Alternative Substrate Kinetics of Escherichia coli Ribonuclease P

Background: RNase P acts on multiple tRNA precursors, but little is known about substrate competition. Results: Alternative substrate kinetics reveal a simple competitive mechanism allowing relative rate constants to be quantified. Conclusion: The relative rates of processing of different substrates are restricted to a narrow range and reflect association. Significance: RNase P processing is tuned for uniform specificity and coupling to tRNA precursor biosynthesis. A single enzyme, ribonuclease P (RNase P), processes the 5′ ends of tRNA precursors (ptRNA) in cells and organelles that carry out tRNA biosynthesis. This substrate population includes over 80 different competing ptRNAs in Escherichia coli. Although the reaction kinetics and molecular recognition of a few individual model substrates of bacterial RNase P have been well described, the competitive substrate kinetics of the enzyme are comparatively unexplored. To understand the factors that determine how different ptRNA substrates compete for processing by E. coli RNase P, we compared the steady state reaction kinetics of two ptRNAs that differ at sequences that are contacted by the enzyme. For both ptRNAs, substrate cleavage is fast relative to dissociation. As a consequence, V/K, the rate constant for the reaction at limiting substrate concentrations, reflects the substrate association step for both ptRNAs. Reactions containing two or more ptRNAs follow simple competitive alternative substrate kinetics in which the relative rates of processing are determined by ptRNA concentration and their V/K. The relative V/K values for eight different ptRNAs, which were selected to represent the range of structure variation at sites contacted by RNase P, were determined by internal competition in reactions in which all eight substrates were present simultaneously. The results reveal a relatively narrow range of V/K values, suggesting that rates of ptRNA processing by RNase P are tuned for uniform specificity and consequently optimal coupling to precursor biosynthesis.

Ribonuclease P (RNase P) 2 is an essential ribonucleoprotein enzyme that is responsible for catalyzing the maturation of the 5Ј end of transfer RNAs (tRNAs) through site-specific hydrolysis of a phosphodiester bond in precursor tRNAs (ptRNAs) (1)(2)(3). The RNA subunit, termed P RNA, contains the active site (4,5), whereas the smaller protein subunit (C5 in Escherichia coli) is required for optimal molecular recognition and catalysis in vitro and is essential in vivo (6 -13). Although P RNA is a ribozyme, its mode of molecular recognition differs from other catalytic RNAs in two important ways. First, its biological role in ptRNA processing requires that it act in trans as a multiple turnover enzyme (14), whereas, other ribozymes, with the exceptions of the ribosome and spliceosome, undergo single turnover self-splicing or self-cleavage reactions (15)(16)(17). Second, RNase P processes multiple RNA substrates, including all ptRNAs in the cell, whereas other ribozymes, again with the exceptions of the ribosome and spliceosome, have one specific substrate (18,19). These characteristics are essential to RNase P function, as they are to the ribosome and spliceosome, and are common to many enzymes involved in RNA metabolism (20 -23). Therefore, understanding the multiple substrate recognition properties of RNase P can shed light on general principles of molecular recognition by other ribonucleoproteins and multisubstrate enzymes.
The ptRNA nucleotides contacted by RNase P have been determined by chemical interference and structure-function studies ( Fig. 1) (14,18,24,25). The recognition elements near the cleavage site include the 3Ј-RCCA sequence, a G(ϩ1)/ C(ϩ72), as the first base pair in the acceptor stem and the 2Ј-OH and nucleobase of a U(Ϫ1) residue 5Ј to the cleavage site. The substrate binding domain of P RNA also contacts 2Ј-OH groups in the T stem loop (26,27). The spacing of these contacts in the T stem loop in relation to the cleavage site results in an overall shape recognition of the substrate (28 -31).
Comparative analysis of E. coli tRNA gene sequences shows significant variation among the nucleotides identified as contact points with the enzyme. As shown in Fig. 1, alignment of the 87 ptRNA genes of E. coli K12 (19) reveals that the leader sequences (region I) and the acceptor stem (regions II and III) show only minimal sequence conservation. An exception is the 3Ј-CCA sequence that is recognized by the ribosome (32), aminoacyl-tRNA synthetases (33,34), and elongation factor Tu (35). Only two-thirds of E. coli ptRNAs (66/87) contain a G(ϩ1)/C(ϩ72), and a similar fraction (63/87) have an optimal U at the N(Ϫ1) position (19). The population of ptRNAs that contain all of the recognition elements is significantly smaller (ϳ50%; 42/87). These ptRNAs make up a canonical sequence, whereas a noncanonical ptRNA is missing one or more of these recognition elements. The adjacent base pair to these recognition elements is often a G(ϩ2)/C(ϩ71); however, this position is not known to contact RNase P. The 5Ј leader sequence shows no conserved motif; however, both binding and cleavage of model substrates by E. coli RNase P are sensitive to changes in the sequence of the 5Ј leader (36,37). Indeed, recent studies identified a protein-RNA interaction between the leader sequence and the Bacillus subtilis RNase P (38). A structure from Mondragón and colleagues (31) of the Thermotoga maritima RNase P bound to tRNA and leader products is consistent with the experimentally defined interface between enzyme and substrate drawn from biochemical studies. Although specific leader contacts are not resolved in the crystal structure, it generally corresponds with the perspective from cross-linking and structure-function studies (10,36).
Central to achieving a complete understanding of multiple substrate recognition by RNase P is the observation that catalysis by P RNA alone is sensitive to natural structural variation among ptRNAs that results in loss of RNA-RNA contacts between P RNA and ptRNA (36, 39 -41). Catalysis by the ribonucleoprotein holoenzyme, which forms additional leader sequence interactions, is less sensitive to sequence and structure variation among endogenous ptRNAs (36). A conformational change during substrate recognition has been documented for B. subtilis RNase P by Fierke and colleagues (9,25) in which the protein subunit facilitates via leader sequence contacts. This two-step mechanism for substrate binding may give rise to threshold effects resulting in similar rate constants for catalysis for substrates lacking optimal contacts with the enzyme (36,39,40,42).
