Structural asymmetry does not indicate hemiphosphorylation in the bacterial histidine kinase CpxA

Histidine protein kinases (HKs) are prevalent prokaryotic sensor kinases that are central to phosphotransfer in two-component signal transduction systems, regulating phosphorylation of response regulator proteins that determine the output responses. HKs typically exist as dimers and can potentially autophosphorylate at each conserved histidine residue in the individual protomers, leading to diphosphorylation. However, analyses of HK phosphorylation in biochemical assays in vitro suggest negative cooperativity, whereby phosphorylation in one protomer of the dimer inhibits phosphorylation in the second protomer, leading to ∼50% phosphorylation of the available sites in dimers. This negative cooperativity is often correlated with an asymmetric domain arrangement, a common structural characteristic of autophosphorylation states in many HK structures. In this study, we engineered covalent dimers of the cytoplasmic domains of Escherichia coli CpxA, enabling us to quantify individual species: unphosphorylated, monophosphorylated, and diphosphorylated dimers. Together with mathematical modeling, we unambiguously demonstrate no cooperativity in autophosphorylation of CpxA despite its asymmetric structures, indicating that these asymmetric domain arrangements are not linked to negative cooperativity and hemiphosphorylation. Furthermore, the modeling indicated that many parameters, most notably minor amounts of ADP generated during autophosphorylation reactions or present in ATP preparations, can produce ∼50% total phosphorylation that may be mistakenly attributed to negative cooperativity. This study also establishes that the engineered covalent heterodimer provides a robust experimental system for investigating cooperativity in HK autophosphorylation and offers a useful tool for testing how symmetric or asymmetric structural features influence HK functions.

Two-component systems, the prevalent signaling pathways in bacteria, are one of the best-studied models of signal trans-duction schemes (1,2). A conserved phosphotransfer reaction between the sensor histidine kinase (HK) 3 and the response regulator (RR) is used to couple a large variety of inputs and outputs. HKs, usually functioning as homodimers, sense stimuli through their variable sensing domains and modulate phosphorylation levels of their cognate RRs. HKs display multiple enzyme activities, including autokinase, phosphotransferase that is catalyzed in conjunction with the RR protein, and often phosphatase activity toward the phosphorylated cognate RR. The conserved catalytic core of an HK consists of a dimerization and histidine phosphotransfer (DHp) domain that contains the conserved histidine residue for receiving and transferring the phosphoryl group and a catalytic ATP-binding (CA) domain that contains residues critical for kinase activity. Structures of HKs and HK-RR complexes representing different enzymatic states have been captured, providing mechanistic details of HK activities. Signal-dependent regulatory mechanisms have been investigated for HKs in response to ligand binding (3)(4)(5)(6) or light sensing (7,8). The structures and mechanisms have been extensively reviewed (2, 9 -12). Distinct structural features are often linked to individual catalytic functions and biochemical behaviors of HKs.
Except for several atypical HKs with unusual oligomeric or monomeric states (13)(14)(15), one predominant emerging theme in HK signaling is the symmetry/asymmetry transitions in HK dimer structures. The symmetric or asymmetric HK structures involve similar or different arrangements of structural elements between individual protomers within an HK dimer. Structures with both symmetric and asymmetric conformations have been observed in the periplasmic sensing domains (3)(4)(5), the signaltransducing transmembrane helices and HAMP domains (6), and the catalytic core domains (16 -20). Transitions between the two conformations have often been associated with signaldependent switching of HK activities (16 -18). Bhate et al. (10) analyzed more than 20 HK structures and revealed a general trend of symmetry/asymmetry transitions in different HKs. Symmetry or asymmetry in the catalytic core domains refers to the packing of DHp helices and the relative positioning of the two CA domains. Although the phosphatase state of an HK is often symmetric, with two CA domains held at positions unfavorable for phosphorylation, the autokinase state harbors an asymmetric conformation with one CA domain in close prox-imity of one phosphorylatable histidine, whereas the other CA domain is located far from the other histidine. The CA domain that provides the reactive ATP and the histidine receiving the phosphoryl group can be from the same or different protomers, resulting in a cis-or a trans-phosphorylation mechanism in different HKs. Nevertheless, both mechanisms make use of similar asymmetric conformations that only allow phosphorylation of one histidine at a time (16,17,19,21,22).
Such asymmetric structures are often intuitively associated with asymmetric phosphorylation, in which phosphorylation of one protomer hinders phosphorylation of the second protomer, leading to hemiphosphorylation in the extreme case, with a single phosphorylation event per dimer. For example, observation of asymmetric conformations in CpxA led to implication of hemiphosphorylation despite the experimental observation of a 70% total phosphorylation level, where the phosphorylation exceeding 50% was attributed to subunit exchange of protomers within HK dimers (17). As structural asymmetry is repeatedly demonstrated for the kinase state, is phosphorylation asymmetry also a general trend in HKs?
Asymmetric phosphorylation, or negative cooperativity, has been biochemically explored in several HKs (19,23,24). Early studies on NRII indicated that the equilibrium constant for phosphorylation of the first protomer is ϳ78-fold larger than that of the second protomer (23). Negative cooperativity has been attributed to an exceptionally rapid reverse reaction, with transfer of the phosphoryl group from the diphosphorylated HK to ADP generating the hemiphosphorylated HK; thus, ADP has a large inhibitory effect on diphosphorylation of HK dimers. Hemiphosphorylated HKs have also been observed on native gels in studies of HK853 (19). A complete diphosphorylation of HK853 dimers was not achieved unless ADP present in the reaction mixture was continuously recycled back to ATP. An even stronger negative cooperativity has been demonstrated for DesK (24). The observed phosphorylation stoichiometry of DesK was ϳ0.5, and full phosphorylation was not achieved even in the presence of a coupled enzyme system that continuously converted ADP to ATP, indicating an extremely high negative cooperativity. Such extreme negative cooperativity may be uncommon for HKs because full phosphorylation at high ATP levels or in the presence of ATP regeneration has been documented for many HKs (19,23,25,26). On the other hand, analyses of the hybrid HK ShkA indicate no cooperativity in autophosphorylation (25).
Biochemical analyses of negative cooperativity of phosphorylation often rely on deriving equilibrium constants by measuring HK phosphorylation levels across a wide range of ATP concentrations. However, likely due to the spontaneous hydrolysis of ATP, even the "high-purity" commercial ATP reagent contains a trace amount of contaminating ADP (26 -28). The initial amount of ADP, relative to that generated during the phosphorylation reaction, is nontrivial when high concentrations of ATP are used. Under such conditions, the inhibitory effect of the contaminating ADP might not be negligible, as presumed in prior analyses, and could impact interpretation of negative cooperativity. Here, we take account of the initial ADP concentration in the kinetic equilibrium modeling and show that the neglect of ADP contamination can lead to significant overesti-mation of negative cooperativity. We develop a strategy to examine the phosphorylation cooperativity by measuring the un-, mono-, and diphosphorylated HK dimer species using a covalently linked HK dimer. Applying this strategy to E. coli CpxA, we demonstrate that autophosphorylation of CpxA is not negatively cooperative, or asymmetric, despite the structural asymmetry.

