Examination of the nucleotide‐linked assembly mechanism of E. coli ClpA

Abstract

Escherichia coli ClpA is a AAA+ (ATPase Associated with diverse cellular Activities) chaperone that catalyzes the ATP‐dependent unfolding and translocation of substrate proteins targeted for degradation by a protease, ClpP. ClpA hexamers associate with one or both ends of ClpP tetradecamers to form ClpAP complexes. Each ClpA protomer contains two nucleotide‐binding sites, NBD1 and NBD2, and self‐assembly into hexamers is thermodynamically linked to nucleotide binding. Despite a number of studies aimed at characterizing ClpA and ClpAP‐catalyzed substrate unfolding and degradation, respectively, to date the field is unable to quantify the concentration of ClpA hexamers available to interact with ClpP for any given nucleotide and total ClpA concentration. In this work, sedimentation velocity studies are used to quantitatively examine the self‐assembly of a ClpA Walker B variant in the presence of ATP. In addition to the hexamerization, we observe the formation of a previously unreported ClpA dodecamer in the presence of ATP. Further, we report apparent equilibrium constants for the formation of each ClpA oligomer obtained from direct boundary modeling of the sedimentation velocity data. The energetics of nucleotide binding to NBD1 and NBD2 are revealed by examining the dependence of the apparent association equilibrium constants on free nucleotide concentration.

Introduction

ATP‐dependent proteases play critical and diverse roles in the proteome maintenance of prokaryotes and eukaryotes. Diverse cellular pathways such as heat shock response,1 posttranslational protein triaging,2 and regulation of Gram‐positive bacteria pathogenesis3 depend on the activity of ATP‐dependent chaperone systems. A hallmark of these systems is the ATP‐dependent coordination between a multimeric AAA+ (ATPases associated with diverse cellular activities) molecular chaperone and an associated protease for the regulated degradation of targeted polypeptide substrates.4, 5, 6 Escherichia coli ClpA is the AAA+ molecular chaperone component of the bacterial energy‐dependent chaperone system, ClpAP. Multiple rounds of ATP binding and hydrolysis by ClpA catalyze the translocation of polypeptide substrates. In the presence of its proteolytic counterpart ClpP, translocated polypeptide clients are threaded into a solvent excluded proteolytic cavity of ClpP for degradation. ClpA oligomers competent for ClpP binding form only in the presence of ATP.7, 8

ClpA is subclassified as a Class I Hsp100/Clp molecular chaperone due to the presence of two nucleotide binding domains (NBDs) within each ClpA protomer.9 Structurally, the ATP‐binding pocket of each protomer contains canonical Walker A and B motifs.10 In the absence of nucleotide, we have shown that wild type ClpA (ClpA_WT) resides in a distribution of monomers, dimers, and tetramers at 25 °C.11, 12 The functional oligomer of ClpA capable of polypeptide substrate unfolding and interaction with ClpP is a hexamer.8, 13 The structure of the ClpA hexameric state has not been solved independent of ClpP. However, Guo and coworkers proposed a model reconstruction of the hexamer based on the low‐resolution electron micrographs of the adenosine diphosphate (ADP) monomer crystal structure.10 Based on this model, the hexamer is arranged as a planar ring with an axial pore through which polypeptide substrates are threaded for unfolding.

ATP binding and hydrolysis by ClpA is coupled to both oligomeric assembly and the translocation of polypeptide substrates. In the presence of ATP, Kress and coworkers showed that ATP binding but not hydrolysis drives the oligomerization of ClpA into hexamers (ClpA₆) capable of binding polypeptide substrate and tetradecameric ClpP (ClpP₁₄).8 In addition to driving oligomerization, ATP binding and hydrolysis drives the translocation of polypeptide substrates down the axial channel of ClpA hexamers. Repeated rounds of ATP binding and hydrolysis are proposed to modulate the conformational switching of a P‐loop that connects the Walker A and Walker B motifs within each NBD that extends into the axial channel of ClpA hexamers.14 Using crosslinking studies Hinnerwisch et al. observe the NBD2 axial loops to be in direct contact with a polypeptide substrate and find that translocation activity can be abolished by mutations in the NBD1 axial loops.

Once populated in the presence of ATP, ClpA hexamers have been shown to catalyze the unfolding and translocation of polypeptide substrates both in the absence and presence of ClpP.15, 16 Yet, importantly, multiple studies observed a different ClpA translocation rate when ClpP is present relative to when it is not. Using a single turnover polypeptide translocation assay, we observe that in the absence of ClpP, ClpA translocates polypeptide substrates at a rate of ~20 aa s⁻¹.17 In contrast, when ClpP is present, we observe that ClpA translocates with a faster overall rate of ~36 aa s⁻¹.18 Using Förster resonance energy transfer (FRET)‐based assays to monitor ClpA‐catalyzed polypeptide unfolding others have observed differences for the catalytic rate of unfolding by ClpA in the absence and presence of ClpP.16, 19

The molecular basis for the observations of ClpP modulating ClpA catalytic activities is not well understood. One proposed model for these observed differences is that ClpP changes the rate of the physical up and down movements of the ClpA loops. However, an alternative and not necessarily mutually exclusive, explanation is that ClpP perturbs the ClpA assembly state. Changes to the binding affinity or hydrolysis rate of ATP at each ClpA NBD could lead to differences in the population of ClpA hexamers available to catalyze polypeptide translocation in the absence or presence of ClpP. Because ATP binding and oligomerization are coupled in ClpA, testing whether ClpP modulates the macromolecular assembly state of ClpA requires deconvolution of the affinity constants for the formation of hexamers and the affinity of ATP binding to each of the 12 ATP‐binding sites within the hexameric ring.

In this study, we use sedimentation velocity experiments to quantify the self‐assembly equilibrium constants for the formation of ClpA oligomers. Since ATP binding, but not hydrolysis is required for ClpA assembly, we used the ATP hydrolysis inactive variant ClpA_E286A/E565A to characterize the assembly state in the presence of ATP. Surprisingly, we observe that the hexamer is not the highest order oligomer populated in the presence of nucleotide. We find that ClpA_E286A/E565A resides in a distribution of monomers, dimers, tetramers, hexamers, and dodecamers in the presence of ATP.

