
trans-cleavage reaction using 5
-32P-substrate.
The end-labeled 5
cleavage product was then gel purified as described
(25). Ligation reactions were carried out with a small amount of
5
-32P 5
cleavage product (less than 1 nM) and
saturating excess of 3
cleavage product and ribozyme (8 µM each). The fraction of 5
cleavage product ligated to
the 3
cleavage product (substrate formation) was plotted
versus time and fitted to the double-exponential equation
shown above (Equation 2). The amplitudes and rates of the biphasic time
course were estimated as described for the cleavage reaction.
A
small amount of 5-32P-substrate (less than 1 nM) was incubated with a saturating excess of ribozyme (200 nM) in the reaction buffer for 2 min (wt ribozymes) or
30 s (SV5 ribozymes) at 25 °C. These incubation times allow
essentially complete formation of the ribozyme·substrate complex
since the binding half-times under these conditions are about 30 and
1 s, for the wt and the SV5 ribozymes, respectively (see
"Results"). The chase step is initiated by adding a large excess (5 µM final concentration) of either a DNA oligonucleotide
that is fully complementary to the wt substrate or, alternatively, a
nonradiolabeled SV5 substrate for reactions carried out with wt or SV5
ribozymes, respectively. A complementary DNA oligonucleotide was used
instead of the unlabeled wt RNA substrate because this molecule forms
stable dimers at high concentrations. During the chase period, aliquots
were removed and quenched with an equal volume of loading buffer (15 mM EDTA, 97% formamide). Samples were analyzed and
quantified as described above. Parallel control reactions were carried
out in the absence of the chase molecule. The efficiency of the chase
step was evaluated by mixing the labeled substrate with the chase
molecule (either the complementary DNA oligonucleotide or the unlabeled
RNA substrate) prior to the addition of ribozyme. No significant
cleavage of the labeled substrate was observed under these conditions,
indicating that there is no rebinding of the labeled substrate during
the chase step.
Typically, time courses carried out in the presence of the chase molecule displayed monophasic behavior and, therefore, were fitted to single-exponential equations (Equation 1). Control reactions in the absence of chase showed biphasic kinetics, and hence double-exponential equations (Equation 2) were used. Estimation of the kinetic parameters (amplitudes and rates) was carried out as described above.
Pulse-chase Experiment to Measure Substrate AssociationRate constants for substrate association were
measured using a series of pulse-chase experiments, similar to those
used to evaluate substrate dissociation. Several ribozyme
concentrations, ranging from 12.5 nM to 200 nM
for wt ribozymes or from 1 nM to 10 nM SV5
ribozymes, were combined with a trace amount (less than 0.1 nM) of the corresponding 5-32P-substrate in
reaction buffer at 25 °C. For each ribozyme concentration, several
chase reactions were initiated at different times, ranging from 10 s to 4 min. The chase molecule was a complementary DNA oligonucleotide,
in the case of the wt substrate, or unlabeled RNA substrate, in the
case of the SV5 substrate. The final concentration of the chase
molecule was 5 µM or 1 µM for reactions
carried out with wt or SV5 substrates, respectively. Reactions were
incubated for 1 h at 25 °C after addition of the chase
molecule. This time is sufficient to ensure a quantitative cleavage of
the 5
-32P-substrate·ribozyme complexes (the half-time
for the cleavage reaction is about 5 min). Time courses of the cleavage
reaction were fitted to single-exponential equations, and the observed rates were plotted versus ribozyme concentration to obtain
association (kon) and dissociation
(koff) rates (2).
Using the four ribozymes described above (wt, wt EH4, SV5, and SV5 EH4 ribozymes; Fig. 1) with corresponding substrates, we have carried out pre-steady-state and steady-state kinetic analyses. Pre-steady-state kinetics were used to measure individual rates for substrate binding (association and dissociation) and catalysis (cleavage and ligation). Steady-state analysis was used to assess rate-limiting steps and to estimate the interconversion rates between different conformations of the ribozyme (see below).