Impact of ADP contamination on interpretation of negative cooperativity
Commercial ATP is typically contaminated by its hydrolysis product ADP, and even ultrapure ATP (e.g. Sigma) contains ϳ0.4% ADP (27,28). The exact value of ADP contamination may vary depending on the provider, lot, storage conditions, and storage time. We measured the ADP level in our ATP reagent using the NADH-coupled enzyme assay (26). Approximately 1% ADP was present in the ATP stock solutions (Fig.  S1). In phosphorylation equilibrium assays with ATP concentrations often exceeding 1 mM, 1% ADP contamination would provide more than 10 M ADP and could significantly impact HK phosphorylation.
To assess the inhibitory effect of the contaminating ADP, we modeled the HK phosphorylation equilibrium with the simple bi-bi reaction model (Fig. 1A) that has been previously used to derive equilibrium constants and cooperativity (23). The Figure 1. Impact of ADP on interpretation of phosphorylation cooperativity. A, model of HK phosphorylation. K ma and KЈ ma are macroscopic equilibrium constants for sequential phosphorylation of the two sites in an HK dimer. Kisthemicroscopicconstant.crepresentsthecooperativityconstant.B,dependence of steady state phosphorylation levels on ADP contamination. The gray-shaded area indicates a range (40 -60%) that is often experimentally considered to be ϳ50% total phosphorylation. C, misinterpretation of negative cooperativity due to neglect of ADP contamination. The black line and circles represent data simulated with ADP contamination at 1%. Circles reflect data variations simulated with Gaussian-distributed S.D. at 5%. The red line is the fitted line assuming no ADP contamination (0%). D, determination of the cooperativity constant from populations of individual HK dimer species. Populations of the mono-(dotted lines) and diphosphorylated (dashed-dotted lines) dimer species differ greatly for the noncooperative (black) and the negatively cooperative (magenta) systems. ADP contamination was 1% (black) or 0% (magenta). Values of the composite parameter (solid lines) calculated by 4 ϫ U ϫ P 2 /(P ϫ P) remain constant across different ATP levels and are wellseparated for the two cooperative systems. All data were simulated with the indicated parameter values and the HK dimer concentration at 1 M. EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative monophosphorylated species contains two indistinguishable forms, with phosphorylation occurring at each individual protomer. Thus, the macroscopic equilibrium constant for phosphorylation of the first His, K ma , equals twice the microscopic constant K, whereas the constant for phosphorylation of the second His, KЈ ma , is half K if the cooperativity constant c is equal to 1 (see details in supporting information and Fig. S2A).
The steady-state phosphorylation percentages of all phosphorylatable His sites, which are often readily quantifiable by various experimental methods, such as assays with radiolabeled ATP or Phos-tag gels, were simulated at different ATP concentrations. Unsurprisingly, increasing the contaminating ADP percentage, ADP 0 /ATP 0 , has a negative impact on total phosphorylation levels (Fig. 1B). Despite a noncooperative system simulated with the c value at 1, at high ATP concentrations, ADP contamination at 2% yields a total phosphorylation level within the range of 40 -60%, a range often estimated as ϳ50% phosphorylation and intuitively associated with hemiphosphorylation. Clearly, a total phosphorylation level close to 50% does not indicate hemiphosphorylation or negative cooperativity, and a range of 40 -60% phosphorylation can be achieved with different combinations of equilibrium constants and ATP and ADP concentrations ( Fig. 1B and Fig. S2B, shaded area).
Because both ADP contamination and negative cooperativity can negatively impact the total phosphorylation level, we examined whether the inhibitory effect of ADP contamination could be misinterpreted as negative cooperativity. Our simulations indicate that ATP-dependent phosphorylation profiles can be extremely similar for distinctly different scenarios, one with negative cooperativity and the other with no cooperativity but with a higher ADP contamination percentage (Fig. 1B, magenta and black dashed-dotted curves) or with a lower value of the equilibrium constant (Fig. S2C, magenta and black lines). Generally, stronger negative cooperativity causes the ATP-dependent phosphorylation to be more graded than that with no cooperativity, but such distinction can be obscured by data variations. Within the range of experimental error, different combinations of cooperativity, ADP contamination, and equilibrium constants can result in curves that are highly similar to each other (Fig. S2D) and thus prone to misinterpretation. As shown in Fig. 1C, data were simulated (black line) with no cooperativity, ADP contamination at 1% and an equilibrium constant of 0.1, a value within the same magnitude of measured constants for some HKs (23,25). Total phosphorylation percentages simulated with small S.D. values under the above conditions (circles) could be fitted to a different set of parameters (magenta line) if the initial ADP contamination is neglected and assumed to be zero, leading to a conclusion of negative cooperativity. The fitted cooperativity constant c has a value at 0.14, corresponding to a nearly 30-fold difference between the two macroscopic constants K ma and KЈ ma . Thus, neglect of ADP contamination can lead to significant overestimation of negative cooperativity for HK autophosphorylation.
Although the total phosphorylation levels shown in Fig. 1C are similar, populations of individual phosphorylated species differ remarkably between the two scenarios, with or without negative cooperativity (Fig. 1D). More importantly, a composite parameter h, defined as 4 ϫ U ϫ P 2 /(P ϫ P) calculated from concentrations of individual phosphorylated species (Fig. 1A), is equal to the cooperativity constant c under the bi-bi reaction scheme (see Equation 7 under "Modeling"). The value of h is constant across different ATP concentrations independent of ADP contamination or the equilibrium constant K. Thus, the cooperativity of HK phosphorylation can be derived from the concentrations of differently phosphorylated HK dimer species if the individual forms can be robustly quantified.

