Asymmetric Allosteric Activation of the Symmetric ArgR Hexamer

Asymmetric Allosteric Activation of the Symmetric ArgR Hexamer

doi:10.1016/j.jmb.2004.11.031 J. Mol. Biol. (2005) 346, 43–56 Asymmetric Allosteric Activation of the Symmetric ArgR Hexamer Lihua Jin1*, Wei-Feng X...

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doi:10.1016/j.jmb.2004.11.031

J. Mol. Biol. (2005) 346, 43–56

Asymmetric Allosteric Activation of the Symmetric ArgR Hexamer Lihua Jin1*, Wei-Feng Xue2, June Wong Fukayama3, Jaclyn Yetter1 Michael Pickering1 and Jannette Carey3 1

Chemistry Department DePaul University, Chicago IL 60614, USA 2

Biophysical Chemistry Department, Lund University SE-22100 Lund, Sweden 3 Chemistry Department Princeton University, Princeton NJ 08544-1009, USA

Hexameric arginine repressor, ArgR, bound to L-arginine serves both as the master transcriptional repressor/activator at diverse regulons in a wide range of bacteria and as a required cofactor for resolution of ColE1 plasmid multimers. Multifunctional ArgR is thus unusual in possessing features of specific gene regulators, global regulators, and non-specific gene organizers; its closest functional analog is probably CAP, the cyclic AMP receptor/activator protein. Isothermal titration calorimetry, surface plasmon resonance, and proteolysis indicate that binding of a single L-arginine residue per ArgR hexamer triggers a global conformational change and resets the affinities of the remaining five sites, making them 100-fold weaker. The analysis suggests a novel thermodynamic signature for this mechanism of activation. q 2004 Elsevier Ltd. All rights reserved.

*Corresponding author

Keywords: global analysis; cooperativity; c value; ligand occupancy

Introduction Many prokaryotic transcriptional regulators are activated allosterically by small-molecule effectors that increase the affinity and specificity of operator recognition. Structural analysis of several such proteins has revealed important features of activation by comparison of the end states with and without bound ligand and DNA, but the biology and mechanism of allosteric activation are not understood in detail. Although most of these proteins function as symmetric multimers, it is not always clear how many bound effector molecules are required for activation, or if effector binding is cooperative. These features, together with binding affinity, determine the effective range of ligand concentration for activation.1 Direct study of the concentration dependence of effector occupancy states is thus the first step in relating ligand binding to function. The classic example of allosteric transcriptional control is CAP, the cAMP receptor/activator protein that regulates a wide range of metabolic operons involved in response to changes in carbon source.2 Rising concentrations of cAMP increase, Abbreviations used: L-can, L-canavanine; ITC, isothermal titration calorimetry; SPR, surface plasmon resonance. E-mail address of the corresponding author: [email protected]

then decrease, gene expression. The textbook explanation of CAP allosteric activation is that binding of cAMP to the nucleotide-binding domains of the symmetrical dimer causes conformational changes propagated to its distant DNAbinding domains.3 Ligand-binding studies of CAP/ cAMP suggested that the first cAMP-binding event decreases affinity for the second by 100–1000-fold, thus explaining the biphasic response by extreme negative cooperativity between the two identical cAMP-binding sites of CAP.4,5 Surprisingly, recent structural analysis revealed an additional pair of cAMP molecules bound at the CAP/DNA interface, suggesting that the biphasic response may be better explained by a four-site model, with one pair of strong sites and one pair of weak sites.6 However, persistent difficulties in determining the CAP/ cAMP ligand-binding isotherm in solution have led to conflicting reports about stoichiometry, cooperativity, and occupancy states,7–9 and the relevance of the new sites for CAP function is still unclear. Thus, even our most widely accepted example of allosteric activation cannot be explained in biological or mechanistic terms. The arginine repressor, ArgR, shares a large number of features with CAP. ArgR is the direct sensor and transcriptional transducer of the concentration of L-arginine, controlling the arg regulon in Escherichia coli and many other bacteria.10 Recently, ArgR has been implicated in modulating more distantly related operons,11–14 and its target

0022-2836/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

44 sites have been identified in archaebacteria.15 The protein functions also as an accessory factor in the resolution of plasmid ColE1 multimers at cer sites, where its ability to bend DNA apparently facilitates intramolecular recombination.16 The many structural and functional similarities between ArgR and CAP motivated use of the CAP/DNA cocrystal structure as a template for modeling ArgR/DNA interactions based on biochemical and biophysical data.17 The results suggested that ArgR uses only one or two pairs of its six equivalent DNA-binding domains to bind its targets, which typically contain one or two palindromic sequences. The crystal structure of intact ArgR from Bacillus stearothermophilus18 is consistent with this unusual mode of DNA binding, corroborating the relevance of CAP as a model for ArgR despite the different strategies for symmetry-matching used by the two proteins. Binding of L -Arg to ArgR is required for transcriptional control and recombination, but its effects on the protein are not clear. The L-Arg binding sites of ArgR are buried deep within the C-terminal domain of the protein, ArgRC,19 distant from the peripheral DNA-binding domains. The location of the ligand binding sites at the trimer interface suggests that L-Arg binding stabilizes the ArgR hexamer, but hexamer stabilization by L-Arg or by DNA was ruled out as the mechanism of ArgR allosteric activation by showing that hexamers are already assembled when they bind to DNA, even in the absence of L-Arg.20 Although L-Arg binding to ArgR increases affinity for both operator and nonoperator DNAs, the increase is greater for operator DNA, indicating that both L-Arg and DNA act together to achieve full activation.20 Recent structural comparison between intact ArgR apo-protein from B. stearothermophilus and its ArgRC domain fragment bound to L-Arg suggested that L-Arg activation involves a dramatic relative rotation of the two trimeric halves of the symmetric hexamer,18 but the E. coli ArgRC domain structures with and ˚ in only without L-Arg bound differ by less than 1 A 19 a few residues near the L-Arg binding site. Thus, it is presently unclear if the differences observed for B. stearothermophilus ArgR are due to the N-terminal domains or to binding of L-Arg. The studies reported here were carried out to establish the quantitative basis for activation in the ArgR regulatory system. Although arginine is a ubiquitous signaling precursor whose metabolites are crucial to a number of physiological processes in both prokaryotes and eukaryotes, quantitative studies of its binding to target proteins have been hampered by lack of applicable methods. Studies of bacterial arginine regulatory systems date to the 1950s, but this report presents the first elucidation of affinity, stoichiometry, cooperativity, and thermodynamic profile for L -Arg binding to ArgR, achieved by exploiting the complementarity of isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR). Multiphasic ITC isotherms virtually identical with those observed in

