Catalytic Cooperativity among Subunits of Escherichia coli Transcription Termination Factor Rho

Escherichia coli transcription termination factor Rho shows a 30-fold faster rate of ATP hydrolysis when all three catalytic sites are filled with ATP than when only a single site is filled (Stitt, B. L. and Xu, Y. (1998) J. Biol. Chem. 273, 26477–26486). To study the structural requirements of the substrate for this catalytic cooperativity, rapid mix/chemical quench experiments using various ATP analogs were performed. The results indicate that it is the configuration of the β- and γ-phosphoryl groups of ATP that is of primary importance for the rate enhancement. Our results also show that there are kinetically slow branches of the enzyme mechanism that are not seen when the chemistry step of the catalytic cycle is fast. These branches become prominent, however, when two of the three Rho active sites are empty or bear non-hydrolyzable compounds. A first-order step that is slow compared with Vmax catalysis enables a single ATP molecule bound in any one of the three Rho active sites to be hydrolyzed and defines the kinetically slow branches. This first-order step could be a protein conformation change or a rearrangement of bound RNA. The results reinforce the importance of catalytic cooperativity in normal Rho function and suggest that several protein conformations exist along the catalytic pathway.

Catalytic cooperativity occurs in multisubunit enzymes when a catalytic step in one active site affects the catalytic cycle in another active site. It is best documented in F 1 -type ATPases of mitochondria. When ATP is bound in only one of the three active sites, it is reversibly hydrolyzed by the enzyme without release of products until ATP binds in at least one additional catalytic site. The binding of the additional ATP molecule(s) increases the rate of product release from the first active site, completing the catalytic cycle there (1,2).
Catalytic cooperativity has been reported for Escherichia coli transcription termination factor Rho (3). Rho aids in the release of newly synthesized RNA from paused transcription complexes (reviewed in Ref. 4). The homohexameric Rho protein binds nascent RNA and, with the RNA-dependent hydrolysis of ATP, travels 5Ј 3 3Ј along the RNA to disrupt the ternary transcription complex, releasing product RNA and al-lowing RNA polymerase to recycle. RNA-dependent ATP hydrolysis by Rho can be studied in a simplified system, requiring only Rho, RNA, and MgATP. During the course of pre-steadystate rapid mix/chemical quench experiments carried out with such a simplified system, Stitt and Xu (3) found that Rho exhibits catalytic cooperativity. The steady-state rate of RNAdependent ATP hydrolysis is 30-fold slower when a single ATP molecule is bound to the Rho hexamer than when all of the ATPase sites are filled.
Here, the molecular features that are required of a nucleotide for it to enhance or "promote" the hydrolysis rate of a single Rho-bound ATP molecule are explored. Results from experiments using various ATP analogs and related compounds are considered in relationship to the present model for ATP hydrolysis by Rho.

EXPERIMENTAL PROCEDURES
Enzymes, Buffers, and Substrates-Wild type Rho from E. coli was purified as described previously (5) from strain AR120/A6 containing plasmid p39ASE (6). The concentration of Rho was spectrophotometrically determined using ⑀ 280 nm 1% ϭ 3.25 cm Ϫ1 (7). The enzyme preparations used had specific activities with poly(C) at 37°C of 10 -20 units mg Ϫ1 . A unit of activity is defined as that amount of enzyme that hydrolyzes 1 mol of ATP in 1 min.
Buffers were TKME (40 mM Tris-HCl, pH 7.7 at 25°C, 50 mM KCl, 1 mM MgCl 2 , 0.1 mM EDTA) and TAGME (40 mM Tris acetate, pH 8.3 at 25°C, 150 mM potassium glutamate, 1 mM Mg acetate, 0.1 mM EDTA). Buffers were supplemented with MgCl 2 or Mg acetate at a concentration equimolar with that of any added nucleotide or phosphate ester. Poly(C) RNA with an average length of 400 bases was from Amersham Biosciences and was dissolved in water at 5 mg/ml.
[␥-32 P]ATP at a specific activity of 1-10 Ci mmol Ϫ1 was synthesized from [ 32 P i ] and ATP according to the exchange method of Glynn and Chappell (8) as modified by Grubmeyer and Penefsky (9). Following purification, these preparations typically had Ͻ3% of their radioactivity in compounds other than ATP. [␥-32 P]CTP was prepared similarly, although the reaction was slow (ϳ3 h rather than 30 min) and only ϳ50% exchange was achieved rather than Ͼ90%.
[ 32 P]Sodium pyrophosphate (PP i ) 1 was NEX019 from PerkinElmer Life Sciences and was purified by ion-exchange chromatography to remove 32 P i . PP i , ACS grade, was from Fisher Scientific.
ADP (disodium salt, Roche Applied Science) was found to contain sufficient ATP to affect results. The contaminating ATP was decreased by conversion to ADP ϩ glucose 6-phosphate as follows. To 1.5 ml of 85 mM ADP adjusted to pH 7.5 with Tris base was added equimolar Mg acetate, glucose to 11 mM, and 5 units of hexokinase (H-4502, Sigma). Following incubation at 30°C for 5 h, hexokinase was removed by filtration using Amicon Centricon-30 concentrators at 6000 rpm in an SS34 rotor for 20 min. The removal of hexokinase was confirmed by the stability of a trace amount of [␥-32 P]ATP that was added to a portion of the filtrate.
