Recycling of bacterial RNA polymerase by the Swi2/Snf2 ATPase RapA

Significance

RNA synthesis is an essential conduit of genetic information in all organisms. After transcribing an RNA, the bacterial RNA polymerase (RNAP) must be reused to make subsequent RNAs, but the steps that enable RNAP reuse are unclear. We directly observed the dynamics of individual molecules of fluorescently labeled RNAP and the enzyme RapA as they colocalized with DNA during and after RNA synthesis. Our studies show that RapA uses ATP hydrolysis to remove RNAP from DNA after the RNA is released from RNAP and reveal essential features of the mechanism by which this removal occurs. These studies fill in key missing pieces in our current understanding of the events that occur after RNA is released and that enable RNAP reuse.

Abstract

Free-living bacteria have regulatory systems that can quickly reprogram gene transcription in response to changes in the cellular environment. The RapA ATPase, a prokaryotic homolog of the eukaryotic Swi2/Snf2 chromatin remodeling complex, may facilitate such reprogramming, but the mechanisms by which it does so are unclear. We used multiwavelength single-molecule fluorescence microscopy in vitro to examine RapA function in the Escherichia coli transcription cycle. In our experiments, RapA at <5 nM concentration did not appear to alter transcription initiation, elongation, or intrinsic termination. Instead, we directly observed a single RapA molecule bind specifically to the kinetically stable post termination complex (PTC)—consisting of core RNA polymerase (RNAP)-bound sequence nonspecifically to double-stranded DNA—and efficiently remove RNAP from DNA within seconds in an ATP-hydrolysis-dependent reaction. Kinetic analysis elucidates the process through which RapA locates the PTC and the key mechanistic intermediates that bind and hydrolyze ATP. This study defines how RapA participates in the transcription cycle between termination and initiation and suggests that RapA helps set the balance between global RNAP recycling and local transcription reinitiation in proteobacterial genomes.

DNA transcription into RNA by RNA polymerases (RNAP) is essential for protein synthesis and is universal in all domains of life. In Escherichia coli, transcription is regulated at each step to control initiation (1), elongation (2, 3), and importantly, efficiency of termination (4, 5). Intrinsic termination occurs at sites on DNA which typically encode a hairpin structure followed by a short uridine-rich sequence. The formation of this RNA hairpin in the RNAP exit channel causes spontaneous transcript release as a result of melting and shearing of the RNA-DNA hybrid (6–9). The canonical scheme depicts transcript release followed by RNAP dissociation from DNA as the final step in the transcription cycle (5, 8), with RNAP free to bind a σ factor and initiate another round of transcription. RNAP recycling after termination is essential to maintain an adequate rate of steady-state transcription in vivo.

Contrary to the canonical scheme, recent single-molecule studies on the behavior of RNAP at intrinsic terminators demonstrate the formation of a long-lived RNAP-DNA complex, the post termination complex (PTC), that persists on DNA after transcript release in >90% of transcription events in vitro (10–13). Consistent with these observations, ensemble experiments show that the PTC must undergo further conformational changes to drive RNAP dissociation from DNA (14). There is evidence that the same PTC can alternatively be formed in vitro by sequence nonspecific association of core RNAP with DNA (10, 11, 15), but termination-independent PTC formation is likely not prominent in vivo because of the low steady-state concentration of free core RNAP in the bacterial cytoplasm (16). While in the PTC state, RNAP may hop or slide along DNA in a random walk and flip 180 degrees on DNA, allowing reinitiation of either sense or antisense transcription from a suitably situated promoter upon σ factor binding (10, 12, 13). However, these reinitiation pathways are limited to 1-D diffusion to proximal promoters on the same template, and the efficiency of reinitiation through this pathway depends on terminator–promoter distance and σ factor availability (15). The mechanism by which RNAP dissociates from DNA after intrinsic termination and is efficiently recycled to the cytoplasmic pool of RNAP holoenzyme remains unknown.

RapA, RNAP-associated protein ATPase, is a 109-kDa protein that is present across eubacteria and is as abundant in the cell as the housekeeping sigma factor σ⁷⁰ (17). RapA stably associates with core RNAP (K_D ~5 to 10 nM) (17) but not with holoenzyme (σ⁷⁰RNAP) due to the overlapping binding regions of RapA and σ⁷⁰ on RNAP (18). The ATPase activity of RapA is significantly enhanced upon binding to RNAP compared to its apo (unbound) form (19) but is unaffected by the presence of DNA. RapA is a bacterial homolog of eukaryotic Swi2/Snf2 proteins, which bind to and remodel nucleosomes on DNA (20). However, unlike some Snf2 family members, RapA binds dsDNA only weakly (K_D ~ 22 μM) (21, 22).

In bulk transcription reactions with purified RNAP and σ⁷⁰, the addition of RapA strongly stimulates multiround transcription cycling and transcript production, raising the possibility that it acts following termination (18, 23–26). However, multiple other activities for RapA have been proposed, including stabilizing open-promoter complexes during transcription initiation (27), promoting nascent transcript release from elongation complexes (25), preventing binding of RNAP on nonpromoter DNA (28), and removing stalled elongation complexes via backtracking (29).

To directly examine the role of RapA in transcription in real time, we performed colocalization single-molecule spectroscopy (CoSMoS) (30, 31) and single-molecule fluorescence resonance energy transfer (FRET) (32) studies. These experiments allowed us to define the binding target of RapA in the transcription cycle, establish how RapA reaches this target, observe the formation of key RapA·RNAP·DNA complexes, and quantitatively characterize the kinetic pathways by which they form and resolve the roles of nucleotide binding and hydrolysis. Together, the studies define a molecular mechanism for RapA function in bacterial transcription.

Results

RapA Binds to the PTC and Promotes PTC Dissociation.

To observe the behavior and function of RapA during the transcription cycle by single-molecule fluorescence, we first tethered fluorescently labeled circular DNA molecules (DNA^Cy5) containing a transcription promoter and two consecutive terminators to the surface of a glass flow chamber (Fig. 1A). Locations of the DNA^Cy5 molecules were recorded by single-molecule TIRF microscopy, and the attached Cy5 dye moieties were then photobleached (Materials and Methods). We then added to the chamber a solution containing σ⁷⁰RNAP holoenzyme fluorescently labeled on the RNAP β′ subunit (σ⁷⁰RNAP⁵⁴⁹). We observed the appearance of discrete RNAP fluorescent spots colocalized at DNA^Cy5 locations, indicating the formation of open promoter complexes on DNA (11). Excess unbound RNAP was then flushed from the chamber.

Fig. 1.

