The thioredoxin system and not the Michaelis–Menten equation should be fitted to substrate saturation datasets from the thioredoxin insulin assay

Abstract

Introduction: The thioredoxin system, consisting of thioredoxin reductase, thioredoxin and NADPH, is present in most living organisms and reduces a large array of target protein disulfides.

Objective: The insulin reduction assay is commonly used to characterise thioredoxin activity in vitro, but it is not clear whether substrate saturation datasets from this assay should be fitted and modeled with the Michaelis-Menten equation (thioredoxin enzyme model), or fitted to the thioredoxin system with insulin reduction described by mass-action kinetics (redox couple model).

Methods: We utilized computational modeling and in vitro assays to determine which of these approaches yield consistent and accurate kinetic parameter sets for insulin reduction.

Results: Using computational modeling, we found that fitting to the redox couple model, rather than to the thioredoxin enzyme model, resulted in consistent parameter sets over a range of thioredoxin reductase concentrations. Furthermore, we established that substrate saturation in this assay was due to the progressive redistribution of the thioredoxin moiety into its oxidised form. We then confirmed these results in vitro using the yeast thioredoxin system.

Discussion: This study shows how consistent parameter sets for thioredoxin activity can be obtained regardless of the thioredoxin reductase concentration used in the insulin reduction assay, and validates computational systems biology modeling studies that have described the thioredoxin system with the redox couple modeling approach.

Keywords:

• Redoxin
• Systems biology
• Redox regulation
• Kinetic model

Introduction

The thioredoxin system consisting of NADP(H), thioredoxin, and the enzyme thioredoxin reductase is widely distributed in nature and plays a major role in intracellular redox regulation.¹ In this system, thioredoxin reductase, a member of a family of pyridine nucleotide-disulfide oxidoreductases, uses NADPH to reduce thioredoxin, which in turn reduces a wide array of protein and non-protein targets, forming a large redox-regulated network.^2,3 This network connects key cellular processes including DNA synthesis, hydrogen peroxide metabolism, and sulfur assimilation,^4,5 and perturbations in this network are associated with distinct physiological processes and are correlated with a number of pathologies.^1,6–8

While several assays for measuring thioredoxin activity have been developed using substrates such as 5,5ʹ-dithiobis(2-nitrobenzoic acid) (DTNB)^9,10 or fluorescently labeled proteins,¹¹ insulin with a single intrachain and two interchain disulfide bonds¹² still remains the most popular substrate for characterising thioredoxin activity in vitro.¹³ In this assay, insulin is reduced by thioredoxin and the reaction can be monitored turbidimetrically by following the aggregation of the free B-chain¹⁴ or by coupling the reaction to NADPH oxidation (Scheme I).¹³

Scheme I: Thioredoxin enzyme model.(1) (2) (3) where TrxSS and TrxSH represent oxidized and reduced thioredoxin, respectively. Insulin (ox) and Insulin (red) represent oxidized and reduced insulin, respectively, and TR represents thioredoxin reductase.

Increases in the insulin concentration result in a classical substrate saturation profile and Michaelis–Menten parameters have consequently been assigned to thioredoxin.^13,15–19 Despite mammalian insulin not being the physiological substrate for all the thioredoxins characterised with this assay, it is readily reduced by most thioredoxins. This common substrate therefore allows for semi-quantitative kinetic comparisons between different thioredoxins. However, in many of these studies it was not always clear whether thioredoxin reduction or thioredoxin oxidation was the rate-limiting step in the assay (Scheme I). The activities of other redoxins (glutaredoxins and peroxiredoxins) have also been described using Michaelis–Menten kinetic parameters (see for example Refs. 20–22).