ATP␥S from Sigma (A1388) was also treated with hexokinase. To avoid consumption of the ATP␥S during this treatment, the incubation period with hexokinase was minimized as determined by trials in which the hydrolysis of [␥-32 P]ATP added at 8 M final concentration to a sample of the ATP␥S stock solution was monitored. Depletion of the labeled ATP was measured (10) by quenching reactions with trichloroacetic acid, adding charcoal to precipitate adenine nucleotides, centrifuging, and measuring radioactivity in [ 32 P]glucose 6-phosphate in the supernatant by liquid scintillation spectrometry. The treatment thus determined for 1.8 ml of a 14 mM solution of ATP␥S in 10 mM Tris-HCl, pH 8, 5 mM dithiothreitol, 14 mM Mg acetate, 14 mM glucose was incubation for 20 min at 32°C with 50 units of hexokinase followed by ultrafiltration as described above to remove the enzyme. Following thin-layer chromatography, the resulting ATP␥S appeared visually to contain ϳ10% ADP.
For AMP-PNP (A-2647 from Sigma), 2.4 ml of 33 mM AMP-PNP in 10 mM Tris-HCl, pH 8.0, 42 mM Mg acetate, 12.5 mM glucose was treated for 16 h at 25°C with 10 units of hexokinase. For ddATP (lithium salt, D5413, Sigma), 130 l of an 8 mM solution in TAGME buffer with additional Mg acetate to 12 mM and glucose to 15 mM was treated with 2.5 units of hexokinase at 30°C for 10 min.
Rapid mix/chemical quench experiments (11) were carried out at 23°C as described (3). Typically, one syringe of the Update Instruments System 1010 apparatus contained 6.6 M Rho hexamer (1.76 mg/ml) in TAGME buffer with 2 M [␥-32 P]ATP at 100 -600 cpm/pmol (0.3 ATP/ hexamer). The background of 32 PO 4 in this syringe increased during the course of an experiment as Rho slowly hydrolyzed [␥-32 P]ATP in the absence of RNA. This rate was measured in each experiment (values were 1-3 ϫ 10 Ϫ6 hexamer Ϫ1 s Ϫ1 ), and the RNA-dependent ATP hydrolysis data were corrected by subtracting the appropriate background. The second syringe of the rapid mix apparatus contained 400 g/ml poly(C) and 2-20 mM Mg 2ϩ nucleotide in TAGME buffer. Following reagent mixing, after aging times from 5 ms to 30 s, the ϳ100-l reaction was quenched by injection into 400 l of 5% (w/w) trichloroacetic acid. A sample (50 l) was taken for measurement of total radioactivity, and unreacted [␥-32 P]ATP substrate was removed from 350 l of the quenched reaction by absorption to charcoal followed by centrifugation (10). 32 P i product was measured in the supernatant by liquid scintillation spectrometry.
For some experiments, such as those using ddATP, the rapid mix instrument was used slightly differently. Its syringes were filled with TAGME buffer, and one reagent was loaded into each of the 25-l tubings that connect the syringes to the mixer. The tubings were removed, rinsed, dried, and reloaded after each time point. This protocol resulted in minimal consumption of reagents and also permitted mixing of Rho with [␥-32 P]ATP immediately before loading the tubing. Because in this procedure the execution of a time point occurred ϳ2 min after Rho was combined with [␥-32 P]ATP, the significant RNA-independent hydrolysis of [␥-32 P]ATP described above was avoided.
K D determinations by competition were carried out for PP i , PPP i , AMP-CPP, ATPP, AMP-PNP, AMP-PCP, and 2Ј-dATP. Equilibrium binding mixtures (200 l) containing 0.35 M Rho hexamer, 0.1 M [␥-32 P]ATP, 2 mM Mg acetate, and varying concentrations of unlabeled ligand (5 M-2 mM) in TAGME buffer were prepared and sampled to measure total radioactivity. A centrifugal ultrafiltration method was then employed to separate free ligand (12), and the amount of free [␥-32 P]ATP was measured by liquid scintillation counting. K D values were obtained by fitting the data using a linear least-squares analysis, the program Ultrafit (Biosoft), and Equation 1, where n ϭ number of ATP binding sites per hexamer. K D determina-tions through direct binding measurements were carried out for [␥-32 P]ATP and [␥-32 P]CTP by centrifugal ultrafiltration (12). 32 PP i Hydrolysis Experiments-10 l of reaction mixtures contained, in TAGME buffer, 2 M Rho hexamer, 5 g of poly(C), and 10 M PP i including 5000 cpm of [ 32 P]PP i with or without 10 M ATP. Mixtures were pre-warmed at 37°C, and Rho was added last to start the reactions. Samples (1 l) of the reaction mixture were spotted on polyethyleneimine cellulose TLC sheets on top of previously applied 0.5-l carrier spots of a mixture of 1 mM P i ϩ 1 mM PP i and chromatographed in 2 M formic acid, 0.5 M LiCl. Radioactivity on the dried sheets was visualized by phosphorimaging using a Packard Cyclone instrument and quantitated using Packard OptiQuant software.