Cleavage Activity Follows Biphasic BehaviorExperiments in which ribozyme was in large excess over substrate (single-turnover conditions) were used to measure the first-order rate for cleavage of substrate (see "Materials and Methods"). Under these conditions, the observed rate will reflect the rate of the cleavage step, unless both cleavage products remain bound to the ribozyme long enough as to be ligated (reverse reaction). However, product dissociation is much faster than ligation in the hairpin ribozyme (14), preventing the interference of the ligation activity in a cleavage assay carried out in the presence of ribozyme excess.
Time courses for cleavage catalyzed by wt, wt EH4, SV5, and SV5 EH4
ribozymes were followed at 25 °C. An excess of 200 nM ribozyme was used with picomolar concentrations of their corresponding [-32P]ATP radiolabeled substrates to monitor cleavage
rates under single-turnover conditions (see "Materials and
Methods"). A typical time course for such a cleavage reaction, as
catalyzed by the wt ribozymes is shown in Fig. 2. For
all four ribozymes, the experimental data were fitted to single- and
double-exponential equations (see "Materials and Methods"). As
shown in Fig. 2, the data are much better described as biphasic rather
than monophasic reactions. This was evident by visual inspection of the
data and from the comparison of statistical error parameters (standard
deviation,
2, and determination coefficient,
R2).
Table I lists the values of the rates and amplitudes for the two different reaction phases for all four ribozymes. For the rest of this paper, we will refer to these phases as "fast" and "slow" according to their corresponding rates. The amplitudes and rates of both the phases were independent of ribozyme concentrations (25-200 nM) under single turnover conditions (Fig. 3). This rules out the possibility that the biphasic behavior of the ribozymes is due to the aggregation of two or more molecules. Before initiation of the reaction, both the ribozyme and the radiolabeled substrate were incubated separately at 37 °C for 10 min. To induce different folding conditions, different preincubation protocols were followed before the cleavage reactions were initiated. These conditions included preincubation at 90 °C for 1 min, 65 °C for 10 min, 37 °C for 10 min, and no preincubation. In all cases, biphasic kinetics were observed.
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Except in the case of the wt ribozyme, approximately 75% of the substrate was cleaved in the fast phase of the reaction. The rate of the fast phase was generally at least 10-fold greater than the rate of the slow phase. Although the reaction rates follow a similar trend for the wt ribozyme, the amplitudes of the fast and slow phases were almost equal. This indicates that the partitioning of the two phases in the case of the wt ribozyme is different from the other three variants of the hairpin ribozyme.
Rate Constants for LigationThe rates of ligation for all
four constructs of the hairpin ribozyme were measured using two
different approaches, cis- and trans-ligation.
Cis-ligation was carried out using a self-cleaving version
of the hairpin ribozyme that is covalently attached to the 5-product
through a short pentacytidine linker (28), as described under
"Materials and Methods." The cis-ligation rate was
measured using a trace quantity of the internally labeled ribozyme (10 nM) with a saturating excess of 3
-product (10 µM). In contrast, the trans-ligation reaction
was monitored using a trace amount of 5
-32P 5
-product
(<1 nM) in the presence of saturating concentrations of 8 µM ribozyme and 3
-product (see "Materials and
Methods"). In both cases (cis- and
trans-reactions), the observed ligation rate will reflect an
approach to the equilibrium between cleavage and ligation since
cleavage is much faster than dissociation of the ribozyme·substrate
complex (see below). Therefore, the observed rate will be the sum of
cleavage and ligation rates.
Cis-ligation kinetics were studied for each of the four
ribozymes, and reaction profiles followed single-exponential kinetics (Fig. 4A and Table II). On the
other hand, the ligation reaction in trans catalyzed by SV5
and SV5 EH4 ribozymes clearly showed biphasic kinetics (Fig.
