Requirements for and Regulation of Origin Opening of Plasmid P1*

Origin opening is essential for the initiation of DNA replication in the theta mode and requires binding of initiator proteins. Using reactivity to KMnO4 in vivo as an assay, we find that, like initiation, origin opening of the Escherichia coli plasmid P1 requires the host initiators DnaA and HU and the plasmid-encoded initiator RepA. The ability to detect opening at the P1ori in vivo allowed us to study this activity at various copy numbers in chimeric replicons. The opening was prevented when the P1ori was cloned in high copy vectors or when excess RepA binding sites (iterons) were provided in trans. However, when RepA supply was also increased, the opening was efficient. A further increase in RepA prevented opening. Replication of an incoming P1 under these conditions correlated with opening. These results demonstrate that initiation is possible even at abnormally high origin concentrations and that oversupply of RepA, relative to iterons, can prevent replication by blocking origin opening. It appears that plasmid overreplication can be prevented either by limiting RepA or by accumulating RepA at a rate higher than that of the origin.

Initiation of DNA replication has been staged into discrete steps primarily from the work in vitro on plasmids carrying the Escherichia coli origin, oriC. Binding of initiators first opens the origin, and the opening provides the stage for the DnaCmediated loading of the DnaB helicase (1). In the absence of the DnaB-DnaC complex, a stable open state of the origin could be obtained in vitro. Using a dnaC(ts) mutant host at the nonpermissive temperature, a stable open structure could also be obtained in vivo as assayed by reactivity to KMnO 4 (2). Reactivity was lost rapidly when the culture was shifted down to permissive temperature. It appears that once DnaB is loaded, the subsequent steps of priming and elongation can proceed rapidly and are unlikely to be the steps for controlling initiation frequency.
We have examined whether origin opening of plasmid P1 can be used to follow regulation of initiation in vivo. Plasmid P1 belongs to a family of plasmids characterized by the presence of short repeating sequences, called iterons (3). The iterons are binding sites for the plasmid-encoded initiator, RepA. Iterons cover about half of the minimal origin (ori) of P1 and also constitute the control locus, incA (see Fig. 1). The incA locus can be deleted, and such plasmids are maintained at an 8-fold higher copy number. The locus therefore plays only a negative regulatory role in plasmid replication. The origin iterons (called incC; see Fig. 1) are essential for initiation and are believed to be important for the control of copy number as well. The incC locus also includes the promoter of the initiator gene. Consequently, RepA binding to incC results in efficient repression of the RepA promoter. Autoregulated initiator synthesis is generally a conserved feature of iteron-carrying plasmids, implying that maintenance of initiator concentration is critical to the copy number control process.
We find that the requirements for the appearance of KMnO 4reactive bases in P1ori are well correlated with the genetic determinants of P1 plasmid replication. Two host proteins, DnaA and HU (4,5), and P1 RepA (6) are essential for initiation of P1 replication, and excess iterons or excess RepA inhibit P1 replication (7)(8)(9). These characteristics of plasmid replication were found to be also true for the opening reaction, validating the use of the opening assay to study initiation control.
We show that normally inhibitory concentrations of cloned origins or iterons were tolerated both for opening as well as replication, provided RepA concentration was correspondingly high. Further increases of RepA can be inhibitory. Thus, under the conditions of our experiments, the inhibitory activities of iterons and RepA depend upon their relative concentrations.
Plasmids supplying various amounts of RepA were pALA197 (3ϫ), pALA198 (7ϫ) and pALA169 (40ϫ). Initially, repA was cloned in pBR322 under the control of a constitutive promoter bla-p2 (13). The resultant plasmid, pALA162, produced 40ϫ more protein than the wild type P1 plasmid as determined by Western blotting. RepA production was reduced to 7ϫ and 3ϫ by interposing a transcription terminator (T1) in two orientations between the gene and the promoter. Finally, fragments containing the repA(ϮT1)bla-p2 region were cloned into a pBR322 compatible vector, pST52 (14) to generate plasmids pALA169, pALA198, and pALA197. Another 7ϫ RepA source was pKP116, constructed by cloning a SspI-EcoRV fragment of pALA176 (15) into the HincII site of pGB2, a pSC101-derived vector with a spectinomycin resistance gene (16). The source of P protein was pRLM75 (pBR322 ϩ cI857p L OP) (17).