Thus, detailed in vitro structure-function studies measuring binding and catalysis for model substrates have revealed basic principles of molecular recognition by RNase P. Nonetheless, information on the competition between different alternative substrates is needed to understand function in vivo. Here, we test a simple competitive model to describe the relative rates of ptRNA processing by RNase P and apply this model to evaluate the effect of natural, genomic variation in ptRNA substrate structure on relative processing rates. The results provide insight into the features of the kinetic mechanism of RNase P that govern its function in vivo that are relevant for other multiple substrate enzymes.

EXPERIMENTAL PROCEDURES
RNA Synthesis and RNase P Holoenzyme Reconstitution-E. coli P RNA and ptRNAs were generated by in vitro transcription from cloned DNA or PCR DNA templates. The ptRNA fMet47 and ptRNA Met82 substrates were synthesized from plasmids ptRNA605 and ptRNA608, respectively, as described previously (39). The ptRNA His37 , ptRNA Gln85 , ptRNA Gly62 , ptRNA Ser80 , ptRNA Leu76 , and ptRNA Ile1 substrates were synthesized from PCR products generated from E. coli genomic DNA using primers that introduce a T7 promoter and nine nucleotides of 5Ј leader sequence to generate the RNA sequences shown in Fig. 2: ptRNA Gln85 , forward, 5Ј-TAATACGACTCACTATAGGCCGGTTATTGGGGTA-TCGCC-3Ј, and reverse, 5Ј-TGGCTGGGGTACCTGGATTC-G-3Ј; ptRNA Gly62 , forward, 5Ј-TAATACGACTCACTATAG-GATCTCGAAGCGGGCGTAGTTC-3Ј, and reverse, 5Ј-TGG-AGCGGGCGAAGGGAATCG-3Ј; ptRNA Ser80 , forward, 5Ј-TAATACGACTCACTATAGGGTCATTCCGGAAGTGTG-GCCG-3Ј, and reverse, 5Ј-TGGCGGAAGCGCAGAGATTCG-3Ј; ptRNA Ile1 , forward, 5Ј-TAATACGACTCACTATA-GGACCTCTACAGGCTTGTAGCTC-3Ј, and reverse, 5Ј-TGGTAGGCCTGAGTGGACTTG-3Ј. PCR reactions contained 100 mM KCl, Tris-HCl, pH 8, 5 mM MgCl 2 , 100 M dNTP and were performed at 95°C, 30 s, 60°C, 60 s, and 72°C, 90 s for 30 cycles. The resulting DNA was purified by phenol and chlo-FIGURE 1. Secondary structure and sequence conservation of E. coli (K12) ptRNAs at regions contacted by RNase P. A, the conserved secondary structure of tRNA is shown. The RNase P ribonucleoprotein interacts with the acceptor stem and TC stem and loop of tRNA (black circles). The enzyme also contacts in the 5Ј leader (gray circles). The sequences identified as forming RNA-RNA contacts with the RNase P enzyme are shown as letters and include a U at N(Ϫ1), a G(1)-C(73) base pair at the top of the acceptor stem, and the 3Ј-RCCA sequence as described in the Introduction. B, the linear sequences of tRNA involved in substrate binding are separated into three regions for presentation of sequence variation. Genomic tRNA sequences and alignments were obtained from the genomic tRNA database (19). Sequence logos for regions I, II, and III were created using WebLogo (88). Region I (N(Ϫ10 to N(Ϫ1)) includes the protein binding site in the 5Ј leader and the nucleotide at N(Ϫ1) that contacts P RNA. Region II (N(1) to N(7)) is the 5Ј side of the acceptor step including the RNase P cleavage site 5Ј to N(1). Region III (N (66) to N(76)) includes the 3Ј side of the acceptor stem and the conserved RCCA sequence that interacts with P RNA. roform extraction and precipitated with ethanol as described previously (40).
In vitro transcription reactions contained ϳ10 g of plasmid or PCR template, 5 mM each NTP, 50 mM Tris-HCl, pH 8, 17.5 mM MgCl 2 , 10 mM DTT, 2 mM spermidine, and 1 unit/l of T7 RNA polymerase (Ambion) and were incubated overnight at 37°C. The resulting RNA products were recovered by phenol/ chloroform extraction and ethanol precipitation. The fulllength transcription products were purified by PAGE as described (40).