Hydrolysis tests for PPP i , ddATP, ATPP, ATP␥S, and AMP-CPP were set up and chromatographed similarly to those for 32 PP i except that the final concentration of test substrates was 1-2 mM. PPP i and its hydrolysis products were visualized using a molybdate spray reagent (13). For adenine nucleotides, visualization on Polygram Cel 300 polyethyleneimine/UV254 TLC plates (Macherey-Nagel) was under UV light.
Data Simulations Using KINSIM (14)-Previous results indicate that the three ATP binding sites of Rho are equivalent (10) and that RNA binding to Rho⅐ATP 3 complexes leads to sequential hydrolysis of the bound ATP molecules (3,12). A preexisting asymmetry in the Rho hexamer and/or asymmetry conferred by the binding of RNA must permit discrimination among the three Rho active sites and results in their ordered firing. Thus, we can designate them as site 1, site 2, and site 3. We modeled the results from experiments in which there was at most one molecule of bound [␥-32 P]ATP per hexamer as follows. Onethird of the initially bound [␥-32 P]ATP was assumed to be in the Rho active site where the first of the sequential hydrolyses occurs, one-third was in the site of the second hydrolysis, and one-third was in the third active site. Poly(C) RNA was assumed to bind randomly with respect to bound ATP. Because chase compounds were used at final concentrations of 1-10 mM, their on-rates were presumed not to be rate-limiting (a test confirming this assumption was done using PP i ; see "Results").
[␥-32 P]ATP bound to Rho can dissociate at any stage. At longer times (1-30 s) after components were mixed, slow hydrolysis of [␥-32 P]ATP was sometimes seen in experiments because the concentration of the chase compound was insufficient. These portions of the data were not included during modeling. In most cases, only the first 350 ms of data were used.
We note that, when a numerical integration program like KINSIM is used, multiple-step mechanisms are written and rates are assigned to each step so that, among sequential catalytic cycles of a three-cycle mechanism, the same steps can have the same rates. The arrangement of steps and the flow of substrates and products among them create sequentiality. In contrast, when a curve-fitting program such as Ultrafit (Biosoft) is used as in Stitt and Xu (3), because a single equation composed of multiple first-order steps generates the fit, sequential hydrolyses can only be modeled by using different rates for repeated occurrences of the same processes.

RESULTS
The basic experiment to determine the features of the ATP molecule that are needed for promotion employed rapid mix/ chemical quench techniques. Rho⅐[␥-32 P]ATP 1 complexes were pre-formed by combining [␥-32 P]ATP with excess Rho so that on average there was 0.3 [␥-32 P]ATP molecule per Rho hexamer. The Rho⅐[␥-32 P]ATP 1 complexes were mixed in a chemical quench apparatus with a solution of poly(C) RNA (required for catalysis) plus a large excess (final concentration, 1-10 mM) of Mg 2ϩ complex of unlabeled nucleotide or other compound of interest ("chase"). The extent and rate of [␥-32 P]ATP hydrolysis were determined by quenching the reaction after various times (5 ms-30 s) and measuring the amount of product 32 P i (see "Experimental Procedures"). The rates of the chemistry step for [␥-32 P]ATP hydrolysis and of other events in the catalytic cycle were obtained from simulations of the data using KINSIM (see "Experimental Procedures" and Table I) (14), employing a model that is described below.
Promotion by an ATP Chase-When a high concentration of ATP (2-20 mM) is included with the RNA that is mixed with Rho⅐[␥-32 P]ATP 1 complexes, the conditions are closest to the normal in vivo functioning of Rho. All of the vacant catalytic sites rapidly fill with ATP, and RNA binding permits V max hydrolysis. 20 -30% of the total [␥-32 P]ATP is hydrolyzed in a burst by 10 ms after mixing, and more than two-thirds is turned over by 200 ms (Fig. 1A). A model that successfully simulates the data is presented in Scheme 1 (also see "Experimental Procedures"). According to this model, the substoichiometric [␥-32 P]ATP that is initially bound to Rho is hydrolyzed when, as previously concluded (3,12), the three active sites fire sequentially. A preexisting asymmetry in the Rho hexamer and/or asymmetry conferred by RNA binding differentiates among the three Rho active sites, defining sites 1, 2, and 3 and resulting in their ordered firing. [␥-32 P]ATP and initial RNA binding are at random with respect to one another; hence, one-third of the [␥-32 P]ATP is in each of the three sites. The chemistry step of the catalytic cycle is fast (Ն300 s Ϫ1 ), so up to one-third of the total [␥-32 P]ATP (which is in site 1) is hydrolyzed rapidly (burst) and is found as product 32 P i at the earliest experimental time points (5-10 ms) ( Fig. 1 and Table I). For [␥-32 P]ATP molecules initially bound in Rho active site 2 or 3, one and two complete catalytic cycles, respectively, precede the hydrolysis of the labeled substrate molecule. In the simulations, the same steps in each of the three catalytic cycles have the same rates. [␥-32 P]ATP can dissociate at any time from Rho (at 3 s Ϫ1 ). Its rebinding is prevented by the high concentration of non-radioactive chase ATP. The steady-state hydrolysis rate usually found for Rho is 30 s Ϫ1 ; however, rates of ϳ10 s Ϫ1 were obtained from modeling.