4B and Table II). These ligation time courses were fitted to
double-exponential equations, which allowed estimation of amplitudes
and rates of both phases (Table II). Rates of trans-ligation
for wt and wt EH4 ribozymes could not be measured since the high
ribozyme concentration required for these reactions led to accumulation
of ribozyme dimers (23).
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The observed ligation rates were about 15-fold faster than the cleavage rates (compare Table I with II). Therefore, the rates shown in Table II essentially reflect the ligation step since the reversal reaction (cleavage) is negligible. This indicated that the hairpin ribozyme is an efficient ligase. A similar observation was reported from a previous kinetic study with the hairpin ribozyme (14). Ligation rates were generally faster for the constructs with EH4, with the exception of the cis-ligation reactions carried out with the SV5 ribozymes (see Table II).
Substrate Dissociation RatesPulse-chase experiments were
designed to obtain upper limits for substrate dissociation rates. As
shown in Fig. 5A, this method evaluates the
partitioning of a ribozyme·substrate complex between substrate
dissociation and cleavage (product formation). The
ribozyme· substrate complex is formed by incubating a trace amount
of 5-32P-labeled substrate with an excess of ribozyme
(pulse step). This incubation is long enough to ensure quantitative
binding of substrate (see below for substrate association rates) but
short enough so that most of the substrate remains uncleaved. The chase
step is initiated by adding an excess of a DNA oligonucleotide
complementary to the substrate or an excess of unlabeled substrate (see
"Materials and Methods"). Under these conditions, dissociation of
labeled substrate is irreversible. Therefore, the accumulation of
product over time during the chase step allows estimation of the
competition between cleavage and substrate dissociation.
These experiments were carried out with the four ribozymes under study (wt, wt EH4, SV5, and SV5 EH4 ribozymes). A representative result obtained with SV5 ribozyme is shown in Fig. 5B. The nonchased control reaction presented the biphasic behavior described above. However, reactions carried out in the presence of the chase showed clear monophasic behavior. Values for amplitudes and rates were obtained by fitting the experimental data to double (reactions without chase) or single exponential equations (reactions with chase). Results are shown in Table III and indicate that the single phase observed in the presence of chase corresponds with the fast phase of the nonchased reaction, taking into account both amplitudes and rates. Therefore, when reassociation of substrate molecules is prevented, the slow phase is abolished while the fast phase remains virtually unchanged. This behavior was observed with different ribozymes possessing a variety of values for amplitudes and rates (not shown).
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These results clearly suggest that there are two populations of ribozyme·substrate complexes. One population undergoes cleavage at a much faster rate than substrate dissociation and is responsible for the fast phase of the biphasic kinetic behavior. In contrast, the other population favors dissociation rather than cleavage and is responsible for the slow phase observed in cleavage reactions. Specific kinetic schemes that take into account these two populations will be discussed below.
Rate of Substrate AssociationThe results presented in the
previous section permitted us to measure the association rate for
ribozyme·substrate complex. The experimental strategy is outlined in
Fig. 6A. A trace amount of
5-32P-labeled substrate was incubated with an excess of
ribozyme for varying times to allow formation of the two kinds of
complexes discussed above (pulse step). An excess of a DNA
oligonucleotide complementary to the substrate or an excess of
unlabeled substrate was then added to prevent further binding (chase
step). Reactions were allowed to proceed until essentially all bound
5
-32P-substrate was either cleaved or dissociated (see
"Materials and Methods"). As indicated above, one population of
ribozyme· substrate complexes undergoes cleavage without
significant dissociation during the chase step, whereas substrate
dissociates quantitatively in the other population. Taking this into
account, the amount of labeled substrate cleaved during the chase step
represents the formation of the catalytically proficient complex during
the pulse step (see Fig. 6A).