By quantifying the self‐assembly equilibrium constants for the formation of each oligomer in the presence of varying ATP concentrations, we constructed binding isotherms that allowed us to separate ATP‐binding affinity from macromolecular assembly. The binding isotherms for the formation of each oligomer as a function of [ATP] were analyzed to determine the affinity and stoichiometry for ATP binding to each oligomer. We report binding constants for ATP binding each ClpA oligomer. On average, we find that ClpA monomers, dimers, tetramers, hexamers, and dodecamers bind 1, 3, 6, 10, and 20 ATP molecules, respectively. Notably, none of the ClpA oligomers are observed to be saturated with ATP. This observation lends support to the previously proposed stochastic or probabilistic model for ATP hydrolysis by ClpA.15

Results

ClpA_E286A/E565A exhibits dynamic assembly in the presence of ATP

We have previously shown that ATPγS binding will drive the formation of ClpA_WT hexamers competent for binding to peptide.20 Although AMPPNP will drive the formation of hexamers, we found that substantially higher concentrations of AMPPNP, compared to ATPγS, were required to do so, indicating weaker binding of AMPPNP. Moreover, AMPPCP, ADP, and ADP‐BeF did not drive the formation of hexamers with polypeptide binding activity. With these results in mind, we initiated a study to examine the ligand‐linked assembly equilibrium using ATPγS and wild‐type ClpA (data not shown). However, due to slow ATPγS hydrolysis these experiments are both irreversible and poorly reproducible. To overcome this problem, we chose to examine the ligand‐linked assembly process using ClpA_E286A/E565A, a Walker B variant that binds but does not hydrolyze ATP. Since this ClpA variant binds but does not hydrolyze ATP, we initiated an examination of the ligand‐linked assembly process using hydrolysable ATP.

We recently examined the self‐assembly mechanism and hydrodynamic properties of ClpA_E286A/E565A in the absence of nucleotide. We observe that in the absence of nucleotide, ClpA_E286A/E565A resides in a distribution of monomers, dimers, tetramers, and hexamers.21 As a next step, here we sought to quantify the ATP‐linked self‐association reaction of ClpA_E286A/E565A using sedimentation velocity experiments.

Initially, sedimentation velocity experiments were performed on 6 μM ClpA_E286A/E565A in the absence of ATP or in the presence of 500 μM or 1 mM ATP in H500 (see Materials and Methods). Figure 1(a) shows a representative set of sedimentation boundaries collected for 6 μM ClpA_E286E/E565A in the presence of 1 mM ATP monitoring fringe displacement as a function of radial position and time. Sedimentation boundaries collected in the absence and presence of ATP were subjected to c(s) analysis in SedFit (Peter Schuck, NIH). An overlay of the resulting c(s) distributions is shown in Figure 1(b).

Figure 1.

c(s) distributions for ClpA_{E286A/ E565A} in the absence and presence of ATP. (a) Sedimentation velocity experiments performed on 6‐μM ClpA_{E286A/ E565A} monitoring fringe displacement as a function of radial position and time. Sets of sedimenting boundaries collected (black, open circles) were subjected to c(s) analysis (red, solid traces) to obtain c(s) distributions. (b) c(s) distributions are shown for 6 μM ClpA_{E286A/ E565A} in the absence of ATP (black) and in the presence of 500 μM (blue) and 1 mM ATP (purple).

In the absence of nucleotide [Fig. 1(b), black], the c(s) distribution of 6 μM ClpA_E286A/E565A is dominated by a single species at s _20,w = (4.1 ± 0.2) S. In our recent examination of the hydrodynamic properties of ClpA Walker B variants, we observe a sedimentation coefficient for s _20,w = (4.3 ± 0.2) S for ClpA_E286A/E565A monomers. Consistent with those findings, Figure 1(b) shows that in the absence of nucleotide, the distribution of 6 μM ClpA_E286A/E565A is largely in the monomeric state.

When ATP is added to 6 μM ClpA_E286A/E565A [Figure 1(b), blue and purple traces], there is a clear shift in the c(s) distribution toward larger sedimentation coefficients. To examine the impact of nucleotide addition on the c(s) distribution of 6 μM ClpA_E286A/E565A, weight average sedimentation coefficients ($\overline{s}$ _20,w) were obtained by integrating the c(s) distributions shown in Figure 1(b) over the entire sedimentation coefficient range shown. In the absence of nucleotide a $\overline{s}$ _20,w ~ 4.5 S is obtained. In contrast, when ATP is present [Fig. 1(b), blue and purple traces], the weight average sedimentation coefficient shifts to $\overline{s}$ _20,w ~ 13.1 S and 14.9 S for 500 μM ATP and 1 mM ATP, respectively. This is a clear indication that ATP binding drives the assembly of ClpA_E286A/E565A toward higher order oligomers.

Further inspection of Figure 1(b) shows that in the presence of ATP, the distributions of 6 μM ClpA_E286A/E565A contain peaks spanning a range of s _20,w ~ 4–22 S. As expected, the peak at ~4.1 S consistent with ClpA monomers decreases when ATP is present, relative to the c(s) distribution obtained in the absence of ATP. In addition, a broad reaction boundary at s _20,w ~ 6–11 S and a peak at ~15 S emerge. The broad reaction boundary spans a sedimentation coefficient range consistent with the previously reported sedimentation coefficients of ClpA_E286A/E565A dimers and tetramers. This likely indicates the presence of a mixture of dimers and tetramers at both ATP concentrations tested. Similarly, the ~15 S peak is consistent with our previously observed sedimentation coefficient of 15.5 S for peptide‐bound ClpA_WT hexamers in the presence of ATPγS.20 These data support previous observations that ATP binding drives the hexamerization of ClpA.