Asymmetric Allosteric Activation

other complex systems, including CAP, were deconvoluted by integrating extensive biophysical data on the ArgR system, including SPR; by studying protein and ligand variants; and by applying binding theory to reveal features ascribable to inherent limitations of weak-affinity systems. The results suggest an unexpected manifestation of cooperativity that is consistent with independent biochemical data: binding of a single L-Arg triggers a global conformational change in the ArgR hexamer and resets the affinities of the remaining five sites, making them 100-fold weaker. The analysis suggests that the complex thermodynamic profile revealed by ITC may represent a signature for global conformational change. The strong analogies to CAP suggest that the approaches used here may be applicable to understanding the stoichiometry and cooperativity of cAMP binding, which remain unresolved despite textbook acceptance of CAP as a paradigm for our understanding of molecular mechanisms of allosteric transcriptional activation.

Results Isothermal titration calorimetry Titration of 22 mM ArgR hexamer with 2 mM displays a multiphasic heat response, as shown in Figure 1(a) and as reported.21 The apparent midpoint in the rising part of the exotherm is near six equivalents of L-Arg per ArgR hexamer (Figure 1(b)), the expected stoichiometry at L-Arg saturation based on the crystal structure, although the multiphasic nature of the heat response complicates interpretation of the midpoint as the overall stoichiometry of binding. Close examination of the first few injection peaks (Figure 1(a) and (c)) reveals a small endothermic component of the heat response with a slightly longer evolution time than the exothermic component. The total magnitudes of the endothermic and exothermic components are unknown because they are apparently mutually offsetting, resulting in the net magnitude for the exothermic component observed in the first few peaks. The endothermic component of the heat response thus contributes to the multiphasic nature of the isotherm. The endotherm is not due to instrument overcompensation since in the conditions used net heat is being supplied to the reaction cell. All ITC titrations conducted in this work under the experimental conditions discussed below display the multiphasic heat response. Because measured heats can arise from a very wide range of sources, many potential artifactual causes of the complex heat response were evaluated during the course of this work. ArgR solutions remained optically clear during titration to final concentrations of L-Arg comparable to those used to precipitate ArgR during purification,22 perhaps because the conditions used for ITC were optimized L-Arg

Asymmetric Allosteric Activation

45

Figure 1. ITC response of ArgR to L-arginine. (a) Raw data. Typical results of titration at 25 8C when ArgR is at w22 mM hexamer in the reaction cell and L-Arg is at w2 mM in the syringe. (b) Integrated heats and fitting. The integral of each heat spike shown in (a) was determined with manual baseline adjustment; the molar ratio is the cumulative total concentration of L-Arg added, divided by total concentration of ArgR in the cell, adjusted for dilution (points). Lines are best fits to models with two classes of sites, 1 and 2, that differ in affinity; total number of sites NtotalZ6; and number of sites in each class, N1 and N2, constrained to integer values. The red line is best fit to the N1Z1, N2Z5 model discussed in the text, with parameters N1Z1, Kd1Z0.81 mM, DH81ZK0.47 kcal/mol L-Arg bound, and N2Z5, Kd2Z77 mM, DH82Z K2.6 kcal/mol. Blue and green lines, respectively, are best fits to the N1Z2, N2Z4 and N1ZN2Z3 models discussed in the text. (c) Early endothermic component of reaction heat: x-scale and y-scale expansion of the first several injections from an L-Arg titration similar to that in (a) but with ArgRC in the reaction cell. (d) Effect of raising the concentration of L-Arg. Integrated heats and fitting to typical results obtained when ArgR is at w22 mM hexamer in the reaction cell and L-Arg is at w15 mM in the syringe. The green line is the best fit to a model with one class of sites and no constraint on the total number of sites; best-fit model parameters are NtotalZ5.4, DH8ZK2.7 kcal/mol, KdZ77 mM. The red line is with the number of sites constrained at NtotalZ6; best-fit model parameters are DH8ZK2.4 kcal/mol, KdZ83 mM. The blue line is the best fit to a model with N fixed at 7; best-fit model parameters are DHZK2.0 kcal/mol, KdZ68 mM.

46 for solubility (see Materials and Methods). Corrections for heats of ligand dilution used control titrations collected immediately before or after each experimental titration, and yielded heats small enough for accurate subtraction (not shown). Poor buffer matching was ruled out because control titrations of buffer into buffer yielded negligible heats, as did titrations of buffer into protein (not shown). Protonation events were ruled out because experiments in Tris and phosphate buffers yielded essentially identical results (not shown) although the two buffers differ by nearly tenfold in protonation enthalpy, with opposite signs. The range of plausible explanations for the complex heat response is further limited because similar behavior was found for L-Arg analogs and for protein variants purified by alternative methods from different hosts, including the cyteine-less mutant Arg-RC68S, which was purified and studied in buffers containing only sodium phosphate and salt. The only factors observed to be correlated with the multiphasic heat response were the absolute and relative concentrations of protein and ligand in the titrations and, as shown below, these factors are correlated with the multiphasic heat response not only qualitatively but also quantitatively. Various concentrations of L-Arg and ArgR were titrated over the range accessible with ArgR, which is limited due to both abundancy and solubility. In a series of experiments at w15 to w40 mM hexamer, the position of the trough shifts to the left as protein concentration is raised (not shown), reflecting changes in the relative contributions of the endothermic and exothermic components. The apparent midpoint in the rising part of the exotherm also shifts to the left at higher concentrations of protein. Raising the concentration of titrant (L-Arg) is expected to make the early endothermic component of the reaction a smaller fraction of the total response by confining its contribution to the first injection. A titration conducted at 22 mM ArgR hexamer and 15 mM L-Arg is shown in Figure 1(d). The descending phase of the heat response, and thus also the trough (minimum) between descending and ascending phases of the exotherm, is absent from this titration because the endothermic component is masked within the first injection of ligand. The steeply rising isotherm displays no obvious midpoint. Thus, the ITC isotherms are highly sensitive to very small changes in concentration of protein or ligand. Formation of ArgR hexamers upon L-Arg binding could contribute to the observed heats if a population of dissociated hexamers pre-exists at the beginning of the titration. The maximum potential size of such a population was calculated using the hexamer dissociation constant derived from analytical ultracentrifugation experiments conducted under the solution conditions used for ITC,20 which showed no dissociation of ArgR hexamers in the presence or in the absence of L-Arg at the lowest detectable concentrations of ArgR, leading to a