There have been a number of conflicting reports on the interpretation of the plots generated in these experiments.^23,24 For example, unlike most enzymes, thioredoxin is inactivated by its substrate and requires thioredoxin reductase to regenerate it. Further, in the original description of the thioredoxin insulin assay, it appeared that varying concentrations of thioredoxin reductase in the assay led to changes in the observed turnover number for thioredoxin activity.¹³ Moreover, in other studies, reduced and oxidized thioredoxin have been detected in vivo,^25,26 suggesting that the thioredoxin redox couple's activity should be characterised by redox potentials and not enzyme kinetic parameters. For computational systems biology studies, in particular, these discrepancies posed a serious limitation as it was not clear whether thioredoxin should appear in the stoichiometric matrix or rate vector of the equation describing the kinetic model of the system.²⁷

Using a computational model, we suggested that these disparate observations could be reconciled by proposing that the saturation observed in the insulin assay was due to a limitation in the thioredoxin redox cycle.²³ As the insulin concentration was increased, thioredoxin oxidation increased and the activity of the thioredoxin reduction reaction correspondingly increased until it was limited by the availability of oxidized thioredoxin or by saturation of the thioredoxin reductase, or both. This in turn limited the reduced thioredoxin available for insulin reduction and the flux through the system saturated.²³ We further proposed that mass-action kinetics appeared to be sufficient to describe insulin reduction by thioredoxin. Substrate reduction by thioredoxin proceeds via the formation of a mixed-disulfide complex between the redoxin and its substrate.²⁸ Once formed, the breakdown of these redoxin–substrate complexes is highly favorable and therefore the intermediate steps involving the mixed-disulfide complex were not explicitly modeled but were instead combined into a single second-order rate constant.²³ The validity of this simplification was tested by fitting a computational model of the Escherichia coli thioredoxin system to a published in vitro dataset.¹³ Collectively, these findings suggested that the kinetic parameters for thioredoxin should be obtained by fitting a kinetic model of the entire thioredoxin system (Scheme II) to a given substrate saturation dataset and that mass-action kinetics could adequately describe insulin reduction.

Scheme II: Thioredoxin redox couple model.(4) (5) A number of systems biology studies have since used this approach to describe thioredoxin activity in large-scale kinetic models.^29–31 However, Lin³² found a discrepancy between the model output and the insulin reduction profile obtained when using a minimal model²³ of the yeast thioredoxin system (equation (6(6) )):(6) In this minimal description of the entire thioredoxin system (Scheme II), the thioredoxin reductase reaction was described by mass-action kinetics with a second-order rate constant (k₁), Trx_tot refers to the total thioredoxin concentration and insulin reduction was also described by a second-order rate constant (k₂). Note that equation (6(6) ) has the same form as the Michaelis–Menten equation with a V_max described by k₁·NADPH·Trx_tot, an apparent k_cat described by k₁·NADPH and an apparent K_m described by k₁·NADPH/k₂; therefore the ratio k_cat/K_m is equal to k₂, the true rate constant for insulin reduction.²³

As thioredoxin reductase is fully saturated by NADPH in the insulin assay, the flux through the system is effectively zero-order with respect to the NADPH concentration and therefore equation (6(6) ) has limited value for fitting datasets under these conditions. Lin³² nonetheless proposed that thioredoxin was indeed an enzyme whose activity could presumably be described with Michaelis–Menten parameters. Thus, it is not clear whether substrate saturation datasets from the thioredoxin insulin assay should be fitted with the Michaelis–Menten equation or whether they should be fitted with the entire thioredoxin system (Scheme II). In this study, we employed computational modeling and in vitro kinetic assays of the thioredoxin insulin system to determine which of these approaches should be used to characterise thioredoxin activity.