Notably, reaction boundaries spanning the range of s _20,w ~ 4–11 in Figure 1(b) indicate that oligomers smaller than the hexamer persist at thermodynamic equilibrium under conditions where ATP is in large excess over the macromolecule concentration. Thus, quantifying the population of hexamers present at any given nucleotide concentration requires examination of the nucleotide‐linked assembly equilibrium, as previously done for the closely related AAA+ molecular chaperone, ClpB.22

Surprisingly, the hexamer is not the largest oligomer observed in the c(s) distributions determined for ATP‐bound ClpA_E286A/E565A shown in Figure 1(b). In addition to the features described above, there is a peak that emerges at s _20,w ~ 22.5 S. A similar 23 S species has been observed before from absorbance sedimentation velocity experiments performed on ClpA_WT in the presence of ADP.20 Although the authors speculated this to be a ClpA dodecamer, there were not enough constraints in the absorbance sedimentation velocity data and sedimentation equilibrium data collected to model dodecamer formation. In absorbance sedimentation velocity experiments, sedimenting boundaries are collected by scanning across the radial length, which takes minutes. In contrast, in an interference experiment the entire radial length is captured instantaneously by a CCD camera. Thus, it is possible that with greater temporal resolution in the sedimenting boundaries collected here (see Materials and Methods) the data contain enough information to characterize the energetics of dodecamerization.

ClpA_E286A/E565A resides in a monomer‐dimer‐tetramer‐hexamer‐dodecamer equilibrium in the presence of ATP

To investigate the ATP‐linked assembly mechanism of ClpA_E286A/E565A, we first sought to determine the ATP concentration dependence of the formation of each ClpA oligomer in the assembly pathway. To do this, sedimentation velocity experiments were collected for 6 and 10 μM ClpA_E286A/E565A at fixed nucleotide concentrations ranging from approximately 20 μM to 1 mM ATP. The resulting sedimentation boundaries were directly modeled using the time difference curve method (see Materials and Methods). From this analysis, apparent equilibrium constants (L _n,app) were obtained for the formation of each ClpA_E286A/E565A oligomer as a function of ATP. Here L _n,app is defined as Eq. 1,

$$L_{n,\mathrm{app}}=L_{n,0}\frac{P_n}{{\left(P_1\right)}^n},$$ (1)

where L _n,0 represents the equilibrium constant for ClpA n‐mer formation in the absence of nucleotide and P _n represents the partition function for ClpA n‐mer binding ATP. Importantly, the partition function is only a function of free ligand, in this case [ATP]_free. Thus, we devised an experimental strategy to be able to measure [ATP]_free.

Prior to subjecting ClpA_E286A/E565A to sedimentation velocity, protein samples and ATP were equilibrated using equilibrium dialysis. For each reaction, protein and nucleotide samples were placed in separate chambers of an equilibrium dialyzer separated by a membrane permeable to nucleotide but not protein as described (see Materials and Methods). After a 14 h incubation at 25 °C, the protein chamber contains the total concentration of ATP (ATP_total) which is equal to the sum of the concentration of free and ClpA‐bound ATP. Since all chambers are permeable to ATP, the chambers impermeable to protein contain equilibrium concentrations of ATP_free. The contents of each chamber were separated and the [ATP]_free was measured spectroscopically. In addition to allowing us to directly measure the [ATP]_free, this strategy results in a gradual exposure of ClpA to ATP. That is to say, ClpA is exposed to ATP at a rate that is limited by diffusion across the semipermeable membrane. Thus, this strategy represents the best approximation to reversible addition of ATP to the system over a 14 h period.

The protein‐nucleotide sample from the equilibrium dialysis experiment was then subjected to sedimentation velocity. The free ATP concentration, measured from the equilibrium dialysis experiments to be in the range of 17 μM–1.1 mM, remained constant throughout each sedimentation velocity experiment. Time difference curves were subsequently obtained from sedimenting boundaries collected at fixed protein and nucleotide concentrations. These data were subjected to non‐linear least squares (NLLS) analysis using a model that assumes the presence of monomers, dimers, tetramers, hexamers, and dodecamers (1‐2‐4‐6‐12 model) at thermodynamic equilibrium Eqs. 18, 19, 20, 21. Figure 2 shows representative sets of difference curves for 6 and 10 μM ClpA_E286A/E565A in the presence of 62.3 and 68.5 μM ATP_free, respectively, analyzed using the 1‐2‐4‐6‐12 model (Fig. 2, green traces).

Figure 2.

Analysis of representative time‐difference curves fit to a 1‐2‐4‐6‐12 stepwise assembly model. Time curves obtained for (a) 6 μM ClpA_{E286A/ E565A} in the presence of 62.3 μM ATP and (b) 10 μM ClpA_{E286A/ E565A} in the presence of 68.5 μM ATPfree were subjected to analysis using the 1‐2‐4‐6‐12 model. Sedimentation boundaries were collected every 30 s and all boundaries collected in the first 2 h of sedimentation were included in the analysis. Every 10th boundary is shown. The data are shown in black open circles and the fit is shown in green. Fitting residuals randomly distributed about zero, shown underneath each plot, and fitting RMSD of (a) 0.0268 and (b) 0.0186, respectively, indicate the data are well described by the 1‐2‐4‐6‐12 assembly model.

For difference curves collected in the presence of ≥200 μM ATP_free, the measured [ATP]_free was assumed to be approximately equal [ATP]_total. In these cases, difference curves for 6 and 10 μM ClpA_E286A/E565A at one fixed [ATP]_free were globally analyzed using the 1‐2‐4‐6‐12 model. In contrast, sets of time difference curves collected at one fixed protein and free ATP concentrations <200 μM were individually modeled using the 1‐2‐4‐6‐12 model.

Stepwise equilibrium constants, K ₂, K ₄, K ₆, and K ₁₂ were obtained at each concentration of ATP_free, from the analysis of difference curves using the 1‐2‐4‐6‐12 model. These were used to calculate stoichiometric equilibrium constants, L _2,app, L _4,app, L _6,app, and L _12,app using Eqs. 2, 3, 4, 5, where A _n represents a ClpA n‐mer. Table 1 shows average L _n,app and standard deviations from the independent analysis of three experimental replicates.

$$L_{2,\mathrm{app}}=\frac{\left\{A_2\right\}}{{\left\{A_1\right\}}^2}=K_2$$ (2)

$$L_{4,\mathrm{app}}=\frac{\left\{A_4\right\}}{{\left\{A_1\right\}}^4}={K_2}^2{K}_4$$ (3)

$$L_{6,\mathrm{app}}=\frac{\left\{A_6\right\}}{{\left\{A_1\right\}}^6}={K_2}^3{K}_4{K}_6$$ (4)

$$L_{12,\mathrm{app}}=\frac{\left\{A_{12}\right\}}{{\left\{A_1\right\}}^{12}}={K_2}^6{K_4}^2{K_6}^2{K}_{12}$$ (5)

Table 1.