Phages were DKC234ϭP1:5RcI857Kan r , carrying the entire P1repϩpar region, and DKC274ϭP1oricI857Kan r (21). The control phage, DKC275, was isogenic to DKC274 except that the P1ori was replaced with incC. KMnO 4 Footprinting in Vivo-The bacterial cultures were grown in M9 medium (22) supplemented with 0.2% Casamino acids, 0.002% thymine, and 0.001% vitamin B1. When desired, 100 g/ml ampicillin, * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 20 g/ml chloramphenicol, 30 g/ml kanamycin, 15 g/ml tetracyclin, and 40 g/ml (400 g/ml for PC2) spectinomycin were added to the medium in various combinations. Fresh overnight cultures were diluted 100-fold in the same medium and grown at 30°C to A 600 of Յ0.3. The culture was distributed into 10-ml aliquots. One set was maintained at 30°C as controls, while the other set was shifted to 42°C for inactivation of DnaC or induction of the P protein. The induction was at 38°C for EH3827, because its growth reduces above 37°C. Incubations were for 1 h. When desired, rifampicin (Rif) 1 was added to a final concentration of 0.1 mg/ml, 5 min prior to KMnO 4 treatment. KMnO 4 was diluted to a final concentration of 3 mM and incubated for 1 min at 42°C for all cells. (A 0.37 M KMnO 4 stock solution was made in water by boiling for 5 min and used up to a month.) The reaction was terminated by mixing the culture with an equal volume (10 ml) of ice-cold STE buffer (100 mM NaCl, 10 mM Tris, pH 8.0, and 1 mM EDTA) with 5 mM dithiothreitol and chilling the mixture on ice. The cells were pelleted at 3000 rpm in a GLC-4 centrifuge (Sorvall) at 4°C for 15 min, and the pellet was washed with 1 ml of 50 mM Tris buffer, pH 8.0, and resuspended in 100 l of TE buffer (10 mM Tris, pH 8.0, 1 mM EDTA). Plasmid DNA was isolated using a INSTA-MINI-PREP kit (5 Prime 3 3 Prime, Inc., Boulder, CO) and used for polymerase chain reaction without further purification.
Lysogeny-Freshly saturated cultures grown as described for KMnO 4 footprinting were simultaneously titered for viable counts and used for lysogeny. Typically, 100 l of cells were mixed with phage at a multiplicity of infection of Յ 10. After 30 min of incubation at room temperature, 0.5 ml of L broth was added to each tube. The mixtures were incubated at 30°C for 2 h for expression of drug resistance and, after appropriate dilution, plated on media selective for resident plasmids and infecting phage (plasmid prophage).

Stabilization of P1 Origin Opening by Blocking of DnaB
Loading-In exponentially growing cells, KMnO 4 reactivity of P1ori was found to be minimal, probably because only a small fraction of the plasmids were undergoing replication initiation at the time of KMnO 4 probing. To accumulate plasmids at the initiation step, an E. coli host with a dnaC(ts) mutation was used at the nonpermissive temperature. Inactivation of DnaC was expected to accumulate the open complexes at P1ori by blocking the loading of DnaB because a similar strategy was used to catch opening in oriC ( Fig. 1

and Ref. 2).
dnaC(ts) cells carrying a miniP1 plasmid, pSP102, were incubated at 42°C for 1 h before treatment with KMnO 4 . When the plasmid DNA was probed for the bottom strand, a patch of modified bases could be seen within a stretch of about 20 base pairs (P1 coordinates 405-422) at one end of the AϩT-rich region of P1ori ( Fig. 1, upward arrows, and Fig. 2, lanes 3 and  4). Higher reactivity in this region was usually accompanied by reduction in reactivity in the surrounding regions. This relative change made the recognition of the opening signal unambiguous. When probed for the top strand, a patch could also be seen, but it was shifted more to the middle of the AϩT-rich region ( Fig. 1, downward arrows, and Fig. 2, lanes 10 and 11). To determine the role of transcription elongation, cells were treated with Rif at a final concentration of 0.1 mg/ml, 5 min prior to adding KMnO 4 . The presence of Rif did not change the pattern of KMnO 4 reactivity significantly (Fig. 2, lanes 1-4 and 8 -11). Thus, continued transcription does not seem to be re-quired for the reactivity. The reactive patches apparently represent initiation intermediates because the signal disappeared within 10 min of return to the permissive temperature ( Fig. 2, lanes 5-7 and 12-14).
