Breaking the covalent connection: Chain connectivity and the catalytic reaction of PMM/PGM

Abstract

Fragment complementation has been used to investigate the role of chain connectivity in the catalytic reaction of phosphomannomutase/phosphoglucomutase (PMM/PGM) from Pseudomonas aeruginosa, a human pathogen. A heterodimer of PMM/PGM, created from fragments corresponding to its first three and fourth domains, was constructed and enzyme activity reconstituted. NMR spectra demonstrate that the fragment corresponding to the fourth (C-terminal) domain exists as a highly structured, independent folding domain, consistent with its varied conformation observed in enzyme–substrate complexes. Steady-state kinetics and thermodynamics studies reported here show that complete conformational freedom of Domain 4, because of the break in the polypeptide chain, is deleterious to catalytic efficiency primarily as a consequence of increased entropy. This extends observations from studies of the intact enzyme, which showed that the degree of flexibility of a hinge region is controlled by the precise sequence of amino acids optimized through evolutionary constraints. This work also sheds light on the functional advantage gained by combining separate folding domains into a single polypeptide chain.

Introduction

Fragment complementation, also called protein reconstitution, has been widely used in investigations of protein structure–function relationships.^1–4 In many systems, fragmentation of the native, covalently linked polypeptide backbone into multiple pieces permits the reassembly of native-like structure and function. These studies, and related ones like circular permutation, have led to new insights into the relationships between chain connectivity and protein structure. Fragment complementation has also been used to study domain organization and assembly,⁵ protein folding,⁴ protein evolution,⁶ and to better understand the factors that govern the native states of proteins.⁷ Fragment complementation has also gained widespread use in the visualization of protein–protein interactions in cells.⁸

We describe herein the use of fragment complementation to investigate a specific aspect of catalysis: the effect of conformational freedom on catalytic efficiency. Previously, we have established the importance of conformational change and flexibility of the polypeptide backbone in the reaction of the enzyme phosphomannomutase (PMM)/phosphoglucomutase (PGM) from Pseudomonas aeruginosa.^9–12 PMM/PGM catalyzes the reversible, intramolecular transfer of a phosphoryl group from the 1- to the 6-position of its phosphosugar substrates and participates in the early steps of several biosynthetic pathways of this organism.^13,14 Crystallographic studies of PMM/PGM–substrate complexes revealed that the protein changes conformation relative to the apoenzyme, with Domain 4 rotating by ∼10° to enclose bound ligand in the active site.⁹ A recent study by our laboratory showed that site-directed mutants of PMM/PGM designed to increase the flexibility of a hinge region of the protein, distant from the active site, exhibit decreased catalytic efficiency.¹² Thermodynamic analyses revealed that this was primarily due to entropic effects, consistent with greater conformational freedom due to increased flexibility of the polypeptide backbone. This work prompted the question: what would be the effect of introducing a covalent break in the polypeptide backbone (i.e., complete conformational freedom) on the kinetic and thermodynamic parameters of the enzyme?

Here, we report construction of a heterodimeric version of P. aeruginosa PMM/PGM, created from two fragments that correspond to the first three domains of the enzyme and the fourth, C-terminal domain. Using this approach, we have successfully produced homogeneous preparations of the two fragments, reconstituted enzyme activity, and determined the thermodynamic parameters of activation for the reaction. We also show that the Domain 4 fragment constitutes a highly structured, independent folding unit. Characterization of reconstituted, heterodimeric PMM/PGM allows us to assess the importance of chain connectivity in catalysis, in a system where protein flexibility and conformational change are important for function.