Materials and methods

Plasmids and chemicals

Clones harboring the plasmid pET28a expressing thioredoxin reductase were generously supplied by Miss M.M. Photolo.³³ Thermoscientific Taq DNA polymerase and the InsTAclone kit were obtained from Inqaba Biotech (Johannesburg, South Africa), the Qiagen Ni-NTA agarose matrix from Whitehead Scientific (Pty) Ltd (Cape Town, South Africa), and the New England Biolabs HindIII and NdeI restriction enzymes were obtained from The Scientific Group (Midrand, South Africa). Trichloroacetic acid (TCA), methoxypolyethylene glycol maleimide (PEG-maleimide M_n 5000), 4-(2-aminoethyl)benzenesulfonyl fluoride hydrochloride (AEBSF), and dithiothreitol (DTT) were obtained from Sigma (Capital Labs, Johannesburg, South Africa) and all other common chemicals were from Saarchem/Merck (Johannesburg, South Africa) and were of the highest purity available.

Kinetic modeling

Kinetic modeling experiments were carried out using the open source Python Simulator for Cellular Systems (PySCeS) modeling software³⁴ (http://pysces.sourceforge.net) as described previously.^23,29 Detailed models were created to analyse the E. coli and Saccharomyces cerevisiae thioredoxin systems and were parameterised with realistic parameter sets (Table 1) which were obtained from either primary literature sources, the BRENDA kinetic parameter database³⁵ (http://www.brenda-enzymes.info), or from our in vitro kinetic assays. In these models, thioredoxin reductase was modeled with a two-substrate Michaelis–Menten kinetic expression and insulin reduction was modeled with mass-action kinetics as described previously.²³ Kinetic models of the entire thioredoxin system or the Michaelis–Menten equation were fitted to in vitro datasets using non-linear least squares regression with the Levenberg–Marquardt algorithm as previously described.²³ The PySCeS and SBML versions of the kinetic models are available in the Supplementary information.

Table 1 Kinetic parameters and species concentrations used for building computational models of the E. coli and baker's yeast thioredoxin systems

Species	E. coli (μM)	S. cerevisiae (μM)
NADPH*	400	400
NADP*	1.0	1.0
TrxSS*	0.05	0.75
TrxSH*	0.05	0.75
Insulin (oxidized)*	30	20
Insulin (reduced)	1.0	1.0
Kinetic parameters	TR	TR
[TR]*	0.1 μM	0.05–0.25 μM
kcat	22.8 s^−1	66.6 s^−1
KNADPH	1.2 μM	1.2 μM
KTrxSS	2.8 μM	4.4 μM
Insulin reduction
k2*	0.064 μM/s	0.003 μM/ s

Note: TR, thioredoxin reductase.

*This study; other model parameters were obtained from Refs. 13, 23, 35, 45–47.

Cloning, expression, and purification of thioredoxin and thioredoxin reductase

The TRX1 gene (Saccharomyces genome database (SGD) (http://www.yeastgenome.org), Gene ID 850732) was directly amplified from S. cerevisiae BY4743 genomic DNA using the primers AGCCATATGGTTACTCAATTCAAAACTGCC and ACGAAGCTTAAGCATTAGCAGCAATGGC (NdeI and HindIII restriction sites underlined), cloned into a pTZ57R/T vector (InsTAclone kit, Thermoscientific) and then subcloned into a pET28a expression vector. The nucleotide sequences of the TRX1 and TRR1 clones were confirmed by automated sequencing (Central Analytical Facility, Stellenbosch University). To purify these recombinant proteins, transformed E. coli (DE3) cells containing the appropriate plasmid were cultured in LB media with kanamycin (30 µg/ml) and protein expression was induced by IPTG (final concentration 0.5 mM) for 6 hours for thioredoxin expression or 1 hour for thioredoxin reductase expression. Cells were then harvested, resuspended in 10 volumes of extraction buffer (20 mM Tris–HCl (pH 7.5), 10 mM NaCl, 1 mM EDTA, 0.2 mM AEBSF, and 5 mM DTT), disrupted by sonication, and centrifuged (12 000 × g, 30 minutes, 4°C). The thioredoxin containing supernatants were heat-treated (75°C, 30 minutes) and clarified by centrifugation (12 000 × g, 30 minutes, 4°C). Thioredoxin and thioredoxin reductase were then purified by Ni-NTA affinity chromatography and protein purity was confirmed by SDS-PAGE while protein concentration was determined using the Bradford assay and the extinction coefficients for thioredoxin and thioredoxin reductase (10 095 and 49 320 M⁻¹ cm⁻¹, respectively). During the purification, thioredoxin activity was monitored using the insulin aggregation assay with DTT as a reducing agent³⁶ and thioredoxin reductase was assayed using a DTNB reduction assay.³⁷