To assay P1ori opening in other hosts, an alternative method of blocking DnaB loading was devised. The method utilized the strong DnaB binding property of the bacteriophage protein P (17). The P protein was supplied from a plasmid (pRLM75) under the control of a heat-inducible promoter (17). After 30 min of induction, a KMnO 4 reactive patch appeared similar to that seen in the dnaC(ts) host (Fig. 3A, lane 3). The signal was stable at least up to 70 min (Fig. 3A, lane 6). We conclude that P1ori opening can be conveniently assayed also in dnaC ϩ strains by blocking the loading of DnaB with the P protein.
Requirements of DnaA, HU, and RepA Initiators for P1ori Opening-Host initiator proteins DnaA and HU, and the P1 RepA being essential for P1 plasmid replication, their role in the opening of P1ori was tested to validate the KMnO 4 reactivity assay as a reporter for initiation. Because miniP1 cannot replicate in a ⌬dnaA host, P1ori was cloned in a DnaA-independent vector, pACYC184 (23). RepA was provided in trans from another DnaA-independent vector, pST52 (14), at 3ϫ, 7ϫ, and 40ϫ where 1ϫ is the amount that a wild type P1 plasmid produces normally.
In a ⌬dnaA host, the KMnO 4 reactive patch was absent (Fig.  3B, lanes 1-4). When the dnaA gene was re-introduced by lysogenizing the ⌬dnaA host with a dnaA transducing phage DKC365 (a imm 21 derivative of KO32, (24)), the reactive patch could be seen (Fig. 3B, lanes 6 -8). The intensity of the signal was weaker than that seen in dnaA ϩ cells. Although the basis for the quantitative difference remains to be determined, a correlation of the requirement of DnaA for the KMnO 4 reactivity of P1ori with the requirement of DnaA for P1 replication could be made (4). These experiments also revealed that the KMnO 4 reactivity is sensitive to RepA concentration. The 7ϫ source was optimal, and reactivity decreased at both higher and lower RepA (Fig. 3B, lanes 5-8). As will be discussed, the requirement for RepA at higher than physiological concentrations is most likely due to the presence of the P1ori in a high copy vector. Otherwise, the dependence of the opening signal 1 The abbreviation used is: Rif, rifampicin. on DnaA and RepA and decrease of the signal with increase of RepA concentration are consistent with earlier replication studies (4,21).
We next determined the requirement for HU protein on the appearance of the KMnO 4 reactive patch. E. coli HU protein consists of two subunits, ␣ and ␤, encoded by hupA and hupB genes, respectively. The protein normally exists as a heterodimer, but homodimers of either subunit can also be functional (12). For the KMnO 4 reactivity of P1ori, either of the homodimers was sufficient (Fig. 3C, lanes 2 and 4), but there was no apparent reactivity in the absence of both subunits (Fig.  3C, lanes 2 and 4 versus lane 6). These results provide further correlation of KMnO4 reactivity with initiation and encouraged the use of the assay to study initiation control.
P1ori Opening in the Presence of Excess Iterons-As stated earlier, in miniP1 plasmids devoid of the incA locus (e.g. pSP102), although the mean copy number increases, it is still controlled. This is believed to be due to the origin (incC) iterons. When their concentration reaches some threshold, further in-creases in copy number are not allowed. The plasmid used in experiments of Fig. 3 (B and C), pKP104, a clone of P1ori in pACYC184 vector, had a copy number very similar to that of pSP102. Because the concentration of incC iterons was comparable in the two cases (pSP102 and pKP104), the appearance of the opening signal in pKP104 was not surprising (Fig. 4A, lane  2). However, when the iteron concentration was significantly increased by providing incA in trans from pALA18 (pBR322ϩincA), our expectation from replication studies was that the opening would be totally inhibited. Such was the observation (Fig. 4A, lane 6). However, increased RepA concentration did allow opening (Fig. 4A, lanes 7 and 8). Thus, under the conditions of the present experiment, it appears that incA inhibition of opening can be overcome by excess RepA.