Results and Discussion

Fragment design and production

Wild-type PMM/PGM is a 463-residue protein that has been well characterized structurally and kinetically.^{9–12,15–19} The intact protein has four structural domains (Fig. 1),¹¹ is highly soluble (>2 mM), and stable to proteolysis (Beamer, unpublished). Key residues for activity, including the catalytic phosphoserine residue and the metal-binding loop reside within the first three domains of the protein. Domain 4, in contrast, contains no residues directly involved in catalysis, although several residues make direct interactions with bound ligands in the enzyme–substrate complexes.⁹ Upon ligand binding, Domain 4 rotates by ∼10° via conformational changes in a hinge region (residues 367–369), enclosing substrate in the active site and correctly positioning it for catalysis. Because the hinge region of PMM/PGM coincides with both a site of conformational change and a domain–domain junction, it was conceptually simple to envision creation of a heterodimeric enzyme via a break in the polypeptide chain at this location.

Figure 1.

(A) A tube diagram of intact PMM/PGM (1P5D) showing the four structural domains of the protein in different colors (green—Domain 1, yellow—Domain 2, red—Domain 3, and blue—Domain 4) and bound substrate (G1P) in a space filling model. The site of fragmentation at the juncture of Domains 3 and 4 is indicated by arrow and blue rectangle; the width of the tube corresponds to the conformational differences between apoenzyme and enzyme–substrate complex. (B) Space filling representation of intact PMM/PGM, shown in two relative orientations at 0° and 90°, highlighting the interface between Domain 4 (white carbons) and the rest of the protein (yellow carbons).

Two fragments of PMM/PGM corresponding to the first three structural domains (d1–3) of PMM/PGM and its 95-residue C-terminal domain (d4), respectively, were produced and purified as described in Materials and Methods. Both fragments were highly expressed, and SDS-PAGE of Ni²⁺ affinity purified proteins (data not shown) revealed a primary band of the expected MW (41.8 kDa for d1–3 and 12.8 kDa for d4) at >95% purity. The d4 fragment was well behaved during purification (Fig. 2) and highly soluble (>50 mg/mL). Isotopically labeled samples of d4 were prepared to further assess sample quality via NMR (see below).

Figure 2.

Chromatograms of PMM/PGM and the d1–3 and d4 fragments on a Superdex200HR analytical size exclusion column. Column buffer was 200 mM NaCl, 10 mM MOPS, pH 7.4, and 0.5 mM DTT. (A) Top: The d1–3 fragment after preparative ultracentrifugation, showing remaining high-molecular-weight peaks (*) as well as a peak (**) corresponding to the d1–3 monomer based on calibration with column standards; Bottom: rerun of peak (**) above on size exclusion column. (B) A comparison of intact (full-length) PMM/PGM, d1–3, and d4 elution profiles. The retention times on x-axis in both panels represent direct conversion from elution volume based on an elution flow rate of 1 mL/min. Also, for data in Panel A the sample was injected at 3.44 min compared with 0 min in Panel B. (C) CD spectra of the d1–3 fragment (solid black line) and intact PMM/PGM (triangles), indicating very similar secondary structure content. Protein concentrations were 1.25 M (intact) and 2.1 M (d1–3).

In the case of the d1–3 fragment, however, protein precipitation was observed during initial attempts at sample concentration, prompting additional investigation of its homogeneity. Size exclusion chromatography showed that a significant fraction of the d1–3 fragment (after Ni²⁺ affinity purification) was present as aggregates of high molecular weight [Fig. 2(A), top chromatogram]. To prepare a homogeneous sample for fragment complementation studies, preparative ultracentrifugation was followed by size exclusion chromatography to remove the aggregates. This combined approach was successful, resulting in a single peak of the correct molecular weight that remained homogeneous in size, as assessed by a second run on the size exclusion column [Fig. 2(A), bottom chromatogram]. Ultracentrifugation and size exclusion chromatography were incorporated into the purification protocol for this fragment to remove protein that had self-associated. The resulting monomeric d1–3 fragment was used for the complementation studies below. Efforts to isolate a complex of d1–3/d4 by mixing of the fragments before size exclusion chromatography were not successful (data not shown).