Asymmetric Allosteric Activation

limiting value of Kd%2.5 nM for a putative trimer– hexamer equilibrium. This Kd value predicts that no more than 1 pmol of ArgR trimers (0.7 nM in the 1.4 ml reaction cell) is potentially available for reassociation into hexamers in any ITC injection at 22 mM ArgR. The heat response due to trimer reassociation would have to be thousands of kcal molK1 (1 calZ4.184 J) for this very small trimer population to yield a detectable reaction heat, making this possibility unlikely. Furthermore, ArgR dilution itself is associated with no detectable heat: when ArgR is diluted to generate approximately 2% of the total protein concentration in the form of trimers if Kd is 2.5 nM, heats of dilution are comparable to those of buffer/buffer injections. Higher-order assembly of hexamers was ruled out as a contributing factor by using the ArgRC fragment bearing only the C-terminal hexamerization and L-Arg-binding domain of ArgR.19,23 Like ArgR, ArgRC forms hexamers in solution with an upper limit of Kd%6 nM for dissociation into trimers but, unlike ArgR, it shows no evidence of higher-order multimers at concentrations of up to w300 mM (R. Fairman & J.C., unpublished results). Thus, complex ITC results for ArgRC would not be explainable by higher-order assembly of hexamers. Therefore, such ITC results likely have some other explanation in the case of ArgR also, where small amounts of higher-order multimers are implied by fitting to analytical ultracentrifugation data,20 but are not resolved into discrete species that would permit detailed modeling of their assembly equilibria (R. Fairman & J.C., unpublished results). ITC isotherms for ArgRC binding to L-Arg are multiphasic (Figure 1(c)) and concentration-dependent, like those of ArgR, although, as discussed below, the magnitudes of enthalpy change and heat capacity change differ for the two proteins. Thus, the extreme dependence of ITC isotherms on reaction conditions in the ArgR system is not likely to reflect changes in subunit assembly state accompanying ligand binding. Alternatively, the observed sensitivity of the ITC isotherms could be related to the difficulty of achieving optimal absolute and relative concentrations of titrant and titrate for determination of Kd, DH, and stoichiometry (n), due to a combination of weak affinity and limiting protein concentrations, as discussed recently by Turnbull & Daranas.24 The choice of optimal ITC experimental conditions is guided by the so-called c parameter (cZ(protein concentration!stoichiometry)/Kd).25 In the range of c values where experimental protein concentrations are high relative to affinity, ITC isotherms typically display a sigmoid shape with a midpoint that changes little with protein concentration and approaches n, the molar ratio of interacting components. When experimental concentrations of protein are low relative to affinity, raising the concentration of protein increases the extent of reaction greatly at each injection and alters the shape of the ITC isotherm. In such cases, Kd can generally be determined with confidence, but the

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midpoint of the curve may be difficult to identify, and/or it may not correspond to the molar ratio of interacting components, though sometimes n can be determined by fitting. For systems very far below ideal c values, the difficulty of determining n leads to weak confidence in heat flow per mol of complex formed, even though heat is the observable measured directly. To estimate the c value in the experiments conducted here, and thus to evaluate its contribution to the observed condition-dependence of the ITC isotherms, a confident value for n is needed to establish the correct binding model and determine affinity. A more detailed discussion of n and Kd is deferred to the section below on model-fitting, but reasonable estimates are nZ6 consistent with the apparent midpoint of Figure 1(a), and Kdw100 mM for L-Arg binding to ArgR or ArgRC, consistent with the ITC and SPR results reported here. Thus, given the limited solubility of ArgR, c values of only %10 can be achieved. In the ArgR system, the midpoint of multiphasic ITC isotherms is affected additionally by the condition-dependent contribution of the endotherm through its effect on the depth and position of the trough. As well, the endotherm and its sensitivity to experimental conditions further confound the values of enthalpy change derived for the ArgR system. Thus, the observed strong condition-dependence of ITC isotherms in the ArgR system most likely results from a combination of low-c limitation24 with the effects of a confounding endotherm. A final strategy used in the hope of shedding light on the multiphasic heat response was to study the binding of selected analogs of L-Arg. In ITC experiments with ArgR as titrate and analogs as titrants at concentrations as high as 0.5–1.0 M in the injection syringe, only L-canavanine (L-can) and not L-citrulline or L-ornithine yielded a detectable heat response with ArgR, consistent with previous evidence.21 Just as for L-Arg, the ITC response at low concentrations of L-can is multiphasic and has an endothermic component (Figure 2(a) and (b)), and is more steeply rising at higher concentrations of ligand (Figure 2(c) and (d)). The trough is broader for L -can than for L -Arg when compared at equivalent concentrations of protein and ligand, again consistent with a low-c system but with an affinity for L-can that is even weaker than that for L-Arg, as confirmed below by SPR. The finding that canavanine titrations also display the early endothermic component suggests the assignment of this feature to a process involving the protein or both the ligand and protein, and not the ligand only, and suggests that the endotherm may be related directly to the binding reaction. A direct connection to the binding process itself gains greatest support from the observation that the endotherm appears to be associated quantitatively with addition of the first equivalent of ligand, as determined by fitting various models to the binding data, as discussed below.