Thioredoxin insulin reduction assay

A number of variations of coupled redoxin assays have been presented in the literature. In some assays, NADPH oxidation was monitored by a decrease in absorbance at 340 nm starting at a positive value,^38,39 typically 0.9 for an NADPH concentration of 150 µM,⁴⁰ while in other assays, a decrease in absorbance from the blank was monitored.⁴¹ To compare these methods, insulin reduction was undertaken at 25°C in a final volume of 1 ml in a 100 mM potassium phosphate (pH 7.0) buffer containing EDTA (2 mM), NADPH (0.15 or 0.4 mM), insulin (20–160 µM), thioredoxin (1.5 µM), and thioredoxin reductase (0.05 µM). NADPH oxidation was monitored at 340 nm in a UV-1800 Shimadzu Spectrophotometer and depending on the assay being tested, a sample without the addition of either NADPH or thioredoxin reductase was used as the reference cuvette. To determine the effect of thioredoxin reductase on the rate of insulin reduction, the assay was undertaken as described above with NADPH (0.4 mM), insulin (20–200 µM) and varying thioredoxin reductase concentrations (0.05–0.25 µM). Insulin reduction activity was defined as the concentration of NADPH oxidized per minute using a molar extinction coefficient⁴¹ of 6200 M⁻¹ cm⁻¹. Absorbance measurements were taken for at least 5 minutes, although initial studies showed that the system remained in steady state well beyond this assay period during which no significant insulin precipitation occurred. All assays were undertaken in triplicate and the data obtained was plotted as a mean ± standard error.

Determination of the redox state of thioredoxin

The redox state of thioredoxin was determined using the method described by Hugo et al.⁴² Briefly, the steady-state insulin reduction assay components were added directly into 100% (w/v) ice-cold TCA (100 µl) and incubated on ice for 30 minutes. The TCA-treated samples were then transferred to an Amicon^® Ultra 2 ml centrifugal filter (10 000 NMWL) and centrifuged (7500 × g, 20 minutes, 4°C) to remove the insulin. As a control to ensure that no protein was lost during centrifugation, the eluate was assayed for thioredoxin and thioredoxin reductase activity and was also tested by SDS-PAGE. The remaining concentrate was transferred and centrifuged (22 065 × g, 40 minutes, 4°C). The resulting pellet was washed with ice-cold acetone (100 µl), dried at 37°C and resuspended in 50 µl alkylation buffer (3 mM PEG-maleimide, 50 mM Tris (pH 7.5), 10 mM EDTA (pH 8.0), and 0.1% (m/v) SDS). After a 45-minute incubation period at 45°C, the alkylated samples were mixed with an equal volume of 2× non-reducing sample buffer (125 mM Tris–HCl, 4% (m/v) SDS, 20% (v/v) glycerol, and 0.01% (m/v) bromophenol blue, pH 6.8), the samples boiled and then separated by electrophoresis on a 15% acrylamide Tris–Tricine gel, which was subsequently stained with Coomassie blue. All assays were undertaken in triplicate and representative gel images are shown below. As migration controls, reduced thioredoxin was obtained by incubating thioredoxin (1.5 µM) with DTT (1 mM) at 37°C for 1 hour, while purified thioredoxin served as the oxidized control. The control samples were processed for electrophoresis as described above, and as expected, the reduced form of thioredoxin migrated higher on these gels. The intensity ratio of the bands was determined with ImageJ (http://imagej.nih.gov/ij/) using the reduced control as the standard.