RapA removes post termination RNAP from DNA. (A) Schematic of the single-molecule transcription experiment. Circular DNA^Cy5 molecules tethered to a glass surface (blue) contain the λP_R′ promoter, seven tandem repeats encoding a 21-nt hybridization target (purple), and two consecutive intrinsic transcription terminators (TT). DNA^Cy5 molecules were photobleached (black star) after recording their locations. The presence at the DNA location of σ⁷⁰RNAP⁵⁴⁹ (green), RapA⁶⁵⁰ (orange), or nascent transcript hybridization probe⁴⁸⁸ (blue) is detected by the fluorescence from the attached green-, red-, and blue-excited dye molecules (stars) under alternating blue and green+red laser excitation. The time resolution was 2.6 s. (B) Control transcription experiment without RapA. The plot shows an example two-color record of fluorescence intensity at the location of a single DNA molecule. The presence (color) or absence (black) of a DNA-colocalized fluorescence spot from the specified molecule is indicated. The simultaneous presence of RNAP⁵⁴⁹ and probe⁴⁸⁸ (blue-shaded interval) reports the presence of a transcription elongation complex. Departure of probe⁴⁸⁸ (blue arrow) indicates transcript release and thus termination. RNAP⁵⁴⁹ can persist on DNA for extended times after termination, before its eventual dissociation. The time interval (green shading) between probe⁴⁸⁸ departure and RNAP⁵⁴⁹ departure (green arrow) reports the presence of the PTC. (C and D) Same as B but from a transcription experiment that includes 5 nM RapA⁶⁵⁰. Examples are shown of three-color intensity records at five DNA locations at which RapA⁶⁵⁰ binds and quickly departs (red arrow) during initiation or early elongation (C) or binds shortly before and departs simultaneously with or just after RNAP⁵⁴⁹ leaves the PTC (D). Asterisks mark nonproductive RapA departures that did not drive PTC dissociation. (E) Normalized histograms of PTC lifetimes (green shaded intervals from B–D) in transcription experiments with zero (Top) or 5 nM RapA (Bottom). RNAP⁵⁴⁹ departed either before (gray), simultaneously (±1 s) with (black), or after (green/pink) probe⁴⁸⁸ departure. Curves are exponential fits to lifetimes >1 s yielding the indicated time constants μ. For the zero RapA experiment, the reported time constant underestimates the mean PTC lifetime because 1) for a minority of the observed probe departures, no RNAP departure was observed before the end of the experimental record (26 of 113 total; these were not included in the plot and not fit), and 2) the measured RNAP⁵⁴⁹ photobleaching rate of 2.4 ± 0.2 × 10⁻⁴ s⁻¹ (SI Appendix, Fig. S4) reduces the measured characteristic lifetime by ~15%.

We first did a control experiment without RapA in which we initiated transcription at time zero upon the addition of a solution containing 0.5 mM each of ATP, CTP, GTP, and UTP (NTPs), and 10 nM of an oligonucleotide probe labeled with Alexa Fluor 488 (probe⁴⁸⁸) which hybridizes to a repeat cassette sequence near the 5′ end of the nascent transcript. At a typical DNA location that started with bound RNAP⁵⁴⁹ (e.g., Fig. 1B), we observed fluorescence resulting from probe⁴⁸⁸ hybridization to the nascent RNA, indicating the existence of a transcript elongation complex (11, 33, 34). During the time that probe fluorescence was present, we sometimes observed that RNAP⁵⁴⁹ intensity gradually decreased as observed previously for transcription with linear DNA templates (11). We attribute this change to gradual movement of the RNAP⁵⁴⁹ away from the chamber surface in the direction of decreasing TIRF field intensity. On other DNAs, we saw little intensity change during transcription, suggesting that some DNA circles might be oriented largely along the surface rather than normal to it. In either case, we usually observed the all-at-once disappearance of the probe fluorescence (Fig. 1B, blue arrow) suggesting that transcription had terminated via release of the probe-bound RNA. The mean duration of probe⁴⁸⁸ fluorescence was 59 ± 7 s (±SE; N = 113) for our experiment conducted at 33.1 °C, which is similar to the time (~42 to 60 s) for E. coli RNAP to transcribe the 2,334 bp DNA estimated from literature elongation rates [39 to 55 nt s⁻¹ at 37 °C (35–37)]. After termination, RNAP typically persisted on the DNA for hundreds of seconds as a PTC.

To examine the role of RapA, we prepared the fluorescently labeled construct RapA⁶⁵⁰. When we added 5 nM RapA⁶⁵⁰ and 1 mM ATP to a chamber containing only DNA with no RNAP, we observed little RapA binding to DNA; 4% (9 of 226) of DNA molecules were observed to interact with RapA for at least two consecutive frames (2 s) over 500 s. In contrast, in a transcription experiment with 5 nM RapA⁶⁵⁰ (Fig. 1A), 66% (184 of 280) of the DNA locations exhibited RapA binding, suggesting a direct interaction of RapA with polymerase molecules bound to the DNA. Furthermore, RapA binding at DNA locations depended on the phase of the transcription cycle. For the 180 of the 280 DNA molecules that exhibited transcript production, (i.e., probe appearance and later disappearance), we observed in 55 cases (31%) brief RapA association just prior to probe appearance (e.g., Fig. 1C). The significance of this short-lived binding during initiation or early elongation is not known (Discussion). Importantly, RapA rarely bound to mature elongation complexes. RapA presence during intervals when the probe was colocalized, which requires a transcript length of >47 nucleotides, was seen on only 10% (18 of 180) of DNAs that exhibited probe binding. Furthermore, the average dwell time of RapA on the elongation complexes to which it did bind was brief, 13 ± 3 s (±SEM; N = 18). Consistent with these observations, the presence of 5 nM RapA⁶⁵⁰ had little effect on the rate of transcript elongation: the mean duration of the probe⁴⁸⁸ fluorescence was 68 ± 3 s (±SEM; N = 180), similar to that seen in the absence of RapA.

In contrast to the minimal binding observed during transcript elongation, most (76%; 136 of 180) transcription events displayed RapA binding that occurred simultaneously with (within the ±2.6 s time resolution of the experiment) or after transcription termination detected by probe⁴⁸⁸ departure (examples shown in Fig. 1D). Notably, the majority of RNAP releases were preceded by RapA binding and occurred simultaneously with RapA departure from DNA (60%; 107 of 180 transcription events). Occasionally, RapA⁶⁵⁰ stayed bound on DNA after RNAP⁵⁴⁹ departure (Fig. 1 D, Bottom Left), but these events were rare (4%; 7 of 180) and were determined to be due to RNAP⁵⁴⁹ photobleaching (Discussion). Thus, RapA appears to bind to the PTC and remove RNAP from the DNA. This effect is confirmed by measurements of PTC lifetimes. Without RapA, PTCs had a characteristic lifetime of >600 s (Fig. 1 E, Top), similar to that observed previously (10). These measurements of PTC lifetimes without RapA are underestimates of the true mean because 23% (26 of 113 transcription events) of RNAP molecules stayed bound until the end of the experimental record. Not all RapA binding events triggered RNAP release; many were nonproductive events that ended with RapA departure from DNA with RNAP remaining behind (e.g., Fig. 1D, stars). Nonetheless, inclusion of 5 nM RapA⁶⁵⁰ in the experiment decreased PTC lifetimes by more than four-fold (Fig. 1 E, Bottom). In summary, the data establish via direct observation of transcription complexes that low nanomolar concentrations of RapA preferentially bind the PTC, are present when core RNAP departs, and always or almost always leave with the departing RNAP.