Kinetic Analyses of Single ptRNA Substrate Reactions-The ptRNA substrates were 5Ј-end-labeled with [␥-32 P]ATP and T4 polynucleotide kinase after dephosphorylation by alkaline phosphatase. RNase P holoenzyme reaction kinetics were measured under the following conditions: 50 mM Tris-HCl, pH 8, 100 mM NaCl, 17.5 mM MgCl 2 , and 0.005% Triton X-100. The P RNA and 5Ј-32 P-end-labeled ptRNA were renatured separately in the above buffer (omitting the Mg 2ϩ ) by incubation at 95°C for 4 min followed immediately by incubation at 37°C for 10 min. MgCl 2 was added to a concentration of 17.5 mM, and the incubation was continued for an additional 10 min. C5 protein was purified, and activity was tested by titrations into multiple turnover reactions containing a constant concentration of P RNA as described previously (43). C5 protein was added to a concentration equal to that of P RNA, and the 37°C incubation was continued for an additional 10 min. Reactions were initiated by mixing equal volumes of enzyme and substrate. Aliquots were removed at specific time intervals and quenched with 50 mM EDTA. The residual ptRNA substrate and 5Ј leader cleavage product were resolved by denaturing PAGE (15%). The conversion of substrate to product was quantified by Phos-phorImager analysis using a GE Healthcare Storm system and ImageQuant software. The fraction of reaction was determined as F ϭ For multiple turnover reactions, initial rates were measured and plotted versus ptRNA concentration and fit to the Michaelis-Menten equation as described under "Results." Transient kinetic experiments were performed in a similar manner, with the substrate and enzyme concentrations indicated in the figure legends. Single turnover kinetic analyses were performed as described previously (44) using the following reaction conditions: 50 mM MES, pH 6, 100 mM NaCl, 17.5 mM MgCl 2 , and 0.005% Triton X-100. F was plotted versus time and fit to a single exponential function, where F o is the maximal fraction of reacted substrate. Experiments were measured using the single turnover conditions described above at pH 6 with either 1 nM ptRNA fMet47 or 1 nM ptRNA Met82 and 100 nM RNase P. At 30 s after initiating, the reaction the volume was divided in half. One aliquot was added to a tube containing a substrate quench giving a final concentration of 5 M B. subtilis ptRNA Asp . Both reactions were continued, and the kinetic data for both pre-chase and post-chase were fit to Equation 1 (45).

Determination of Relative Rate Constants by Internal
Competition-To detect the formation of products from two substrates independently in the same reaction, ptRNA fMet47 and ptRNA Met82 were modified by the addition of two extra G nucleotides to the 5Ј end of the leader sequence, giving rise to ptRNA fMet47 (ϩ2) and ptRNA Met82 (ϩ2). The two additional residues allow their products to be separated on 15% PAGE and quantified independently from the products of the other ptRNAs used in this study.
Internal competition reactions contained two, three, or eight ptRNAs as indicated in the text and in the legends for Figs. 6 -9. Reactions containing both ptRNA fMet47 and ptRNA Met82 at a range of concentrations from 10 to 100 nM were performed with one or the other substrates containing the two extra G residues in the 5Ј leader. Additional reactions containing ptRNA fMet47 and ptRNA Met82 (ϩ2) at 100 nM in the presence of increasing concentrations of nonradiolabeled ptRNA Leu76 from 10 to 3000 nM were also analyzed by monitoring the formation of the 5Ј end-labeled ptRNA fMet47 and ptRNA Met82 (ϩ2). Similarly, reactions containing all eight of the substrates shown in Fig. 2 were conducted with each ptRNA present at 100 nM (800 nM total). For these reactions, trace concentrations of radiolabeled reference substrate ptRNA Met82 (ϩ2) and one of the remaining seven substrates were included to follow product formation. Relative rate constants ( r k ϭ (V/K)/(V/K) reference ; see below) were determined using analytical methods based on Equation 2 and Scheme 1, as described in the following sections.

RESULTS
Application of Competitive Alternative Substrate Kinetics to ptRNA Processing by RNase P-As illustrated in Scheme 1, a simple competitive multiple turnover mechanism allows the competition between different ptRNA substrates for processing by RNase P to be quantified (46 -48). A single population of RNase P (E) combines with multiple ptRNA substrates (S 1 , S 2 , S 3 . . . S N ) to form individual RNase P-ptRNA complexes (ES 1 , ES 2 , ES 3 . . . ES N ) that react with rate constants V 1 , V 2 , V 3 . . . V N to form tRNA and leader products that together are represented by P 1 , P 2 , P 3 . . . P N . We apply the convention of using V and V/K as the fundamental multiple turnover kinetic parameters. The parameter V is the rate constant for reaction of ES to form products and regenerate free enzyme and is equivalent to k cat . The V/K is the second order rate constant at limiting substrate concentrations (i.e. k cat /K m ) (49, 50). Importantly, both S 1 and S 2 must compete with the remaining population of sub- SCHEME 1 strates, which act as competitive inhibitors (46 -48, 51). As a result, the expression for the ratio of the rates for conversion of S 1 and S 2 to products simplifies to Thus, the ratio of the observed rates of product formation for the two substrates depends on the ratio of their V/K values and their concentrations. The designation r k is used below to refer to the ratio of the V/K values for an experimental or unknown substrate relative to a reference substrate ( r k ϭ (V/K)/ (V/K) reference ) (51). As indicated under "Experimental Procedures," the ptRNA Met82 (ϩ2) substrate is used as the primary reference in this study.
There are two key consequences of Scheme 1 and consequently Equation 2 that are important in considering the in vivo function of RNase P (46 -48, 51). First, the relative V/K values and consequently the observed rates of any two substrates will be independent of the presence or concentration of alternative substrates. The reason for this is that the additional substrates act as competitive inhibitors decreasing the concentration of free enzyme available for all substrates equally. Second, the relative processing rates will depend on the V/K values of the two substrates regardless of the enzyme concentration or whether either substrate concentration is saturating. These considerations highlight that the second order rate constant at limiting substrate is an essential parameter in understanding the biological function of RNase P, as it is with other enzymes.
Accordingly, we set out to test whether this simple competitive model describes the relative rates of ptRNA processing by RNase P and to evaluate the effect of natural, genomic variation in ptRNA substrate structure on the kinetics of competi-tion reactions containing multiple substrates. As described in the following sections, we first measured the V and V/K values for two well characterized canonical and noncanonical ptRNAs using standard steady state reactions of uniform RNA populations. We used pre-steady state and single turnover kinetic analyses to determine the reaction steps that limit V and V/K. Reactions containing mixtures of both substrates were analyzed, and the simple competitive model described above was validated. Using an internal competition approach based on this model, we determined the relative rate constants for eight different ptRNAs representing the range of ptRNA structural variation at sites of RNase P contact occurring in the E. coli genome.