Surface plasmon resonance To provide independent information about ligand binding in the ArgR system, SPR was chosen as a second method that uses a distinct physical observable and has different experimental criteria for successful implementation. There has been no reports of immobilizing ArgR onto SPR chip surfaces, although a study of ArgR/DNA binding by SPR using immobilized DNA has been published.26 ArgR was immobilized using carbodiimide-activated amine coupling so that the chip surface might present random orientations of ArgR molecules, in the hope that at least some orientations would be compatible with its hexameric assembly state and preserve its L-Arg binding capability. Individual attached species are likely to be physically isolated from one another by the dextran matrix of the chip surface, so subunit assembly equilibria are unlikely to contribute to binding processes detected by this method. SPR is not inherently sensitive to modest changes in levels of immobilized protein but, unlike ITC, it typically offers no direct information about stoichiometry. Only species that are active for binding can register an SPR response; no evidence of heterogeneity due to partially active forms was observed here. Figure 3(a) shows a series of sensorgrams, the output of the SPR measurement, corrected for the change in refractive index detected on an adjacent mock-immobilized surface on the same chip. The kinetics of both association and dissociation are near the limit of being too fast to be analyzed quantitatively with confidence. This result suggests that the relatively slow endothermic process detected in ITC does not reflect a change in mass. The response values at the steady-state plateau were taken as a measure of the amount of ligand bound in the sensor cell. The sensorgrams show increasing response to concentrations of ligand in the range 10 mM–1 mM, consistent with the doseresponse behavior for a ligand capable of binding to the immobilized protein with an affinity of the order of w100 mM (Figure 3(b)). Essentially identical results were obtained for the super-repressor variant ArgR from E. coli B,27 in agreement with its ITC isotherm determined here, (not shown). The binding of L-Arg to ArgRC was studied using SPR (not shown) but, despite similar levels of immobilized protein, ArgRC surfaces were far less active than ArgR surfaces in L-Arg binding, yielding only partial isotherms suggesting an affinity of KdS1 mM. Although all SPR titrations conducted in this work consistently yielded affinities two to three times weaker than those obtained from ITC, the difference in ArgRC/L-Arg binding affinities found by SPR and by ITC is much larger than this and is well outside the relatively large range of errors of the two measurements (see Materials and Methods). Attachment of the L-Arg-binding domain directly to the chip surface may impose a distortion or proximity effect that interferes with ligand binding; attachment of intact ArgR to the chip

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Figure 2. ITC response of ArgR to L-canvanine. (a) Raw data at a low concentration of L-can. Typical results of titration at 25 8C when ArgR is at w29 mM hexamer in the cell and L-can is at w14 mM in the syringe. (b) Integrated heats and fitting. The red line is the best fit to a model with two classes of sites, 1 and 2, that differ in affinity; total number of sites NtotalZ6; number of sites in each class, N1 and N2, constrained to integer values; and Kd2 constrained to the value derived from fitting to the data in (c). Best-fit model parameters are N1Z1, Kd1Z325 mM, DH1Z6.8 kcal/mol of L-can bound, and N2Z5, Kd2Z714 mM, DH2ZK3.0 kcal/mol. (c) Raw data at a high concentration of L-can. Typical results when ArgR at w16 mM hexamer in the reaction cell is titrated with L-can at w45 mM in the syringe. (d) Integrated heats and fitting. The red line is the best fit to a model with one class of sites and number of sites constrained to NtotalZ6. Bestfit model parameters are DHZK1.7 kcal/mol, KdZ714 mM.

almost certainly proceeds through amine groups located in the peripheral N-terminal DNAbinding domains, and may shield its C-terminal L-Arg-binding domain from interference at the chip surface. Binding of L-can to ArgR studied by SPR (Figure 3(c)) yielded incomplete isotherms very

similar to those for ArgRC/L-Arg, consistent with an affinity of S2 mM for ArgR/L-can; a value of 2 mM would be within error of the values derived by model-fitting from ITC data. This agreement suggests that the same ArgR/L-can binding process is observed by both SPR and ITC, whereas for

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49

Figure 3. SPR titration of ArgR with L-Arg. (a) Dose-response sensorgrams. ArgR immobilized on the chip surface was titrated with L-Arg at concentrations from 1 mM (bottom) to 10 mM (top) in successive analyte injections at 25 8C. RU, instrument response in arbitrary units after subtraction of response in a parallel mock-immobilized channel of the flow cell. (b) ArgR/L-Arg binding isotherm. The response value at steady-state (points) was derived from the flat part of sensorgrams like those in (a). The continuous line is the best fit to a 1:1 binding model yielding KdZ255 mM. The broken line is the best fit to a model with two classes of sites with N1Z1, Kd1Z3 mM, and N2Z5, Kd2Z276 mM. (c) ArgR/L-can binding isotherm. The continuous line is the global best fit (see (d)) to three independent datasets, yielding KdS2 mM for a 1:1 binding model. (d) Global analysis of SPR data. Each set of colored points represents one chip surface with unique amount of ArgR immobilized, then titrated with L-Arg as in (a). The continuous lines are the best fit to all 16 independent datasets simultaneously, yielding KdZ283 mM for a 1:1 binding model.

ArgRC/L-Arg the two methods may not report on the same process and their results should not be compared. SPR experiments were repeated at 5 8C–40 8C in 5 deg. C increments (not shown) in an effort to derive values of the enthalpy and heat capacity changes in the ArgR system from the temperature-

dependence of Kd. Values of DH8 derived independently from van’t Hoff analysis of SPR data could provide input parameters for fitting ITC data to elucidate the complex ITC isotherm. Useful values were obtained only for ArgR/ L -Arg: DH8ZK3.0(G1.7) kcal/mol and DCp8w0, consistent with the values determined directly by ITC. SPR

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isotherms for ArgRC/L-Arg and ArgR/L-can were incomplete at all temperatures, and did not yield confident values of DH8 or DCp8. The partial isotherms for ArgR/L-can did not vary significantly with temperature, indicating that DH8 is relatively small, like that for ArgR/L-Arg. Model-fitting and data analysis Standard mathematical approaches28 to modelfitting were used to analyze ITC binding data. In addition, complementary results were taken into account to help choose among models that offered

similar fits. For example, DH8 for each protein– ligand pair under study was estimated independently from direct calorimetric titration of protein into excess ligand, and from van’t Hoff analysis of SPR binding data where possible. Table 1 organizes the parameters derived from various models discussed below and the other factors that were considered in evaluating each model. Direct information about the molar ratio of interacting components, n, is a requirement for molecular interpretation of binding data by modelfitting. Because the assembly state of ArgR is known from analytical ultracentrifugation in the ITC

Table 1 Parameters Model Equivalent sites

Data

ArgR/L-Arg

Monophasic

KdZ77 mM; DHZK2.7 kcal molK1; nZ5.5

ArgRC/L-Arg

ArgR/L-can

KdZ340 mM; DHZK10.4 kcal molK1; nZ3.1

DH by direct measurement ZK5.8 kcal molK1 KdZ550 mM; DHZK0.13 kcal molK1; nZ52

Six equivalent sites

Monophasic

Comments

Unrealistic n

KdZ83 mM; DHZK2.4 kcal molK1 KdZ290 mM; DHZK5.2 kcal molK1

3C3 sites

Multiphasic

Kd1Z2.1 mM; DH1ZK1.1 kcal molK1 Kd2Z130 mM; DH2ZK3.8 kcal molK1

KdZ710 mM; DHZK1.7 kcal molK1 Kd1Z47 mM; DH1ZC7.5 kcal molK1 Kd2Z83 mM; DH2ZK52 kcal molK1

DH by direct measurement ZK2.3 kcal molK1 DH by direct measurement ZK5.8 kcal molK1.