Equilibrium Constants as a Function of [ATP]_free

[ATP] free (μM)	log(L 2,app)	log(L 4,app)	log(L 6,app)	log(L 12,app)
17.0	4.0 ± 0.1	15.1 ± 0.1	23 ± 1	51 ± 1
17.9	4.0 ± 0.4	15.7 ± 0.1	26 ± 0.2	57 ± 3
26.8	4.0 ± 0.1	16.1 ± 0.2	26.3 ± 0.5	57 ± 3
27.0	4.5 ± 0.5	16.1 ± 0.3	27.1 ± 0.3	59.5 ± 0.8
62.3	5.0 ± 0.8	17.2 ± 0.5	28 ± 1	63 ± 2
68.5	4.2 ± 0.4	16.9 ± 0.2	27.7 ± 0.5	61.3 ± 0.8
120.3	4.6 ± 0.5	17.3 ± 0.1	29.1 ± 0.1	63 ± 2
120.3	4.0 ± 0.4	17.3 ± 0.2	29.0 ± 0.3	63.0 ± 0.7
203.2	3.88 ± 0.08	17.7 ± 0.3	29.6 ± 0.5	64.3 ± 0.8
536.2	4.8 ± 0.1	19 ± 0.3	32 ± 0.4	69.2 ± 0.8
1100	5.1 ± 0.5	19 ± 1	32 ± 1	69 ± 2

In sedimentation velocity experiments, dissociation rate constants are measurable if they occur in the range of ~10⁻²–10⁻⁵ s⁻¹.23 The L _n,app values in Table 1 were obtained assuming a dissociation rate constant of 0.01 s⁻¹. This assumes that all oligomers exhibit instantaneous dissociation on the time‐scale of sedimentation. To test whether oligomer dissociation occurs on the timescale of sedimentation, the kinetic rate constants for the dissociation of each oligomer, k _r,n in Eqs. 18, 19, 20, 21 were floated as a fitting parameter in the analysis of difference curves.

Table S1 shows L _n,app and k _r,n values obtained when equilibrium and dissociation rate constants are floated parameters in the analysis of difference curves. The error reported in the table for each parameter is the standard deviation obtained from the independent analysis of three replicates. On average, the reverse rate constants reported in Table S1 fall outside of the measurable range. However, dimers and tetramers appear to be outside of the measureable range in the limit of dissociating very fast. In contrast, hexamers and dodecamers appear to be in the range of dissociating very slowly. In fact, it appears as though dissociation of hexamers and dodecamers may be slowing with increasing [ATP]. Nevertheless, more direct measures of the kinetics of dissociation are needed to draw conclusion about the kinetics of dissociation.

To examine the impact of assuming k _r,n ≥ 0.01 s⁻¹ on L _n,app, the apparent equilibrium constants reported in Tables 1 and S1 are plotted as a function of [ATP]_free in Figure S1. Figure S1 shows that the L _n,app reported in Tables 1 and S1 are within error. This observation suggests that there is no additional information obtained about the energetics of assembly by floating k _r,n terms as fitting parameters. Thus all k _r,n were constrained to 0.01 s⁻¹ in the analysis of difference curves.

Model‐independent determination of the ClpA_E286A/E565A ATP‐binding density

The ATP‐binding stoichiometry of each ClpA_E286A/E565A oligomer was determined by model‐independent Wyman analysis.24 This strategy has been previously employed by us to determine the ATPγS binding density of ClpB oligomers.22 As shown previously, Eq. 6 is obtained by first taking the log of Eq. 1 and subsequently taking the first derivative of the resulting expression with respect to the log([ATP]_free).

$$\frac{\partial \log \left(L_{n,\mathrm{app}}\right)}{\partial \log \left({\left[\mathrm{ATP}\right]}_{\text{free}}\right)}={\overline{X}}_n-n{\overline{X}}_1$$ (6)

$\overline{X}$ _n represents the extent of binding to the n‐mer. Extent of binding is defined as the ratio of the concentration of ligand bound to the concentration of total macromolecule.25 In this analysis, $\overline{X}$ _n is the extent of binding to a ClpA_E286A/E565A oligomer ([ATP]_bound/[A_n]_total) and $\overline{X}$ ₁ represents the extent of binding to ClpA_E286A/E565A monomer ([ATP]_bound/[A₁]_total). The difference expressed in Eq. 6 is equal to the slope of a plot of log(L _n,app) as a function of the log([ATP]_free), known as a Wyman plot.24

Four Wyman plots were constructed using the L _n,app values shown in Table 1. Figure 3(a–d) shows the linear region of each plot fit to a line. The slopes obtained from the linear regression analysis can be expressed as the system of linear equations shown in Eqs. 7, 8, 9, 10.

$${\overline{X}}_2-2{\overline{X}}_1=1.2\pm 0.1$$ (7)

$${\overline{X}}_4-4{\overline{X}}_1=2.4\pm 0.3$$ (8)

$${\overline{X}}_6-6{\overline{X}}_1=4.7\pm 0.4$$ (9)

$${\overline{X}}_{12}-12{\overline{X}}_1=9\pm 1$$ (10)

Figure 3.

Wyman plots of log(L _n,app) as a function of log[ATP]free. The linear region of each plot of log of (a) L _2,app, (b) L _4,app, (c) L _6,app, and (d) L _12,app as a function of log[ATP]free. The data in each plot were individually fit to a linear regression (red) resulting in slopes reported in Eqs. 7, 8, 9, 10.

Equations (7–10) represent a system of four linear equations with five unknowns. The simplest way to solve this system of equations is to make assumptions about the monomer extent of binding and solve for the others. The reason for making assumptions about the extent of binding for the monomer is that each ClpA monomer contains two nucleotide binding sites. Consequently, there are only three possibilities for the stoichiometry of ATP binding the monomer: zero, one, or two. By constraining $\overline{X}$ ₁ equal to either zero, one, or two, we can easily solve Eqs. 7, 8, 9, 10 to determine the extent of binding to dimers, tetramers, hexamers, and dodecamers.