Comparison of the Multiple Turnover Kinetics of ptRNA Met82 and ptRNA fMet47 Processing by E. coli RNase P-The substrates ptRNA Met82 and ptRNA fMet47 (Fig. 2) were selected as representative examples of canonical and noncanonical ptRNAs, respectively. Both ptRNAs have similar sequence length and base composition; however, they differ significantly at the nucleotides contacted by the P RNA subunit of RNase P. The ptRNA fMet47 , an initiator tRNA, has an A instead of an optimal U at N(Ϫ1) and a C(ϩ1)-A(ϩ72) pair at the cleavage site that results in a Ͼ900-fold decrease in the rate of catalysis by the P RNA subunit alone (36). In contrast, the RNase P holoenzyme binds both ptRNA Met82 and ptRNA fMet47 with equivalent equilibrium binding constants and processes them with similar single turnover rate constants (36). The metal ion and pH dependence of the single turnover reactions of both substrates are also comparable (37). To isolate the effects of tRNA sequence and structure that contact RNase P from secondary effects due to flanking sequences that are idiosyncratic to individual ptRNAs, we used a standard substrate structure containing the tRNA and 10 additional leader sequences (Fig. 2).
To evaluate the V/K for processing of ptRNA Met82 and ptRNA fMet47 by RNase P, the observed initial rates for both substrates were plotted against their concentrations and fit to the Michaelis-Menten equation (Fig. 3).
The steady state kinetic parameters V and K for both substrates are highly similar (V Met82 ϭ 0.11 Ϯ 0.01 s Ϫ1 ; V fMet47 ϭ 0.14 Ϯ 0.01 s Ϫ1 and K Met82 ϭ 310 Ϯ 60 nM; K fMet47 ϭ 280 Ϯ 40 nM), resulting in an r k ratio near unity (ϳ0.9, where r k ϭ (V fMet47 / K fMet47 )/(V Met82 /K Met82 )) ( Table 1). Fitting complete time courses of the multiple turnover reactions of ptRNA Met82 and ptRNA fMet47 to the integrated Michaelis-Menten equation shows evidence of product inhibition (Fig. 4). An additional approach to measure V/K from multiple turnover reactions is to analyze progress curve data using the integrated Michaelis-Menten equation.
Although the multiple turnover time courses for RNase P cleavage of ptRNA Met82 and ptRNA fMet47 fit well to the above equation, the values of V/K determined using the initial rate data do not predict the observed time courses for either substrate (Fig. 4, dotted lines). It is observed that the kinetics are significantly slower and that a much larger K value is obtained from fitting. These features are hallmarks of product inhibition, and thus we fit the progress curve data to the integrated equation including product inhibition.
Equilibrium binding studies as well as competitive single turnover inhibition experiments indicate that the K d for the   tRNA Met82 is 150 nM and that the K d for the tRNA fMet47 is 100 nM (36,39). Using these values for K i in the above equations provides a much improved fit of the data (Fig. 4, solid line). The values of V and K for the two substrates obtained by this method are ϳ2-fold lower than those obtained from analysis of the initial rate data; however, the values of V/K are highly similar.
The multiple turnover kinetic parameters, V and V/K, estimated by both approaches are highly similar for both substrates despite their significant difference in structure (Table  1). Next, we asked whether the similar V and V/K values for the two substrates reflect the same or different rate-limiting steps.
Pre-steady State Kinetic Analyses to Evaluate the Reaction Step That Limits V-The kinetics of ptRNA cleavage at increasing concentrations of RNase P were examined to determine the predominant form of the enzyme that is populated at steady state (ES or EP, in Scheme 1). As shown in Fig. 3B, for reactions in which RNase P (5 and 10 nM) and the ptRNA substrate (500 nM) are both present at concentrations in excess of K d (Ͼ1 nM), there is a linear increase in product concentration that extrapolates back to the origin. Reactions with either 5 nM or 10 nM RNase P result in product formation that increases linearly with no evidence for a pre-steady state burst. A simple interpretation of this result is that the net rate constant for dissociation of products and regeneration of free enzyme (k 3 in Scheme 2) is faster than substrate cleavage (k 2 ). Therefore, ES is the predominate form of the enzyme that accumulates at steady state. This result contrasts with the kinetic mechanism of B. subtilis RNase P, which is limited by product release for a canonical ptRNA Asp substrate (52).
Single Turnover Kinetics to Evaluate the Reaction Step That Is Rate-limiting for V/K-An important observation relevant to the reaction mechanism of E. coli RNase P is that the observed K (where K ϭ (k off ϩ V)/k on in Scheme 1; i.e. K m ) (53) from multiple turnover kinetic analyses is greater than the independently measured equilibrium dissociation constant, K d (310 nM versus 0.5 nM for ptRNA Met82 and 280 nM versus 0.3 nM for ptRNA fMet47 ) (Tables 1 and 2). This result implies that the net rate constant for cleavage to regenerate free enzyme (V ϭ k 2 k 3 /k 2 ϩ k 3 ) in Scheme 2) is fast relative to substrate dissociation (k Ϫ1 ) (53)(54)(55). It follows that at limiting substrate concentration, the rate of multiple turnover could therefore be limited by substrate association (50).