No convergence 2C2C2 sites

Multiphasic

1C1C1C1C1C1 sites

Multiphasic

2C4 sites

Multiphasic

Kd1Z29 mM; DH1ZK0.3 kcal molK1 Kd2Z11 mM; DH2ZK3.3 kcal molK1 Kd3Z3.2 mM; DH3ZK26 kcal molK1 Kd1Z30 mM; DH1ZK0.7 kcal molK1 Kd2ZK860 mM; DH2Z91 kcal molK1 Kd3ZK180 mM; DH3ZK72 kcal molK1 Kd4Z2.0 mM; DH4ZK23 kcal molK1 Kd5Z230 mM; DH5ZK6.0 kcal molK1 Kd6Z220 mM; DH6ZK4.9 kcal molK1 Kd1Z2.7 mM; DH1ZK0.74 kcal molK1 Kd2Z91 mM; DH2ZK3.1 kcal molK1

Unrealistic heats and Kd values

Unrealistic heats and Kd values

See Figure 1(a)

Kd1Z8.3 mM; DH1ZK0.06 kcal molK1 Kd2Z130 mM; DH2ZK6.0 kcal molK1

Trough fits poorly. No convergence

1C5 sites

Multiphasic

Kd1Z0.81 mM; DH1ZK0.47 kcal molK1 Kd2Z77 mM; DH2ZK2.6 kcal molK1 Kd1Z7.6 mM; DH1ZC0.80 kcal molK1 Kd2Z150 mM; DH2ZK5.3 kcal molK1 Kd1Z320 mM; DH1Z6.8 kcal molK1 (Kd2Z710 mM) DH2ZK3.0 kcal molK1

Kd2 must be fixed.

Asymmetric Allosteric Activation

conditions,20 molar ratios that can be resolved unambiguously from the L-Arg binding data can be equated with reaction stoichiometries. Monophasic ITC isotherms for ArgR/L-Arg have no obvious midpoint (Figure 1(d)). Therefore, an initial estimate for n was obtained by assuming all sites are equivalent (Table 1), yielding nZ5.5, a value consistent with the apparent midpoint in the rising part of the multiphasic isotherms (Figure 1(b)). The estimated uncertainty in n is 10–20%, due to experimental constraints on precision (see Materials and Methods). The general agreement of ArgR/ L-Arg molar ratio between datasets obtained at high and low concentrations of ligand suggests that the total reaction stoichiometry in solution is indeed likely to be six ligands per hexamer in either concentration regime, in agreement with the crystal structure.19 When the number of sites is constrained at 6 so as to be a physically reasonable integer, the quality of fits to the monophasic datasets is not degraded significantly (Figure 1(d)) and DH8 agrees better with the value measured directly (K2.3 kcal/ mol; Table 1). The results obtained in this work rule out additional binding sites for ArgR/L-Arg with affinities stronger than Kdw1 mM. For ArgRC/L-Arg and ArgR/L-can, monophasic ITC data constrain n less well. The best-fit value of n for equivalent sites on ArgRC is 3.1 with DH8Z K10.4 kcal/mol, nearly twice the value measured directly (K5.8 kcal/mol). The covariance between n and DH8 results in similar fit with n fixed at 6, yielding DH8 in much better agreement with the value measured directly. For ArgR/L-can, n, DH8 and Kd are poorly constrained by monophasic ITC datasets, presumably due to the weaker affinity noted above. With n fixed at 6, both Kd and DH8 values are consistent with other data. To analyze multiphasic ITC datasets, a range of models was tested that are plausible for ArgR given its known properties, including models with six sites of inequivalent affinity, or six sites with two or three classes of affinities (Table 1); the molar ratios for each affinity class were constrained to integral numbers to be physically meaningful. No multiphasic isotherms could be fit by models in which all binding sites belong to a single affinity class, regardless of the total number of sites. Both multiphasic and monophasic isotherms could be fit very well by a model of six nonequivalent sites. This model would be physically reasonable if the structurally equivalent sites of apoArgR are rendered inequivalent by cooperative interactions, which is plausible because each ligandbinding site contains residues from three of the six polypeptide chains and thus has the means for communicating its ligand-occupancy state to unoccupied sites. However, the 12 independent parameters of this model might fit many datasets by chance, and some physically unreasonable negative affinities were returned from the fit (Table 1). A model with three sets of sites and two equivalent sites per set yielded a reasonable fit to the ITC data but returned physically unreasonable parameter values with strong covariance, indicating that the information

51 content of the data is too low to constrain models with six parameters. Two-sets-of-sites models used four independent parameters (two values each of Kd and DH; Table 1) and fixed, integral N1 and N2 to fit multiphasic ITC datasets, but most such models fit the ArgR/L-Arg ITC data poorly, especially in the trough region (Figure 1(b)). Models with two sites in one set and four in the other fit poorly, regardless of how many sites were designated as higher affinity (N1Z2 or N1Z4). The two-sets-of-sites model with three sites in each set (N1ZN2Z3) also did not give a good fit to the data. All these models offered acceptable fits with multiphasic ArgRC/L-Arg and ArgR/L-can ITC data, which offer less constraining datasets than ArgR/L-Arg. Only one model with two sets of sites provided an acceptable fit to all multiphasic datasets for both ArgR/L-Arg and ArgRC/L-arg, although its fit is not ideal and its asymmetry makes it seemingly less plausible than the others. This model includes one site of high affinity (Kd1w1 mM) and five sites of lower but equivalent affinity (K d2 w100 mM). Although the fitted curve does not pass through all ITC data points exactly (Figure 1(b)), the deviations were observed to vary with the relative magnitude of the descending part of the exotherm in the many datasets obtained in the course of this work, suggesting that the endothermic component of binding governs the fit with this model. Deviations are detected as saturation is approached, suggesting that the low-affinity sites may differ slightly from each other in affinity. The fitted values of DH8 are in good agreement with those obtained from ITC titrations at high concentrations of ligand where binding is stoichiometric, and with those from van’t Hoff analysis of the SPR data, and the fit is not altered substantially when the van’t Hoff value for ArgR/L-Arg is used as an input. This model also fits the SPR binding isotherms for ArgR/L-Arg (Figure 3(b)), returning values of Kd1Z3 mM and Kd2Z276 mM, in reasonable agreement with the ITC data considering the relatively large experimental errors. In an effort to better restrict models for the binding process, a new method was developed to permit global analysis of SPR data. Widely different amounts of ArgR were immobilized on separate chip surfaces so as to vary the signal-to-noise ratio over a wide range. Typical results of a series of 16 such experiments for ArgR/L-Arg binding are shown in Figure 3(d), where each set of points represents a titration on one independent surface. The continuous lines represent the best-fit value of KdZ283 mM for all datasets fit simultaneously to a simple 1:1 model (equivalent to binding of six L-Arg per hexamer). The global analysis method used here differs from that reported for SPR kinetic data by Myszka and co-workers,29 who treated the maximum value of response as a global parameter in the fit. In the present case, individual values of pretransition and post-transition response are fit to each dataset while satisfying the condition that all