Table 2 shows the extent of binding to each oligomer obtained assuming a monomer extent of binding of zero, one, or two. Each ClpA oligomer contains 2n nucleotide binding sites. In the case of $\overline{X}$ ₁ = 2, the extent of binding predicted for each oligomer is greater than the number of nucleotide binding sites present in each oligomer. From this analysis, we can rule out a monomer extent of binding of two. In contrast, assuming a monomer extent of binding equal to either zero or one results in extent of binding values for all other oligomers that are less than the number of nucleotide binding sites present in each oligomer. With this in mind, we devised a sedimentation velocity experiment to determine whether monomers bind ATP.

Table 2.

Extent of ATP Binding to Each ClpA Oligomer Predicted from Wyman Analysis

	${\overline{X}}_1=0$	${\overline{X}}_1=1$	${\overline{X}}_1=2$
${\overline{X}}_2$	1.2	3.2	5.2
${\overline{X}}_4$	2.4	6.4	10.4
${\overline{X}}_6$	4.7	10.7	16.7
${\overline{X}}_{12}$	9	21	33

ClpA_E286A/E565A monomers bind ATP

To determine whether ClpA monomers bind nucleotide, sedimentation velocity experiments were performed on ClpA_E286A/E565A in the presence of 2,4,6‐trinitrophenol adenosine triphosphate (TNP‐ATP). TNP‐ATP is a fluorescent nucleotide analog of ATP. Here TNP‐ATP was used as a chromophore that absorbs in the visible wavelengths. Consequently, we can detect TNP‐ATP absorbance at 408 nm where the absorbance is insensitive to the absorbance of the protein. Any peaks present in the resulting c(s) distributions only reflect TNP‐ATP bound species.

Figure 4 shows the c(s) distributions from 6 μM ClpA_E286A/E565A in the presence of 30 μM TNP‐ATP (pink). For comparison, the distribution from 6 μM ClpA_E286A/E565A in the absence of nucleotide (Fig. 1, black) is also shown in Figure 4. In the presence of TNP‐ATP, Figure 4 (pink) shows a distribution at ~4 S. This ~4 S peak overlays well with the monomer population that dominates the distribution in the absence of nucleotide (Figs. 1 and 4, black trace). Since the signal collected in the presence of TNP‐ATP is only sensitive to absorbance from TNP‐ATP, we conclude that ATP must bind monomers. Populations at ~7.5 S and ~14.6 S are also present when TNP‐ATP is added, consistent with higher order ClpA oligomers, as expected. Importantly, these additional peaks indicate that TNP‐ATP drives assembly of ClpA_E286A/E565A into higher order oligomers, analogous to ATP.

Figure 4.

c(s) distributions of 6 μM ClpA_{E286A/ E565A} in the absence and presence of TNP‐ATP. Sedimentation velocity experiments were collected for 6 μM ClpA_{E286A/ E565A} in the absence of ATP monitoring interference (black) and in the presence of TNP‐ATP monitoring absorbance at 408 nm (pink). Because protein does not absorb in the visible region of the UV–vis spectrum, peaks present in the distribution collected monitoring absorbance at 408 nm represent TNP‐ATP bound ClpA_{E286A/ E565A} species.

The results shown in Figure 4 allow us to rule out a monomer extent of binding equal to zero. A monomer extent of binding of two has also been ruled out from the model‐independent analysis discussed above. From data shown in Figure 4 and the results from the Wyman analysis, we conclude a monomer extent of binding equal to one. From Table 2, we obtain extent of binding values of ~3, ~6, ~10, and ~21 for ATP binding to dimers, tetramers, hexamers, and dodecamers, respectively. With estimates for the stoichiometry of ATP binding to each oligomer in hand, we next sought to determine the average affinity of ATP binding to monomers, dimers, tetramers, hexamers, and dodecamers.

NLLS analysis of L _n,app as a function of [ATP]_free

In order to determine the ATP‐binding affinity to each oligomer, binding isotherms were constructed by plotting log(L _n,app) as a function of ATP_free. Figure 5 shows the binding isotherms for L _2,app, L _4,app, L _6,app, and L _12,app on [ATP]_free. In order to model the binding isotherms globally, we need a partition function that describes ATP binding to the monomer, dimer, tetramer, hexamer, and dodecamer, respectively [Eq. 1].

Figure 5.

Global analysis of L _n,app‐binding isotherms. (a) Log(L _2,app), (b) log(L _4,app), (c) log(L _6,app), and (d) log(L _12,app) as a function of [ATP]free were subjected to global NLLS analysis using Eqs. 13, 14, 15, 16. The black closed circles represent the data presented in Table 1. The solid red lines represent the result from NLLS analysis obtained by constraining m ₁ = 1 and m ₂ = 3. The best‐fit values obtained for m ₄, m ₆, m ₁₂, κ ₁, κ ₂, κ ₄, κ ₆, and κ ₁₂ are summarized in Table 3.

The simplest way to model ATP binding to each oligomer is with a n‐independent and identical sites model. This model assumes that ATP binding to each site within an oligomer is independent of the other sites and can be described by the same ATP‐binding constant. Equation 11 describes the general form of the partition function for a ClpA n‐mer binding ATP, assuming n‐independent, identical sites.

$$P_n={\left(1+{\kappa }_n{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_n}$$ (11)

In Eq. 11, κ _n describes the average stepwise equilibrium constant for ATP binding a ClpA n‐mer and m _n represents its ATP‐binding stoichiometry. Following substitution of Eq. 11 into Eq. 1, we arrive at a general model for L _n,app shown in Eq. 12.

$$L_{n,\mathrm{app}}=L_{n,0}\frac{{\left(1+{\kappa }_n{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_n}}{{\left({\left(1+{\kappa }_1{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_1}\right)}^n}.$$ (12)

The binding isotherms shown in Figure 5 were subjected to global NLLS analysis using the logarithmic form of Eq. (12) for each L _n,app, shown in Eqs. 13, 14, 15, 16.

