Traditionally, ribozyme activity is determined through in vitro cleavage followed by gel electrophoresis; the latter most often uses a radiolabeled substrate RNA combined with autoradiography 39, although non-radioactive detection by ethidium bromide staining has also been employed 40. For both methods, quantification then requires densitometry of the cleavage products on the gel. Here, we wished to evaluate whether ribozyme cleavage activity can also be measured via quantitative RT-PCR. Accordingly, ribozyme GUC7 was incubated for varying lengths of time with the appropriate substrate RNA, and the remaining substrate was analyzed either by agarose gel electrophoresis followed by densitometry, or else by real time RT-PCR on the LightCycler. As shown by Figure 2, the results from these two methods are in good agreement. We concluded that quantitative RT-PCR is a valid method by which to determine ribozyme activity in vitro; thus, all activity measurements for our study were therefore made by this method.

For the 15 ribozymes tested in vitro, we performed both correlation and regression analyses, using the ribozyme catalytic activity measured by (1-Su3600), and each of the computational parameters (see Methods). First, we observed that there were two outliers, namely, ribozymes GUC3 and GUC11, which behaved differently from the other 13 ribozymes. We thus initially focused on the analyses for the 13 "normally behaving" ribozymes, and then investigated possible explanations for the two outliers.

For the 13 well behaved ribozymes, we found, among the structural and thermodynamic parameters, that ΔG_disruption and ΔG_total are significantly correlated with ribozyme activity (Table 2). The correlation coefficient for ΔG_disruption is 0.6839 with a P-value of 0.0099, and the correlation coefficient for ΔG_total is -0.7901 with a P-value of 0.0013. Ribozyme activity, however, was not significantly correlated with ΔG_switch, or ΔG_hybrid. Because ΔG_total is computed from ΔG_disruption, ΔG_switch, and ΔG_hybrid (see Methods), ΔG_total and ΔG_disruption are significantly correlated (correlation coefficient = -0.6349, and P-value = 0.0110). Thus, the significance of the correlation with the ribozyme activity for ΔG_total is mainly due to ΔG_disruption. From linear regression analysis, either ΔG_disruption or ΔG_total is significantly predictive of the ribozyme activity (Table 2, Figure 3). Furthermore, in a comparison of the R² values for ΔG_disruption and ΔG_total, a relative improvement of about 33.5% is observed for ΔG_total. This suggests that, although ΔG_switch and ΔG_hybrid are insignificant as individual predictors, they do contribute to the improved predictability by ΔG_total. The R² for ΔG_total indicates that over 60% of the variability in the ribozyme cleavage activity can be attributed to ΔG_total.

To understand the behaviors of the two outliers, ribozymes GUC3 and GUC11, we examined the structures predicted by Sfold for each of the ribozymes. In the case of ribozyme GUC3, we found that, for 79.1% of the structures, there are at least four base pairs formed by nucleotides in the two binding arms and the ends of the catalytic core sequence (Figure 4). In the "active" ribozyme binding conformation (Figure 1B), all of not only the binding arms but also the end sequences of the catalytic core are single-stranded. Thus, substantial intramolecular structure involving these regions can hinder target binding by the ribozyme, despite the correct formation of helix II (Fig 1A). For GUC11, we found that 33.5% of sampled structures have the catalytic core misfolded so that it lacks a correctly formed helix II (Figure 5). This could explain the observation that GUC11 was the least effective for target cleavage (Table 1, Figure 3), despite a moderately accessible target site as indicated by ΔG_disruption (Table 1). In contrast, for each of the other 14 ribozymes in our study, the percentage of the sampled structures having a misfolded core is less than 1%.

For creation of the ribozymes in vitro, two complementary oligonucleotides containing the hammerhead ribozyme core sequence flanked by the sequences for the two binding arms and a T7 RNA polymerase promoter sequence were annealed into duplex DNA in 10 mM Tris, pH 8.0, and 50 mM NaCl, by incubation at 94°C for 5 min, followed by slow cooling to room temperature. All oligonucleotides were obtained from Integrated DNA Technology (IDT, Coralville, IA).