Structural integrity of the fragments

To assess the folded structure of the fragments, ²H/¹⁵N-labeled samples were prepared for NMR studies. Limited solubility and excessive line broadening compromised NMR spectra of the d1–3 fragment (data not shown). The propensity of the d1–3 fragment for aggregation and its limited solubility suggests that this construct could have exposed hydrophobic patches on its surface and/or be partially unfolded when present in isolation in solution. These possibilities are consistent with the line broadening observed in ¹⁵N TROSY and HSQC peaks in the NMR spectra, which could result either from self-association and/or dynamic equilibria between states. Nonetheless, a circular dichroism spectrum of the d1–3 fragment shows that its secondary structure content is remarkably similar to that of the intact enzyme [Fig. 2(C)]. Moreover, upon mixing d1–3 with d4, enzyme activity was successfully reconstituted, with a 1:1 molar ratio of fragments producing maximal activity (see following sections).

The ²H/¹⁵N-labeled sample of d4 proved to be highly amenable for NMR characterization. A (¹H,¹⁵N) HSQC spectrum is shown in Figure 3, demonstrating excellent dispersion of the peaks that are sharp, without obvious line broadening from conformational exchange. These are all hallmarks of a monodisperse sample with well-ordered tertiary structure and a predominant low energy conformation.

Figure 3.

HSQC spectrum (800 MHz) of the uniformly ²H/¹⁵N-labeled d4 fragment. The sample was at ∼1.1 mM in 10 mM MOPS, pH 7.3, and 5% D₂O and at 298 K.

The ability of the d4 fragment of PMM/PGM to exist as an independent and highly structured domain in the absence of the remainder of the protein is a novel result from this study. This observation is consistent with the movement of d4 upon ligand binding, seen in our structural studies.⁹ Relative to the first three domains of PMM/PGM, which have extensive domain–domain interfaces with each other [Fig. 1(B)], Domain 4 stands out for its limited interface with the rest of the enzyme: only 11% of its total surface area is involved in interactions with Domain 3 in the apoenzyme structure.¹¹ Domain 4 is also structurally distinct within PMM/PGM: Domains 1–3 of the protein share a common mixed 〈/® core fold, whereas Domain 4 is structurally unrelated and is a member of the TATA-box–binding protein-like fold family.¹¹ The fact that d4 is an independent folded domain in solution lends support to the idea that this structural unit was fused to an ancestral PMM/PGM protein during evolution to create the present-day four-domain enzyme. On the other hand, the rest of the enzyme (Domains 1–3) appears to have become at least somewhat dependent during evolution on Domain 4 for stability, solubility, and/or maintaining a folded structure in solution.

Reconstitution of enzyme activity

To determine if enzymatic activity could be reconstituted from the two fragments of PMM/PGM, each fragment was assayed individually, and then a titration of d1–3 with varying amounts of d4 was performed (Materials and Methods). No measurable activity was present for either isolated fragment (data not shown). In the titration experiments, however, enzymatic activity was clearly apparent, and the reaction rate increased with increasing amounts of d4 relative to d1–3 [Fig. 4(A)]. The maximum reaction rate was observed when equimolar ratios of the two fragments were added to the reaction mixture (k_cat, 0.0017 s⁻¹). Increasing the amount of d4 beyond the 1:1 ratio with d1–3 did not produce an increase in activity (e.g., for a d1–3 to d4 molar ratio of 1:3, k_cat 0.0014 s⁻¹), possibly because of substrate trapping by excess d4. Therefore, a 1:1 mixture was used to determine the steady-state kinetic parameters [Fig. 4(B) and Table I]. These showed a K_m of the reconstituted heterodimer for glucose 1-phosphate (G1P) of 62 µM and a k_cat of 0.003 s⁻¹.

Figure 4.