To test these predictions, we determined the relative magnitudes of the rate constant for catalysis, k 2 , and the rate constant for substrate dissociation, k Ϫ1 , using a "sequential mixing" or "isotope trapping" experiment (45). The RNase P-ptRNA complex was formed by mixing limiting substrate (1-2 nM) with a saturating concentration of enzyme (100 nM). At an intermediate time, an excess of nonradiolabeled substrate was added. If k 2 is fast relative to k Ϫ1 , then there will be little dissociation of the remaining RNase P-ptRNA complexes over the remaining time course of the reaction, and correspondingly no effect on the accumulation of product. Alternatively, if substrate dissociation is fast relative to catalysis (k Ϫ1 Ͼ Ͼ k 2 ), then the addition of nonradiolabeled substrate will quench the formation of radiolabeled product.
The dependence of the observed pseudo-first order rate constant on enzyme concentration showed saturable behavior as predicted based on Scheme 1 (data not shown). These data allowed reaction conditions to be determined under which all of the radiolabeled ptRNA is present in the ES complex. As shown in Fig. 5, A and B, the addition of a cold substrate chase after formation of ES did not result in quenching or a change in reaction kinetics. In contrast, the addition of the excess nonradiolabeled substrate at the start of the reaction resulted in the expected slow, multiple turnover kinetics. Therefore, we concluded that substrate dissociation is negligible over the remaining time course of the reaction (k 2 Ͼ Ͼ k Ϫ1 ).
An important implication of this result is that the substrate association rate constant, k 1 , can be measured from the concentration dependence of the single turnover reaction (k obs versus [E]) (54). Fitting the dependence of k obs to [E] at concentrations below K 1/2 permits k 1 and k Ϫ1 to be estimated as the slope and intercept (Fig. 5C). The kinetic parameters for both substrates are similar (1.9 Ϯ 0.1 ϫ 10 6 and 1.5 Ϯ 0.4 ϫ 10 6 M Ϫ1 s Ϫ1 for ptRNA Met82 and ptRNA fMet47 , respectively) ( Table 2). The estimates for k Ϫ1 from second order analyses are less than the V for both substrates. In this case, the observed K for the multiple turnover reaction will be approximated by V/k 1 (53). The experimentally measured values of these kinetic parameters result in calculated K values of 57-172 nM for ptRNA Met82 and 71-117 nM for ptRNA Met47 . These calculated values are within 2-fold of the experimentally observed K determined from analysis of initial rate data (Tables 1 and 2). It is possible that differences in the reaction pH or errors in the determination of concentrations of substrate and enzyme account for this difference.
From the definitions for V and K, above, it follows that V/K ϭ k 2 k 1 /(k Ϫ1 ϩ k 2 ) (50). Thus, when k 2 Ͼ Ͼ k Ϫ1 , then V/K Ϸ k 1 . Therefore, the most simple interpretation of the pre-steady state and single turnover results is that the cleavage step (k 2 ) is rate-limiting for V (i.e. at saturating substrate concentrations) and that V/K reflects the association step (k 1 ) for both ptRNAs at limiting substrate concentrations.   MARCH 22, 2013 • VOLUME 288 • NUMBER 12

JOURNAL OF BIOLOGICAL CHEMISTRY 8347
Competitive Alternative Substrate Kinetics of ptRNA Met82 and ptRNA fMet47 Processing by RNase P-As introduced above, in competitive multiple turnover reactions, the relative rates for two competing ptRNAs are expected to be determined by their relative V/K values ( r k ϭ (V/K)/(V/K) reference ) and their concentrations (46 -48, 51). Also, it follows that the presence of additional substrates will decrease the observed rates for all substrates in the reaction due to competition for free enzyme, but should not affect the r k value for any two substrates (46,56,57). We tested the competitive alternative substrate model for RNase P by analyzing the competitive kinetics of reactions containing both ptRNA Met82 and ptRNA fMet47 .
To simultaneously measure the reaction kinetics of two ptRNAs in the same reaction, we used a reference substrate in which two additional G residues are added to the 5Ј end of the leader sequence. This modification allows the products of the ptRNAs to be distinguished by their mobility on denaturing PAGE and quantified individually. An example of the primary data from this approach for ptRNA Met82 (ϩ2) and ptRNA fMet47 is shown in Fig. 6A. The precursor band contains both substrates as these species are not resolved under these gel conditions. However, the products from the two substrates are readily distinguished and quantified, allowing relative rates of product formation to be measured. To address the effect of the additional nucleotides on ptRNA processing, the relative rate constants for comparison of ptRNA Met82 with ptRNA Met82 (ϩ2) and comparison of ptRNA fMet47 with ptRNA fMet47 (ϩ2) were also measured (data not shown) and were observed to be 0.9 -1.3. Thus, the presence of the additional nucleotides required to distinguish the products from two substrates has essentially no effect on the rate of RNase P processing.
To compare the competitive kinetics of ptRNA fMet47 and ptRNA Met82 , the observed rates of product formation were determined for reactions containing substrate concentration ratios (in nM) of 10:100, 100:10 10:10 and 100:100 (ptRNA fMet47 : ptRNA Met82 ). The product ratios from at least three time points taken under steady state conditions were averaged and then corrected for the relative substrate concentrations. Additionally, the collection of data for the observed rates as a function of the relative rates of the two substrates were fit to the logarithmic form of Equation 2, log(v 2 /v 1 ) ϭ log r k ϩ log͑S 2 /S 1 ͒ (Eq. 6) where v 2 /v 1 is the ratio of the observed initial rates for ptRNA fMet47 relative to ptRNA Met82 (ϩ2). Analysis of the data in this manner allows determination of r k from the combined data set. As shown in Fig. 6B, the data for both the ptRNA fMet47 / ptRNA Met82 (ϩ2) and the ptRNA fMet47 (ϩ2)/ptRNA Met82 combination of substrates fit this relationship as predicted. Fitting to Equation 4 yields an r k value of 0.5 ((V/K) fMet47 /(V/K) Met82 ) for the reaction in which the ptRNA Met82 was modified to contain the additional two leader nucleotides. As a control, the r k was measured in competitive reactions in which ptRNA fMet47 instead of ptRNA Met82 was lengthened to distinguish the products from the two substrates. A similar value of 0.6 was observed consistent with the value measured in which the ptRNA Met82 (ϩ2) was used for the reference substrate.