PTC Lifetimes Are RapA Concentration- and ATP-Dependent.

To further investigate the mechanism of PTC dissociation, we next reconstituted PTCs. The PTC consists of core RNAP-bound sequence nonspecifically to DNA. Available data suggest that the same complex can be made directly by mixing core RNAP directly with DNA. Like PTCs, these reconstituted PTCs (rPTCs) have long lifetimes (>600 s), exhibit RNAP sliding on DNA, are dissociated by treatment with heparin, and can bind σ⁷⁰ (10, 11, 15). rPTCs can be efficiently made in large quantities at the beginning of an experiment, allowing us to systematically investigate the effect of RapA concentrations and ATP on rPTC lifetimes.

We first tethered to a coverslip fluorescently labeled DNA circles that lack known transcription promoters, npDNA^Cy5, and then preincubated with RNAP⁵⁴⁹ (Fig. 2A). Free RNAP was flushed from the chamber and replaced by a solution containing various concentrations of RapA and/or ATP at time zero. We then measured the dwell times of RNAP⁵⁴⁹ spots at npDNA^Cy5 locations (Fig. 2B). At zero RapA and 1 mM ATP, the rPTC mean dwell time was 1,271 ± 26 s (SEM; N = 1,063), but this underestimates the true mean since 41% (442 of 1,063) of measurements were censored by the end of the experimental record. This value is consistent with the >600 s lifetime observed for PTCs (Fig. 1). When RapA in the 1 to 10 nM range was added, the reciprocal mean dwell time increased steeply (Fig. 2C, green circles). In contrast, no change in the mean dwell time was observed at increasing concentrations of RapA in the absence of ATP (Fig. 2C, green diamonds).

Fig. 2.

Nanomolar RapA disrupts rPTCs in an ATP-dependent manner. (A) Schematic of the single-molecule rPTC disruption experiment. Circular npDNA^Cy5 molecules [tethered to a glass surface (blue)] contain no known promoter sequences and were photobleached (black star) after recording their locations. At time zero, RapA or RapA⁶⁵⁰ (orange) was added either together with RNAP⁵⁴⁹ (green; premix) or after free RNAP⁵⁴⁹ was removed from the chamber (washout). Presence at the DNA location of RNAP⁵⁴⁹ is detected by the fluorescence from the green-excited dye molecule (star) under continuous laser excitation. Time resolution 1 s; 532 nm laser power 400 µW; RNAP⁵⁴⁹ photobleaching rate (SI Appendix, Fig. S3) 0.0006 s⁻¹. (B) Example RNAP⁵⁴⁹ fluorescence intensity record at the location of a single DNA molecule from a washout experiment, plotted as in Fig. 1 B–D. (C) Reciprocal of the mean RNAP⁵⁴⁹ dwell time τ at various RapA or RapA⁶⁵⁰ concentrations. Experiments were conducted using the premix or washout protocols in the presence or absence of 1 mM ATP. Data were fit to hyperbolic (solid line) or linear (dashed lines) models yielding fit parameters given in SI Appendix, Table S1. Inset: Magnified view of the low concentration range with additional data at zero RapA.

rPTCs dwell times were the same with 5 nM unlabeled RapA and 5 nM RapA⁶⁵⁰ (SI Appendix, Fig. S1), indicating that the presence of the fluorescent dye label on RapA does not alter its PTC disruption activity.

At RapA concentrations >10 nM in the presence of ATP, the dwell time of RNAP on DNA became sufficiently short that significant dissociation occurred during the washout fluid flow. To measure short dwell times accurately under these conditions, we used an alternative “premix” protocol in which 0.7 nM RNAP⁵⁴⁹ and various concentrations of RapA or RapA⁶⁵⁰ were premixed with or without ATP and then loaded all together over the surface-tethered npDNA^Cy5 molecules. RNAP⁵⁴⁹ molecules were continuously recorded as they bound and released from DNA surface locations, allowing measurements of dwell times as short as 2 s. When the two protocols were compared under the same conditions, they produced similar results (Fig. 2C, orange and green). The dwell times measured in the premix experiment exhibited saturation kinetics and fit well to a hyperbolic model with a half-saturating RapA concentration K_0.5 = 21 ± 3 nM and extrapolated maximum rate at saturation of k_max = 0.043 ± 0.004 s⁻¹ (SI Appendix, Table S1). These parameters imply an effective second-order rate constant for RapA-mediated rPTC disruption of k_max/K_0.5 = (2.1 ± 1.3) × 10⁶ M⁻¹ s⁻¹, close to that expected for a diffusion-limited association step. Taken together, these data indicate that nanomolar concentrations of RapA potently disrupt rPTCs in an ATP-dependent manner; RapA is able to decrease rPTC lifetime by a factor of at least 20-fold (k_max/b; see SI Appendix, Table S1).

Washout experiments in which we observed fluorescence from both RNAP⁵⁴⁹ and RapA⁶⁵⁰ (Fig. 3A) exhibited similar behavior on rPTCs to that seen on PTCs (Fig. 1D). RapA bound to rPTCs and usually departed simultaneously with RNAP. In rare cases, RapA⁶⁵⁰ remained briefly after RNAP⁵⁴⁹ fluorescence vanished, but as previously noted, these uncommon events may be a consequence of RNAP⁵⁴⁹ photobleaching rather than true sequential departure of the two proteins. With both PTCs (Fig. 1D, asterisks) and rPTCs (Fig. 3A, asterisks), we sometimes observed nonproductive RapA binding that did not remove RNAP from DNA.

Fig. 3.