In vitro transcription of the substrate and ribozyme RNA was performed using the MEGAscript and MEGAshortscript kits (Ambion-ABI, Austin, TX), respectively, following the manufacturer's instructions. Either 2.5 μg of linearized plasmid (pTRIamp19, Ambion) containing the target ABCG2 cDNA sequence, or 1.5 μg of ribozyme DNA were used as template. After transcription, the DNA templates were digested with RQ1 RNase-free DNase. Unincorporated nucleotides were removed from the RNA transcripts by size-exclusion chromatography with a ProbeQuant G-50 Micro Column (GE-Healthcare, Piscataway, NJ) or by phenol/chloroform extraction, both of which were followed by an ethanol precipitation. The purified in vitro-transcribed RNAs and ribozymes were then quantitated spectrophotometrically, and their quality verified by gel electrophoresis (see Additional file 1). Two separate substrate RNAs were made, one from nucleotides -225 to +1011, and one from nucleotides +586 to +1708, relative to the A of the ATG start codon of the full length ABCG2 cDNA (GenBank accession no. NM_004827). Individual ribozymes are numbered consecutively in the order of occurrence of the GUC cleavage sites to which they bind, starting from nucleotide -285. Thus, for example, GUC1 refers to the first GUC triplet after nucleotide -285. A total of 15 hammerhead ribozymes targeted to GUC sites were designed and prepared (Table 1). These ribozymes were constructed with the same ribozyme core sequence, but with different sequences for binding arms that were complementary to the target sequences at the binding site (Figure 1A; also see Additional file 2). For each of these ribozymes, the 3' binding arm had 11 nucleotides, and the 5' binding arm had nine nucleotides.

The target RNA (10 pmol) and ribozyme (50 pmol) under study were mixed in 50 mM Tris, pH 8.0, and the in vitro cleavage reaction was initiated by the addition of 20 mM MgCl₂. One μl of RNaseGuard was also added, and the mixture was incubated at 37°C. 10-μl aliquots were removed after 0, 5, 10, 15, 30, and 60 min, and the reaction was terminated by the addition of 50 mM EDTA. The cleavage products were then analyzed by electrophoresis in a 2% (v/v) formaldehyde/2.0% (w/v) agarose gel for 3–4 hr at 70 V. The separated products were stained with SYBR Green or ethidium bromide and photographed under UV light 40.

Since a ribozyme irreversibly cleaves its substrate, we reasoned that the cleavage reaction could be quantified through measurement of the amount of substrate remaining by real-time RT-PCR, using primer pairs that span the cleavage site. Accordingly, an aliquot of the cleavage reaction containing both the remaining, uncleaved substrate and the cleavage products was added to a one-step real-time RT-PCR reaction mix containing SYBR Green (Sigma, St. Louis, MO) according to the manufacturer's instructions, and amplification was carried out for 35–45 cycles in a LightCycler^® (Roche, Indianapolis, IN), under conditions appropriate for each primer pair (see Additional file 3). Primers flanking each cleavage site were chosen such that the PCR products were between 600 and 400 bp long. The amount of uncleaved substrate present was determined from the crossing point values (C_T) calculated by the Lightcycler software from the amplification curve. The relative amount of template remaining at each time point (Su(t)) was then calculated by 2−(CT(t)−CT(0)) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaeGOmaiZaaWbaaSqabeaacqGHsislcqGGOaakcqqGdbWqdaWgaaadbaGaeeivaqLaeiikaGIaeeiDaqNaeiykaKcabeaaliabgkHiTiabboeadnaaBaaameaacqqGubavcqGGOaakcqaIWaamcqGGPaqkaeqaaSGaeiykaKcaaaaa@3B27@, where C_T(t) is the C_T value at time t, and C_T(0) is the C_T value at time 0. Each time point was assayed in duplicate, and each cleavage reaction was repeated at least four times independently with different batches of substrate RNA. Selected ribozymes were also analyzed with differing ribozyme preparations. No significant activity differences were observed between separate ribozyme and/or substrate preparations. For the subsequent calculations, the relative amount of substrate cleaved at 3600 sec (1-Su3600) was used as the measure of ribozyme activity. In preliminary experiments, we determined that the RT-PCR reaction was linear with the amount of substrate present (data not shown).