Time courses of complex formation obtained at different concentrations of SV5 EH4 ribozyme are shown in Fig. 6B. The observed rates of complex formation (kobs) reflect the rate of approach to equilibrium, which is the sum of association and dissociation rates (kobs = kon [Rz] + koff; where kon and koff stand for association and dissociation rates, respectively, and [Rz] represents ribozyme concentration). The plot of kobs versus SV5 EH4 ribozyme concentration is shown in Fig. 6C. The y-intercept was equal to 0, within error, indicating that substrate dissociation (koff) is very slow. The substrate association rates (kon) obtained for the four ribozymes under study are shown in Table IV. The interpretation of these substrate association rates is complicated because of the fact that two different ribozyme·substrate complexes are being formed. As discussed below, the value for kon that is measured in this manner can be considered as a weighted average of the substrate association rates of both complexes.
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To test the validity of some of the kinetic parameters obtained from the pre-steady-state analyses, we carried out cleavage reactions under steady-state conditions in which the rate-limiting step is assessed. This analysis is especially pertinent when two populations of ribozyme·substrate complexes are present since exchange rates between them may be reflected in the rate-limiting step.
Under multiple-turnover conditions (substrate excess), cleavage reactions were carried out with SV5 and SV5 EH4 ribozymes (see "Materials and Methods"). Accurate steady-state measurements were not possible with wt or with wt EH4 ribozymes since the wt substrate forms dimers by means of self-complementarity at the concentrations required for multiple-turnover analysis.1
For both SV5 and SV5 EH4 ribozymes, the maximal rate constant for
product formation at saturating substrate concentration (kcat) was 0.15 min1, and the
substrate concentration at which half of the maximal velocity is
achieved (Km) was 1.4 nM
(Fig. 7). The rate of product formation remained
constant for up to at least 5 h, as long as excess substrate
remained, and no initial burst of product formation was observed (not
shown). These observations suggest that the ribozyme is not being
trapped into an inactive conformation during this time interval and
allow us to impose constraints to the different kinetic models
describing populations of ribozyme·substrate complexes (see
below).
In studies of ribozyme kinetics, the presence of alternatively folded structures of ribozymes and substrates is a significant problem that frequently makes an accurate kinetic description of the reaction difficult or, in some cases, impossible. In most studies to date, investigators have avoided this problem by testing various combinations of ribozymes and substrates and discarding those that are not kinetically well behaved. Alternatively, and more commonly, workers in the field have focused only on the fastest phase of the reaction by measuring initial rates of reaction.
Studies on various hairpin ribozyme constructs led us to the conclusion that conformational heterogeneity was likely to be an inherent property of the hairpin ribozyme. Therefore, an adequate understanding of the kinetic mechanism requires quantitative consideration of the kinetic heterogeneity that is as rigorous as possible.
We have determined individual rate constants for substrate binding and catalysis for four structural variants of the hairpin ribozyme in an effort to understand the structural basis for conformational heterogeneity together with its implications for the catalytic activity of the ribozyme. It is important to point out that each of these four ribozymes migrated as single bands in nondenaturing polyacrylamide gels (data not shown). However, two major activity forms (active and inactive) were detected for all of them through kinetic analysis. At the present time, we do not know whether these two conformations co-migrate in native gels or if only one of them is stable under the electrophoretic conditions. In either case, it is clear that native gel electrophoresis should be used with caution as a diagnostic tool for the conformational homogeneity of RNA.
Kinetic Mechanism of the Hairpin Ribozyme
Competition between Cleavage and DissociationThe biphasic nature of the cleavage reactions catalyzed by the four hairpin ribozymes under investigation (wt, wt EH4, SV5, and SV5 EH4 ribozymes) is very clear. Biphasic or multiphasic kinetics have been observed in numerous other ribozyme reactions (5, 9, 29-32). However, only in a very few cases, the multiphasic character of the reactions was incorporated into the analysis of the authors (5, 9, 32). In our particular case, biphasic kinetics were observed at different ribozyme concentrations and with different protocols for RNA folding prior to reaction. Therefore, this behavior seems to reflect an inherent property of the hairpin ribozyme.