$$\log \left(L_{2,\mathrm{app}}\right)=\log \left(L_{2,0}\right)+\log {\left(1+{\kappa }_2{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_2}-2\log {\left(1+{\kappa }_1{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_1}$$ (13)

$$\log \left(L_{4,\mathrm{app}}\right)=\log \left(L_{4,0}\right)+\log {\left(1+{\kappa }_4{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_4}-4\log {\left(1+{\kappa }_1{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_1}$$ (14)

$$\log \left(L_{6,\mathrm{app}}\right)=\log \left(L_{6,0}\right)+\log {\left(1+{\kappa }_6{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_6}-6\log {\left(1+{\kappa }_1{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_1}$$ (15)

$$\log \left(L_{12,\mathrm{app}}\right)=\log \left(L_{12,0}\right)+\log {\left(1+{\kappa }_{12}{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_{12}}-12\log {\left(1+{\kappa }_1{\left[\mathrm{ATP}\right]}_{\text{free}}\right)}^{m_1}$$ (16)

The L _n,0 terms were constrained in the NLLS analysis of L _n,app ATP‐binding isotherms. The self‐association equilibrium constants, L _2,0, L _4,0, and L _6,0 were recently determined for ClpA_E286A/E565A in the absence of nucleotide.21 In the absence of nucleotide, we do not observe ClpA_E286A/E565A dodecamers and therefore could not experimentally measure L _12,0. Instead, we calculated an upper limit of L_12,0 ≤ 1 × 10⁵⁰  M ⁻¹¹. We obtained this limit by generating species fractions for the formation of each ClpA oligomer using the experimentally determined L _2,0, L _4,0, and L _6,0 while constraining L _12,0 to finite values. A L _12,0 = 1 × 10⁵⁰ M ⁻¹¹ was determined to be the largest value for which a dodecamer would not be populated at 20 μM ClpA_E286A/E565A, the highest concentration used to determine the energetic parameters for the self‐association in the absence of nucleotide. Thus a value of L _12,0 = 1 × 10⁵⁰ M ⁻¹¹ was constrained in the global analysis of L _n,app‐binding isotherms (Fig. 5).

The binding stoichiometry terms (m ₂, m ₄, m ₆, and m ₁₂) and average ATP‐binding constants (κ ₁, κ ₂, κ ₄, κ ₆, and κ ₁₂) were floated as fitting parameters in this analysis. Note that m ₁ and κ ₁ are global parameters, while m ₂, m ₄, m ₆, m _12, κ ₂, κ ₄, κ ₆, and κ ₁₂ are local parameters in the analysis. Given that, we conclude a binding stoichiometry of 1 for the monomer from the results discussed above (Table 2, Fig. 4), m ₁ was constrained to 1 in the NLLS analysis of the binding isotherms. When all other m _n and κ _n are floated parameters, the data are well described by the fit (Fig. 5, red traces). The parameters obtained from NLLS analysis are summarized in Table 3.

Table 3.

Results from NLLS Analysis of L _n,app‐binding Isotherms

Floating parameters	m 1 constrained	m 1 and m 2 constrained
m 1	1*	1*
m 2	5 ± 1106	3*
m 4	5.3 ± 0.4	5.7 ± 0.3
m 6	9.1 ± 0.6	9.6 ± 0.5
m 12	20 ± 1	21 ± 1
k 1 (M −1)	(2.5 ± 0.9) × 103	(4 ± 2) × 103
k 2 (M −1)	(5 ± 3) × 103	(2.0 ± 0.6) × 103
k 4 (M −1)	(1.2 ± 0.1) × 105	(1.3 ± 0.2) × 105
k 6 (M −1)	(8 ± 1) × 104	(1.1 ± 0.2) × 105
k 12 (M −1)	(8 ± 1) × 104	(9 ± 2) × 104

The error on each fitted parameter in the analysis was determined from the standard deviation of Monte Carlos simulations (1000 iterations). From this analysis we find that m ₄, m ₆, m ₁₂, κ ₂, κ ₄, κ ₆, and κ ₁₂ are well constrained (Table 3). However, we also find the binding stoichiometry of the dimer to be unconstrained. This is not surprising given that the L _2,app does not have a clear ATP dependence for ATP_free concentrations <200 μM (see Fig. 5 and Table 2). That is likely due to the low population of dimers present at low ATP concentrations.

With this in mind, the data were modeled again, constraining m ₂ = 3, the stoichiometry for ATP binding the dimer obtained from Wyman analysis (see Table 2). The resulting fitting parameters for m ₄, m ₆, m ₁₂, κ ₂, κ ₄, κ ₆, and κ ₁₂ (Table 3) are within error of that obtained when m ₂ is floated in the analysis, as expected given that m ₂ is not a well‐constrained parameter in the analysis. Comparing the resulting stoichiometries, the NLLS analysis done with m ₂ constrained results in stoichiometries for ATP‐binding dimers, tetramers, and hexamers that agree with the values obtained from the Wyman analysis (compare Tables 2 and 3) as expected.

The next level of complexity for modeling the L _n,app‐binding isotherms would be to incorporate cooperativity between the binding sites. A hallmark of cooperative binding is a sigmoidal dependence on ligand concentration and steep binding isotherms that span fewer than two log units. As shown in Figure 5, this analysis does not result in steep binding isotherms that would indicate the ATP‐binding sites are cooperative. Therefore, there is no justification in the data to warrant incorporating this complexity into the model. From this we conclude that the simplest model of n‐independent, identical sites is sufficient to describe the data.

Discussion

ATP binding has been shown to drive the formation of ClpA hexamers competent for binding to ClpP and polypeptide substrates for ATP‐driven substrate unfolding and degradation.8, 17, 26 Thus, quantifying the hexamer population and the affinity of ATP binding to ClpA hexamers is an important aspect of determining the molecular basis for ClpA‐catalyzed substrate unfolding and translocation in the absence and presence of ClpP. With this in mind, we examined the ATP‐linked assembly mechanism of an ATP hydrolysis inactive ClpA variant in the presence of hydrolysable ATP.

The self‐association of ClpA_WT has been previously examined in the presence of the slowly hydrolysable ATP analogue, ATPγS.8 Maurizi and coworkers observed a single ClpA oligomer, modeled as a hexamer, from the analysis of absorbance sedimentation velocity boundaries collected for ClpA in the presence of saturating [ATPγS] at 4 °C. In contrast to this, we observed a distribution of ClpA oligomers from similarly low resolution absorbance sedimentation velocity experiments performed on ClpA in the presence of 1 mM ATPγS at 25 °C.11, 20 Here, using sedimentation velocity experiments with higher temporal resolution, we similarly observed and quantified the distribution of ClpA oligomers at thermodynamic equilibrium, present even in the presence of excess nucleotide.