Dynamics of labeled RapA interacting with rPTCs. (A) Example fluorescence intensity records from the locations of four individual rPTCs in the presence of 0.75 nM RNAP⁵⁴⁹, 5 nM RapA⁶⁵⁰, and 1 mM ATP. Experiments used the design shown in Fig. 2A with the washout protocol, and data were collected with simultaneous green and red laser excitation; time resolution 0.2 s. Asterisks and arrowheads, respectively, indicate nonproductive binding events by RapA and protein departure, respectively, as in Fig. 1. (B) Cumulative fraction of rPTC locations from the experiment in A that bound at least one RapA⁶⁵⁰ molecule by the indicated time (blue) and analogous data from non-DNA control locations in the same experiment. Plot truncated at 500 s for clarity. Also shown are data from an analogous experiment without RNAP that show binding to npDNA^Cy5 locations (orange) and non-DNA control locations. Fits to model that includes exponential non-specific surface binding and exponential DNA-specific binding (dashed lines) yielded the kinetic parameters shown in SI Appendix, Table S2. (C) Experiment with the same conditions as in A, except that data were recorded with only 532 nm laser excitation. Example records from four different PTC locations show donor emission with donor excitation (D_exD_em), acceptor emission with donor excitation (D_exA_em), effective FRET efficiency [E_FRET = D_exA_em/(D_exD_em + D_exA_em)], and total emission (D_exD_em + D_exA_em). Galleries show excerpts of the rPTC location image recordings in the D_exD_em and D_exA_em channels. (D) Histograms of E_FRET values from the experiment in C at times when both RNAP⁵⁴⁹ and RapA⁶⁵⁰ were detected on rPTCs. Shown separately are data from RapA dwells that ended with simultaneous RapA and RNAP dissociation [Left, mean E_FRET = 0.404 ± 0.004 (SEM), N = 932 time points from 46 dwells] and those that ended with nonproductive RapA dissociation [Right, mean E_FRET = 0.370 ± 0.002, N = 4,253 time points from 189 dwells).

RapA Binds Directly to Core RNAP on DNA.

We next investigated the steps in the process by which RapA disrupts PTCs. Since RapA has putative DNA-binding domains (18, 19), we first asked whether the protein initially binds DNA or alternatively whether it goes directly to the DNA-bound RNAP in the PTC. In the Fig. 3A experiment, RapA⁶⁵⁰ bound to rPTCs with a second-order rate constant of 1.8 ± 0.4 × 10⁶ M⁻¹ s⁻¹ (Fig. 3B and SI Appendix, Table S2). This is similar to the effective second-order rate constant for rPTC disruption in the limit of low RapA concentrations (k_max/K_M = 2.1 ± 1.3 × 10⁶ M⁻¹ s⁻¹; Fig. 2C and SI Appendix, Table S1), confirming that the observed binding is kinetically competent to be the initial step in PTC disruption.

In contrast to its rapid binding to rPTCs, 5 nM RapA⁶⁵⁰ in 1 mM ATP exhibited no detectable background binding to the slide surface or to DNA molecules without bound RNAP (Fig. 3B, compare orange and gray distributions; SI Appendix, Table S2, compare A_f values). This is consistent with the very weak binding of dsDNA by RapA in solution [K_D = 15 µM (19)]. Thus, RapA likely reaches its PTC target by direct binding from solution, not by long-distance random sliding on DNA until RNAP is encountered.

To verify that RapA and RNAP are in close proximity when RapA binds to rPTCs, we checked for FRET between RNAP⁵⁴⁹ (donor) and RapA⁶⁵⁰ (acceptor). When washout protocol experiments were repeated using only donor (532 nm) excitation, we observed appearance of DNA-colocalized spots in the acceptor emission channel and concomitant reduction of donor emission, both indicative of FRET (Fig. 3C). The effective FRET efficiency (E_FRET) distribution was unimodal (Fig. 3 D, Left), with mean <E_FRET> = ~0.4, a plausible value given the proximity of the SNAP-tag attachment points in the two labeled proteins in RapA-elongation complex structures (SI Appendix, Fig. S2).

Just as we observed for PTCs (Fig. 1D), binding of RapA to rPTCs was sometimes productive, ending with simultaneous release of RapA and RNAP, and sometimes nonproductive, ending with just RapA release (Fig. 3 A and C, red arrows and asterisks, respectively). E_FRET distributions for the productive and nonproductive RapA·RNAP·DNA complexes were similar (Fig. 3D), consistent with the idea that productive and nonproductive events reflect different breakdown pathways of the same types of RapA-rPTC complexes.

RapA Association with PTCs Is Independent of Nucleotide.

Many members of the Snf2 family are motor enzymes that use ATP hydrolysis to drive translocation of the Snf2 homology domain relative to DNA. To check whether RapA translocates along DNA to reach DNA-bound RNAP, we compared RapA recruitment to rPTCs in experiments with ATP, with no added nucleotide, or with the non-/slowly hydrolyzable ATP analog AMPPNP (Fig. 4A). For each rPTC present at the beginning of the washout experiment (e.g., as seen in Fig. 4A, D_exD_em records), we measured the interval up to the time that RapA associated with the rPTC as judged by the onset of FRET (D_exA_em). Fitting demonstrates that the rPTC-specific binding intervals are exponentially distributed (Fig. 4B), as expected for a simple, one-step binding process. Importantly, the RapA-rPTC association rate constants k₁ determined from the fits were identical within experimental uncertainty (Fig. 4C). Thus, the absence of nucleotide or nucleotide hydrolysis does not alter the kinetics of RapA association with the PTC, implying that translocation driven by RapA ATP hydrolysis is not required for RapA recruitment to the PTC. Furthermore, the onset of RapA⁶⁵⁰ binding detected by direct excitation (Fig. 4A, A_exA_em) was simultaneous (to within the ±1.4 s experimental time resolution) with the onset of the same binding event detected by FRET (D_exA_em). This was the case for almost every RapA⁶⁵⁰ binding examined: 100.0% (645 of 645) in 1 mM ATP, 98.7% (639 of 647) in 1 mM AMPPNP, and 99.7% (1,302 of 1,305) with no nucleotide. The appearance of FRET simultaneously with binding is consistent with direct association of RapA with DNA-bound RNAP. The lack of a detectable delay between RapA arrival and FRET shows either that there is no intermediate state in which RapA searches along DNA or that this intermediate is too short lived to detect at the ~1.4 s time resolution of the experiment.

Fig. 4.

RapA-rPTC association kinetics under different nucleotide conditions. (A) Example fluorescence intensity records from nine individual rPTC locations in washout experiments (as in Fig. 2 A and B) with either 1 mM ATP (Left), 1 mM AMPPNP (Center), or no added nucleotide (Right). Alternating excitation with green and red lasers (0.2 s duration frames) allowed detection of RNAP⁵⁴⁹ (D_exD_em), RapA⁶⁵⁰ excited via FRET (D_exA_em), and RapA⁶⁵⁰ excited directly (A_exA_em). The average interval between consecutive frames with the same excitation wavelength was 1.39 ± 0.03 (SD) s. Note the expanded horizontal scale for the 1 mM ATP condition. Departure or photobleaching of core RNAP⁵⁴⁹ is marked by green arrows; departure of RapA⁶⁵⁰ without simultaneous RNAP⁵⁴⁹ release is marked by an open arrow. Asterisks mark nonproductive RapA binding intervals (RapA binding without catalyzing an RNAP departure). (B) Kinetics of specific RapA-rPTC association detected by FRET (i.e., D_exA_em). For the same three experiments from which the examples in A were taken, plots show the cumulative fraction of rPTCs that exhibited at least one RapA⁶⁵⁰ binding by the indicated time (rPTC) and analogous data from control locations without DNA molecules in the same samples (non-DNA control). Fits to data from both the rPTC (solid lines) and off-DNA data (dashed lines) using the same model as in Fig. 3B yield the parameters in SI Appendix, Table S3. (C) Second-order association rate constants for RapA binding to rPTCs (SI Appendix, Table S3).