Several different kinetic mechanisms could give rise to biphasic cleavage reactions. Such models include multi-step reactions and heterogeneous populations of reactants. Determination of the actual mechanism is necessary for the accurate derivation of rates for association, dissociation, cleavage, and ligation steps.
In the case of the hairpin ribozyme, the slow phase of the cleavage reaction is abolished when substrate reassociation is prevented (Fig. 5, pulse-chase experiment), and yet the fast phase remains unchanged. The simplest explanation that accounts for these results implies the presence of two populations of ribozyme·substrate complexes. The fast phase would result from the cleavage activity taking place in one of the populations. In these molecules, the rate of cleavage would be much faster than the rate of substrate dissociation since neither the amplitude nor the rate of the fast phase is affected when substrate reassociation is prevented. The other population of complexes would undergo slow dissociation rather than cleavage. Dissociated substrate molecules would then be free to partition again between both populations since ribozyme is in excess in this kind of assay. Therefore, the second phase would result from the slow substrate dissociation taking place in this second population. Based on the competition between cleavage and dissociation, the former population might be considered as the active one in terms of product formation, whereas the latter one would represent an inactive population.
Once a model has been partially defined, it is possible to extract some
information from the amplitudes and rates of the biphasic kinetics
(Fig. 8). According to the two-population model
presented above, the amount of active and inactive complexes formed
upon substrate binding corresponds to the amplitudes of the fast and slow phases, respectively. The actual cleavage rate
(kcleav) can be directly obtained from the rate
of the fast phase of the biphasic kinetics, being 0.15 min1 as average (Table I). As discussed above, the
dissociation rate from the active complex (k
1)
has to be much slower than the cleavage rate. Hence the upper limit of
k
1 can be estimated to be one-tenth of
kcleav (0.01 min
1). This value is
in agreement with previous kinetic studies of the hairpin ribozyme (14,
42). On the other hand, the dissociation rate of the inactive complexes
(k
2) is not equivalent to the rate of the slow
phase since substrate is expected to partition between active and
inactive populations after each dissociation event, and only substrate
molecules that are turned over to the active complexes will contribute
to the slow phase of the reaction. Therefore, the actual dissociation
rate is the proportion of the rate of the slow phase to the substrate
fraction that partitions to active complexes, which is the amplitude of
the fast phase (k
2 = rate of slow
phase/amplitude of fast phase). Applying this calculation to the data
presented in Table I, k
2 can be averaged as
0.01 min
1, ranging from 0.006 min
1 (SV5 EH4
ribozyme) to 0.026 min
1 (wt EH4 ribozyme).
Exchange between Active and Inactive Conformations
Some
information about the exchange rates between the two populations can
also be extracted from the pulse-chase experiment shown in Fig. 5. The
fact that the slow phase of the biphasic reaction virtually disappears
when substrate reassociation is prevented suggests that substrate
quantitatively dissociates from the inactive complex rather than
isomerizing to form active ones. In other words, substrate dissociation
(k2) is estimated to be at least 10-fold
faster than a putative exchange rate (k
3). Hence, an upper limit of 0.001 min
1 can be calculated for
k
3 (Fig. 8).
To get more information about exchange rates, the kinetic scheme has to be defined with more precision. As schematized in Fig. 8, active and inactive populations of ribozyme·substrate complexes can be formed, either when a substrate molecule is able to bind the ribozyme in two different conformations (Fig. 8A) or when two populations of ribozymes are present prior to substrate binding (Fig. 8B). These two models predict different behaviors for a cleavage reaction carried out in steady-state conditions, that is, with an excess of substrate over ribozyme. According to the former scheme, ribozyme molecules will partition into active and inactive complexes after each cleavage cycle, and, therefore, the amount of active ribozyme·substrate complexes will decrease with successive turnovers. Eventually, this will lead to a reduction in the rate of product formation as the ribozyme becomes trapped into inactive complexes.