Kinetic and thermodynamic analysis of PMM/PGM heterodimer activity. (A) Reaction time course of G1P conversion to G6P using reconstituted PMM/PGM. Each trace represents the change in absorbance at 340 nm versus time at the indicated ratios of d1–3 to d4 and using the coupled assay described in Materials and Methods. The absorbance values recorded at 2-min intervals were extracted from the original time course dataset and plotted. The corresponding reaction rates determined from the initial slopes were as follows: d1–3 to d4 ratio of 1:0.25 (•; k, 0.0006 s⁻¹); 1:0.5 (○; k, 0.001 s⁻¹); 1:1 (▾; k, 0.0017 s⁻¹), and 1:3 (▵; k, 0.0014 s⁻¹). (B) Michaelis–Menten plot for the conversion of G1P to G6P by the reconstituted PMM/PGM heterodimer. Points are experimental and line shows fit to the Michaelis–Menten equation with the k_cat 0.003 s⁻¹ and K_m 62 μM. (C) Temperature dependence of reaction rate for the WT PMM/PGM (•, r² 0.98) and the reconstituted PMM/PGM heterodimer (○, r² 0.97). Error bars on this panel are included but fall within the symbols.

Table I.

Kinetic and Thermodynamic Parameters for Intact and Reconstituted PMM/PGM

Protein	kcat (s−1)	Km (μM)	kcat/Km (μM−1/s)	ΔG‡ (kcal/mol)	ΔH‡ (kcal/mol)	TΔS‡ (kcal/mol)
Wild typea	7.8 ± 0.8	27.2 ± 4.5	0.28	17.0 ± 1.7	13.9 ± 0.3	−3.0 ± 0.2
Heterodimer	3 × 10−3 ± 2 × 10−4	62 ± 13	4.8 × 10−5	21.7 ± 1.3	9.8 ± 0.6	−11.9 ± 0.7

Errors for ΔH^‡ were calculated based on the errors in the slope of the Arrhenius plots for WT and d1–3/d4 heterodimer; errors in ΔG^‡ reflect errors in k_cat shown in this table, and errors for TΔS^‡ were calculated on the basis of the averaged errors for ΔH^‡ and ΔG^‡.

^aPublished in Ref. 18.

Comparison with the steady-state kinetic parameters of intact PMM/PGM (Table I) shows a remarkably small, approximately twofold increase in the K_m of the heterodimer. In contrast, k_cat of the heterodimer is greatly decreased (2600-fold), such that k_cat/K_m for the reconstituted enzyme is only 0.02% that of intact, wild-type PMM/PGM. Thus, reconstitution of the enzyme has a profound effect on catalytic efficiency, while only a limited effect on substrate binding. Several factors could contribute to the ∼2600-fold reduction in k_cat relative to the intact enzyme. Two possible explanations include intrinsic loss of catalytic efficiency and/or incomplete reconstitution the d1–3/d4 heterodimer, resulting in a low active-site concentration. The requirement for a 1:1 ratio of d1–3 to d4 to achieve maximum activity and the dependence of the saturation behavior of the reaction rate on the concentration of d4 suggest that the active-site concentration is equal or close to the protein concentration. Moreover, the thermodynamic parameters derived from temperature dependence studies (see following section) indicate that the decreased activity of the heterodimer is due largely to entropic factors, consistent with an intrinsic loss in catalytic efficiency.

Thermodynamic characterization

To further investigate the effects of the lack of chain connectivity on catalysis, temperature dependence studies of the reaction rate were performed and the thermodynamic parameters associated with the reaction catalyzed by the d1–3/d4 heterodimer were determined using an Arrhenius plot [Fig. 4(C)]. The activation energy (E_a) for the PMM/PGM heterodimer was determined from the slope of ln k versus 1/T as previously done for wild-type enzyme¹² and described in Materials and Methods. Subsequent data analysis by transition-state theory allowed the determination of the enthalpy, entropy, and free energy of activation for the PMM/PGM heterodimer (ΔH^‡, ΔS^‡, and ΔG^‡, respectively). Details of the analysis are described in Materials and Methods, and the results are summarized in Table I. These results show that although the enthalpy of activation (ΔH^‡) for the heterodimer is somewhat reduced compared with that of the wild-type reaction, the entropy of activation (ΔS^‡) is significantly more negative, resulting in a substantial increase in ΔG^‡ by ∼5 kcal/mol.