An additional prediction of the internal competition model is that the addition of a third substrate will not affect the r k value for these two substrates. Accordingly, we tested the effect of increasing concentrations of a third substrate on the observed rates of ptRNA Met82 (ϩ2) and ptRNA fMet47 product formation. In Scheme 1, additional substrates act as competitive inhibitors that decrease the observed rate of processing of both substrates by competing for free enzyme. In Fig. 6C, ptRNA Leu76 is added as a competitive alternative third substrate in reactions containing ptRNA fMet47 and ptRNA Met82 (ϩ2) as the reference substrate. Increasing concentrations of nonradiolabeled ptRNA Leu76 , which binds to RNase P with similar affinity as the FIGURE 5. Single turnover kinetics of ptRNA Met82 and ptRNA fMet47 processing by RNase P. A, single turnover sequential mixing experiment with initial concentrations of 1 nM ptRNA Met82 and 100 nM RNase P. At the time indicated by the vertical dotted line, the reaction was divided, and one fraction was combined with a high concentration (5 M) of nonradiolabeled ptRNA (circles). Time points were continuously collected from the remaining fraction (squares). As a control, an identical reaction was combined with nonradiolabeled substrate before the addition of enzyme (triangles). B, single turnover sequential mixing experiment using ptRNA fMet47 performed as described in panel A. C, second order analysis of RNase P binding of ptRNA Met82 and ptRNA fMet47 to increasing concentrations of RNase P. The pseudo-first order rate constants (k obs ) determined for a single turnover reaction containing 2.5-10 nM RNase P concentrations are plotted versus [E]. These data are fit to a linear function k obs ϭ k 1 [E] ϩ k Ϫ1 to determine the rate constants reported in Table 2. Error bars indicate S.D.
other two ptRNAs in the reaction, decrease the observed rates of ptRNA fMet47 and ptRNA Met82 (ϩ2) processing as expected. The data fit to a simple competitive inhibition model derived from Scheme 1, where S 1 is the concentration of the labeled substrate and S 2 and S 3 are the concentrations of the competitive alternative, unlabeled substrates in Fig. 6C. Analysis of the observed rates data for ptRNA Met82 and ptRNA fMet47 in the presence of 10 -3000 nM ptRNA Leu76 allows the K value for ptRNA Leu76 to be estimated. A value of ϳ300 nM is obtained, which is similar to the values measured by analysis of initial rate data for reactions containing ptRNA Met82 or ptRNA fMet47 alone (Table 1). Nonetheless, as demonstrated in Fig. 6C, inset, the ratio of the observed rates, the r k for ptRNA fMet47 referenced to ptRNA Met82 (ϩ2), is independent of the presence and concentration of a competing substrate. Because the r k value for two competing substrates is insensitive to a third competing substrate, the internal competition approach could be used to determine the r k values for substrates in reactions containing more complex populations.

Determination of Relative Rate Constants for ptRNAs in Complex Substrate Populations by Internal Competition-It follows
from Scheme 1 and the observations documented above that the presence of additional substrates, regardless of their number or concentration, should also have no effect on the relative rates of processing of any two substrates in the population. To test this concept, we generated five ptRNA substrates in addition to ptRNA Met82 , ptRNA fMet47 , and ptRNA Leu76 . Substrates were selected to span the range of ptRNA structure variation encountered by E. coli RNase P in vivo, and their secondary structures are shown in Fig. 2. Among these, similar ptRNA His and ptRNA Ser substrates have served as substrates for analyzing the determinants of specificity adjacent to the site of 5Ј processing (58).
We used the same approach, described in the preceding section, of distinguishing between the products of two substrates by analyzing the relative rate constants of ptRNA Met82 (ϩ2) and ptRNA fMet47 . Because the two substrates of interest are the only species that are radiolabeled, their products alone are detected. As shown in Fig. 9, the r k determined by this method (0.3) is within error of the value of 0.5 determined by analysis of the two substrates alone. Thus, the presence of additional competing substrates in the reaction does not have an appreciable effect on the magnitude of the relative V/K for ptRNA fMet47 and ptRNA Met82 (ϩ2).
Next, we determined the r k values for the remaining seven substrates using the ptRNA Met82 (ϩ2) as the reference substrate. As shown in Fig. 7, the r k value for the ptRNA Leu76 substrate is readily determined by this approach. This substrate has an r k of 3.5, indicating faster processing of ptRNA Leu76 over the reference ptRNA Met82 when they compete for RNase P processing. For this particular substrate, the ptRNA can be resolved from the unreacted reference ptRNA Met82 (ϩ2). This allows the change in the relative concentrations of the residual substrates to be quantified as well. As shown in Fig. 7B, we took advantage FIGURE 6. Competitive multiple turnover reactions containing both ptRNA fMet47 and ptRNA Met82 (؉2). A, PAGE analysis of the products of a reaction containing 5Ј 32 P end-labeled ptRNA fMet47 and ptRNA Met82 (ϩ2). The two precursors run as a single band indicated by a bracket denoting the presence of both substrates. The two leader sequence products are indicated by lines with or without the additional guanosines that identify the product from ptRNA Met82 (ϩ2). B, plot of the observed multiple turnover rate constants (v obs ) for ptRNA fMet47 (open symbols) and ptRNA Met82 (filled symbols) as a function of the relative concentrations of the two substrates. The data are fit to the log form of Equation 2 (Equation 5). C, plot of the observed multiple turnover rate constants (v obs ) for ptRNA fMet47 (open symbols) and ptRNA Met82 (filled symbols) as a function of the concentration of the third substrate ptRNA Leu76 . The data are fit to a mechanism in which ptRNA Leu76 acts as a competitive inhibitor (Equation 6). The inset shows the individual r k values determined from dividing the observed rate for ptRNA fMet47 by the observed rate for ptRNA Met82 at each of the different ptRNA Leu76 concentration. The solid line and dashed lines represent the average and standard deviation, respectively, calculated from this data set.