Formation of covalently linked CpxA c dimers
Creation of covalent dimers provides a robust strategy for separating multiple phosphorylated forms of HKs based on their mobility difference on Phos-tag SDS-polyacrylamide gels. Furthermore, the covalent linkage eliminates potential subunit exchange of protomers among dimers. Instead of using an engineered disulfide linkage that could potentially introduce conformational strain or might interfere with naturally occurring cysteine residues in HKs, we employed Spycatcher-Spytag chemistry, a technology that utilizes two separate protein fragments that spontaneously form a covalent bond between a lysine and an aspartate residue (29). This strategy was used to create covalent dimers of cytoplasmic fragments of Escherichia coli CpxA, an HK in which structural asymmetry has been observed (17,22). Spycatcher (SpyC-) or Spytag (SpyT-) was genetically fused to the N terminus of CpxA C , the cytoplasmic fragment (residues 188 -457) of CpxA that was shown to have asymmetric domain arrangements (17), creating SpyT-CpxA C and SpyC-CpxA C (Fig. 2A). These domains were fused with CpxA C using flexible linkers at residue 188, a position spatially distant from the catalytic center, so it is unlikely that they will constrain the conformational changes of the DHp and CA domains or interfere with the enzymatic functions.

EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative
Formation of covalent dimers occurred rapidly after mixing SpyT-CpxA C and SpyC-CpxA C proteins (Fig. 2B). The majority of monomers were converted to covalent dimers after 5 min of incubation at room temperature, and dimers remained stable over time. However, this SDS-PAGE analysis does not exclude the existence of tetramers, specifically dimers of dimers that have been shown to exist in solutions at high protein concentrations (17) and could potentially be formed by covalent linkage of pairs of SpyT-CpxA C and SpyC-CpxA C noncovalent dimers. To address this possibility, the oligomerization states of the proteins in solution were examined using size-exclusion chromatography. Retention times of SpyT-CpxA C and SpyC-CpxA C proteins corresponded to apparent molecular masses of 68 and 88 kDa, in close correlation with the calculated molecular masses of the noncovalent homodimers, 67 and 86 kDa, respectively. The covalent dimer formed by mixing SpyT-CpxA C and SpyC-CpxA C eluted at a retention time corresponding to an apparent molecular mass of 78 kDa, similar to the calculated molecular mass of 79 kDa for the heterodimer. No peaks were observed at early retention times, as might be expected for higher-order oligomers. However, a small shoulder peak was observed, presumably corresponding to the noncovalent dimer of SpyT-CpxA C that likely resulted from a small excess of this protein in the mixture used to form the heterodimer. Collectively, the data indicate that SpyT-CpxA C and SpyC-CpxA C exist primarily as noncovalent homodimers and form a covalent heterodimer when mixed. The rapid formation of the heterodimer suggests that the noncovalent dimers of CpxA cytoplasmic domains are dynamic, allowing exchange of protomers within the dimer.