No Chase-As previously reported (3), when only one of the three ATP binding sites of Rho is occupied and RNA is added in the absence of chase nucleotide, hydrolysis of the bound [␥-32 P]ATP differs in two ways from the results with the ATP chase. 1) The rate of catalysis is slow, and 2) there is essentially no burst (Fig. 1A). This result was general for NTPs as dem-onstrated by experiments in which [␥-32 P]CTP was the substrate (Fig. 1, filled triangles).
Although the data when there is no chase appear to be fit by a first-order equation (as in Ref. 3), greater complexity is probably involved. First, some degree of dissociation and rebinding of [␥-32 P]ATP during the experiment is expected to occur and  1 complexes with various chase compounds Rho⅐͓␥-32 P͔ATP 1 complexes were mixed in a chemical quench apparatus with poly(C) RNA plus mM levels of chase compounds. Samples were quenched after various times, and the product 32 P i was measured. Experiments were carried out between one and five times. The results were simulated using KINSIM. See "Experimental Procedures" for details. Burst magnitude indicates the fraction of ͓␥-32 P͔ATP hydrolysis found at the earliest quench time (5-10 ms).  1B and data not shown) requires that [␥-32 P]ATP initially bound in any Rho site eventually can undergo catalysis. With the goal of a single kinetic model that with appropriate rate choices successfully simulates all of the experimental results, the ordered sequential model described above for an ATP chase was applied to this situation with no chase. Two inconsistencies were found. (i) Because there is no substrate or other molecule in two of the active sites, hydrolysis of the [␥-32 P]ATP molecules bound in enzyme sites 2 and 3 cannot be preceded by any catalytic cycles. Although it could reasonably be thought that this situation precludes hydrolysis of [␥-32 P]ATP initially bound in sites 2 and 3, simulations show that hydrolysis by site 1 alone, including hydrolyses following dissociation and random rebinding of [␥-32 P]ATP from other sites, would produce far less product 32 P i than was observed (Fig. 1B, dashed line). Therefore, it is clear that the enzyme must be able to hydrolyze [␥-32 P]ATP initially bound in site 2 or 3 without catalysis in the preceding site(s). Stated another way, enzyme with site 2 or 3 occupied must become like enzyme with [␥-32 P]ATP in site 1 where RNA binding is followed by slow (because two active sites are empty) catalysis. Branches are necessary in the kinetic pathway for these proposed additional first-order events involving enzyme with [␥-32 P]ATP site 2 or 3 (see Scheme 2). Simulations indicate that the rates of such first-order steps are in the range of 2.2-2.4 s Ϫ1 . (ii) The second inconsistency when the model for an ATP chase is used for the no-chase situation is that, without energy input from previous catalytic cycles, ordered sequential active site firing must become random. In enzyme molecules with [␥-32 P]ATP bound in site 1, site 1 fires first but enzyme molecules with [␥-32 P]ATP in site 2 or 3 must now behave similarly to one another with a first-order step followed by slow catalysis. When the ATP chase model is modified to accommodate these two inconsistencies (Schemes 2 and 3), the data are closely fit (Fig. 1B). As previously found (3), the rate of the chemistry step of [␥-32 P]ATP hydrolysis is slow  (Table I). [␥-32 P]ATP dissociation was at 3 s Ϫ1 , and its rebinding was at 0.02 s Ϫ1 .
In the absence of a chase compound, no burst was found. Only 3-4% of the radioactivity initially in [␥-32 P]ATP was detected as 32 P i . This quantity is of the same magnitude as the background 32 P i in the [␥-32 P]ATP and is not considered significant. A burst of product formation is expected from those Rho hexamers that have all three catalytic sites filled with [␥-32 P]ATP; however, under the experimental conditions of 0.1 [␥-32 P]ATP per active site, only 0.1% of the total Rho will have 3 molecules of [␥-32 P]ATP bound and only one of those three bound [␥-32 P]ATP molecules will be hydrolyzed in the burst.
To summarize, in the absence of a chase nucleotide, the kinetics of hydrolysis of a single [␥-32 P]ATP molecule bound to Rho are not only slower than when ATP is saturating but the three Rho active sites no longer necessarily act sequentially. An additional first-order step is required in the enzyme mechanism to permit hydrolysis by enzyme molecules with [␥-32 P]ATP in site 2 or 3.
Other Promoters-ATP analogs and the related compounds that we tested to determine the features of a molecule that are important for promotion fell into three classes: 1) those that behaved like ATP; 2) those that enhanced the rate of hydrolysis of [␥-32 P]ATP but not as well as ATP and with a smaller extent of initial hydrolysis; and 3) those that did not promote the hydrolysis of [␥-32 P]ATP or show significant initial 32 P i product formation. Nucleoside monophosphates were not tried since previous work established that AMP binds poorly (10).