Results

Computational models with thioredoxin described either as an enzyme, or as a redox couple, have contrasting kinetic properties

To determine whether it really mattered if thioredoxin activity was described with Michaelis–Menten parameters or with mass-action kinetics, two distinct kinetic models in which thioredoxin acts as an enzyme (equation (3(3) ), Scheme I) or as a redox couple (Scheme II) were both fitted to a previously published in vitro insulin reduction dataset.¹³ As mammalian insulin contains three disulfide bonds and reduction was followed by NADPH oxidation, we also wanted to determine whether it made a difference to the fitting results if the insulin or the disulfide bond concentration was considered as the ‘substrate’ in these experiments. In addition, we used our computational models to highlight the key differences between the thioredoxin enzyme and redox couple fitting approaches.

Both the Michaelis–Menten equation and the redox couple model showed excellent fits (r² ≥ 0.996) to the insulin saturation profile (Fig. 1A), suggesting that both models were apparently consistent with the dataset (Table 2). As the redox couple model predicted that substrate saturation was due to a limitation in thioredoxin reductase activity, the effect of increasing the thioredoxin reductase concentration on the rates within the system was also tested. Increasing the thioredoxin reductase concentration increased the insulin reduction rate in the thioredoxin redox couple model (Fig. 1A), confirming that its activity was limiting in this system. Note that in our kinetic model, thioredoxin reductase was described with Michaelis–Menten kinetics, which would not be accurate at thioredoxin and thioredoxin reductase concentrations of 1.5 and 0.1 µM, respectively, as the thioredoxin concentration was only 15-fold larger than the thioredoxin reductase concentration. Nonetheless, the fitted second-order rate constant obtained over a range of thioredoxin reductase concentrations showed very little variation (Table 2), suggesting that this method is robust in obtaining kinetic parameters.

Figure 1 The Michaelis–Menten equation and the thioredoxin redox couple model both fit an in vitro insulin reduction dataset¹³ but the resulting kinetic models show distinct responses to thioredoxin reductase concentration and substrate saturation. In (A) the Michaelis–Menten equation and the thioredoxin redox couple kinetic model (black line) both showed excellent fits (r² ≥ 0.996) to an insulin substrate saturation dataset (•). Increasing the thioredoxin reductase concentration (0.05 µM) in the thioredoxin redox couple model to 0.15 (blue) or 0.25 µM (green) increased the flux within the system at a given insulin concentration. Substrate saturation (black) within a fitted thioredoxin redox couple model (0.05 µM TR) was accompanied by the redistribution of thioredoxin from its reduced (blue) to oxidized (red) form (B). In (C) disulfide bond rather than insulin concentration was used to determine the kinetic parameters for thioredoxin-dependent insulin reduction.

Table 2 The Michaelis–Menten parameters and second-order rate constants (k₂) for insulin reduction from computational modeling of the E. coli thioredoxin system at varying thioredoxin reductase concentrations

Substrate	TR (µM)	Apparent Michaelis–Menten parameters				Redox couple model
		Km ± SE (µM)	kcat ± SE (s^−1)	kcat/Km (µM^−1 s^−1)	r^2	k2 ± SE (µM^−1 s^−1)	r^2
Varying insulin concentrations	0.1	11.52 ± 1.12	0.75 ± 0.02	0.06	0.996	0.06 ± 0.005	0.997
	0.5	57.37 ± 1.41	3.88 ± 0.04	0.06	0.999	0.07 ± 0.001	0.999
	1.0	110.09 ± 4.27	7.53 ± 0.17	0.06	0.999	0.07 ± 0.001	0.999

Note: TR, thioredoxin reductase.