Two Different RapA·RNAP·DNA Complexes Form during PTC Disruption.

The forgoing experiments imply that the mechanism of PTC disruption by RapA starts with RapA binding to the RNAP component of the PTC and ends with simultaneous departure of RapA and RNAP from the DNA. We next examined the characteristics of the RapA·RNAP·DNA complexes that exist in the time interval between these two events. In contrast to the similar rates of RapA·RNAP·DNA complex formation in different nucleotide conditions, RapA·RNAP·DNA lifetimes were markedly different. Notably, 1 mM AMPPNP caused a >50-fold increase in the average RapA·RNAP·DNA lifetime relative to ATP [373 ± 22 (SEM) s, N = 645 and 7.1 ± 0.4 s, N = 647, respectively]. Under all three nucleotide conditions, individual RapA·RNAP·DNA complexes were observed to have a broad distribution of lifetimes. Each distribution had two (or more) exponential components (Fig. 5A). This demonstrates that during the PTC disruption reaction, at least two different RapA·RNAP·DNA complexes are formed.

Fig. 5.

Kinetic analysis of PTC disruption by RapA. (A) Lifetime distributions of all RapA⁶⁵⁰·RNAP⁵⁴⁹·DNA complexes (circles; ±SE) for the different nucleotide condition experiments shown in Fig. 4. Also shown (lines) are maximum-likelihood fits to a two-exponential equation (Materials and Methods); fit parameters are provided in SI Appendix, Table S7. (B) Summary of the proposed kinetic scheme for RNAP (green) dissociation from the PTC by RapA (orange). The RapA·RNAP·DNA and RapA·RNAP·DNA^† complexes are indistinguishable by fluorescence, but the presence of two such species is inferred from the kinetics (see text). Experimental data were fitted with a full scheme that includes additional steps accounting for photobleaching of RapA⁶⁵⁰ and RNAP⁵⁴⁹ (SI Appendix, Fig. S5). In our working model of the mechanism, ATP binds to RapA in the RapA·RNAP·DNA state and is cleaved upon entrance into or exit from the RapA·RNAP·DNA^† state (Discussion). (C) Rate constants for the steps in the scheme (B) and for the photobleaching steps (SI Appendix, Fig. S5). Rate constants were determined by fitting the full kinetic scheme (SI Appendix, Fig. S5) to the RapA·RNAP·DNA paired lifetime and fate data summarized in SI Appendix, Fig. S6 and Table S6, except for k₁ values which are from SI Appendix, Table S3. Gray highlights designate values that are indistinguishable from zero within experimental uncertainty. The given photobleaching rate constants were determined from the fits, but they are roughly similar to photobleaching rate constants measured independently: k′_{pb, RNAP} = (0.043 ± 0.003) × 10⁻² s⁻¹ (SI Appendix, Table S4) and k′_{pb, RapA} = (0.26 ± 0.09) × 10⁻² s⁻¹ (SI Appendix, Table S5). The lifetime distributions and fate partition ratios predicted by the fits to the model are shown in SI Appendix, Fig. S6 and Table S6.

Kinetic Mechanism of PTC Disruption by RapA.

We propose (Fig. 5B) a minimal kinetic scheme consistent with our observations, one in which the two ternary complexes (designated RapA·RNAP·DNA and RapA·RNAP·DNA^†) are sequential intermediates in PTC disruption. We speculate that the two intermediates may differ in conformation, nucleotide state of the active site, or both. To test the agreement of this scheme with the experimental data, we first classified by its fate and measured its lifetime each individual observed RapA·RNAP·DNA complex. Three fates were observed: 1) the unproductive fate, in which RapA departs by itself (e.g., the RapA·RNAP·DNA complexes marked “*” in Fig. 4A); 2) the productive fate where RapA and RNAP leave simultaneously (e.g., Fig. 4A, red and green arrowheads); and 3) the fate in which RNAP departure precedes RapA departure (e.g., Fig. 4A, open arrowhead). We then fit the model and determined the values of the rate constants that gave the best agreement with the lifetime and fate data independently for each of the three experiments in Fig. 4A.

The model accurately reproduced the molecular behaviors observed for the RapA·RNAP·DNA complexes. In particular, it reproduced the partitioning between the three fates (SI Appendix, Table S6) and the lifetime distributions for RapA·RNAP·DNA complexes segregated according to fate (SI Appendix, Fig. S6). In our model, we considered the possibility that disappearance of the RapA⁶⁵⁰ or RNAP⁵⁴⁹ fluorescent spots can be caused either by protein dissociation or by photobleaching (SI Appendix, Fig. S5 and Materials and Methods). For RapA, we explicitly modeled dissociation (k_-1) and photobleaching (k_{pb, RapA}) processes. For RNAP, we found that it was not necessary to include a process in which RNAP dissociates from a RapA·RNAP·DNA complex leaving RapA behind to give good agreement with the data, so such a step was omitted from the kinetic scheme (Fig. 5B and SI Appendix, Fig. S5). The validity of the photobleaching analysis is confirmed by independent measurements of the photobleaching rates of RNAP⁵⁴⁹ (SI Appendix, Fig. S3 and Table S4) and RapA⁶⁵⁰ (SI Appendix, Fig. S4 and Table S5) which agree with the corresponding rate constants determined by fitting the RapA·RNAP·DNA lifetime and fate data to the kinetic scheme (Fig. 5C).

The kinetics revealed in the quantitative analysis of the reaction scheme (Fig. 5C) emphasize the kinetic significance of the two RapA·RNAP·DNA complexes: both k₂ and k₃ are partially rate limiting for RapA function at 1 mM ATP, and the reverse reactions k_-1 and k_-2 significantly compete with the k₂ and k₃ forward processes. Thus, the RapA binding step and the subsequent isomerization step are readily reversible, and this accounts for the significant number of nonproductive RapA binding events seen in the presence of ATP. In both AMPPNP and no nucleotide conditions, even more nonproductive events are observed, although it is possible that some of these events are due to photochemical blinking of the dye on RapA⁶⁵⁰.

Discussion

Early work on RapA showed that it facilitated multiround transcription in vitro, including switching between different template molecules. Jin and coworkers proposed that RapA allows recovery of RNAP from a “posttranscription or post termination” refractory state, but the composition of this refractory state and its position in the transcription cycle remained unclear (18, 23, 24). Here, we provide direct evidence that RapA binds to the post termination RNAP-DNA complex (PTC), an intermediate in the transcription cycle that follows intrinsic termination (10, 12, 13, 15). Within seconds of its binding to the PTC, RapA effectively removes core RNAP from DNA. This process is driven by a single RapA molecule, occurs even at low nanomolar concentrations of RapA, is ATP-dependent, and does not require a sigma factor. The refractory state of the early studies seems similar to the PTC but may not be identical to it. Notably, entrance into the refractory state appears largely irreversible, whereas PTCs can slowly dissociate even without RapA, especially in the presence of free σ⁷⁰ (15).