ATP-like Promotion-Chase nucleotides CTP, GTP ( Fig. 2A,  filled circles), and UTP, all known Rho substrates (15), behaved like ATP in promoting the hydrolysis rate of [␥-32 P]ATP in Rho⅐[␥-32 P]ATP 1 complexes in the presence of poly(C) and showed an elevated initial product level (burst) ( Table I). Among known NTP substrates, the features of the base portion of the nucleotide thus are not critical to promotion. ATP analogs variant in the sugar, 2Ј-and 3Ј-dATP, ddATP (Fig. 2B, filled circles), SCHEME 2. No chase. SCHEME 3. Boldface arrows are ordered sequential V max catalysis. A, ATP; D, ADP. and adenine arabinoside-5Ј-triphosphate, which are good Rho substrates, also behaved like ATP (Table I). Although Richardson and Conaway (15) reported that ddATP does not support the release of RNA from ternary transcription complexes, we found from steady-state time course experiments monitored by TLC (see "Experimental Procedures") that it is hydrolyzed at approximately half of the rate of ATP. Thus, the hydroxylation state of the ribose 2Ј-and 3Ј-carbons of the nucleotide substrate is also not of great importance in promotion. In the KINSIM model, off-rates of 3 s Ϫ1 and catalytic cycle rates of 5-11 s Ϫ1 (for the catalytic cycle in site 1 preceding chemistry in site 2 and the cycles in sites 1 and 2 preceding chemistry in site 3) accommodated the data with the exception of 3Ј-deoxy-ATP where the catalytic cycle was 3 s Ϫ1 .
Non-promoting Nucleotides-Hydrolysis products ADP and CDP used as chase agents at ϳ30ϫ K D were ineffective. The results resembled those obtained in the absence of chase with no rate enhancement or burst (Table I), indicating the importance of the ␥-phosphoryl group to promotion. The inclusion of 1 mM P i with a 1 mM ADP chase did not change the results ( Fig.  2A, triangles). This finding is not surprising because the K D for P i is ϳ30 mM (10), so at 1 mM there would be little P i bound. The use of significantly higher concentrations of P i and accompanying Mg 2ϩ led to the formation of a precipitate, so the effect of the simultaneous presence in Rho active sites of both ATP hydrolysis products is not known. Non-hydrolyzable ATP analogs AMP-PNP (Fig. 2B, triangles) and AMP-PCP (Fig. 2B, open circles) also failed both to promote hydrolysis and to show a significant burst (Fig. 2B and Table I). In KINSIM models, the rates of catalytic cycles preceding chemistry in sites 2 and 3 were set to zero as was done above in the absence of chase but other parameters were close to those for promoting nucleotides. Ligand off-rates were 1.5 s Ϫ1 , and the added first-order step for enzyme molecules with [␥-32 P]ATP in site 2 or 3 was 0.5-1.3 s Ϫ1 . The chemistry step of the catalytic cycle was again slow (1.6 -5.0 s Ϫ1 ) (Table I).
Slower Promotion-Several ATP analogs and related compounds used as chase molecules produced appreciable but lower initial bursts than did ATP and also showed significant rate enhancements during subsequent catalysis. ATP␥S, ATPP, AMP-CPP, PP i , PPP i , and PNP all behaved in this manner (Fig. 3). The most important contributor to this behavior is an increase in the rate of the chemistry step for [␥-32 P]ATP hydrolysis, modeled by KINSIM as 45-120 s Ϫ1 (Table I).
K D values were obtained for many of the chase compounds by ultrafiltration measurements in competition experiments where [␥-32 P]ATP was initially bound (see "Experimental Pro- . C, as in A except that the chase compound was 1 mM MgATP␥S (filled circles). Results from a MgATP chase (ϩ) are included for comparison. Lines were fit as described in Fig. 1. cedures"). The values obtained are given in Table II and show that, at 1 mM final concentrations, Rho active sites will be saturated. The possibility that slower on-rates contributed to the slower promotion was tested with PP i by repeating the experiment at a 4-fold higher MgPP i concentration. No change was seen in the results (Fig. 3B, open versus filled triangles), indicating that the on-rate was not limiting.
Slower Promoters Are Not Significantly Hydrolyzed-The slower promotion of ATP hydrolysis by these compounds prompted us to determine whether they are substrates for Rho. We found very slow hydrolysis of [ 32 P]PP i at 37°C of 0.5 ϫ 10 Ϫ4 s Ϫ1 measured by quantitation of product 32 P i following TLC of reaction samples (see "Experimental Procedures"). Including a small amount (10 M) of ATP to more closely mimic the conditions of the chase experiments yielded a similar result (data not shown). This extremely slow PP i hydrolysis rate indicates that, although PP i is able to promote ATP hydrolysis, its own hydrolysis is not part of the process. An analysis of PPP i found no evidence for its hydrolysis by Rho after 60 h at room temperature (see "Experimental Procedures"), whereas AMP-CPP was a slow substrate with an estimated turnover rate on the order of 0.1-1 s Ϫ1 . AMP-CP product was visible after 1 h of reaction at room temperature with complete hydrolysis by 4 h under conditions where the same initial concentration of ATP was fully hydrolyzed by ϳ5 min (see "Experimental Procedures"). Under similar conditions, ATPP was a very slow substrate, requiring overnight incubation for ϳ50% hydrolysis (analyzed by TLC). These results indicate that these compounds promote the rate of [␥-32 P]ATP hydrolysis without being hydrolyzed over the time period of promotion. This conclusion is supported by the similar behavior of PNP, a non-hydrolyzable PP i analog (Table I and Fig. 3B).