In this study, obtaining interreference sedimentation velocity data on an ATPase inactive ClpA variant allowed us to model the in solution distributions of ClpA oligomers for a range of ATP concentrations. Our results indicate that in the presence of ATP, ClpA resides in a dynamic equilibrium of monomers, dimers, tetramers, hexamers, and dodecamers. The populations of each oligomer depend on both the free nucleotide concentration and the protein concentration, as predicted from Eq. 1. Further, we observe that the apparent equilibrium constant for oligomer formation exhibits a dependence on [ATP]_free (Fig. 5). These observations indicate that a different concentration of hexamers will be present at various concentrations of ATP. In addition to quantifying apparent equilibrium constants for ClpA oligomerization, the binding isotherms constructed as a function of [ATP]_free provide insight about ATP binding to each oligomer present at thermodynamic equilibrium. Here, for the first time, we report an average apparent ATP‐binding affinity and stoichiometry for each ClpA oligomer.

Our findings have important implications for the interpretation of ClpA steady‐state ATPase assays. In a steady‐state ATPase assay the initial velocity would be determined at several fixed total ATP concentrations. The initial velocity would be plotted as a function of ATP concentration and the V _max determined. The V _max would subsequently be divided by the total enzyme concentration to determine k _cat. In the case of ClpA, if one divides the V _max by the total monomer concentration of ClpA, then this assumes that all ATPase sites hydrolyze ATP with the same rate constant regardless of whether they reside in a monomer, dimer, tetramer, hexamer, or dodecamer. This may or may not be a reasonable assumption. The alternative is to divide the total monomer concentration by six and use this concentration to divide V _max. However, this assumes that all of the monomers reside in the hexameric state, which is clearly not the case. In fact, our results indicate that there will be a different distribution of oligomers at each ATP concentration assayed. This too will not be an issue if all of the ATPase sites hydrolyze ATP with the same rate constant regardless of what oligomer they reside within. However, it seems unlikely that this would be the case. Moreover, our stoichiometry measurements indicate that monomers only bind one ATP so there is a subset of ATPase sites that do not hydrolyze at all.

Together, the self‐association constants, as well as the stoichiometry and apparent affinity of ATP for each oligomer reported here allow one to determine the concentration of active ClpA hexamer present at any concentration of protein and ATP. This predictive power is essential to the interpretation of functional assays designed to characterize ClpA‐catalyzed polypeptide substrate unfolding. For example, in previous work from Baytshtok and coworkers, a cleverly designed FRET assay was used to characterize the substrate unfolding kinetics of ClpA using 1.2 μM ClpA (monomer concentration units) in the presence of 5 mM ATP.16 Equally important, steady‐state ATPase experiments are performed under the same conditions. In this work, 100% of the ClpA population is assumed to reside in the hexameric state, and accordingly the hexamer concentration is reported to be 0.2 μM. Yet, under these conditions, our model predicts that ClpA would reside in a distribution of oligomers consisting of 8% monomers, 5% tetramers, 36% hexamers, and 51% dodecamers.

Various groups have observed differences in substrate unfolding and/or translocation rate by ClpA in the absence versus the presence of ClpP.16, 18, 26 These differences have been proposed to result from changes to the ATP hydrolysis rate of each ClpA NBD when ClpP is bound. Given that ClpA resides in an oligomeric distribution in the absence of ClpP as shown here, we hypothesize an alternative, and not mutually exclusive explanation for these observed differences: ClpP binding tunes the ATP‐binding affinity of ClpA hexamers. As shown in Eq. 12, the apparent equilibrium constant for the formation of each ClpA n‐mer (L _n,app) is proportional to the average stepwise equilibrium constant for ATP binding that n‐mer. It is possible that ClpP binding to ClpA hexamers structurally alters the ATP‐binding pocket in a way that would perturb the ATP‐binding affinity to the hexamer and thereby shift the ClpA assembly state. Thus in principle, it is possible that ClpP binding can affect ClpA substrate translocation activity via a combination of modulating both its NTPase activity as well as perturbing its assembly state. Future experiments will be needed to deconvolute these ClpP‐induced effects.

Materials and Methods

Buffers and reagents

All buffers used in the experiments described were prepared using reagent grade materials and ultrapure water obtained from a Purelab Ultra System (Evoqua Water Technologies). The ATP used was purchased from Sigma‐Aldrich. All experiments with purified protein were carried out in buffer H500 containing 25 mM HEPES, pH 7.5 at 25 °C, 10 mM MgCl₂, 2 mM 2‐mercaptoethanol, 500 mM NaCl, and 10% (v/v) glycerol.

Protein isolation

ClpA_E286A/E565A was overexpressed in E. coli ΔClpA_WT‐BL21(DE3) cells as previously described.21 After overexpression, the protein was isolated following the same isolation protocol as that used to isolate ClpA_WT, previously described.11 Purified stocks of ClpA_E286A/E565A were stored in 25 mM Tris base (pH 7.5 at 4 °C), 100 μM EDTA, 2 mM 2‐mercaptoethanol, 1M NaCl, and 50% (v/v) glycerol for long term storage at −80 °C. Prior to performing experiments, protein samples were dialyzed against buffer H500 at 4 °C. After dialysis, protein concentration was determined spectroscopically using a monomer molar extinction coefficient of 31,000 M ⁻¹ cm⁻¹ at 280 nm. All concentrations are reported in monomer units.

Equilibrium dialysis

Equilibrium dialysis experiments were conducted to gradually equilibrate ClpA_E286A/E565A samples with ATP. The experiments were carried out using a 3‐chamber microequilibrium dialyzer system purchased from The Nest Group. In the 3‐chamber system, a central chamber is separated from two adjacent chambers by a dialysis membrane. The central chamber was loaded with 500 μL of the protein solution and separated from the other two chambers with a 25 kDa molecular weight cut off (MWCO) cellulose membrane. Both external chambers were supplemented with 500 μL aliquots of an ATP solution. In this experimental design, the central chamber containing ClpA_E286A/E565A was permeable to the exchange of ATP. On the other hand, ClpA_E286A/E565A, with a molecular weight of ~84,100 g/mol per protomer, was kept within the central chamber by the 25 kDa MWCO dialysis membrane.