A similar finding was made in a different experiment. In this experiment, P1ori was cloned in pUC19, and the copy number of the resultant plasmid, pALA658, was 2.5-fold higher than that of pSP102 or pACYC184. However, opening was efficient in the presence of the 40ϫ source (Fig. 4B, lane 3). We conclude FIG. 2. KMnO 4 reactivity of P1ori of the miniP1 plasmid pSP102 in a dnaC(ts) host, as visualized by primer extension. The host was used to block loading of DnaB to P1ori by inactivation of DnaC at 42°C. A patch of reacted bases is apparent when the culture was incubated at 42°C for 60 min (bracket), regardless of the presence of Rif. Rif was used to assess the role of transcription to ori opening. Note that the patches were shifted with respect to each other in the top and the bottom strands (lanes 3, 4, 10, and 11 and Fig. 1). The reactivities were lost within 5 min upon returning to 30°C, the permissive temperature for the dnaC(ts) host (lanes 5-7 and 12-14). Dideoxy guanosine and cytosine sequencing reaction products are shown in lanes G and C. The landmarks on the sequencing lanes have been described in Fig. 1. To ensure uniform template DNA concentrations for primer extension reactions, plasmids were extracted from cultures of identical optical density. that at high concentrations of iterons, present either in cis as in the pUC19ϩP1ori plasmid or in trans as in the pBR322ϩincA plasmid, need not be inhibitory, provided sufficient RepA is also present. From these results it appears that the replication of pSP102 could be limited by the availability of RepA.

P1 Plasmid Replication in the Presence of Excess Iterons-If excess
RepA could allow simultaneous opening of an abnormally high concentration of P1ori (as in pUC19ϩP1ori plasmid) and if the open-complexes were intermediates of initiation, as suggested by their rapid disappearance when the block to DnaB loading was removed (Fig. 4B, lanes 4 -6), we argue that excess RepA would also allow replication of miniP1 plasmids in the presence of excess origins in trans. Functioning of the P1ori was tested by lysogeny of P1 chimeric phages, which are defective in recombination and depend on a functional P1ori to maintain themselves as plasmid prophages. In a recA host, the lysogeny of a P1ori phage increased 4 orders of magnitude in the presence of RepA but was inhibited in the presence of the 40ϫ source of RepA, as expected (Table I, column 1, rows 1-4).
In the presence of extra iterons provided by a pACYC184ϩincC plasmid, only the 7ϫ but not the 3ϫ source of RepA allowed lysogeny (Table I, column 1, rows 6 -7). Results were similar when pACYC184ϩincC was replaced with pACYC184ϩP1ori plasmid (Table I, column 1, rows 9 -12). This is evidence that incC suffices for control in the absence of incA. When the incoming phage was miniP1, which in addition to P1ori had the autoregulatory repA gene and the incA locus, lysogeny became dependent on additional (trans source of) RepA only when excess iterons were present (Table I, column 2). The results of lysogeny with miniP1 were otherwise similar to P1ori. These experiments showed that an excess of origin iterons (incC) in trans can inhibit miniP1 replication and that this inhibition can be overcome by providing excess RepA.
Similar experiments were also done in the dnaC(ts) host used in some of our origin opening studies (Table II). In this case, extra iterons were provided at a higher concentration using a pUC19ϩincC plasmid, whose copy number was 2.5 times higher than the pACYC184ϩincC plasmid used in the experiments of Table I. The 7ϫ RepA source was not enough; efficient lysogeny required the 40ϫ source (Table I, Tables I and II, because the copy number of the plasmids depended on the strain background. The copy numbers were lower in the dnaC(ts) host, which may explain why the so-called 40ϫ source was not inhibitory (Table II, row 4). We conclude that replica- FIG. 3. KMnO 4 reactivity of P1ori in dnaC ؉ hosts. In these hosts, block to DnaB loading was accomplished by thermal induction of P protein synthesis from pRLM75 (pBR322 ϩ cI857p L OP). A, kinetics of reactivity of pSP102 in DH5⌬lac. The reactivity was optimal at 30 min of induction at 42°C. B, requirement of DnaA in a ⌬dnaA host. The P induction was done at 38°C to avoid temperature sensitivity of the strain. P1ori was present in pKP104 (pACYC184-derived), and RepA was provided in trans from constitutive sources at 3ϫ, 7ϫ, and 40ϫ physiological concentrations from pALA197, pALA198, and pALA169, respectively. Note that the reactivity is apparent only when the host had an integrated dnaA phage (lanes 6 -8). Note also that the opening was optimal at 7ϫ RepA (lane 7), the concentration at which opening at the Ϫ10 region of prepA (horizontal arrow) was optimally repressed. Promoter repression is a reliable indicator of RepA binding to origin iterons, as evidenced by footprinting in vivo (10). C, requirement of HU protein. The origin was present in pKP104, as in Fig. 3B, and RepA protein was provided at 7ϫ concentration from pKP116. The host was deleted either for one of two genes of the heterodimeric HU protein, hupA and hupB, or for both the genes. Upon temperature shift to induce P to block DnaB, reactivity became more pronounced in ⌬hupA and in ⌬hupB (lanes 2 and 4) and remained unchanged in ⌬hupA⌬hupB (lane 6).