As in the situation with no chase, more than one-third of the [␥-32 P]ATP is eventually hydrolyzed. In these slower promoter chases, this occurs before 400 ms (Fig. 3). Unlike the situation with no chase, rebinding and hydrolysis of dissociated [␥-32 P]ATP cannot account for a significant portion of this product formation. Again, the enzyme must be able to achieve conformations in which [␥-32 P]ATP bound in site 2 or 3 can be hydrolyzed without catalysis in the previous site(s). KINSIM yields rates for these first-order steps of 1-4 s Ϫ1 .
Lower Bursts with Slower Promoters Arise from the Slower [␥-32 P]ATP Hydrolysis Rates-To explain the lower bursts of [␥-32 P]ATP hydrolysis found with the slower promoters, we reasoned as follows. Essentially all of the [␥-32 P]ATP in these experiments is initially bound at random to Rho active sites. As in the case where there is an ATP chase, the hydrolysis of one-third of the total [␥-32 P]ATP in a burst can be understood as the hydrolysis of [␥-32 P]ATP bound in Rho site 1, for which there is no required preceding catalytic cycle. However, in the case of the slower promoters, clearly less than one-third of the total [␥-32 P]ATP is hydrolyzed in a burst but more is hydrolyzed than with non-promoting chase compounds (Figs. 2 and 3 and Table I). The burst is smaller than with an ATP-like promoter, because slower chemistry permits more [␥-32 P]ATP dissociation from site 1 prior to hydrolysis. Optimal KINSIM simulations for the [␥-32 P]ATP dissociation rate for this class of compounds were similar to those obtained in other experiments of this type (from 1.5 to 4 s Ϫ1 ).
The case of ATP␥S as chase is illustrative. Although the results come close to the promotion achieved using ATP as chase (Fig. 3C), experiments carried out side-by-side using as close to the same materials as possible consistently showed less initial 32 P i product and slower promotion. ATP␥S has been previously characterized as a Rho substrate (3,16). It is hydrolyzed at 23°C in the presence of poly(C) at ϳ1 s Ϫ1 versus 30 s Ϫ1 for ATP. KINSIM modeling of the results with ATP␥S as chase failed to match the data when its hydrolysis at 1 s Ϫ1 was forced to precede that of [␥-32 P]ATP in Rho sites 2 and 3 (ordered sequential mechanism). If this were the mechanism, a plateau after hydrolysis of approximately onethird of the total [␥-32 P]ATP is expected as the slow hydrolysis of ATP␥S permits time for [␥-32 P]ATP dissociation at 3 s Ϫ1 . However, the data could be well fit (Fig. 3C) by a 100-s Ϫ1 [␥-32 P]ATP chemistry step together with a 3-4-s Ϫ1 first-order step preceding [␥-32 P]ATP hydrolysis in active site 2 or 3. Thus, ATP␥S hydrolysis at ϳ1 s Ϫ1 is too slow to be a significant step in ATP␥S-promoted 32 P i production from [␥-32 P]ATP. ATP␥S must, like the other slow promoters that are not appreciably hydrolyzed, enable the enzyme active sites to achieve a conformation close to that when ATP is present in all active sites. A comparison of the results of [␥-32 P]ATP hydrolysis with an ATP␥S chase and [ 35 S]ATP␥S hydrolysis with ATP chase revealed, as expected, that ATP does not promote fast hydrolysis of ATP␥S (data not shown), consistent with a slow chemistry step for this analog (17).

New Enzyme Behavior under Substoichiometric Substrate
Conditions-When poly(C) is added to Rho that has ATP bound, ATP hydrolysis is 30-fold faster when all three active sites contain ATP than it is when only one site is occupied (3). The kinetics and extent of [␥-32 P]ATP hydrolysis with no chase, non-promoting chase, or with slowly promoting chase compounds reinforce the concept introduced by the finding of ordered sequential catalysis among its three active sites that the Rho hexamer is functionally asymmetric and illuminate two additional facets of Rho behavior. First, ATP or other strong promoter binding in all of the active sites permits the enzyme to adopt optimal active site configurations and results in ordered sequential substrate hydrolysis with fast chemistry steps (Schemes 1 and 3 and Table I). The slower promoters allow Rho active sites to achieve configurations competent for chemistry but at lower rates. Second, when [␥-32 P]ATP or other strong promoter occupies only active site 2 or 3, the enzyme can undergo a slow conformation change that essentially converts it to the form with [␥-32 P]ATP bound in site 1 and then catalysis can occur (Scheme 2). ATP-saturated enzyme can probably also undergo these conformation changes (Scheme 3), but they are so slow relative to the steps of the ordered sequential firing pathway that their contribution to hydrolysis is minimal. These kinetic branches only achieve visibility when chemistry is slow. When there is no chase or with chase compounds that are not hydrolyzed, the slow branches are the only routes to hydrolysis of [␥-32 P]ATP initially bound in site 2 or 3. Thermodynamic considerations mandate that hydrolysis by enzymes with ATP in site 2 or 3 without catalysis in preceding sites must occur in a random, rather than an ordered sequence, because there is no energy input from preceding catalysis that can impose order.