of internal competition analyses typically used to measure the relative rate constants for isotope effect measurements (51). The slower reacting ptRNA will become progressively enriched in the residual substrate population, and the relative rate constant can be determined by analyzing the change in substrate ratio as a function of the fraction of reaction. Using the ratio of residual precursor concentrations derived from the ratio of radiolabeled precursor bands, the r k for ptRNA Leu76 was determined by fitting to where R 0 is the ratio at the start of the reaction and R s is the ratio at the fraction of reaction (f) of the reference substrate (Fig. 7B)  (51, 59). The fraction of reaction for ptRNA Met82 (ϩ2) is determined from the intensity of its precursor and product bands. As expected, the faster rate constant for the ptRNA Leu76 substrate results in faster depletion of this substrate from the residual precursor population relative to the slower reacting ptRNA Met82 (ϩ2). As a result, the ptRNA Leu76 /ptRNA Met82 (ϩ2) ratio becomes progressively smaller as the reaction progresses. An essentially identical r k value of 3.4 is obtained from the fitting of the data shown in Fig. 7B.
Interestingly, in the course of experiments to determine the r k for ptRNA Ser80 , we detected two cleavage products in addition to correct RNase P cleavage at the mature tRNA 5Ј end. As shown in Fig. 8A, the reaction of ptRNA Met82 (ϩ2) yields a single product as expected, whereas the ptRNA Ser80 substrate   Fig. 2. The large variable arm of ptRNA Ser80 results in a substrate that is 15 nucleotides longer than ptRNA Met82 (ϩ2), which can be resolved under these gel conditions (15% PAGE). The ptRNA Ser80 substrate is cleaved by RNase P to give three products: the correct cleavage product resulting from cleavage 5Ј to N(ϩ1) (SER P1), miscleavage one nucleotide 5Ј into the leader sequence (SER P2), and miscleavage four nucleotides 5Ј to the correct cleavage site (SER P3). All of these products are resolved from the single cleavage product resulting from processing at the authentic 5Ј end of ptRNA Met82 (MET82). B, plot of product accumulation versus time for the products indicated in panel A showing the initial rates of product formation for the Ser P1 (open circles), Ser P2 (filled circles), and Ser P3 (open triangles) products relative to the accumulation of the product from ptRNA Met82 processing (squares). C, secondary structure of ptRNA Ser80 with arrows indicating the location of the three cleavage sites in ptRNA Ser80 by RNase P.
gives rise to three products (Fig. 8, labeled P1, P2, and P3). The P1 product maps to the expected site for RNase P processing between N(Ϫ1) and N(1). The P2 product is derived from miscleavage one nucleotide 5Ј to the authentic site, yielding a product one nucleotide smaller. Cleavage to give the P3 product occurs five nucleotides upstream of the correct site. RNase P cleavage in the leader sequence is not expected, although several studies have demonstrated the ability of the RNase P holoenzyme to cleave unstructured RNA, but with sequence or structure specificity that is not yet well defined (29,60). Alternatively, cleavage may result from alternative RNA folding (61,62). The r k for the miscleavage at P2 occurs at essentially the same rate as P1 (both have an r k of ϳ0. 6). Surprisingly, the r k value for miscleavage of the ptRNA Ser80 substrate at P3 occurs with an r k that is significantly higher (2.2). Although the precursors of both substrates can be resolved, the fact that ptRNA Ser80 reacts to form multiple products precludes determination of its relative rate constant by analysis of precursor ratios by Equation 6.
Nonetheless, as demonstrated in Fig. 8B, the relative rates of accumulation of the three products of ptRNA Ser80 are readily distinguished. For the ptRNA Gly62 , ptRNA Ile1 , ptRNA His37 , and ptRNA Gln85 substrates, the r k values were determined relative to ptRNA Met82 (ϩ2) from analyzing the initial rates of formation of the products. The r k values for all eight substrates, shown as the natural log to provide a linear scale, are compared in Fig. 9 together with the values for the alternative products for ptRNA Ser80 .

DISCUSSION
Understanding the competition between multiple, different cognate ptRNAs for processing by RNase P is important for understanding its function in vivo. This point is similarly true for the broad class of RNA-processing enzymes that recognize multiple cognate substrates. In this study, steady state kinetic analyses of two representative canonical and noncanonical ptRNA substrates were used to provide a framework for establishing a basic alternative substrate kinetic model for E. coli RNase P. For both substrates, the rate-limiting step for V is the substrate cleavage step; however, the rate-limiting step for V/K is substrate association. Because substrate binding is essentially irreversible relative to cleavage, both substrates compete for RNase P processing based on their relative rates of association. Using internal competition reactions, in which two or more substrates are present in the same reaction, we validated the basic features of the alternative substrate kinetic model. The results demonstrated that the relative rates of processing of two substrates directly reflect their relative V/K values (i.e. the specificity constant) and their concentrations. Also, the presence of additional substrates reduced the observed rate of processing of individual ptRNAs, but did not affect the observed r k for the two substrates being compared. Thus, for the set of substrates examined here, the E. coli RNase P enzyme follows simple alternative substrate kinetics; assuming that the results for ptRNA fMet47 and ptRNA Met82 are representative, the competition is governed by similar association rate constants. The results represent an important advance because they shed light on the biological function of RNase P in tRNA biosynthesis and provide a framework for quantifying relative processing rates in complex populations of competing tRNA precursors.