FIG. 4. Requirement of higher RepA for KMnO 4 reactivity in the presence of incA (A) or at increased P1ori copy number (B).
The host was dnaCts. RepA sources were same as in Fig. 3. A, P1ori plasmid was pKP104. In the absence of incA, opening was optimal at 3ϫ RepA (lane 2), whereas in the presence of incA, provided from a pBR322 vector, opening was best at 40ϫ RepA (lane 8). B, P1ori plasmid was pALA658 (pUC19-derived). The cells also contained a source of LacI to repress the lac promoter present in pUC19. The reactivity was optimal at 40ϫ RepA (lane 3) and was lost within 5 min of returning to 30°C (lane 5) as seen in Fig. 2. tion inhibition by excess iterons can be overcome by controlled overproduction of RepA. DISCUSSION Here we show that opening of the P1 plasmid origin in vivo can be detected efficiently by probing with KMnO 4 , provided the DnaB helicase loading to the origin is blocked. This has been achieved either by inactivating DnaC (2) or by sequestering DnaB with P protein (17). The opening was taken to represent initiation of DNA replication for the following reasons. It 1) required the presence of all three proteins that are essential for plasmid replication: host initiators DnaA and HU and plasmid-encoded initiator RepA, 2) was site-specific, localized to an AϩT-rich region of the origin, 3) was transient, because it reversed when the block to DnaB loading was lifted, and 4) was regulated by iterons and RepA, the known regulators of P1 plasmid replication.
Opening of plasmid origins has been studied primarily in vitro. For P1, some opening was observed with DnaA alone (25). RepA alone was not effective, but it greatly stimulated opening when present together with DnaA. Results were similar with miniF plasmids except that these experiments also included HU (26). Although individually ineffective, a combination of RepE (the P1 RepA equivalent) and HU allowed opening, which was further stimulated by DnaA. Results were different for plasmid RK2 in one respect (27). DnaA alone, which was effective in opening the P1 and F origins, was ineffective for the RK2 origin. From our present results in vivo, it is seen that any of the pairwise combinations of DnaA, HU, and RepA were insufficient. A reproducible signal required cooperation of all three proteins, indicating that one reason the three are essential in replication is for opening the origin.
The ability to detect opening allowed us to study P1ori activity at various copy numbers in chimeric replicons and test the applicability of models that have been proposed for the negative feedback control of plasmid copy number by iterons.
In the initiator titration model, the concentration of plasmidencoded initiator protein that binds the iterons is assumed to be limiting (8,15,19,28,29). With increase of copy number, the limiting amount of initiator is believed to distribute to different origins, preventing saturation of any one origin. Thus, the increase of origin (or, more precisely, iteron) concentration relative to initiator provides the negative feedback signal. The model was questioned when extra initiators did not increase copy number significantly in many iteron-carrying plasmids: R6K (30), P1 (21), RK2 (31), pSC101 (32), and Rts1 (33), although not R1162 (34).
A second model, the handcuffing model, is based on the finding that the initiators can pair iterons in trans (21,35). It is assumed that the pairing causes a steric hindrance to origin activity, increases with increased origin (iteron) concentration and cannot be relieved by increasing the concentration of RepA. As discussed above, this model was invoked when the titration model was found inadequate to explain insensitivity of copy number to increases of initiator concentration.