By directly observing transcription events in real time, we were able to distinguish the step(s) during which RapA preferentially binds in the transcription cycle. We saw essentially no RapA binding to mature elongation complexes in our experimental conditions. This observation argues against suggestions that RapA acts directly on elongation complexes (29, 38, 39). Our finding is consistent with structures of the RapA·RNAP complex showing that RapA binds at the RNAP RNA exit channel and displaces the RNAP β-flap tip, thereby partially blocking the RNA exit channel. This likely makes RapA binding incompatible with the protruding RNA present in mature elongation complexes and also with the presence of elongation-complex-bound NusA (28, 38). Nevertheless, prior studies taken together with our results support an indirect RapA effect on elongation complexes. Portman et al. (29) observed RapA disrupt stalled elongation complexes, but primarily on positively supercoiled DNA, and only slowly (the minimal lifetime of elongation complexes with 100 nM RapA in solution was ~1,000 s, not the 23 s we infer for PTCs at saturating RapA (1/k_max; see SI Appendix, Table S1)). Importantly, they provided strong evidence that this activity of RapA requires elongation complex backsliding on RNA/DNA. Based on the structural data and our observations that RapA does not bind stably to mature elongation complexes, we propose that for an elongation complex to be disrupted, it must first backslide either off the 5′-end of the RNA or at least to within 8 nt from the 5′ end, the point at which the RNA-DNA heteroduplex starts to be disrupted. In either case, the result would be a PTC-like structure in which core RNAP is bound to DNA without RNA protruding from the exit channel and which is vulnerable to at least partial bubble closing induced by positive superhelical twist. RapA could then bind the PTC-like structure and execute the ATP-dependent PTC-disruption activity that we demonstrate here. The fact that both elongation complex disruption and PTC disruption have half-maximal rates at similar RapA concentrations (~7 nM) is consistent with this interpretation.

In addition to PTC binding, we also see in ~24% of transcription events that RapA transiently (typically for <4 s) associated with the RNAP·DNA complex during the interval before the nascent transcript was detected by probe hybridization. These complexes are likely to be initiation complexes (e.g., the open-promoter complex) or very early elongation complexes that have not yet synthesized the part of the nascent transcript containing the probe hybridization sequences. When RapA dissociates from these complexes, the nascent RNA, and hence the elongation complex, is detected within seconds (Fig. 1C). A function of RapA during initiation was reported for Pseudomonas putida RapA, which is thought to stabilize the open complex during initiation and/or to rescue stalled initiation complexes, possibly in addition to its PTC disruption activity (40). Our data are consistent with a possible additional activity of E. coli RapA during initiation, although our experiments did not reveal an effect of nanomolar RapA on initiation kinetics.

The proposed kinetic scheme for disruption of the PTC by RapA (Fig. 5B) is a minimal scheme: It has the minimum number of states needed to explain our experimental results. The full mechanism for RapA function is necessarily more complex; in particular, it must also include ATP binding, hydrolysis, and ADP and P_i release steps. Our experiments conducted under various nucleotide conditions give some insight into the way that ATP hydrolysis is coupled to PTC disruption by RapA. The rate at which RapA associates with the PTC (k₁ in Fig. 5 B and C) is identical whether or not nucleotide is present, consistent with a mechanism in which RapA binds the PTC in its apo (no nucleotide) form, even when millimolar nucleotide is present. This is supported by structural work showing that the position of the RapA N-terminal domain (NTD) in apo-RapA may allosterically inhibit ATP binding (28, 39) and from experiments showing that deletion of RapA NTD significantly activates RapA ATPase activity in the absence of RNAP (41). Upon binding to RNAP either alone or in the context of an elongation complex, the NTD is repositioned, allosterically remodeling the RapA ATPase active site. This suggests that ATP binding to the active site occurs immediately after RapA binds to the PTC, consistent with our observation that all subsequent reactions of the RapA·RNAP·DNA complexes (k_-1 and k₂ in Fig. 5 B and C in particular) have nucleotide-dependent rates. Thus, ATP binding likely occurs between the k₁ and k₂ steps.

In contrast to the nucleotide-independent effect on k₁, the nucleotide effect on k₃ is profound. In the absence of nucleotide or in the presence of AMPPNP, k₃ is not significantly above zero (Fig. 5C, gray). Based on the calculated uncertainties, we estimate that k₃ is at least 150-fold faster in the presence of ATP than AMPPNP and at least 900-fold faster than without nucleotide. To compare, the nucleotide effect on k₂ is less than 5-fold. Therefore, we propose that the ATPase hydrolysis step is likely at or immediately prior to the step in which RapA-RNAP dissociates simultaneously from DNA, that is, that hydrolysis occurs upon entrance into or exit from the RapA·RNAP·DNA^† state shown in Fig. 5B.

RapA belongs to the Swi2/Snf2 protein family, many members of which are eukaryotic chromatin remodelers (20, 42). Some well-studied examples of these proteins function by a mechanism in which they bind to the histone core and use free energy from ATP hydrolysis to forcibly translocate or rotate the DNA, thereby disrupting histone-DNA contacts and facilitating displacement of the histones from DNA (42). Our data on RapA suggest that it works by an analogous mechanism in which it binds directly to the RNAP-DNA complex, followed by ATP binding and hydrolysis to drive RNAP ejection from DNA. Recent studies show the existence of a partially rewound DNA bubble in RNAP after RNA release during intrinsic termination (43). After binding to the PTC, RapA may mechanically close the bubble, thereby promoting PTC disruption. Further work will be required to determine if RapA drives rotation or translocation of the DNA relative to RNAP during RapA·RNAP·DNA complex disruption and whether hydrolysis of only one molecule of ATP is sufficient for the process.

In bacterial transcription, there is evidence for reinitiation after intrinsic termination from experiments both in vitro and in vivo (10, 12, 13, 15). These studies, among others (44–47), are consistent with the proposal that there is a balance between reinitiation (local) and conventional initiation (global) in cells. Based on the activity and mechanism of RapA described here, we propose that the primary biological function of RapA is to set the balance between these two types of initiation. This phenomenon may be driven by RapA competition with sigma factors for binding to PTCs since the binding sites of the two proteins on the β subunit of RNAP largely overlap (28, 38). Under particular growth conditions (e.g., log phase), transcription is more or less concentrated into particular genomic regions (e.g., rRNA operons) (44, 46, 48). Efficient reinitiation likely helps stabilize this localized transcription. However, when conditions change, it may confer a selective advantage for bacteria to be able to rapidly redeploy the transcription machinery to new genomic regions. In this context, it is noteworthy that RapA knockout mutants do not show any growth defects in unaltered rich medium. However, upon salt stress, sodium deoxycholate treatment, or osmotic shock, deletion of the rapA gene increased the duration of the recovery phase compared to WT (24, 49) and decreased antibiotic resistance in biofilms due to the lower expression of genes implicated in resistance (50). Furthermore, the RapA homolog HepA in Vibrio cholerae is crucial for the acid-tolerance response, where ΔhepA mutants display a >1,000-fold decrease in colonization proficiency (51). Consistent with RapA functioning in reprogramming, RapA is up-regulated when cells transition into heat shock as modulated via the σ³² regulon (52). Further work will be needed to establish the role of RapA in transcriptional reprogramming.