In contrast, the apparent Michaelis–Menten parameters of the system varied significantly at different thioredoxin reductase concentrations, although the k_cat/K_m compared favorably to the second-order rate constant obtained by fitting the redox couple model (Table 2, cf. equation (6(6) )). Thus, if correct, the redox couple model (Scheme II) predicted that the apparent Michaelis–Menten parameters for the system would vary depending on the thioredoxin reductase concentration used in the experiment, while fitting of the entire system should yield a consistent second-order rate constant over a range of thioredoxin reductase concentrations. Conversely, if thioredoxin was indeed limiting in the system and responsible for the substrate saturation profile, increasing thioredoxin reductase should have negligible effects on the insulin reduction rate and the Michaelis–Menten parameters obtained.¹³ An additional distinguishing prediction made by these simulations was that substrate saturation in the redox couple model was accompanied by the progressive redistribution of the thioredoxin moiety into its oxidized form (Fig. 1B). In contrast, if thioredoxin was described as an enzyme, there should be no net change in the steady-state redox state of thioredoxin (equation (3(3) ), Scheme I).

Models using the disulfide bond concentration as the ‘substrate’ were also developed and analysed (Fig. 1C) to determine if it made a difference to the kinetic rate parameters obtained in our fitting experiments. Not surprisingly, we found that the mass-action rate constants (k₂) obtained for the disulfide bond reduction were lower than the rate constants for insulin reduction but again showed a good correlation with the k_cat/K_m values obtained when using this substrate (Table S1). A limitation with such an analysis is that it assumed that all three disulfide bonds in insulin were equally accessible. However, data from insulin aggregation studies have shown that the porcine insulin intrachain A6–A11 and interchain A7–B7 disulfide bonds were more accessible to reduction than the buried A20–B19 disulfide bond.¹² Thus, the second-order rate constant obtained from this analysis and indeed the analysis with insulin as the substrate (above) describes a complex set of reduction events within a single aggregated parameter. As a final control, we modified the redox couple model to determine if another rate expression could be used for the insulin reduction reaction (equation (5(5) )) in these fitting experiments. This reaction was therefore described with reversible mass-action, Hill and Michaelis–Menten kinetics, but we obtained appreciably poorer fits of the data (data not shown), suggesting that irreversible mass-action kinetics were apparently sufficient to describe the reduction of insulin for the concentrations of thioredoxin reductase tested. As these computational modeling observations could be directly tested in vitro, the thioredoxin system was isolated from S. cerevisiae and analysed using the insulin reduction assay.

Purification and assay of the yeast thioredoxin system

Thioredoxin and thioredoxin reductase from S. cerevisiae were cloned, expressed, and purified using standard molecular biology techniques (Fig. 2). To ensure that both proteins were completely active, thioredoxin was assayed using the DTT-dependent reduction of insulin,¹⁴ while thioredoxin reductase was assayed using the DTNB reduction assay.³⁷ The insulin reduction assay with the oxidation of NADPH was used to determine the kinetic parameters for the reaction schemes (I and II). Two variations of the coupling assay to NADPH have been presented in the literature, where NADPH oxidation was monitored by a decrease in absorbance at 340 nm starting at a positive absorbance value^38,39 or by a decrease in absorbance from the blank.⁴¹ We compared both these methods (Fig. 3) and found no differences in the rates obtained over a range of NADPH concentrations (0.15–0.4 mM), but chose to use the former assay as, in our hands, it appeared less noisy over the range of insulin concentrations tested in our experiments.

Figure 2 Ni-NTA affinity purification of recombinant thioredoxin (A) and thioredoxin reductase (B) (details in text).

Figure 3 Similar rates were obtained when the thioredoxin insulin assay was initiated with thioredoxin reductase or NAPDH. Insulin reduction by the thioredoxin system was initiated with either thioredoxin reductase (A) or NADPH (B) and a decrease in absorbance was monitored over negative and positive scales, respectively. The assay contained insulin (80 µM), thioredoxin reductase (0.05 µM), thioredoxin (1.5 µM), and NADPH (150 µM) and was performed in duplicate.