The determination of mRNA secondary structure presents both theoretical and experimental challenges. One major impediment to the accurate prediction of mRNA structures stems from the likelihood that a specific mRNA molecule does not adopt a single structure in solution, but instead likely exists in thermodynamic equilibrium among a population of structures 303145. Thus, the computational prediction of secondary structure based on free energy minimization is not well suited to the task of providing a realistic representation of mRNA structures in vivo.

An alternative to free energy minimization for characterization of the ensemble of probable structures for a given RNA molecule has been developed 32. In this approach, a statistically representative sample is drawn from the Boltzmann-weighted ensemble of RNA secondary structures for the RNA. Such samples of even moderate size can faithfully and reproducibly characterize structure ensembles of enormous size, so that sampling estimates of structural features are statistically reproducible from one sample to another. In particular, in comparison to free-energy minimization, this method has been shown to make better structural predictions 35 and to better represent the likely population of mRNA structures 34, and to yield a significant correlation between predictions and antisense inhibition data 3637. A sample size of 1,000 structures has been shown to be sufficient to guarantee statistical reproducibility in typical sampling statistics and structure clustering features 3234. In applications to modeling RNA target binding by a (partially) complementary nucleic acids, because a single-stranded block of four or five nucleotides is essential for the nucleation step of the hybridization 254647, the probability that such block is single-stranded must be high. Thus, in the current and other related applications, we consider the sample size of 1,000 to be sufficient. In the case that a structural feature of small probability is of interest, a much larger sample would be required. The structure sampling method has been implemented in the Sfold software program for RNA folding and applications 33 and is used here for mRNA folding.

The core of the ribozyme is considered to exist in a mixture of conformations in solution that can interchange rapidly 48495051. In accordance with this established dynamic view of the hammerhead structure, we also employed Boltzmann structure samples generated by Sfold for the prediction of ribozyme secondary structure. Again, a sample size of 1,000 was used for characterizing probable ribozyme structures at equilibrium.

The catalytic activity of a trans-cleaving ribozyme can be affected by many factors. Here, we have focused on a number of structural and thermodynamic parameters. These parameters take into account the secondary structure of the target, the secondary structure of the ribozyme, and the stability of the ribozyme-target duplex. Below, we define these terms in the current context and compute the total free energy change for modeling the hybridization process.

ΔG_disruption is the free energy cost for disruption of the secondary structure at the ribozyme binding site on the target mRNA (Figure 1B), and thus is a measure of accessibility at the target site. For the 15 designed ribozymes, each with nine nucleotides for the 5' binding arm and 11 nucleotides for the 3' binding arm, the binding site involves 20 nucleotides, excluding the unpaired C of the GUC triplet (Figure 1A). To calculate ΔG_disruption, we adopted the simplifying assumption that the binding of a ribozyme to a relatively much longer mRNA should induce a local structural alteration at the target site, but no longer-range effects on overall target secondary structure. In other words, we defined local structural alteration as the breakage of the intramolecular base pairs involving the target site to permit formation of the ribozyme-target duplex (Figure 1). Specifically, ΔG_disruption was calculated as the energy difference between ΔG_before, the free energy of the original mRNA structure, and ΔG_after, the free energy of the new, locally altered structure (ΔG_disruption = ΔG_before- ΔG_after). We calculated ΔG_before from the average energy of the original 1,000 structures predicted by Sfold, and ΔG_after from the average energy of all of the 1,000 locally altered structures. Therefore, under the local disruption assumption, the calculations did not require refolding of the rest of the target sequence.