Materials and Methods

DNA and Plasmids.

Methods for preparing the DNA and plasmids used in this work are described in SI Appendix, Materials and Methods.

Proteins.

The N-terminally His₆-tagged E. coli RapA construct (H₆-RapA) was expressed and purified as described (28).

From the H₆-RapA expression plasmid and pSNAP-tag(T7) plasmid (NEB #101137), we constructed a plasmid pKI1 (Addgene #199118) encoding H₆-SNAP-RapA. The plasmid was transformed into NEBExpress^IQ cells, and the 129-kDa H₆-SNAP-RapA protein was expressed and purified as described (28). The concentration of SNAP-RapA was calculated from absorbance using extinction coefficient, ε²⁸⁰ = 114,590 M⁻¹ cm⁻¹.

To make RapA⁶⁵⁰, the dye-labeled H₆-SNAP-RapA construct, H₆-SNAP-RapA protein and JFX-650 fluorophore SNAP substrate (kind gift of Luke Lavis, Janelia Farm Research Campus) were mixed at a 1:2 molar ratio with 1 mM DTT in SNAP reaction buffer (50 mM Tris–HCl, pH 7.5, 100 mM NaCl, and 0.05% Tween 20). Excess dye was removed from solution using an Amicon Ultra-0.5 mL 30K spin column. The dye-labeling efficiency was 80%, determined using the extinction coefficients of dye (ε⁶⁵⁰ = 160,000 M⁻¹ cm⁻¹ and ε²⁸⁰/ε⁶⁵⁰ = 0.89) and protein (ε²⁸⁰ = 114,590 M⁻¹ cm⁻¹). RapA⁶⁵⁰ was frozen in liquid N₂ and stored at −80 °C in a buffer containing 10 mM Tris–HCl (pH 7.9), 50% glycerol, 0.1 mM EDTA, 0.1 M NaCl, and 1 mM DTT. The functionality of RapA⁶⁵⁰ compared to H₆-RapA was verified through single-molecule washout experiments (SI Appendix, Fig. S1).

E. coli core RNAP (αββ′ω) with an SNAP tag on the C terminus of β´ (RNAP-SNAP) (kind gift from Robert Landick and Rachel Mooney) was labeled with DY-549 dye as described (10). σ⁷⁰RNAP⁵⁴⁹ holoenzyme used in CoSMoS transcription experiments was prepared by incubating 1.33 µM σ⁷⁰ and 240 nM core RNAP⁵⁴⁹ in reconstitution buffer (10 mM Tris–Cl, pH 8.0, 30% glycerol, 0.1 mM EDTA, 100 mM NaCl, 20 mM KCl, 20 μM ZnCl₂, 3 mM MgCl₂, and 0.6 mM DTT) at 37 °C for 30 min and stored at −20 °C for up to 1 h before use.

CoSMoS Transcription Experiments.

All single-molecule fluorescence experiments were performed on a micromirror total internal reflection fluorescence instrument (30) with a ~65-µm-diameter circular field of view. Reported laser powers were measured at a beam position incident to the micromirrors and may be significantly attenuated by the downstream optics. For the transcription experiments (Fig. 1), excitation wavelengths 488, 532, and 633 nm were used for observation of the probe⁴⁸⁸, RNAP⁵⁴⁹, and initial DNA^Cy5 locations before photobleaching and RapA⁶⁵⁰, respectively. Laser powers and acquisition protocols for each experiment are detailed in SI Appendix, Tables S4 and S5. Microscope focus was automatically maintained (53). The temperature of the reaction chamber was maintained at 33.1 ± 0.5 °C using a custom temperature-control system. Transcription reactions were conducted as described (11): In short, single-molecule observations were performed in glass flow chambers (volume ~20 µL) passivated with succinimidyl (NHS) polyethylene glycol (PEG) and NHS–PEG–biotin (Laysan Bio Inc.). Streptavidin (#21125; Life Technologies) was introduced at 220 nM in wash buffer (50 mM Tris–acetate, 100 mM potassium acetate, 8 mM magnesium acetate, 27 mM ammonium acetate, and 0.1 mg mL⁻¹ bovine serum albumin (BSA) (#126615 EMB Chemicals), pH 8.0, incubated 1 min, and washed out (all wash-out steps used two flushes each of four chamber volumes of wash buffer). Streptavidin-coated fluorescent beads (T-10711, Molecular Probes), used as markers for stage drift correction, were loaded in the chamber at a dilution of ∼1:400,000, and excess beads were washed out (30). The chamber was then incubated with 25 pM DNA^Cy5 in wash buffer for 5 min, and excess was washed out with buffer. Locations of surface-tethered DNA^Cy5 molecules were recorded by acquiring five 1 s exposure images with 633 nm excitation at a power of 400 µW (all laser powers measured incident to the objective lens) (53). To photobleach the tethered DNA^Cy5 molecules, we increased the 633-nm laser power to 1.8 mW and watched the bleaching of DNA^Cy5 spots for 25 to 30 min. Photobleaching of the DNA molecules allowed for tracking of RapA⁶⁵⁰ molecules during the subsequent transcription reactions. Next, σ⁷⁰RNAP⁵⁴⁹ holoenzyme was introduced into the chamber at 1 nM in transcription buffer (wash buffer supplemented with 3.5% w/v PEG 8,000 (#81268; Sigma-Aldrich) to mimic the crowding effects of cytoplasmic protein concentrations (54, 55), 1 mg mL⁻¹ BSA, and an O₂-scavenging system (4.5 mg/mL glucose, 40 units/mL glucose oxidase, 1,500 units/mL catalase, and 1 mM DTT), incubated for 10 min to wait for promoter binding and formation of open complexes, and excess unbound RNAP⁵⁴⁹ was washed out. Transcription was initiated by introducing a solution containing 500 µM each of ATP, CTP, GTP, and UTP, 10 nM probe⁴⁸⁸, with or without 5 nM RapA⁶⁵⁰ in transcription buffer. Image acquisition began within 10 s after loading the transcription reagents (at t = 0), with excitation alternating between simultaneous 532/633 nm (400 µW each) and 488 nm (400 µW) with a frame rate of 1 frame/s for 40 min. Based on the measured rate of probe hybridization, 1.1 × 10⁷ M⁻¹ s⁻¹ (33), the seven-repeat target sequence (nucleotides +27 through +174 in the transcript) will on average be detected 9 s or less after its full synthesis.