The results of the temperature dependence studies indicate that the decreased activity of the reconstituted enzyme is due largely to entropic factors, consistent with the notion that the heterodimer exhibits increased conformational freedom upon dissociation into its individual components. As loss of a covalent bond is known to increase the conformational entropy of the unfolded state of proteins more than the folded state,⁷ this may also contribute to the large change in entropic parameters for the heterodimer. Further studies will be needed to elucidate the specific contributions of these various factors, which certainly contribute to a complex, multistate equilibrium.

Comparison with mutants affecting flexibility of the hinge region of PMM/PGM

The behavior of the PMM/PGM heterodimer is consistent with, but considerably more dramatic than, that demonstrated earlier for site-directed mutants of PMM/PGM, including several specifically designed to increase the flexibility of the polypeptide backbone.¹² In this previous study, for example, a conserved proline (P368) in the hinge of PMM/PGM was mutated to both alanine and glycine. Both of these hinge mutants show little change in K_m (less than twofold increase) relative to wild-type enzyme but larger changes in k_cat (approximately sevenfold decrease) and have overall activities (k_cat/K_m) of <10% that of wild-type enzyme. As also seen for the heterodimer, entropic changes dominate the differences in the thermodynamic parameters of the hinge mutants when compared with wild-type enzyme. Our results for the PMM/PGM heterodimer continue the trends observed in these hinge mutants, but in all aspects characterized, the heterodimer shows larger effects, with the entropy of activation (ΔS^‡), in particular, being almost twice as negative as that of the previously characterized mutants. The possible origin of this effect is discussed in more detail below.

Origin of entropic effects

Size exclusion chromatography on mixtures of the d1–3 and d4 fragments failed to give evidence of heterodimer formation in the absence of substrate (see Fragment Design and Production). The more negative ΔS^‡ observed for the PMM/PGM heterodimer, therefore, could result from a relative decrease in the order of the ground state (as d1–3, d4, and substrate must all associate to create the substrate-bound heterodimer complex), a relative increase in the order of the transition state, or some combination thereof. As it is difficult to envision the two-piece heterodimer exhibiting increased order in the transition state relative to intact enzyme, it seems likely that the ground state is less ordered, resulting from a larger ensemble of conformations (including possibly an increase in unfolded or partially unfolded polypeptides). As noted earlier, although Domain 4 of PMM/PGM does not contain amino acids directly involved in catalysis, residues in this domain make an extensive set of interactions with the phosphate group of bound substrates. The importance of these contacts can be clearly seen in the four enzyme–substrate crystal structures of PMM/PGM, where the residues involved and geometry of the contacts are essentially invariant.⁹ Moreover, in the enzyme–ligand complexes, residues in Domain 4 also participate in an interface with residues in Domain 1 of PMM/PGM, creating a “lid” that closes over bound substrate. Thus, the correct positioning of the d4 fragment relative to d1–3 is essential for creating the ligand-binding pocket that positions substrates for catalysis. In this context, the thermodynamic data on the PMM/PGM heterodimer support our previous suggestion that increased flexibility and conformational freedom of Domain 4 reduces the probability of the enzyme adopting a catalytically productive configuration of its active site,¹² an occurrence that would clearly be even less likely in the case of the two-piece heterodimer. To our knowledge, this is the first investigation of the effect of increased conformational freedom via a break in the polypeptide chain on the catalytic energy of activation.

Conclusions

The intrinsic flexibility of proteins is fundamentally limited by many factors, including the amino acid sequence, as well as secondary, tertiary, and (when present) quaternary structures. However, clearly the most fundamental limitation is the connectivity of the polypeptide backbone. In this study, a break introduced into the covalent linkage of the polypeptide chain represents the state with the maximum possible flexibility between polypeptide fragments and reveals an upper limit to the activation energy penalty of gaining complete conformational freedom (entropy). Also, this study highlights the potential functional advantages of joining separate folding domains into a single polypeptide chain during evolution. At least in the case of PMM/PGM, that advantage appears to be primarily in catalytic efficiency, rather than in increased binding affinity for its substrate.