Autophosphorylation of the covalently linked CpxA C dimers
Autophosphorylation kinetics of the noncovalently linked proteins were analyzed for SpyC-CpxA C , SpyT-CpxA C , and CpxA C (Fig. 3). Quantitation of the bands from Coomassie Blue-stained Phos-tag gels produced highly similar autophosphorylation profiles (Fig. 3D), suggesting that the fused Spycatcher and Spytag fragments do not interfere with the autophosphorylation kinase activity of CpxA C . Unlike the noncovalently linked proteins that migrate as two bands corresponding to phosphorylated and unphosphorylated monomer proteins, the covalent CpxA C dimer with two phosphorylatable His residues, one in each of the two WT subunits (Fig. 4A, left), shows triple bands on the Phos-tag gel (Fig. 4B, top), suggesting separation of the di-, mono-, and unphosphorylated dimer species.
To further interrogate autophosphorylation in the covalent dimer, the mode of autophosphorylation was examined with respect to cis or trans mechanisms. Crystal structures indicate that CpxA autophosphorylates in trans, with the CA domain of one protomer making contact with the conserved His residue within the DHp domain of the second protomer (17). The covalent dimer allows biochemical differentiation of the trans and cis autophosphorylation mechanisms. Mutations were introduced to abrogate autophosphorylation either by disrupting the phosphorylation site in the DHp domain (His-248 to Ala, H248A, H*) or by disrupting the ATP-binding site in the CA domain (Asn-356 to Lys, N356K, N*). If CpxA autophosphorylates by a trans mechanism, heterodimers designed with one protomer containing the H248A substitution and the second protomer containing the N356K substitution would be able to phosphorylate a single protomer within the dimer, whereas heterodimers designed with one protomer containing both H248A and N356K substitutions and the second protomer being WT would be unable to autophosphorylate (Fig. 4A). As expected, noncovalent homodimers carrying either H248A or N356K substitutions, or both, displayed no autophosphorylation when incubated with ATP for 30 min (Fig. 4C).
Having verified the expected behavior of the substituted proteins, we examined autophosphorylation in covalent heterodimers. The covalent dimer with WT CpxA C domains, WT:WT (SpyT-CpxA C :SpyC-CpxA C ), migrates as a single species in the absence of phosphorylation. After incubation with ATP, two additional bands are observed (Fig. 4B). The lower band of the triple bands corresponds to the unphosphorylated dimer, and presumably, the middle band is a monophosphorylated species, and the upper band is a diphosphorylated species. A covalent dimer that contains one protomer with a mutation in the DHp domain and the second protomer with a mutation in the CA domain, H*:N* (SpyT-CpxA C H248A:SpyC-CpxA C N356K), displays only a single additional band of lower mobility than the unphosphorylated dimer, corresponding to a monophosphorylated species (Fig. 4B). A covalent dimer that con- These analyses of mutant proteins provide several key validations. First, phosphorylation profiles are consistent with a trans-phosphorylation mechanism as depicted in Fig. 4A, confirming the structural and functional integrity of the covalent dimers. Second, the data support the absence of tetramers because the WT:H*N* complex exhibits no phosphorylation, whereas phosphorylation would be expected for (WT) 2 : (H*N*) 2 tetramers formed by covalent linkage of noncovalent homodimers. Finally, the profiles support the identification of the upper and middle bands that appear upon phosphorylation of the WT dimer as diphosphorylated and monophosphorylated species, respectively.
To characterize the kinetics of autophosphorylation in the covalent dimer, phosphorylation of SpyT-CpxA C :SpyC-CpxA C was followed over time (Fig. 5A). Monophosphorylated species increased initially and then decreased accompanied with a gradual increase of diphosphorylated species. Steady-state levels of phosphorylation were reached after ϳ20 min. At equilibrium, about 55% of dimers exist as diphosphorylated species and 35% as monophosphorylated species, whereas 10% remain unphosphorylated. This corresponds to a total phosphorylation level of ϳ70%, consistent with what was observed for noncovalent dimers (Fig. 3). Full phosphorylation was not reached, likely because of small amounts of ADP present in laboratory stocks or generated as a product of the phosphorylation reaction. Even though the ATP was pretreated to remove ADP, ϳ0.25% of the nucleotide existed as ADP in the ATP stock solution (Fig. S1). The variation in amounts of ADP present in different preparations of ATP likely contributes to variation in results obtained both within and between laboratories.
To eliminate complications arising from the presence of ADP, we used an ATP regeneration system in which pyruvate kinase catalyzes the conversion of ADP to ATP at the expense of its substrate, phosphoenolpyruvate (PEP). In the presence of this regeneration system, CpxA C covalent dimers approach full phosphorylation, with ϳ100% diphosphorylation at 40 min (Fig. 5). This demonstrates full activity of the covalent dimers and eliminates concern about a subpopulation of inactive recombinant protein.

Noncooperative autophosphorylation of the covalent CpxA C dimer
Having established a method for quantifying individual phosphorylated dimer forms, the cooperativity of autophosphorylation for the covalent SpyT-CpxA C :SpyC-CpxA C dimer was examined in the presence of 1500 M ATP and various concentrations of ADP (Fig. 6). With increasing ADP concentrations, levels of the diphosphorylated species (P 2 ) decreased, whereas monophosphorylated species (P) increased initially and then gradually decreased, and the unphosphorylated species predominated (Fig. 6, A and B). Values of the composite parameter h, calculated with concentrations of individual phosphorylated species, 4 ϫ U ϫ P 2 /(P ϫ P), are close to 1 across a wide range of ADP concentrations and approach 2 at the lowest two ADP levels (Fig. 6C). Because the simple bi-bi reaction model predicts equal values of h and the cooperativity constant c, autophosphorylation of the covalent CpxA C dimer appears to be noncooperative, with a cooperativity constant close to 1, whereas h values smaller than 1, corresponding to negative cooperativity, were never observed.
Deviations of h values at low ADP concentrations from those at higher ADP levels are inconsistent with the model prediction that h values would be independent of ATP or ADP. Deviations may be an artifact of large quantification variations present at low ADP levels (Fig. 6C) or reflect inadequacy of the simple bi-bi model. When the simple model with the cooperativity constant c equal to 1 is used to simulate percentages of phosphorylated species (black lines in Fig. 6B), simulated data do not agree well with experimental data, suggesting that the simple model is not accurate in predicting autophosphorylation of CpxA C .
An apparent deficiency of the simple bi-bi model is the lack of consideration of the nucleotide-binding equilibria in HK autophosphorylation. Because the observed K m of ATP for autophosphorylation is ϳ10 -200 M for many HKs (10,30,31), ATP is expected to saturate the HK-binding sites in the above experimental assay with 1500 M ATP. To address the discrepancy between experimental data and the bi-bi model, we developed a complex model that accounts for binding of ATP to the unphosphorylated HK and dissociation of ADP from the phosphorylated HK with their respective association constants K t and K d (Fig. 6D). Further, ATP can compete with ADP for binding to the phosphorylated HK (HKϳP), inhibiting the reverse reaction; vice versa, ADP can inhibit the forward phos- EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative phorylationreactionthroughcompetitivebindingtotheunphosphorylated HK (blue boxes in Fig. 6D). Binding coefficients c t and c d are used to illustrate the two competitive binding events. In addition to the phosphorylation cooperativity constant c, a nucleotide-binding cooperativity constant c 1 is included for developing a cooperative model for nucleotide binding and autophosphorylation of HK dimers (Fig. S3A).
The model predicts that the value of h approximates to c for a large parameter space if the ATP concentration greatly exceeds the binding constant K t (see supporting information for details). If c t is much smaller than 1 and the nucleotidebinding cooperativity constant c 1 is not equal to 1, the value of h deviates from c at low ADP concentrations but converges to c at high ADP concentrations (Fig. S3B), consistent with the observed h values shown in Fig. 6C. The K m of ATP for CpxA C autophosphorylation is ϳ147 M (Fig. S4) and was used to approximate the dissociation constant of ATP for CpxA C for fitting the h values with the complex model. Estimation of multiple parameters based on a limited set of data points is challenging, leading to large S.E. of parameter values (Fig. 6C) except for the autophosphorylation cooperativity constant c. The value of c is 0.98 with the 95% confidence range between 0.93 and 1.03, again suggesting that autophosphorylation of CpxA C is not cooperative. Populations of phosphorylated spe-

EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative
cies simulated with the complex model now agree well with the experimental data (Fig. 6B, blue lines), and inclusion of nucleotide binding appears to resolve the discrepancy between the data and the model.
Simulation with the complex model suggests a value of 0.04 for c t , which would correlate with ATP having a much weaker affinity for the phosphorylated CpxA than for the unphosphorylated CpxA protein. Because the CpxAϳP⅐ATP complex is a nonproductive dead-end complex that competes with the reactive CpxAϳP⅐ADP complex, a weaker affinity of ATP for CpxAϳP will lead to less competition for binding of ADP to form the reverse reaction complex and thus less inhibition of the reverse reaction and more reduction of the overall autophosphorylation activity. As modeled in Fig. 6D, a small c t value has a negative impact on the total phosphorylation level. Nucleotide-dependent phosphorylation is more graded or flat with a smaller c t value. This competition mechanism provides another means of reducing phosphorylation, which potentially could be misinterpreted as negative cooperativity. Calculation of the h value from autophosphorylation of the covalent dimer at different ADP ratios allows accurate determination of the autophosphorylation cooperativity.

Modeling HK phosphorylation at intracellular concentrations of ATP and ADP
To examine how the negative cooperativity or the nucleotide competition might impact HK activities under cellular conditions, we modeled the autophosphorylation and phosphotransfer to RRs at cellular concentrations of ATP and ADP (Fig. 7). An ATP concentration of 1.5 mM and an ADP concentration of 0.2 mM were used based on the reported ATP level and ATP/ ADP ratio in E. coli cells (32,33). If there is no cooperativity (c ϭ 1, c 1 ϭ 1) and nucleotides have equal affinity for HK and HKϳP (c t ϭ 1, c d ϭ 1), the total phosphorylation level of the HK and the concentration of phosphorylated RR (RRϳP) correlate with the autophosphorylation equilibrium constant K pt (black lines in Fig. 7 (A and B)). Under this scenario, with nucleotide competition considered, the complex model appears identical to the simple bi-bi model, and the overall equilibrium constant equals K pt ϫ K t /K d , as shown in Equation 10. A higher affinity of ADP for HKϳP than that of ATP for HK reduces the effective equilibrium constant and shifts the autophosphorylation reaction to the unphosphorylated reactant (dashed line in Fig. 7A). Several HKs, such as CheA (26), NarQ (30), and AgrA (34), have been shown to have a K m for ADP that is about one-tenth of the K m for ATP, suggesting a reduced overall autophosphorylation activity, although phosphorylation cooperativities of these HKs are unknown.
Two additional scenarios were modeled: one with no cooperativity but with less inhibition of the reverse reaction, as suggested by CpxA (c t ϭ 0.04, blue lines) and the other with c t valued at 1 but with negative cooperativity (magenta lines), with c valued at 0.05, which corresponds to an ϳ80-fold difference in macroscopic equilibrium constants observed for NRII (23). Both greatly reduce the total phosphorylation levels of HK (Fig.  7A). In contrast, their effects on RRϳP levels are modest, with only ϳ10% decrease at the measured equilibrium constant values of NRII and CpxA (positioned at the vertical dotted line in Fig. 7B), suggesting that negative cooperativity or reduced reverse reaction inhibition may not impact RR phosphorylation as much as it impacts HK phosphorylation at cellular levels of ATP and ADP. This is due to RRϳP nearing saturation because of a large equilibrium constant for RR phosphorylation, reflecting the fact that phosphotransfer is believed to greatly favor the forward reaction (18). For NRII, it has been shown that disrupting the negative cooperativity effect by removal of ADP has little impact on RR phosphorylation (23), consistent with the model prediction that a greatly favored phosphotransfer minimizes the effect of negative cooperativity on RRϳP. The impact of cooperativity and nucleotide competition on RR phosphorylation could be significant for HKs with smaller values of equilibrium constants for autophosphorylation and phosphotransfer activities. Under the two scenarios described above, the diphosphorylated species remains low across different K pt values, consistent with the monophosphorylated species dominating the phosphorylated HK dimers. However, for an HK without the two phosphorylation-inhibitory effects in the above scenarios, such as ShkA (25), the diphosphorylated species is expected to constitute a nontrivial population of the phosphorylated HK proteins.

Discussion
Negative cooperativity of autophosphorylation, with phosphorylation of one protomer inhibiting the phosphorylation of the other protomer of an HK dimer, has sometimes been presumed when an asymmetric structure corresponding to the kinase state has been observed (17). Our biochemical analyses of the covalent CpxA C dimer indicate that autophosphorylation of CpxA is not negatively cooperative despite observations of hemiphosphorylated and asymmetric structures captured by crystallography (17,22). In addition to CpxA, a cytosolic hybrid HK, ShkA, has also been shown to display no cooperativity in autophosphorylation (25). The biochemical reaction of autophosphorylation appears not always to be negatively cooperative, even though the kinase state of HKs shares common asym- The total HK dimer concentration is 1 M, and the RR concentration is 10 M. The equilibrium constant for the reversible phosphotransfer to RR is set at 10. Magenta lines, data simulated with the negativity cooperativity constant c at 0.05, derived by the macroscopic constants measured for NRII (23). Solid circles indicate HKs with known equilibrium constants K pt : CpxA, 0.35; NRII, 0.35 (23); ShkA, 0.13 (25). Gray symbols indicate HKs with K t /K d valued at 0.1 based on K m and equilibrium constants derived from k cat for both forward and reverse reactions: diamond, NarQ, ϳ0.02 (30); pentagon, AgrA (ϩstimulus), 0.4 (34); circle, CheA, 1 (26).

EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative
metric structures with only one CA domain positioned in a phosphorylation-competent conformation.
Noncooperativity is not necessarily inconsistent with asymmetric catalytic structures. The basis for structural asymmetry is believed to result from asymmetric bending of the DHp helix (10,17,21,35), which leads to asymmetric DHp surfaces that promote different interactions with the two ATP-binding CA domains via the interacting helix in the CA domain, known as the Gripper helix. Such structural asymmetry precludes simultaneous phosphorylation of the two His sites at a single time but does not prevent a proposed sequential phosphorylation mechanism with the two CA domains alternating their interactions with the His sites (21). It is not clear how phosphorylation of one protomer would impact the conformation of the other due to the lack of structures of hemiphosphorylated HKs. One structural snapshot of a hemiphosphorylated (i.e. monophosphorylated) HK is available for CpxA C (22). In this structure, the unphosphorylated His site forms the typical catalytic complex with the CA domain, ready for phosphorylation without any apparent structural hindrance from phosphorylation of the other protomer. Noncooperativity and structural asymmetry appear not to be mutually exclusive, and asymmetric catalytic structures are not equivalent to half-of-sites reactivity.
Biochemical investigations of autophosphorylation cooperativity are often carried out by measuring the total phosphorylation levels of HKs, and ϳ50% phosphorylation is often intuitively associated with half-of-sites reactivity. Our modeling indicates that ϳ50% phosphorylation can result from different combinations of cooperativity, equilibrium constants, and ADP present as contaminants in ATP or generated during reactions. Only when the reverse reaction of autophosphorylation is strongly inhibited by removing ADP with an ATP regeneration system can a 50% total phosphorylation level be used to conclude half-of-sites reactivity. Such a scenario has been reported previously for DesK (24), indicating a strong negative cooperativity. ATP-dependent phosphorylation profiles, often used to derive the two equilibrium constants for autophosphorylation, are also affected by ADP contamination. Higher ADP contamination or larger data variation produces less confidence in predicting negative cooperativity. A sufficiently strong negative cooperativity, as shown for NRII (23), is less prone to misinterpretation caused by the neglect of ADP contamination. Predetermination of the ADP level in ATP reagents can facilitate accurate measurement of the cooperativity of phosphorylation.
Quantification of individual phosphorylated species of CpxA C at different ATP and ADP concentrations revealed the necessity of including the competitive ATP/ADP-binding equilibria for correct modeling of HK autophosphorylation. The overall equilibrium constant, K pt ϫ K t /K d , depends on the ratio of binding affinities of ATP for HK over ADP for HKϳP. This provides additional control over the autophosphorylation equilibrium. No apparent trend in these relative affinities seems to exist for different HKs. Binding of ADP can be stronger than (26,30,34,36), equal to (23,30,37), or weaker than (38,39) binding of ATP to different HKs. Binding of ADP to HKϳP has a negative impact on the overall phosphorylation by promoting the reverse reaction (23,26,38). Competitive binding of ATP to HKϳP results in formation of a dead-end complex, HKϳP⅐ATP, and reduces the amount of HKϳP⅐ADP, a complex that is required for the reverse reaction. Thus, a weaker affinity of ATP for HKϳP will lead to less competition with ADP, a more favored reverse reaction, and less phosphorylation. This mechanism is distinct from negative cooperativity because it involves a dead-end complex of HKϳP⅐ATP and does not require a dimer. Formation of the dead-end complex has been suggested for CheA with ATP having a lower affinity for CheAϳP than for unphosphorylated CheA (40). Much less is known for typical HKs in the common HisKA or HisKA3 subfamilies. A reduced affinity of ATP for HKϳP relative to unphosphorylated HK implies that phosphorylation occurring in the DHp helices impacts nucleotide binding in the CA domains. Because the Gripper helix involved in DHp-CA interaction is directly connected to the ATP lid that is important for nucleotide binding, it is not surprising that phosphorylationinduced changes could propagate to the nucleotide-binding site.
Although both negative cooperativity and reduced inhibition of the reverse reaction can have large negative impacts on HK phosphorylation levels, the two mechanisms are predicted to have modest impact on RR phosphorylation at cellular concentrations of ATP and ADP. A large phosphotransfer equilibrium constant used in our model results in the reaction being heavily favored toward the product side and yields nearly saturating RR phosphorylation, overshadowing the inhibitory effect on HK phosphorylation. Experimentally examined phosphotransfer for typical HKs appears to have an even larger constant than that used in the modeling, with little back-transfer from RRϳP to HK (18,(41)(42)(43)(44). Negative cooperativity would have little effect on RR phosphorylation levels in such systems. For many HKs involved in phosphorelays with a more reversible phosphotransfer (18), negative cooperativity might play a more significant role in determining overall RR phosphorylation levels.
Creation of covalent HK dimers with Spytag-Spycatcher technology has proved to be a successful strategy for examining the biochemical activities of dimeric HK proteins. It provides a robust alternative method to native gels (19) for differentiating the un-, mono-, and diphosphorylated species for analyzing the cooperativity of phosphorylation. Furthermore, because of the covalent complex, the potential complicating effect caused by subunit exchange between HK dimers is eliminated (45,46). Covalent heterodimers of HK mutants enable a straightforward method to differentiate the cis or trans mechanism of autophosphorylation. Here, we demonstrate that autophosphorylation of CpxA C is through a trans mechanism, consistent with the domain arrangement revealed by crystal structures (17,22). Investigations of cis or trans mechanisms often rely on kinase assays of HKs with active-site mutations. In such studies, phosphorylation observed upon mixing H*H* and N*N* mutant proteins is definitive evidence of a trans mechanism, but lack of phosphorylation is not definitive evidence of a cis mechanism, unless it can be demonstrated that subunit exchange produces structurally sound heterodimers. Covalent linkage ensures heterodimer formation, strengthening conclusions of a cis mechanism from a null phosphorylation result with H*:N* covalent dimers and unequivocal identification of a cis mechanism if phosphorylation is observed in WT:H*N* covalent dimers. Fur-EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative ther, because structural asymmetry is a general theme in HK signaling, the Spytag-Spycatcher covalent heterodimer will be a useful tool for testing how individual asymmetric features influence the structure and function of HKs.