Thioredoxin reductase activity is limiting in the insulin reduction assay

According to the thioredoxin redox couple model, increases in the thioredoxin reductase concentration should increase the flux through the system (Fig. 1A). To test this prediction, the rate of NADPH oxidation was measured at varying concentrations of insulin (20–200 µM) and yeast thioredoxin reductase (0.05–0.25 µM). As the concentration of thioredoxin reductase was increased, there was a corresponding increase in the flux through the system (Fig. 4) supporting the thioredoxin redox couple model (Scheme II) and showing that the saturation observed in this assay was due to an apparent limitation in thioredoxin reductase activity.

Figure 4 Changing the thioredoxin reductase concentration altered the kinetic profile and parameters obtained with the yeast thioredoxin insulin reduction assay. The flux obtained for a given insulin concentration increased as the thioredoxin reductase concentration was increased over the range 0.05 (•), 0.15 (▪), and 0.25 µM (♦). The Michaelis–Menten equation and the redox couple model were both fitted to these datasets using either insulin concentration (A) or the disulfide bond concentration (B). All assays were performed in triplicate with standard errors shown.

The computational modeling also predicted that changes in the thioredoxin reductase concentration would cause changes in the Michaelis–Menten parameters if its activity was limiting in the assay (Table 1). We therefore determined the effect of changing the thioredoxin reductase concentration on the Michaelis–Menten parameters (Scheme I) and on the second-order rate constant for insulin reduction obtained by fitting the entire thioredoxin system to the saturation datasets (Scheme II). While the K_m values remained relatively constant, changes in the thioredoxin reductase concentration resulted in changes to the apparent k_cat values, which was also noted in a previous study.¹³ In contrast, the second-order rate constant for insulin reduction (k₂, obtained by fitting the complete system) remained relatively constant and, as expected (Table 2), showed a good correlation with the k_cat/K_m Michaelis–Menten parameters (Table 3). Fitting experiments performed with the disulfide bond concentrations rather than the insulin concentrations also resulted in different Michaelis–Menten and second-order rate constant parameter values. As with the computational modeling studies, there was a good correlation between the k₂ and the k_cat/K_m values obtained (Table S1). We were, however, unable to obtain a satisfactory global fit of all the experimental data, suggesting that our kinetic model could not completely describe the complex set of reduction and aggregation events associated with insulin reduction.^12,43

Table 3 The Michaelis–Menten parameters and second-order rate constants (k₂) for insulin reduction by the baker's yeast thioredoxin system at varying thioredoxin reductase concentrations

Substrate	TR (µM)	Apparent Michaelis–Menten parameters				Redox couple model
		Km ± SE (µM)	kcat ± SE (s^−1)	kcat/Km (µM^−1 s^−1)	r^2	k2 ± SE (µM^−1 s^−1)	r^2
Varying insulin concentrations	0.05	38.21 ± 5.85	0.11 ± 0.01	0.003	0.97	0.003 ± 0.0003	0.97
	0.15	25.81 ± 6.74	0.15 ± 0.01	0.006	0.92	0.005 ± 0.0008	0.94
	0.25	29.27 ± 3.97	0.18 ± 0.01	0.006	0.98	0.005 ± 0.0004	0.98

Note: TR, thioredoxin reductase.

Saturation of the redox cycle and redistribution of the thioredoxin moiety

Over the complete range of thioredoxin reductase concentrations tested, increases in the insulin concentration resulted in observed substrate saturation. According to the redox couple model,²³ this would be due to the saturation of the thioredoxin redox cycle as thioredoxin reductase activity became limiting and the thioredoxin moiety distributed into its oxidized form (Fig. 1B). To experimentally verify whether there was indeed a redistribution of the oxidized and reduced forms of the thioredoxin moiety, the thioredoxin redox state was preserved by rapidly treating the steady-state insulin reduction reactions with TCA and alkylating the extracts with PEG-maleimide.⁴⁴ Increases in the insulin concentration resulted in the progressive redistribution of the thioredoxin moiety into its oxidized form (Fig. 5), which was consistent with our computational model (Fig. 1B). We observed a similar redistribution of thioredoxin into its oxidized form at other thioredoxin reductase (0.15–0.25 µM) and equivalent insulin concentrations (5–200 µM) (data not shown).