Materials and Methods

Design, production, and purification of fragments

Two protein fragments were produced, which correspond to the first three structural domains (d1–3) of P. aeruginosa PMM/PGM and its 95-residue C-terminal domain (d4). The d1–3 construct includes amino acids 1–367 of the protein, and the d4 construct spans residues 369–463. For the d1–3 construct, the gene for intact, wild-type PMM/PGM in a pET14b vector with N-terminal His tag was truncated by inserting a stop codon after residue 367 using the QuikChange site-directed mutagenesis kit (Stratagene) and verified by DNA sequencing. The gene for the d4 fragment was synthesized commercially (GenScript) and inserted into the pET14b vector (Novagen) with an N-terminal hexahistidine tag. An N-terminal location for the tag on d4 was chosen because the hinge of PMM/PGM is in surface-exposed loop of the protein [Fig. 1(A) and figures in Ref. 12] and, thus, would be unlikely to interfere with heterodimer formation, whereas the C-terminus of the protein is involved in extensive interactions with other residues in d4.

For expression of the d1–3 and d4 fragments, Escherichia coli BL21(DE3) cells were transformed with the corresponding plasmid and grown at 37°C to an OD₆₀₀ of 0.6–0.8 in LB medium with 0.1 mg/mL ampicillin. Cells were induced by the addition of IPTG to a final concentration of 0.4 mM, grown at 30°C for 12 h, and harvested by centrifugation. Cell pellets were stored at −80°C.

For protein purification, cell pellets were resuspended in 50 mM sodium phosphate, pH 7.8, 2 mM MgCl₂, 1 mM dithiothreitol (DTT), 0.5 mM p-toluene-sulfonyl fluoride, 0.5 mM N-p-tosyl-l-lysine chloromethyl ketone HCl, and benzonase (Novagen, 50 U/g of cell pellet), lysed with a French press, and centrifuged for 60 min at 4°C. The supernatant was adjusted to 300 mM NaCl, passed sequentially through 0.45 and 0.22 µm filters, and gently mixed with Ni²⁺ affinity resin (His-Select, Sigma) in Buffer A (300 mM NaCl and 50 mM sodium phosphate, pH 7.8) and incubated for 1.5 h on a two-way orbital rocker. The resin was transferred into a column, allowed to settle, and the column washed with Buffer A containing 5 and then 10 mM imidazole, pH 7.8. Protein was eluted with Buffer A containing 125 mM imidazole, pH 7.8. For the d4 fragment, no further purification was done, and the protein was dialyzed into 10 mM 3-(N-morpholino)propanesulfonic acid (MOPS), pH 7.3, and concentrated to 26 mg/mL. Protein concentration was determined by Bradford assay.²⁰

In the case of the d1–3 fragment, the Ni²⁺ column was followed by preparative ultracentrifugation at 100,000 rpm (453,000g) for 2–4 h at 4°C and then by size exclusion chromatography (16/60 Sephacryl S-100 HR) in a buffer of 200 mM NaCl, 10 mM MOPS, pH 7.3, and 1 mM DTT to remove aggregates (see Results and Discussion). For dialysis of d1–3, additional steps were taken because of limited solubility of the sample to ensure phosphorylation of the active site S108 and to remove potential contaminating metals from the Mg²⁺-binding site (residues 242–246). Initial dialysis of the sample was into Buffer B (200 mM NaCl, 10 mM MOPS pH 7.3, and 1 mM DTT). Further dialysis steps were as follows: Buffer B with 2 mM MgCl₂ and 0.2 mM ethylenediaminetetraacetate; Buffer B with 2 mM MgCl₂; buffer B with 1 mM glucose 1,6-bisphosphate and 2 mM MgCl₂, and finally Buffer B with 2 mM MgCl₂. The d1–3 fragment was soluble long term only at concentrations below 5 mg/mL.