After protein and ATP solutions were placed in equilibrium dialyzers, the system was left to equilibrate at 25 °C with gentle shaking at 50 rpm in a benchtop incubator. After a 14‐h incubation, the samples were removed from each chamber. The solutions taken from each external chamber of a given equilibrium dialyzer were combined and its ATP concentration was determined spectroscopically. This was taken to be the concentration of ATP_free for a given experiment. Similarly, a spectroscopic measurement of the protein‐ATP solution recovered from the central chamber was used to determine the concentration of ATP_total (ATP_free + ATP_ClpA‐bound). The central chamber solutions containing ATP and protein were loaded into the sample sector of a dual sector analytical ultracentrifugation cell assembly. The matched ATP_free solution for a given sample solution was loaded into the reference sector.

Sedimentation velocity experiments

Interference sedimentation velocity experiments were collected for 6 or 10 μM ClpA_E286A/E565A in the presence of various ATP_free concentrations. Importantly, each sedimentation velocity experiment was carried out on one fixed protein and nucleotide concentration. Experiments were collected in a ProteomeLab XL‐I analytical ultracentrifuge (Beckman Coulter, Brea, CA). Protein and reference solutions were loaded into each respective sector of a dual channel, Epon charcoal filled centerpiece. Approximately 390 μL of either protein or reference solution was loaded into each sector. Interference boundaries were collected every 30 s at an angular velocity of 40,000 rpm for the duration of sedimentation as previously described.22

Absorbance sedimentation velocity experiments were collected for 6 μM ClpA_E286A/E565A in the presence of 30 μM TNP‐ATP. Boundaries were collected monitoring absorbance at 408 nm as a function of radial position and time. Samples were subjected to an angular velocity of 40,000 rpm and absorbance boundaries were collected every 4 min.

Time corrected sedimentation velocity was subjected to c(s) analysis in SedFit (Peter Schuck, NIH) or difference curve analysis SedAnal, as previously described.21, 27, 28, 29 Sedimentation coefficient values expressed in terms of s _20,w reflect standard conditions of infinite dilution in water at 20 °C as defined in Eq. 17,

$$s_{20,w}=\frac{\left(1-{\rho }_{20,w}\overline{v}\right)}{\left(1-\rho \overline{v}\right)}\cdot \frac{\eta }{{\eta }_{20,w}}\cdot s$$ (17)

where ρ indicates the solution density, η the solution viscosity, and $\overline{v}$ the partial specific volume of the protein. The partial specific volume of ClpA_E286A/E565A was determined from its primary protein sequence to be 0.7405 mL g⁻¹ using Sednterp (David Hayes, Magdalen College, Tom Laue, University of New Hampshire, and John Philo, Alliance Protein Laboratories).30 A correction of 0.00033 mL g⁻¹ was subsequently added to account for the presence of 10% (v/v) glycerol included in the experimental buffer (H500).12, 20 From Eq. 17, a correction factor of 1.501 is obtained to calculate s _20,w from uncorrected sedimentation coefficient values.

Analysis of sedimentation velocity time difference curves

Sets of time difference curves collected at fixed protein and ATP concentrations were modeled in SedAnal. Protein self‐association was modeled using the monomer‐dimer‐tetramer‐hexamer‐dodecamer stepwise assembly model (1‐2‐4‐6‐12 model) shown in Eqs. 18, 19, 20, 21,

$$2\left\{{\text{ClpA}}_1\right\}\underset{k_{r2}}{\overset{k_{f2}}{\leftrightarrows }}\left\{{\text{ClpA}}_2\right\},$$ (18)

$$2\left\{{\text{ClpA}}_2\right\}\underset{k_{r4}}{\overset{k_{f4}}{\leftrightarrows }}\left\{{\text{ClpA}}_4\right\},$$ (19)

$$\left\{{\text{ClpA}}_2\right\}+\left\{{\text{ClpA}}_4\right\}\underset{k_{r6}}{\overset{k_{f6}}{\leftrightarrows }}\left\{{\text{ClpA}}_6\right\},$$ (20)

$$2\left\{{\text{ClpA}}_6\right\}\underset{k_{r12}}{\overset{k_{f12}}{\leftrightarrows }}\left\{{\text{ClpA}}_{12}\right\},$$ (21)

where {ClpA_n} represents all ATP ligation states of a ClpA n‐mer, while k _f,n and k _r,n represent the forward and reverse rate constant for n‐mer formation, respectively. The forward and reverse rate constants are related to the stepwise equilibrium constant (K _n) as shown in Eq. 22. Difference curves were analyzed by floating either both K _n and k _r,n or by floating K _n while constraining k _r,n

$$K_n=\frac{k_{f,n}}{k_{r,n}}.$$ (22)

Sedimentation coefficients were constrained in the analysis of difference curves. Sedimentation coefficient values were previously obtained for the monomer (2.8 S), dimer (4.4 S), tetramer (7.1 S), and hexamer (9.4 S) using the HullRad algorithm as previously described.21, 31 The sedimentation coefficient for the dodecamer was approximated to be 14.4 S (s _20,w = 21.6 S) using Eq. 23 as previously described.32 Note that this prediction is in agreement with the ~22 S population observed in c(s) distributions obtained for 6 μM ClpA_E286A/E565A in the presence of ATP (Fig. 1, blue and purple traces). Importantly, the sedimentation coefficients constrained in the analysis of difference curve were not standardized to s _20,w values.

$$s_n=s_1\left(n^{2/3}\right)$$ (23)

Supporting information

Table S1 Assembly equilibrium and reverse rate constants as a function of [ATP]_free

Figure S1. Comparison of L _n,app‐binding isotherms collected by constraining k _r,n and floating k _r,n in the analysis of time difference curves. Binding isotherms constructed from equilibrium constants listed in Table 1 as a function of ATP_free are shown as black closed circles. These were obtained by constraining oligomer dissociation rate constants (k _r,n) in the analysis of difference curves. For comparison, L _n,app values obtained by floating the equilibrium constants and the reverse rate constants in the analysis of difference curves are also shown (blue, open circles). The apparent equilibrium constants obtained from each fitting strategy are within error of one another.