52 Kd values are equal. The fact that datasets can be fit adequately to a single value of Kd in a global analysis of the SPR binding data provides a very high standard of confidence in the results, despite small responses and widely varying baselines and signal-to-noise ratios. However, these same limitations result in poor ability to restrict the range of models that fit the data (Figure 3(b)), with or without global analysis. The N1Z1, N2Z5 model also fits typical multiphasic ArgR/L-can ITC datasets (Figure 2(b)). However, the model returned unreasonable values of DH8, ten times larger than those for L-Arg and thus inconsistent with the results from van’t Hoff analysis of SPR data, unless Kd2 was fixed using the values obtained from ITC at high concentrations of ligand (e.g. Figure 2(d)) or from SPR (e.g. Figure 3(c)). This behavior is consistent with the poorer optimization of experimental conditions due to weaker affinity for L-can and thus even lower c values than for L-Arg. The fact that L-can affinities are distinct from those of L-Arg yet can be fit by a model that is apparently governed by the endothermic component of the heat response suggests a quantitative link between the endotherm and the first ligand-binding event. The model-dependency of binding analysis limits its usefulness in providing additional independent tests of the binding model, but the affinity constants derived from the model can be used to predict the ligand occupancy state of the hexamer as a function of ArgR and L-Arg concentration for independent biochemical tests. Importantly, the 100-fold difference in binding constant predicted by the 1–5 model should permit essentially complete loading of site 1 at concentrations of L-Arg where sites 2–6 are hardly occupied. This state of occupancy by approximately one L -Arg per ArgR hexamer might have unique biochemical properties. This hypothesis was evaluated using proteolysis. The most sensitive sites of protease cleavage of ArgR are in the linker region between the N and C-terminal domains, 23 and the rate of linker cleavage is enhanced by approximately tenfold in the presence of excess L-Arg (J.C., unpublished results). To probe the rate of cleavage at linker residue Leu82 at defined ligand occupancies, digestion by chymotrypsin was conducted. Values of Kd1Z1 mM and Kd2Z100 mM from the binding model were used to predict the ligand occupancies of site 1 and sites 2K6, respectively, at various concentrations of ArgR and L-Arg. The model predicts that at a total concentration of ArgR of 0.5 mM hexamer, a total concentration of L-Arg of 10 mM yields w88% saturation of site 1 but only w9% saturation of sites 2K6; at 2 mM ArgR hexamer, a concentration of L-Arg of 50 mM yields w98% saturation of site 1 and w32% saturation of sites 2K6. Over this range of predicted ligand occupancies, the rate of ArgR cleavage by chymotrypsin was found to be approximately tenfold faster than for the ArgR apoprotein, and was essentially identical

Asymmetric Allosteric Activation

Figure 4. Effect of L-Arg on proteolytic sensitivity. ArgR at w2 mM monomer was digested for the indicated times by w0.6 mg/ml of chymotrypsin in the presence or in the absence of 50 mM L-Arg, yielding w97% occupancy of site 1 and w30% occupancy of sites 2 to 6. Typical SDS/polyacrylamide gels stained with Coomassie brilliant blue are shown.

with the rate observed at ligand excess (5 mM L-Arg, providing S98% occupancy of all six sites). For example, in Figure 4, intact ArgR (top band) is digested almost completely in w30 minutes in the presence of 50 mM L-Arg, but when L-Arg is absent, nearly half the starting material remains after 30 minutes. Already at three minutes, the extent of digestion in the presence of L-Arg is similar to that at 30 minutes in the absence of L-Arg. Intensities of product bands are difficult to interpret due to further digestion and differential stabilization by 23 L-Arg. Control experiments demonstrate that at these concentrations L-Arg has no general effect on chymotrypsin activity. The proteolytic analysis thus indicates that intact ArgR is cleaved at the same tenfold enhanced rate whether as few as 9% of sites 2–6, or nearly all them, are occupied. This result demonstrates the nonlinear response expected for a cooperative system, suggesting that occupancy of approximately one high-affinity L-Arg site per hexamer is sufficient to convert all subunits to a state of maximum protease sensitivity. This result suggests that binding of the first L-Arg is accompanied by a conformational change that can be detected at the boundary between the N and C-terminal domains and is propagated to other subunits. The results increase confidence in the binding model and its implication that the endothermic component of binding is indeed associated with the first binding event. However, the results do not confidently exclude other binding models. For example, the ligand occupancies predicted by the 2–4 model are similar enough to be probably indistinguishable in these experiments.