Protein purification
Recombinant proteins Spytag-CpxA C , Spycatcher-CpxA C , CpxA C , Spycatcher-CpxA C N356K, Spytag-CpxA C H248A, and Spytag-CpxA C H248A-N356K were produced from E. coli BL21(DE3) containing the plasmids pSB42, pSB58, pSB80, pSB76, pSB77, and pSB79, respectively. Cells from frozen permanents were grown in Luria broth supplemented with 1% glucose and 100 g/ml ampicillin at 37°C with shaking. Overnight cultures were diluted 1:100 into Luria broth containing 100 g/ml ampicillin and incubated at 37°C with shaking. At A 600 ϭ 0.6, isopropyl ␤-D-thiogalactopyranoside was added to a final concentration of 0.5 mM to induce expression of CpxA C and Spytag-CpxA C protein and variants, and incubation was continued for 3 h at 37°C. Expression of Spycatcher-CpxA C protein and variants was induced with 20 M isopropyl ␤-Dthiogalactopyranoside, and incubation was continued for 3 h at 30°C. Cells were harvested by centrifugation, resuspended at a density of 0.3 g cells/ml in binding buffer, and lysed by sonication. Binding buffer for purification of Strep-tagged proteins was composed of 100 mM Tris, pH 8, 150 mM NaCl, 1 mM EDTA. Binding buffer for purification of His-tagged proteins was composed of 24 mM KH 2 PO 4 /Na 2 HPO 4 buffer, pH 6.8, 0.5 M NaCl, 24 mM imidazole supplemented with 0.5 mM phenylmethylsulfonyl fluoride. This and all subsequent purification procedures were performed at 4°C. Lysates were centrifuged at 35,000 rpm for 1 h. The supernatant was collected, passed through a 0.2-m filter, loaded onto Strep-Tactin resin (IBA) for Strep-tagged proteins or HiTrap FF resin (GE Healthcare) for His-tagged proteins, and purified using the manufacturer's recommendations. His-tagged proteins were eluted using Histag binding buffer supplemented with 0.5 M imidazole and Strep-tagged proteins using Streptag binding buffer supplemented with 2.5 mM biotin. Fractions containing the eluted proteins were pooled and concentrated using Amicon Ultra 15-ml centrifugal filters with a cut-off of 10,000 nominal molecular weight limit (MilliporeSigma). Fractions were passed through a 0.2-m filter and loaded onto a Superdex 75 26/60 column (GE Healthcare) equilibrated with 50 mM Tris, pH 7.4, 0.1 M NaCl, and 2 mM ␤-mercaptoethanol. Fractions containing CpxA C proteins were pooled and stored in aliquots at Ϫ80°C.

Formation of covalent dimers
Covalently linked dimers were produced by mixing equimolar quantities of Spytag-CpxA C and of Spycatcher-CpxA C at a final concentration of 3 M each. To determine the kinetics of formation of covalent dimers, aliquots of the reaction mixture were removed at the indicated times, and the linkage reaction was stopped by the addition of concentrated SDS loading buffer. To prepare covalent dimers for kinase assays, Spytag-CpxA C and Spycatcher-CpxA C were incubated at room temperature for 30 min, a point at which kinetics experiments indicated that dimer formation is complete. Trace amounts of nonspecific proteins potentially produced as proteolytic products of tagged proteins or noncovalent CpxA proteins remaining after covalent dimer formation due to a small excess of one of the protomers may be present in the samples, but they did not interfere with phosphorylation analyses because they migrate at positions distinct from the covalent dimers during Phos-tag SDS-PAGE.

Size-exclusion chromatography
Proteins (0.25 ml Spytag-CpxA C at 6 M, 0.3 ml of Spycatcher-CpxA C at 8 M, and a mixture of 0.21 ml of Spytag-CpxA C and 0.29 ml of Spycatcher-CpxA C incubated for 30 min at room temperature to form 5 M covalent dimers of Spytag-Spycatcher CpxA C ) were chromatographed on a Superdex S200 10/30 GL column pre-equilibrated with 100 mM Tris-HCl, pH 7.5, 150 mM NaCl. The column was calibrated using the following standards: 0.3 ml of blue dextran at 5 mg/ml, 0.2 ml of BSA at 6.8 mg/ml, 0.3 ml of lysozyme at 5.9 mg/ml, and 0.3 ml of alcohol dehydrogenase at 1 mg/ml.

Preparation of regenerated ATP
Reactions for regeneration of ATP contained 10 mM ATP, 3 mM PEP, and 20 units/ml pyruvate kinase in 50 mM Tris-HCl, pH 7.4, 4 mM MgSO 4 , 7 mM KCl. After incubation for 1 h at room temperature, the pyruvate kinase was removed using a Microcon 10K centrifugal filter (MilliporeSigma). The concentration of the recovered regenerated ATP was determined using the measured absorbance at 260 nm and an extinction coefficient of 15.4 mM Ϫ1 cm Ϫ1 . PEP remained in the regenerated ATP and was experimentally confirmed not to influence the kinase assay. For regeneration of ATP in kinase assays, 20 units/ml pyruvate kinase was added to the reaction mixture (PEP being present in the regenerated ATP).