It is important to realize that a putative exchange between both
populations would not be fast enough to reequilibrate the amount of
active and inactive complexes since the turnover rate (kcat = 0.15 min1) is much higher
than the upper limit for the conversion of inactive complexes into
active ones (k
3 < 0.001 min
1).
However, the steady-state rate of product formation was constant for up
to at least 5 h, indicating that the model shown in Fig. 8A is not correct. On the contrary, the kinetic scheme shown
in Fig. 8B is compatible with all of our observations from
both pre-steady- and steady-state analyses. According to this model,
the hairpin ribozyme is able to adopt two different conformations. Upon
substrate binding to both populations, active and inactive complexes
are formed. The active ones proceed to cleave substrate while the inactive ones slowly dissociate, giving rise to biphasic kinetics.
Bearing this model in mind and taking into account the results obtained
from the steady-state analysis, it is also possible to set an upper
limit for the conversion rate from active to inactive ribozyme·substrate complexes, k3 (Fig.
8B). Using the same rationale described above, one can see
that a fast k3 would produce a decrease in the
steady-state rate of product formation as the amount of active
ribozyme·substrate complex is diminishing. Considering that the
steady-state rate remains constant after 5 h of cleavage reaction
and assuming an upper limit of 0.001 min1 for
k
3, it can be calculated that
k3 cannot be faster than 0.0008 min
1 (see "Appendix"). Taking these upper limits for
k3 and k
3 into account,
active and inactive ribozyme·substrate complexes seem to be in very
slow exchange, if they exchange at all.
The model shown in Fig. 8B also allows a more precise interpretation of the measured amplitudes and substrate association rates. Substrate binds to active and inactive ribozyme populations with association rates k1 and k2, respectively, giving rise to the corresponding complexes. Taking into account that substrate dissociates very slowly in both cases, it can be demonstrated that the observed rate of complex formation is the same for both populations, being the average of their corresponding association rates (k1 and k2) corrected by the relative abundance of each population (Ra and Ri; see "Appendix"). If we define f as the ribozyme fraction in the active conformation (f = Ra/RT, where RT represents the total population of active and inactive molecules), then the observed rate of complex formation for both populations is as follows.
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(Eq. 4) |
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(Eq. 5) |
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(Eq. 6) |
The validity of this interpretation is also supported by the results obtained with the steady-state analysis. Assuming a fast dissociation of the cleavage products (14) and a null exchange rate between active and inactive complexes (this paper), the steady-state parameters (kcat and Km) can be related with the individual rate constants defined in Fig. 8B as follows.
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(Eq. 7) |
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(Eq. 8) |
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(Eq. 9) |
It is also important to mention that all the derivations of rate constants presented in this section are only valid when the rate of substrate dissociation from both active and inactive complexes is much slower than the cleavage rate. The general analytical solution for the biphasic kinetics, including all the rate constants shown in Fig. 8B, is also available upon request.
Finally, the validity of the model presented in Fig. 8B has been tested by means of computer simulation using measured or calculated values for the rates of substrate binding, dissociation, and cleavage. The experimental results from both pre-steady- and steady-state kinetics were accurately reproduced by these simulations (not shown).
Comparative Analysis of the Cleavage Reaction by Different Hairpin Ribozyme Constructs
The availability of an accurate kinetic scheme, as presented in Fig. 8b, is necessary for a meaningful comparison of the rate constants measured for the hairpin ribozyme derivatives.
One of the first conclusions that can be drawn from the kinetic analysis reported in this paper is the suboptimal cleavage activity of the wt ribozyme. Taking into account the amplitudes of its fast and slow phases, it can be concluded that only 50% of the ribozyme·substrate complexes are found in the active population. On the contrary, the other three ribozymes (wt EH4, SV5, and SV5 EH4) form active complexes in about 75% of the cases. Therefore, two structural changes (extension of helix 4 and modification of substrate specificity) are able to improve the catalytic efficiency of the hairpin ribozyme. However, the effects of these two changes seem to be interdependent. In the context of SV5 substrate specificity, extension of helix 4 did not significantly alter the amount of active and inactive ribozyme·substrate complexes, as reflected in the amplitudes of the biphasic cleavage reaction. Taking into account the kinetic interpretation of the observed association rates and amplitudes (Equations 4-6), these results suggest that extension of helix 4 would have no significant effect in ribozyme folding when the SV5 substrate specificity is considered.