Modeling the Data-We constructed and tested kinetic models for our results with the goal of a single model for all of the data from similar experiments. This goal was achieved. We are aware of the limitations of modeling and attempted to determine the sensitivity of the rates in the best simulations. In general, optimal rates could be varied by less than a factor of two without producing an obviously poorer fit to the data. It is satisfying that similar values were obtained from modeling different data sets for the off-rate for [␥-32 P]ATP and for the slow first-order step permitting catalysis by enzyme with [␥-32 P]ATP in site 2 or 3. The rapid mix/chemical quench results are successfully simulated using the models shown in Schemes 1 and 2 and their composite shown in Scheme 3. (i) When there is promotion of the hydrolysis of a single bound radiolabeled ATP molecule per hexamer, the hydrolysis rate is consistent with random labeled ATP and RNA binding followed by ordered sequential active site firing. An alternative model in which RNA binds preferentially to the Rho subunit that contains [␥-32 P]ATP did not fit the data, producing simulations with faster and larger amplitude hydrolysis than was actually seen (data not shown). (ii) When there is no chase nucleotide present, a non-promoting chase nucleotide, or a slowly promoting chase compound, chemistry is slower, permitting the slow first-order step to emerge, and ordered sequential activity becomes random. Stated differently, enzyme molecules with [␥-32 P]ATP in site 2 or site 3 in the absence of catalysis at normally preceding sites can undergo a slow first-order event that enables them to perform catalysis.
Thus, two conformation changes are implicit in the model. One occurs upon the binding of ATP or other strong promoter molecule to an active site. This conclusion is consistent with the intrinsic Rho fluorescence changes upon ATP binding studied by Jeong et al. (18). If all of the active sites undergo this conformation change, catalysis is fast and ordered sequential. In the KINSIM model, this is reflected in the rate of the chemistry step. If only one site has ATP bound, when it is site 1, slow chemistry (because the other two active sites are empty) follows. If the molecule of ATP is bound in site 2 or 3, an additional first-order isomerization step is needed prior to a slow chemistry step. Different chase molecules lead to very different chemistry step rates (Table I), whereas the slow firstorder step rate does not vary greatly. The slow first-order step could be a protein conformation change, or it might involve the repositioning of bound RNA in relation to an empty active site to a more productive configuration with respect to an active site that is filled with [␥-32 P]ATP.
One notable aspect of the KINSIM model for the ATP chase data (Fig. 1) is the 10-s Ϫ1 rate that provided the best fit for the overall catalytic cycle. Previous work (3,12) led us to expect a rate of 30 s Ϫ1 . It is not clear whether this 3-fold rate difference is significant. However, models employing a catalytic cycle rate of 30 s Ϫ1 gave a poor fit to the data. Those fits could be improved by reducing the rate of the chemistry step from 300 to ϳ80 s Ϫ1 and by increasing the ATP dissociation rate from 3 to 8 s Ϫ1 , but these values deviate from our previous findings. Intermediate values (e.g. 20 s Ϫ1 ) for the catalytic rate provided reasonable fits with corresponding lesser adjustments of the dissociation and chemistry steps. Although this rate discrepancy might reflect an enzymatic property that we do not yet appreciate, it is more likely that it is due to minor differences in mixing order and ligand concentrations in the various experiments compared. It is clear that the kinetics of ATP hydrolysis by Rho depend on the degree of saturation of Rho with ATP (3). There may be other variations of rates that depend, for example, on ligand binding order. It is clear that we do not yet know the details and order of events at all of the catalytic and binding sites on Rho. Much of our current work is directed toward answering these questions.
Substrate Characteristics Needed for Catalytic Cooperativity-A goal of this work was to determine the features of the ATP molecule that are needed for the increased catalytic rate under saturating substrate conditions. Several results illustrate the importance of the phosphoryl chain of the nucleotide relative to that of the base and sugar. 1) There is significant rate enhancement by PP i , PPP i , and PNP, which have no base or sugar.
2) Nucleoside triphosphates with any of the four conventional bases are effective promoters. There is no base specificity.
3) The length of the phosphoryl chain of a nucleotide is critical. Nucleoside diphosphates are ineffective, and the tetraphosphate ATPP is not as efficient as nucleoside triphosphates.