NMR and circular dichroism spectra

Uniformly ²H/¹⁵N-labeled samples of d4 and d1–3 were produced as above, except that cultures were grown in minimal medium prepared with D₂O (final concentration ∼97%) and containing ¹⁵NH₄Cl. For NMR data acquisition, the d4 fragment was at 15 mg/mL (1.3 mM) in 10 mM MOPS, pH 7.3, with ∼5% D₂O. The NMR spectra were acquired at 25°C on an 800 MHz Bruker Avance III NMR spectrometer equipped with TCI cryoprobe. The NMR spectra were processed using NMRpipe²¹ and viewed using SPARKY.²²

CD spectra were recorded at 25°C using an Aviv Model 62DS spectrometer with a 0.1-cm quartz cuvette. Protein samples were dialyzed into 125 mM NaCl, 2 mM MgCl₂, and 10 mM MOPS, pH 7.5. Spectra were run at a scanning rate of 2 nm/min with 1.0 nm wavelength steps from 200 to 250 nm and background subtracted. The dialysate was used as the reference for background subtraction.

Enzyme activity assay and fragment complementation experiments

Enzyme activity for the fragment complementation experiments was assayed as previously described.¹² Briefly, the PGM activity of the fragment mixtures was measured in the direction of glucose 6-phosphate formation, using G1P (Sigma) as a substrate in a coupled assay with glucose 6-phosphate dehydrogenase from Leuconostoc mesenteroides (Sigma). Unless otherwise stated, the reactions were carried out in 50 mM MOPS, pH 7.3, and 1 mM DTT at 25°C and monitored by measuring the rate of production of NADH, based on its absorbance at 340 nm. Neither fragment of PMM/PGM showed any detectable activity in the absence of the other (data not shown).

To determine the optimal ratio of fragments for reconstitution of activity, the d1–3 fragment was first titrated with varying amounts of d4. The substrate (G1P) concentration was 50 μM; d1–3 was at 6.2 µM for each assay with varying amounts of d4. Molar ratios of d4 to d1–3 were 0.25:1, 0.5:1, 1:1, and 3:1.

Steady-state kinetic assays

As maximal activity was observed at equimolar ratios of d4:d1–3, this ratio was used for the determination of the steady-state kinetic parameters. Substrate concentration was varied from 5 to 200 µM; d1–3 was at 6.2 µM with an equimolar ratio of d4. Reactions were conducted in duplicate and were typically monitored for at least 30 min. The data were fitted to the Michaelis–Menten equation to determine the reaction rate (k_cat, s⁻¹) and the Michaelis-Menten constant (K_m, μM). A control experiment was conducted with varying amounts of intact PMM/PGM (at a concentration where its activity is equivalent to that of the heterodimer in our assays) to verify that the amount of the coupled enzyme did not control the velocity of the reaction.

Temperature dependence studies

The temperature dependence of the reconstituted PMM/PGM reaction was determined using the above assay, but at a single substrate concentration of 50 μM G1P.¹² Enzyme activity was measured in duplicate at temperatures ranging from 9 to 29°C; fragment concentrations were as in the steady-state determination above. As wild-type PMM/PGM shows a decrease in enzyme activity between 35 and 40°C,¹² temperatures above 30° were not tested for the reconstituted sample. The temperature dependence of the reaction rate constants for the PMM/PGM heterodimer was analyzed first by the Arrhenius equation to extract the energy of activation, E_a. The E_a parameter was determined from the slope (−E_a/R) of the linear plot of ln k versus 1/T. The activation enthalpy () was calculated as (E_a − RT). The free energy of activation () was calculated as RT[ln(k_BT/h) − ln(k)], where R = 1.9872 cal/(mol K), k_B is the Boltzmann constant (1.38066 × 10⁻²³ J/K), and h is Planck's constant (6.62608 × 10⁻³⁴ J s). The activation entropy () was then calculated as ()/T.^23,24

Glossary

Abbreviations:

DTT

dithiothreitol

G1P

glucose 1-phosphate

MOPS

3-(N-morpholino)propanesulfonic acid

PMM/PGM

phosphomannomutase/phosphoglucomutase