Discussion Multiphasic ITC isotherms similar to those for

Asymmetric Allosteric Activation

ArgR have been resolved in other systems to reveal important features of molecular mechanism including, e.g., kinetic effects in the binding of iron chelates to transferrin;30,31 competition between specific and non-specific interactions in the case of integration host factor binding to DNA;32 and cooperative 2:1 capsule formation by cyclodextrins around camphors.33 One highly similar case that has not been resolved is that of cAMP binding to CAP.7,8 In the ArgR case the complexities of the heat response are attributable to two main causes: the presence of offsetting endothermic and exothermic components of the reaction heat in the early phases of binding, and the difficulty of achieving optimal reactant concentrations for determination of Kd, DH, and n. These two factors conspire to produce highly concentration-dependent isotherms in which the relative magnitudes of endothermic and exothermic components, the position of the trough between them, and the apparent titration midpoint all vary because the initial protein and ligand concentrations govern the extent of reaction in each injection. Despite these complexities, ArgR/L-Arg stoichiometry was determined with reasonable confidence, providing an important constraint in model-fitting. Modeling indicates a single initial binding event with higher affinity than the remaining events that saturate the hexamer, and suggests that the early endotherm is correlated with the first event. This model is consistent with biochemical data suggesting that occupancy of as little as one highaffinity site can induce a conformational change that is detected in other subunits. We regard this model as a testable working hypothesis whose most significant feature is the apparent correlation of the endothermic process with the first binding event. This assignment, however, derives only weakly from the binding model itself. It is supported strongly by the extensive control experiments that ruled out artifactual causes of the endotherm. Another compelling argument is that ArgR/L-Arg, ArgRC/L-Arg, and ArgR/L-can all display the endotherm, despite their many differences. Although the present data do not constrain binding models very narrowly, a binding model is prerequisite to interpreting the thermodynamic results. The analysis presented in the following paragraphs is based on the 1–5 binding model, which appears to best satisfy the collective constraints of all the data on the ArgR system. If the endothermic part of the heat response is associated directly with the initial L-Arg binding event, then it represents an enthalpically unfavorable component of the binding process that must be compensated by favorable contributions, since binding proceeds spontaneously. Indeed, because the affinity in the first binding event is apparently stronger than in subsequent events, favorable contributions to the binding free energy must be larger in the first event than in subsequent events. Presumably, some of the favorable free energy originates in the exothermic component of binding

53 that is also detected in association with the first event, and that must be larger than it appears when offset by the endotherm. One reasonable possibility is that the magnitude of the exothermic part of the enthalpy change due to protein–ligand interactions is no different for binding the first ligand than for all subsequent binding events, consistent with the apparent structural equivalence of the six subunits in both apo- and holorepressors. However, since the net enthalpy change for the first event is less negative than for subsequent events, yet the binding affinity is apparently stronger, there must be favorable entropic changes that accompany the first event. Thus, the picture that emerges from this analysis is that binding of the first L-Arg ligand to the ArgR hexamer initiates a bond-breaking (endothermic) process that is more than compensated by at least two favorable contributions: the exothermic (bondmaking) processes accompanying binding itself, and a release of stored energy in the form of entropy. These thermodynamic contributions give the first binding event a 100-fold higher apparent affinity than any of the subsequent five events. The structural equivalence of the six sites in apo- and holo-ArgR suggests that all sites have equal intrinsic affinities, and that the apparently lower affinity at sites 2–6 results because the first binding event resets the affinity of the subsequent five events, and thus reflects negative cooperativity between site 1 and sites 2–6. One possibility that could be considered likely is that the endotherm and the enhanced proteolytic sensitivity reflect conformational changes associated with repressor activation. The relative rotation of trimers observed by comparing structures of the intact ArgR apoprotein and the ArgRC domain fragment holoprotein from B. stearothermophilus18 would be compatible with the apparent resetting of affinity by the first L-Arg binding event as found in the present work. The assumption made by Ni et al.18 that the observed structural differences are due to ligand binding rather than to the missing N-terminal domains would be consistent with the present results, since both ArgR and ArgRC of E. coli studied here display the endothermic component of binding. The ITC and the SPR results indicate that DH8 is considerably larger for ArgRC than for ArgR, although binding affinities are similar, and the ITC data indicate that DCp8 is larger for ArgRC (w0.1 kcal/mol K versus w0.005 kcal/mol K; not shown). Taken at face value, these results suggest that L-Arg binding at sites in the C-terminal domains of ArgR affects the N-terminal domains in some manner. However, the B. stearothermophilus and E. coli proteins have very different trimer interfaces, and likely different intersubunit and interdomain interactions, and comparison of E. coli apo- and holo-ArgRC proteins shows only very minor structural differences. Finally it is interesting, but likely only coincidental, that Ni et al.18 could identify reasonably strong electron density for only five of the six

54 equivalent DNA-binding domains of intact B. stearothermophilus apo-ArgR. The results from both ITC and SPR suggest that, despite the w100-fold negative cooperativity between site 1 and the remaining five sites of the ArgR hexamer, little or no cooperativity is present among sites 2–6. Weak cooperativity among these five sites cannot be excluded, given the deviation of the model from typical multiphasic ITC isotherms as saturation is approached. The small magnitude of cooperativity allowed by the data means that if intersubunit signaling occurs beyond the first ligand-binding event, it causes little change in affinity among the remaining five sites. A small negative cooperativity might simply reflect increasing electrostatic repulsion at the trimer interface as L-Arg saturation is approached, and not allosteric communication between sites. In biochemical terms, the finding that ligand binding to shared sites 2–6 in ArgR proceeds with little or no allosteric interaction suggests that mechanisms may exist to damp the response of sites that have the means to communicate. The dimeric tryptophan regulon repressor, TrpR, also has ligand-binding sites that share residues from both polypeptide chains,34 but binding of L-tryptophan is non-cooperative.35,36 The damping mechanism for TrpR is not known. In biological terms, the absence of strong cooperativity found for sites 2–6 of ArgR implies a system that responds to rising concentrations of effector with neither the switch-like response of positive cooperativity nor the buffered response of negative cooperativity.37 The present results suggest that the ArgR system is buffered against further increases in the concentration of L-Arg mainly by the affinity switch that is apparently complete upon filling of site 1, perhaps to permit two discrete L-Arg action levels; it is tempting to associate these with repression and activation of anabolic and catabolic operons, respectively, or perhaps with heterologous and autogenous feedback control of the regulon. Determination of binding isotherms as reported here is the required first step in addressing these functional issues, and will aid the design of experiments to elucidate allosteric mechanisms. Given the many biochemical and biophysical properties shared by ArgR and CAP,17 it is possible that some features of the complex ArgR ITC isotherms studied here may be relevant for understanding CAP, where issues about binding stoichiometry, and therefore binding constants, cooperativity, and site occupancy, have been difficult to resolve.38 We note the striking similarity of the multiphasic ITC isotherms observed here for ArgR and those reported for CAP.7,8 In the CAP case, the dominant heat response is generally endothermic, so the isotherms are inverted compared to those of ArgR, but exothermic components are observed in the early injections, and seemingly minor changes in experimental conditions, including the concentration of CAP, alter the appearance of the isotherms drastically, as observed here. Like