A different situation was obtained in the context of wt substrate specificity, where the amount of active complexes was increased by extending helix 4. As shown in Equation 5, this result can be explained by a faster substrate association rate for the active conformation (k1) or by an increase in the amount of properly folded ribozymes (f). Obviously, these two possibilities are not mutually exclusive. Although we cannot rule out the possibility that k1 may be faster, the results presented in this paper suggest that the conformational heterogeneity of the wt hairpin ribozyme is biased toward the active conformation when the length of helix 4 is increased. This concept is also supported by UV cross-linking studies (25). Stabilization of helix 4 may facilitate the alignment of essential functional groups in loop B, therefore stabilizing the catalytic core of the ribozyme. A similar effect of helix extension has been recently proposed for the hepatitis delta virus ribozyme (33). However, the effect of changing the substrate specificity (wt or SV5) is less clear. It is possible that the wt substrate binding strand is directly or indirectly interfering with the proper folding of the ribozyme. In this sense, changing the substrate specificity or stabilizing helix 4 might increase the probability that a ribozyme molecule will adopt the active conformation.
It is worth noting that even the optimized hairpin ribozymes (extended helix 4, SV5 substrate specificity) still displayed biphasic behavior in a cleavage assay. In contrast, monophasic kinetics have been previously reported in a kinetic analysis of the hairpin ribozyme by Hegg and Fedor (14). It is important to realize that biphasic behavior will be observed only when substrate dissociation from the inactive complexes is slower than the cleavage rate. Therefore, the Hegg and Fedor results are also compatible with a two-population model if substrate dissociation from the inactive complexes was relatively fast in their system. This interpretation is supported by the observation of the authors that about 50% of the substrate remains uncleaved at the end of a pulse-chase experiment (14). Hence, we propose that conformational heterogeneity is a general property of the hairpin ribozyme and that it could reflect specific structural constraints of this ribozyme.
The results presented in this paper do not provide information about the specific structure of the inactive conformation. However, recent structural analyses carried out in this laboratory support the concept of an inactive conformation of the ribozyme·substrate complex in which coaxial stacking of helices 2 and 3 results in an extended conformation that prevents interaction of the A and B domains.3 An analogous inactive conformation has been recently proposed for a reversely joined hairpin ribozyme (34).
Comparison of substrate association rates reveals an important difference between the wt and SV5 ribozymes. The rate of formation of the SV5 ribozyme·substrate complex is approximately 50-fold faster than that of the wt complex, regardless of whether or not the extended forms of helix 4 are used. However, the association rates observed with the SV5 substrate were similar to the values obtained for helix formation between oligonucleotides (35-40). The slow association rate of the wt substrate is likely to be related to its ability to adopt hairpin and dimer conformations by means of self-complementarity.1 Assuming that the intrinsic association rate is not significantly altered by substrate sequence, the 50-fold slower rate observed for the wt substrate suggests that most of the molecules are present in a conformation that is not amenable for ribozyme binding. On the other hand, the different conformers of the wt substrate seem to be in rapid exchange since the observed rate of wt substrate association remains second-order at the highest ribozyme concentrations tested. This fact is in agreement with the fast dissociation rates observed for model duplexes and hairpins of comparable lengths (41).