ΔG_switch is the free energy cost for the ribozyme to switch from one conformation to the conformation that is most favorable for target binding and subsequent cleavage. Here, the starting conformation is any conformation predicted by Sfold, and the binding conformation is the one for which the ribozyme core is correctly folded and both binding arms are single-stranded (Figure 1B). Thus, ΔG_switch = ΔG_s - ΔG_b , where ΔG_s is the free energy of the starting conformation, and ΔG_b is the free energy of the binding conformation. In the case that the starting conformation is the binding conformation, ΔG_switch = 0.0 kcal/mol. We calculated ΔG_s by the average free energy of the 1000 structures predicted by Sfold for the ribozyme. ΔG_b is the same for different starting conformations of a given ribozyme sequence, so there is no need to average over a structure sample.

ΔG_hybrid is the energy gain due to the complete intermolecular hybridization between the ribozyme binding arms and the nucleotide sequence of the target binding site. It is calculated by the sum of base-pair stack energies for the two ribozyme arm-target duplexes, an energetic penalty ("initiation energy") for the initialization of bimolecular interaction 52, and other penalties or energies associated with the multi-branched loop formed by the three adjacent helices. Specifically, ΔG_hybrid = ΔG_initiation + ∑_1≤i≤10ΔG_{H3_stacking(i)} + ∑_1≤j≤8ΔG_{H1_stacking (j)} + ΔG_multi-loop+ ΔG_{H3_terminal} + ΔG_{H1_terminal} + ΔG_dangle, where the initiation energy ΔG_initiation = 4.1 kcal/mol 52; ΔG_{H3_stacking (i)} (1 ≤ i ≤ 10) is the stacking energy for the i-th base-pair stack for helix III (Figure 1A); ΔG_{H1_stacking (j)} (1 ≤ j ≤ 8) is the stacking energy for the j-th base-pair stack for helix I; ΔG_multi-loop is a linear penalty for the multibranched loop formed by the three helices; ΔG_{H3_terminal} is a penalty of 0.5 kcal/mole for the terminal A-U pair for helix III, while ΔG_{H1_terminal} applies the same penalty for a terminal A-U or G-U pair 53 for helix I (e.g., A-U for ribozyme GUC19, Figure 1A); and ΔG_dangle is a sum of free energies for dangling ends (i.e., single base stacks)52. More specifically, for the linear multibranched loop penalty, ΔG_multi-loop= a + b(number of unpaired bases)+c(number of helices), where a, b, and c are respectively the offset, the free base penalty and the helix penalty, and a = 3.4 kcal/mol, b = 0.0 kcal/mol, and c = 0.4 kcal/mol 53. In our present context, there are 11 unpaired bases and three helices in the loop, so ΔG_multi-loop= 5.2 kcal/mol, a constant for all ribozymes studied here. For a terminal base-pair N-N' (A-U for ribozyme GUC19, as shown in Figure 1A) for helix I, ΔG_dangle = min [ΔG_3(U-A,C), ΔG_5(N-N',C)] + ΔG_5(A-U,A) + ΔG_3(C-G,G) + ΔG_5(G-C,A) + ΔG_3(N'-N,C), where the free energies for both 5' and 3' dangling ends 53 are used, and min [ΔG_3(U-A,C), ΔG_5(N-N',C) ] is the minimum of the two dangling energies, to take into account two possibilities of single-base stacking for the C of the GUC cleavage triplet. It is assumed that a single unpaired nucleotide between two adjacent helices for a multi-branched loop stacks onto the terminal base pair of the helix possessing the more favorable dangling energy.

Finally, we computed ΔG_total, the total energy change for the ribozyme-target hybridization. ΔG_total can be calculated through consideration of the energy gain due to the complete intermolecular hybridization and the energy costs owing to structure alterations for both the target and the ribozyme. With use of the parameters introduced above, ΔG_total = ΔG_hybrid - ΔG_switch - ΔG_disruption.

The standard univariate linear regression was used for predicting ribozyme activity by each of the parameters listed above. The P-value measures the statistical significance of the parameter, and the R² of the regression indicates the degree of variability in ribozyme activity that is attributed to the parameter. The Pearson's correlation coefficient between a parameter and the ribozyme activity was also computed. We note that the P-value of the correlation is the same as the P-value of the parameter from the standard univariate regression analysis. The software package R 54 was used for the statistical analyses.