Biosynthesis of the translational machinery, including tRNA, consumes most of the resources in rapidly dividing cells (63). Importantly, the distribution of tRNA species is not uniform. The tRNAs that are present at higher concentrations are those that recognize the preferred codons of the genes encoding the highly expressed proteins of rapidly growing bacteria (64,65). This correspondence of codon usage and tRNA abundance is believed to maximize translation efficiency and therefore growth rates (66,67). The turnover of mature tRNA does not appear to be a major mechanism for the modulation of tRNA abundance (68). Thus, the steady state levels of tRNAs are largely set at the transcriptional level. In E. coli, tRNA biosynthesis and rRNA biosynthesis are tightly regulated by the stringent response, which senses the accumulation of uncharged tRNA and negatively regulates the initiation of transcription of tRNA and rRNA operons (69). The ptRNA substrates for RNase P can be transcribed individually or as part of polycistronic RNAs containing additional ptRNAs, rRNA, or mRNA (18,19). Precursors to individual tRNAs that are part of an rRNA primary transcript are thought to be released during the course of rRNA maturation by endonucleolytic cleavage by RNase III or RNase E (70). Separation of individual tRNA precursors from transcripts containing mRNAs or other tRNAs is accomplished primarily by RNase E (71,72).
The narrow range of V/K values for the model ptRNA substrates described here suggests that the relative rates of processing different ptRNAs in the cell will be proportional to the abundance of each precursor, assuming minimal influence of additional flanking RNA sequences. From this perspective, the alternative substrate kinetics of RNase P are tuned to be directly and uniformly proportional to rates of precursor bio- synthesis. It follows that the enzyme has a negligible role in influencing the steady state abundance, but rather functions to maintain the distribution set by precursor biosynthesis despite significant differences in the structure and context of each individual substrate.
This model is specific to ptRNA substrates, and indeed, there may be circumstances under which the rates of RNase P processing are modulated to contribute to regulation of gene expression. There are non-ptRNA substrates of RNase P including riboswitches (73)(74)(75) that are likely to have different kinetic properties related to their unique function and so are not accounted for in the scenario described above for ptRNA substrates. Additionally, the context of different RNase P substrates within larger polycistronic transcripts may influence relative processing rates (19) and clearly deserve further attention. For example, a suppressor tRNA substrate the length of the leader sequence has an effect on cell growth potentially due to effects on in vivo processing efficiency (76). Recently, Mohanty and Kushner (77,78) have identified two tRNA polycistrons in which RNase P is the primary processing event separating the individual tRNA units. RNase P cleaves 4 -7 nucleotides downstream of the CCA determinant, generating a substrate for additional processing nucleases in the substrate for tRNA Leu5 (79). The structures and binding modes that underlie RNase P cleavage at alternative sites in non-ptRNA substrates are poorly understood. Both bacterial (29,60) and eukaryotic (80,81) RNase P have been observed to catalyze cleavage at multiple sites distinct from authentic ptRNA-processing sites, and these forms of alternative specificity clearly deserve further attention. For example, we note that the cleavages of the ptRNA Ser80 substrate demonstrated here occur at a V/K that is within the range of processing at the correct site.
The results not only provide insight into issues specific to RNase P function, but also draw attention to parallels with the recognition capabilities of the ribosome. Studies by Uhlenbeck and colleagues (82,83) demonstrated uniform affinities, dominated by similar association constants, of elongation factor Tu for aminoacyl-tRNAs despite differences in tRNA and amino acid structure and chemical properties. Detailed analysis of misacylated tRNAs revealed thermodynamic compensation between the contributions of the amino acids and the tRNA moieties of the aminoacyl-tRNA to binding. The ribosomal A-site shows specificity for both the amino acid and the tRNA portions of their aminoacyl-tRNA substrates (84,85). Structure-function analysis of chimeric tRNAs presented that each tRNA sequence has coevolved with its anticodon to tune ribosome affinity to a value that is the same for all tRNAs (86). Thus, the observation of similarly uniform rates of ptRNA processing by RNase P provides an additional example of the tuning of RNA recognition to accommodate the structural variation in tRNA necessary for its function in aminoacylation and translation.
Fierke and colleagues (9, 87) demonstrated a conformational change during substrate binding by B. subtilis RNase P. Given the potential for the induced fit model to contribute to specificity, it is important to consider how the occurrence of a conformational change could impact alternative substrate competition. We assume that for cognate ptRNAs, any conformational change upon binding is favorable, whereas for noncognate RNAs, this step is unfavorable. As described previously, induced fit decreases the V/K for both a cognate and a noncognate substrate when the chemical step is rate-limiting and therefore does not intrinsically provide specificity (48). On the other hand, a conformational change can provide specificity when a binding step or product release step is rate-limiting for the cognate substrate, whereas the chemical step is rate-limiting for a noncognate RNA (48). As suggested by our results, association is likely to be broadly rate-limiting for ptRNA processing by E. coli RNase P. Thus, the presence of a conformational change could clearly enhance specificity over noncognate substrates.
In this study, we have taken a new approach to analyzing substrate recognition by RNase P by applying the perspective of alternative substrate kinetics. In addition to providing insight into the enzymatic behavior that underlies its biological function, the framework described here is useful for extracting relative rates by internal competition. With the simple competitive substrate kinetics of RNase P established, more broad application of competitive kinetics may be considered. In principle, internal competition methods are applicable to very large populations of substrates so long as reaction progress and the ratios of their precursors or products can be quantified.