CoSMoS rPTC Experiments.

Microscopy for the experiments in Figs. 2–4 was done the same as for the transcription experiments except that we used excitation wavelengths 532 nm to monitor RNAP⁵⁴⁹ and 633 nm to find DNA^Cy5 locations initially before photobleaching and (in Figs. 3 and 4) afterward to monitor RapA⁶⁵⁰ (33). For the premix experiments in Fig. 2C (orange data), 0.7 nM RNAP⁵⁴⁹, varying concentrations of RapA, and zero or 1 mM ATP were premixed in microcentrifuge tubes and the mixture was then introduced into the chamber in transcription buffer at time zero. For the washout experiments in Figs. 2C (green), 3, and 4, 1 nM RNAP⁵⁴⁹ was introduced into the chamber in transcription buffer, incubated for 10 min to wait for binding to npDNA^Cy5, and excess unbound RNAP⁵⁴⁹ was washed out. Then, varying concentrations of RapA⁶⁵⁰ and 1 mM ATP, 1 mM AMPPNP, or no nucleotide were mixed in transcription buffer and loaded into the glass chamber at time zero. Image acquisition began at time zero for both premix and washout experiments.

Single-Molecule Dwell Time Analyses.

Image analysis was done using custom software and algorithms for automatic spot detection, spatial drift correction, and colocalization (34). Lifetimes τ in Figs. 1 E and 5 A and SI Appendix, Fig. S4 were fit using the maximum likelihood method to the probability density models,

$$p\left(\tau \right)=\exp \left(-\frac{\tau }{\mu }\right),$$

(for Fig. 1E), and to

$$\begin{array}{c}p\left(\tau \right)=a_{\mathrm{f}\mathrm{a}\mathrm{s}\mathrm{t}}\exp \left(-k_{\mathrm{fast}}\tau \right)+(1-a_{\mathrm{f}\mathrm{a}\mathrm{s}\mathrm{t}})\exp (-k_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{w}}\tau ),\hfill \end{array}$$

where k_fast > k_slow (for Fig. 5A and SI Appendix, Fig. S4). Parameter CI were calculated by bootstrapping and error propagation as described (34).

Characteristic lifetimes of RNAP⁵⁴⁹ in Fig. 2 were calculated by taking the average <τ> of all measured intervals where RNAP⁵⁴⁹ is present on DNA. Intervals that are censored by the maximum acquisition time were included but not corrected in the computation of the average lifetime, as follows:

$$<\tau >=\frac{\sum {(\tau }_{\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{d}})+\sum {(\tau }_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{d}})}{N_{\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{d}}+N_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{d}}},$$

And the SE of ${<\tau >}^{-1}$ was calculated as ${<\tau >}^{-2} \mathrm{SEM} (<\tau >)$ . Photobleaching rates in the experiment of Fig. 2 (SI Appendix, Table S4) are too low to significantly affect the mean lifetimes.

To measure the rate of RapA⁶⁵⁰ association to either DNA^Cy5 or RNAP⁵⁴⁹-DNA^Cy5 complexes (Figs. 3B and 4B), we measured the time of first appearance of RapA⁶⁵⁰ at each DNA^Cy5 location, RNAP⁵⁴⁹-DNA location (i.e., DNA^Cy5 locations where RNAP⁵⁴⁹ was already bound), or control no-DNA locations. These data were then fit as described (34) to determine the rate k_ns for the nonspecific association of RapA⁶⁵⁰, the active fraction A_f of DNA^Cy5 locations capable of RapA⁶⁵⁰ binding, and the rate k_{on, app} for association of RapA⁶⁵⁰ with the active fraction of RNAP⁵⁴⁹-DNA sites.

Simulation of the Kinetic Model for RNAP Dissociation from the PTC by RapA.

To analyze our model for dissociation of the RapA·RNAP·DNA complexes based on the SI Appendix, Fig. S5 reaction scheme, we first defined the column-vector P(t) to represent the state of the system at time t, with each element of the vector representing the probability of the system being in a state as shown here:

	P1(t)	P2(t)	P3(t)	P4(t)	P5(t)
Molecular species	RNAP·DNA or RapA*·RNAP·DNA	RapA·RNAP·DNA	RapA·RNAP·DNA†	DNA + RapA·RNAP	RapA·RNAP*·DNA
Initial state	0	1	0	0	0

The asterisks represent photobleached components. The experimentally indistinguishable RNAP·DNA and RapA*·RNAP·DNA were lumped together in species 1 because it was not necessary to consider them separately to analyze RNAP dissociation from the PTC by RapA. The time evolution of P(t) is described by the differential equation,

$$\frac{d\mathbf{P}\left(t\right)}{\mathit{dt}}=\mathbf{Q}\cdot \mathbf{P}\left(t\right),$$

where Q is the transition rate matrix (56)

$$\begin{array}{c}Q=\left(\begin{array}{ccccc}-k_1& k_{-1}+k_{pb,RapA}& k_{pb,RapA}& 0& 0\\ k_1& -\left(\begin{array}{c}{k}_{-1}+k_2+k_{pb,RNAP}+k_{pb,RapA}\hfill \end{array}\right)& k_{-2}& 0& 0\\ 0& k_2& -\left(\begin{array}{c}{k}_{-2}+k_3+k_{pb,RNAP}+k_{pb,RapA}\hfill \end{array}\right)& 0& 0\\ 0& 0& k_3& 0& 0\\ 0& k_{pb,RNAP}& k_{pb,RNAP}& 0& 0\end{array}\right).\hfill \end{array}$$

We set k₁ = 0 because our measured lifetimes end when the system leaves states 2 and 3. For a particular choice of parameter values (k₋₁, k_2, k₋₂, k₃, k_{pb, RNAP}, and k_{pb, RapA}) and expressing the time t = 0 initial state as occupying the molecular species 2 ternary complex [i.e., P(0) = (0, 1, 0, 0, 0)^T], we numerically solved the above differential equation. This yields exact expressions for the time dependence of the P(t) functions. These P(t) fractional occupancies are then computed for each molecular species at integral time values t ranging from 0 to 3,000 s. We numerically differentiate $P_1\left(t\right),P_4\left(t\right),\mathrm{a}\mathrm{n}\mathrm{d}{ P}_5\left(t\right)$ to obtain the time-dependent probability densities for molecular species 1, 4, and 5. The three probability densities and the experimental data were then used to compute the likelihood, which was maximized by adjusting the parameters, yielding the rate constant values k₋₁, k₂, k₋₂, k₃, k_pb, RNAP, and k_pb, RapA given in Fig. 5C. Parameter SEs were computed by bootstrapping (10,000 samples).

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Source data for each experiment is available from Zenodo (10.5281/zenodo.7706033) (57).