Consideration of the Rho crystal structure with bound AMP-PNP (19) is useful in interpreting the ATP analog results, although the presence of six molecules of AMP-PNP per hexamer (in contrast to the three MgATP binding sites that we reproducibly find (10,12)) and the curious absence of Mg 2ϩ in the structure suggest caution in drawing conclusions. The adenine base of AMP-PNP is sandwiched between the side chains of Phe 355 and Met 186 . The hydrophobic interactions involved are not base-specific, consistent with the promotion ability of nucleoside triphosphates with any of the normal bases (Table  I). The ribose hydroxyl groups of AMP-PNP are exposed at subunit interfaces that are splayed open in the available structure but that must close to accomplish catalysis. Our results suggest that specific interactions between the protein and these hydroxyl groups are not of major significance even in a closed protein, because 2Ј-dATP, 3Ј-dATP, ddATP, and adenine arabinoside-5Ј-triphosphate are substrates and promoters ( Fig.  2 and Table I). The phosphoryl group interactions with Rho seen in the co-crystal structure are not what are typically found in proteins with Walker A-and B-sequences, perhaps because of the open configuration at the subunit interfaces (19). Our finding that AMP-PNP is not a promoter further suggests that its phosphoryl groups are not able to interact with the protein in the same way as those of ATP. The subtle structural differences between PNP and PP i , the interaction of AMP-PNP with Mg 2ϩ , or the lower acidity of the terminal phosphoryl group of AMP-PNP compared with ATP (20) may be contributing factors. Although AMP-PNP does not promote [␥-32 P]ATP hydrolysis, the smaller PNP molecule is a slow promoter ( Fig. 3 and Table I). These results indicate that base and ribose contacts with Rho that are available to AMP-PNP thwart productive phosphoryl group interactions with the protein. The fact that AMP-PNP behaves like ADP with respect to promotion ( Fig. 2 and Table I) is consistent with the repeated finding that this analog resembles ADP rather than ATP (18,21).
Consideration of PNP also illustrates the finding that significant rate enhancement does not require coordinated hydrolysis of a phosphodiester bond. PNP and also PP i and PPP i are hydrolyzed at an insignificant rate but are nevertheless slow promoters. These compounds must be able to bind in the place normally occupied by the phosphoryl chain of ATP and interact with moderate efficiency. However, the best promotion is achieved when a hydrolyzable nucleotide is used.
Comparison with Other Enzymes-Catalytic cooperativity in the absence of binding cooperativity, as seen here, has been discussed (22) and is documented, for example, for yeast AMP deaminase, a homotetrameric protein (23,24). Substrate AMP binds with equal affinity to all of the catalytic sites, and in the absence of regulatory ligands, the catalytic rate increases as sites are filled. F 1 ATPase is perhaps the best-known enzyme that exhibits catalytic cooperativity. Its ␣ 3 ␤ 3 ␥␦⑀ structure is reminiscent of Rho. The ␣and ␤-subunits are quite similar and are assembled as a planar hexamer (25), the probable structure for Rho once long RNA is bound (26). The ATP binding portion of the ␤-subunits where the active sites are located is very similar to the ATP binding portion of Rho, both in amino acid sequence and in structure (19,27,28). The enzymes are different in that ATP binding to F 1 , unlike its binding to Rho, exhibits negative cooperativity (e.g. Ref. 29). F 1 has been well characterized as carrying out slow net ATP hydrolysis when a single molecule of ATP is bound and 10 6 -fold faster catalysis when ATP is saturating (2), a far larger difference than is seen with Rho. For F 1 , ATP binding in additional catalytic sites promotes product release from the originally occupied site, whereas for Rho, additional substrate binding promotes the chemistry step of catalysis. F 1 is similar to Rho in that substrates that efficiently promote catalytic cooperativity include other hydrolyzable nucleotides (1). Non-hydrolyzable ATP analogs such as AMP-PNP and ADP, however, behave differently with F 1 , leading to intermediate promotion (1), and additional studies with F 1 (e.g. Ref. 30) suggest greater complexity with this enzyme. These disparities are likely to reflect differences in the details of how the two different proteins interact with nucleotides and their analogs and how the two proteins respond to such interactions.
Similar to the situation with Rho, different degrees of enzyme conformation change depending on whether substrate or a substrate analog binds in the active site have been previously reported as with Ca 2ϩ -ATPase, for example (31). Other enzymes, such as tryptophan synthase (reviewed in Ref. 32; see also Ref. 33), provide additional examples of conformation change in one subunit as a consequence of substrate or substrate analog binding in another subunit.
Summary-The ␤and ␥-phosphoryl groups of ATP play a key role in promoting V max ATP hydrolysis by Rho and are responsible for promoting catalytic cooperativity among the Rho active sites. When a single ATP molecule is bound per Rho hexamer, a slow first-order step that precedes chemistry can occur in the presence of RNA, enabling ATP hydrolysis in any active site. In the absence of saturating hydrolyzable substrate, the rate of catalysis by Rho depends to a significant extent on this slow first-order event, which then emerges together with the chemistry step to kinetic prominence. The first-order step could be a protein conformation change or a rearrangement of Rho-bound RNA.