Asymmetric Allosteric Activation

ArgR, proteolysis of CAP in an interdomain linker region is accelerated in the presence of low concentrations of ligand,39 but a definitive binding isotherm is required to calculate the ligand-occupancy states correlated with proteolytic sensitivity. The two structurally identified sites for cAMP on each CAP monomer are intrinsically inequivalent,6 and could thus provide two action levels even without cooperativity. However, if the cAMPbinding site located directly at the DNA interface6 proves to be relevant for regulation, then it is possible that CAP, like TrpR, might not be considered truly allosteric, because the activating ligand participates directly in formation of the protein–DNA interface. Biological relevance of the new cAMP site cannot be ruled out even if its inferred weak affinity is confirmed by direct analysis: just as for ArgR, CAP/DNA affinity is enhanced by cAMP binding and therefore DNA binding necessarily enhances binding of cAMP, and could bring its affinity into a significantly different range. Multimeric bacterial regulatory systems can have simple ITC isotherms for binding to their effectors. In both the TrpR36 and BirA40 cases, accessible concentrations of protein are sufficiently above Kd to better satisfy the experimental criteria for ITC determination of Kd, DH, and n,24,25 but it is the absence of a confounding heat effect that simplifies their binding isotherms. Consistent with observed structural changes for both TrpR and BirA, ITC data reveal the thermodynamic signature of protein folding coupled to ligand binding. Further work may reveal whether the confounding heat effect seen with ArgR and suggested for CAP may be a thermodynamic signature of global domain rearrangements.

Materials and Methods Protein samples ArgR for ITC analysis was purified according to the protocol of Lim et al.,22 followed by ion-exchange chromatography on DEAE Sephadex-A25 resin as described.20 The hexameric ArgR domain fragment ArgRC was purified according to the protocol of Van Duyne et al.19 Protein concentrations were determined from absorbance as described.20 Pooled fractions were concentrated if necessary by freeze-drying or centrifugal microfiltration (Millipore-Amicon Ultra, cutoff 10,000 Da) and dialyzed against ITC buffer (100 mM Tris–HCl (pH 7.50), 0.20 M NaCl, 10 mM MgCl2, 0.2 mM DTT). Because L-Arg is used for differential precipitation of the protein during purification, early samples of ArgR used for binding analysis were analyzed by 1H-NMR to verify the absence of free L-Arg in the final pools of pure protein. Ligand stocks for titration of each protein were prepared by weight in the corresponding dialysate, and pH was adjusted to 7.50 if necessary. Isothermal titration calorimetry Isothermal titration calorimetry was carried out using a

55

Asymmetric Allosteric Activation

VP-ITC (Microcal) interfaced with a computer running Origin 7.0 software supplied by the manufacturer. The reference cell contained dialysate for all experiments. Solutions of protein and ligand were diluted with dialysate as needed, and degassed under vacuum for five minutes with gentle stirring. The injection syringe volume was 290 ml and the reaction cell volume was 1.4 ml. The stirring speed during titration was 310 rpm and temperature was 25 8C unless specified otherwise. Titrations used a first injection of 1 ml or 1.5 ml that was not used in data analysis, followed by 47 injections of 6 ml each at 0.5 ml/s. The interval between injections was eight minutes. Each experiment using ligand as titrant included a ligand-dilution control into buffer in the reaction cell that was subtracted point-for-point from the corresponding titration into protein. Controls titrating protein into buffer in the reaction cell were similar to water–water or buffer–buffer injections.

Surface plasmon resonance Immobilization of proteins for SPR analysis used Biacore CM5 chips and amine coupling according to the manufacturer’s protocol, and protein stock solutions of 0.1–1 mM hexamer. The experiments were designed according to the general guidelines given by Myszka.41 Protein loadings on the chip ranged from about 1000– 15,000 response units. One of the four flow-cells on each chip was mock-derivatized to serve as a control surface for blank subtraction. Ligand stock solutions were made by weight in ITC buffer with 10 mM instead of 100 mM Tris–HCl, and were serially diluted by hand or by progammed dilution in the instrument, and this buffer was used for binding measurements. For each ligand dilution, 20 ml was injected over the surfaces at a flow rate of 10 ml/minute. Unless specified otherwise, the temperature was 25 8C.

Proteolysis Proteolysis was conducted at room temperature using ITC buffer for dilution of both protein and enzyme. Some samples of ArgR used for these experiments were of lower quality than those used for binding analysis, and contained traces of ArgR domain fragments due to slight (%5%) breakdown over long storage periods. Chymotrypsin was diluted from 2 mg/ml stocks made in 1 mM HCl.42 Reactions were terminated by addition of 5! sample loading buffer and heating at 90 8C prior to resolution on 18% acrylamide (bis-acrylamide/acrylamide, 1:29, w/v) gels using a discontinuous buffer system.43

Precision The experimental errors in all measurements made during this work derive principally from sample handling, including weighing of solid ligands and pipetting of stock solutions of proteins and ligands. Multiple independent replicates of all experiments reported here indicate that these two sources bring substantial errors that limit the precision of all values reported in this work. These errors were propagated into the derived parameters, with the result that Kd values from SPR are reported here to within a factor of 2, and n, Kd or DH8 values from ITC are reported to within 20%.

Acknowledgements We are grateful for the support of the National Science Foundation (DBI-CCLI AI01-26642 to L.J. and MCB01-36094 to J.C.) and DePaul University College of Liberal Arts and Sciences (2003 faculty summer grant research). We thank Sara Linse, Lund University, and Pa¨r Sa¨fsten, Biacore AB, Uppsala, for generously providing access to Biacore-3000 instruments; Jaymie DeWitt, Biacore, Inc. USA, for conducting pilot Biacore experiments; and Danuta Szwajkajzer for her early contributions to analysis of Biacore data. We thank David Remeta and Kenneth Breslauer, Rutgers University, for their generosity in conducting preliminary ITC experiments using their Microcal calorimeter. Undergraduate students Nicole Follmer and Huan Zheng, Princeton University, and Alissa Agnello, Wellesley College, produced many of the preparations of ArgR and ArgRC proteins used in this work. Rita Grandori, Fred Hughson, and Stefano Ricagno provided insightful comments on the manuscript.

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Edited by D. E. Draper (Received 25 August 2004; received in revised form 10 November 2004; accepted 11 November 2004)