A third mode of control is conspicuous in some members of iteron-carrying plasmids: R6K (30), P1 (21), pSC101 (32), and Rts1 (33). In these plasmids, a modest increase of initiator concentration was shown to lead to a decrease in copy number. The mechanism of this mode of control is not clear, but in principle such a mechanism can be an alternative to handcuffing in restraining copy number when RepA concentration becomes excessive.
The results of the present paper are most easily explained by the initiator titration model. When the P1ori was cloned into the pUC19 vector with a copy number about 2.5-fold higher than that normally achieved by miniP1 plasmids (in the absence of the incA locus), the origins could still be opened but required higher concentrations of RepA (Fig. 4B). Such a high concentration of P1ori also did not inhibit replication of an incoming miniP1 plasmid prophage when extra RepA was provided (Table II). These results are consistent with the conclusion from a different set of experiments that origins are poor inhibitors of each other when RepA supply is adequate (8,36).
The inhibitory activity of iterons is clearly seen when they are not part of intact origins (8,15) or when the origin is not functional as in high copy plasmid chimeras used here (Tables  I and II). In some of these experiments, RepA was supplied from an autoregulatory source. One might expect that an autoregulatory source of RepA could promptly compensate for RepA titration. Were that true, the observed inhibition might be attributed to handcuffing. Experiments designed to determine the extent to which titration of RepA by iterons results in additional RepA synthesis showed that the induction of RepA was inefficient (20). This was also observed in the present studies (Tables I and II). The autoregulated source of RepA present in miniP1 did not supply enough RepA to overcome inhibition by extra incC. The inhibition was overcome when extra RepA was provided from a constitutive promoter. One  reason for inadequate RepA supply from the autoregulated source could be due to the capacity of iteron-bound RepA to repress prepA by RepA-mediated handcuffing (20).
In experiments where the source of RepA was not autoregulatory and iteron-mediated inhibition prevails irrespective of the quantity of RepA supply, handcuffing remains the most satisfactory explanation (8,21,36). Even in experiments where the inhibition was overcome by oversupply of RepA (e.g. pBR322ϩincA, Fig. 4A; pACYC184ϩincC, Table I; and  pUC19ϩincC, Table II) and the results are adequately explained by titration, it is possible that handcuffing could have operated at steps after origin opening in experiments where replication was blocked (Fig. 4A) or replication of vector could have interfered with handcuffing (Tables I and II). Similar ambiguity remains in some of our previous experiments where initiator titration appeared to be the simplest explanation. In one, incA inhibition of integrative suppression by miniP1 was overcome by extra RepA (15). In the other, a block to lysogeny by P1ori was overcome by extra RepA (21), as in the present experiments (Tables I and II). In both of these experiments, incA was chromosomally located, and chromosomal replication could have interfered with handcuffing. Thus it is possible to accommodate most of our results as not contradicting the handcuffing model, if the conditions under which handcuffing operates are sufficiently constrained.
How is the copy number of incA-deleted miniP1 plasmids controlled? If origins per se are not inhibitory to each other at high concentrations, the copy number could be limited by the availability of RepA or by some essential host factor(s) (8). We already discussed that RepA supply from an autoregulated source could be limiting. Because RepA requires chaperones for activity (37), their availability could be limiting. Another possibility could be that the supply of too much RepA limits copy number because of an accumulated inhibitor synthesized concomitantly with RepA.
That the inhibitor is not RepA itself is suggested by two lines of evidence. Mutating the translation start codon of repA reduces RepA production drastically but not the synthesis of a replication inhibitor (9). Also excess of purified RepA does not cause replication inhibition in vitro (36,38). When we exceeded the normal copy number of incA-deleted miniP1 in chimeric replicons, the normally inhibitory level of RepA synthesis was not inhibitory, most likely because the inhibitor distributed to different origins. Thus the relative rather than absolute levels of inhibitors and origins seem to be more important, and accumulating RepA at a rate higher than the increase of copy number can be a potential means to prevent runaway replication.
In summary, it appears that in addition to relative concentrations of RepA and iterons, there are probably other players in copy number control. We are interested to know whether the inhibition of replication that is seen when RepA is artificially overproduced happens under normal circumstances. An understanding of the nature and mode of action of the inhibitor(s) may help also to determine the conditions that favor handcuffing and those that favor titration.