It should be noted that the previously reported value for the substrate association rate of the hairpin ribozyme was calculated with a self-complementary substrate (14), and that value is fairly comparable to the one we observed for the wt substrate. Based on this association rate, the authors reported that the binding free energy of a ribozyme·substrate complex was nearly equivalent to that of a ribozyme bound to the cleavage products (14). However, if we take the observed association rate of a nonself-complementary substrate (SV5) to be correct, then the free energy for substrate binding is about 2.0 kcal/mol lower than that for binding of the cleavage products. Therefore, the ribozyme·substrate complex may be structurally different from the complex formed by the ribozyme with the cleavage products.
Comparative Analysis of the Ligation Activity
The ligation reaction catalyzed by the hairpin ribozyme showed
either monophasic or biphasic behavior depending on the assay. Ligation
reactions carried out in cis, that is, when the 5 cleavage product is covalently linked to the ribozyme, followed single exponential kinetics. On the other hand, a biphasic reaction was observed when the ribozyme was not attached to any of the cleavage products. This behavior is in agreement with the two-populations model
presented for the cleavage reaction. Active complexes formed between
the ribozyme and the cleavage products would give rise to the fast
phase of the biphasic kinetics, its rate corresponding to the actual
ligation rate. The second phase would be the result of the slower
dissociation of an inactive population of complexes. Obviously, this
dissociation step cannot produce a second phase when the
cis-ligation activity of the ribozyme is monitored.
It is also noteworthy that the rate of the second phase (derived from dissociation of inactive complexes) was much faster for the ligation reactions than for the cleavage assays. This is probably due to the greater stability of the ribozyme·substrate complex, compared with that of the cleavage products (14).
Most of the ligation rates presented in this paper were about 15-fold greater than the corresponding cleavage rates. These results agree with the observation that the hairpin ribozyme is more efficient as ligase than as an endonuclease (14). We also observed that ligation rates were, in most cases, increased by extending helix 4. The only exceptions were the ligation reactions carried out in cis with the SV5 ribozymes; these were about 3-fold faster than the corresponding cleavage reactions, and no significant difference was observed between SV5 and SV5 EH4 ribozymes. It has been proposed that the efficiency of the ligation reaction of the hairpin ribozyme results from a rigid ribozyme structure, which reduces the entropic advantage of the cleavage reaction (12, 14). According to this, the improved ligation rate observed when helix 4 was extended may reflect a more rigid tertiary structure of the hairpin ribozyme when this helix is stabilized with three extra base pairs. This interpretation would also agree with the faster rate of substrate association measured for wt EH4 and SV5 EH4 ribozymes. It has been proposed that nucleic acid double helix formation is a two-step process composed of a nucleation step (formation of an unstable "nucleus" of two to three base pairs) and a growing step in which the sequential addition of base pairs to the "nucleus" stabilizes the helix (35, 36). In this sense, the rigid tertiary structure provided by the extension of helix 4 might stabilize the formation of the transitory "nucleus" and/or favor the correct alignment for the addition of adjacent base pairs.
Finally, the results presented in this paper provide evidence that modifications of ribozyme structure may have diverse effects on catalytic proficiency. Therefore, determination of the kinetic mechanism of the ribozyme, including the kinetic contributions of conformational heterogeneity, is an important prerequisite for understanding structure-function relationships.
We thank Jillian Amaral for purification of T7 RNA polymerase, David Pecchia for the synthesis of DNA and RNA oligonucleotides, and Joyce Heckman and Nils Walter for fruitful discussions.
When the cleavage assay is carried out at saturating substrate concentrations, it can be considered that both ribozyme populations are always in the form of ribozyme·substrate complex since the cleavage reaction is rapidly followed by product dissociation and binding of a new substrate molecule. Under these conditions, the exchange between active and inactive conformations of the ribozyme can be reduced to the following.
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(Eq. 10) |
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(Eq. 11) |
Since substrate dissociation is much slower than the association rates measured in this study, the process of substrate binding can be reduced to the following.
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(Eq. 12) |
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(Eq. 13) |
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(Eq. 14) |
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(Eq. 15) |
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(Eq. 16) |
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(Eq. 17) |