Measurement of ADP contamination in ATP
An assay was conducted in which NADH oxidation is coupled to ADP consumption via pyruvate kinase and lactate dehydrogenase to measure ADP concentrations in solutions of ATP. Reactions contained 700 M NADH, 3 mM PEP, 30 units/ml lactate dehydrogenase, and 20 units/ml pyruvate kinase in 50 mM Tris-HCl, pH 7.4, 4 mM MgSO 4 , 7 mM KCl, and 25 mM ATP (the sample being assayed for contamination). Reactions were initiated by the addition of pyruvate kinase and incubated for 15 min at room temperature. The decrease in NADH was monitored by absorbance at 340 nm using a Beckman DU 800 spectrophotometer. The difference in A 340 at t ϭ 0 and t ϭ 15 min, a time substantially beyond completion of the reaction, was used to calculate the concentration of oxidized NADH, equivalent to the concentration of ADP in the sample, using an extinction coefficient of 6.22 mM Ϫ1 cm Ϫ1 .

Autophosphorylation assays and kinetics
Autophosphorylation reactions contained 50 mM Tris-HCl, pH 8, 25 mM KCl, 10 mM MgCl 2 , 0.1 M NaCl, and covalent dimers at a final concentration of 1 M. Reactions were initiated by the addition of ATP and/or ADP. Autophosphorylation reactions were always performed using regenerated ATP (described above). Experiments were performed at room temperature; incubation times and ATP/ADP concentrations for individual experiments are specified in the figure legends. Aliquots were removed, and the reaction was quenched by the addition of concentrated SDS loading buffer at a 2:1 sample/ loading buffer ratio.
SDS Phos-tag gels were prepared as described previously with 8% acrylamide, 40 M Phos-tag acrylamide (Wako Chemicals), and 160 M MnCl 2 (48). Electrophoresis was performed at room temperature at a constant voltage of 110 V, and proteins were visualized using Coomassie Blue. Intensities of bands were measured using ImageJ software (National Institutes of Health), and adjacent bands were deconvoluted using the peak analysis algorithm of Origin software.

Modeling
Considering the simplest bi-bi reaction scheme of phosphorylation (Fig. 1A), the reaction proceeds from unphosphorylated HK dimers (U) to monophosphorylated species (P) and eventually to diphosphorylated dimers (P 2 ). This scheme is similar to others described previously (23,25). Because the hemiphosphorylated species contains two indistinguishable microscopic forms with phosphorylation occurring at each monomer, the macroscopic equilibrium constant K ma equals twice the microscopic constant K (see details in supporting information). For the same reason, the macroscopic constant for the second phosphorylation reaction (KЈ ma ) equals half K if no cooperativity is present. A cooperativity parameter c is used to describe how phosphorylation of one site impacts phosphorylation of the second site.
The steady state can be described by the following five equations.
HK 0 , ATP 0 , and ADP 0 are initial concentrations of HK dimers and nucleotides. Equations 1 and 2 describe the equilibria, whereas Equations 3-5 represent mass conservation of HK proteins, nucleotides, and phosphoryl groups. Solutions for the equation system were determined using Matlab for a wide range of parameter values and initial concentrations.Totalphosphorylation fractions of HK proteins were calculated as follows. A composite parameter h is defined with Equation 7. The value of the cooperativity parameter c is equal to h and can be calculated using concentrations of individual HK dimer species.
The reaction scheme used to derive Equation 7 is oversimplified, without considering the binding of ATP or ADP to HK proteins. A more complex model, detailed in the supporting information and illustrated in Fig. 6D and Fig. S3A, accounts for competitive nucleotide binding of ATP and ADP and phosphorylation equilibria. The difference between the two schemes can be illustrated using the following example of the phosphorylation equilibrium of the first site. For the simple scheme, Equation 1 can be rewritten as follows.

EDITORS' PICK: Phosphorylation of HK CpxA is not cooperative
For the complex scheme, considering the nucleotide binding constants K t (ATP to unphosphorylated HK) and K d (ADP to HKϳP), in which ␣ ϭ K t ϫ [ATP], ␤ ϭ K d ϫ [ADP], and F 1 and F 0 are composite factors related to the cooperative and competitive binding of nucleotides (see details in supporting information), whereas K pt is the equilibrium constant of phosphorylation. If there is no cooperativity in nucleotide binding, and nucleotides have equal affinity to HK and HKϳP, then the value of F 1 /F 0 equals 1, and Equation 9 can be rewritten as follows.
This equation is essentially identical to Equation 8 derived from the simple bi-bi reaction scheme except that the nucleotide association constants are now considered, and the overall equilibrium constant K equals K pt ϫ K t /K d . If nucleotides have different affinities for HK and HKϳP, or if there is cooperativity in nucleotide binding, the value of F 1 /F 0 will be different from 1; thus, Equation 8 and the simple bi-bi reaction scheme are no longer applicable.
The value of h, calculated from concentrations of individual phosphorylated species, can still be used to derive the phosphorylation cooperativity with the following equation, in which F 2 , F 1 , and F 0 are composite factors related to the cooperative and competitive binding of nucleotides to the di-, mono-, and unphosphorylated HK dimer species (see details in supporting information). When there is no cooperativity in nucleotide binding, the value of F 2 ϫ F 0 /F 1 2 equals 1 and h equals the phosphorylation cooperativity constant c. When ATP and ADP concentrations are both very high, saturating the binding sites, the value of h converges to c. When one is high and the other is low, such as occurs in the common in vitro phosphorylation experiment in which ATP is high and ADP is low, the value of h may deviate from c. If nucleotide binding is positively cooperative, the value of h is larger than c; vice versa, h is smaller than c for a system with negative cooperativity in nucleotide binding. Thus, measuring the values of h at different concentrations of ATP and ADP can be used to determine the phosphorylation cooperativity constant c.