Figure 5 Substrate saturation is associated with redistribution of the thioredoxin moiety into its oxidized form in the insulin reduction assay. Reduced thioredoxin in the insulin reduction assay was alkylated with PEG-maleimide. As migration controls, reduced thioredoxin was obtained by incubating thioredoxin (1.5 µM) with DTT (1 mM), while purified thioredoxin served as the oxidized control. The experiment was performed in triplicate over a range of thioredoxin reductase concentrations (0.05–0.25 µM) and a representative gel image is shown here.

Discussion

The insulin reduction assay is one of the most commonly used methods to determine thioredoxin activity in vitro, but the classical substrate saturation profile generated with increasing insulin concentrations has usually been fitted to the Michaelis–Menten equation (Scheme I),^13,15–19 although we recently proposed that these datasets should be fitted to a model of the entire system of reactions (i.e. the redox couple model approach, cf. Scheme II).²³ To distinguish between these approaches, we used a computational model of an E. coli thioredoxin system which yielded three key predictions. If the redox couple model fitting approach was correct, (a) the second-order rate constant for insulin reduction (k₂) would remain constant but the apparent Michaelis–Menten parameters would change at varying thioredoxin reductase concentrations (Table 2), (b) thioredoxin reductase activity would be limiting in the system (Fig. 1A), and (c) the thioredoxin moiety would redistribute into its oxidized form with increasing substrate concentration (Fig. 1B). On the other hand, if fitting with the Michaelis–Menten equation (Scheme I) was correct, the thioredoxin reductase concentration would have a negligible effect on the rate and Michaelis–Menten parameters for insulin reduction, and thioredoxin should remain in its reduced, active enzymatic form with increasing substrate concentration.

To test the predictions in vitro we used the classical insulin reduction assay for thioredoxin activity.¹³ Our data showed that increasing the thioredoxin reductase concentration resulted in an increased flux through the system (Fig. 4) and also caused a significant change to the k_cat values while the second-order rate constant for insulin reduction (k₂) obtained from fitting the redox couple model remained relatively constant over a range of thioredoxin reductase concentrations (Table 3). Further, using an alkylation assay, the steady-state oxidation of the thioredoxin moiety was observed with increasing insulin concentrations (Fig. 5). Collectively, the data obtained from the in vitro analysis support the redox couple model for saturation in the thioredoxin system and suggest that fitting experiments on insulin reduction assay datasets should use models of the entire system of reactions under study. A potential limitation of our combined experimental and modeling approach is that it might be possible that other kinetic models may also fit these datasets. We therefore tested a number of other rate expressions for insulin reduction (equation (5(5) ), Scheme II), but these fitting experiments were unsuccessful. Irreversible mass-action kinetics for thioredoxin-dependent insulin reduction appeared to be sufficient to describe the data for each concentration of thioredoxin reductase used in our experiments. While several studies have shown that fitting of other redoxin systems to substrate saturation datasets does indeed yield consistent and reproducible parameter sets,^24,31 we were unable to obtain a satisfactory global fit with all our datasets. This result suggests that the differences in the kinetic profiles obtained for different thioredoxin reductase concentrations could not be completely explained by our computational models, which was not surprising given the complex reduction and aggregation kinetics of insulin.^12,43

The results presented here make two important contributions to our understanding of redoxin kinetics and analysis. First, we should now be able to obtain consistent second-order rate constants for thioredoxin-dependent insulin reduction regardless of the thioredoxin reductase concentration used in the assay. We did note a good correlation between the k_cat/K_m values and the second-order rate constant obtained by direct fitting of the entire system (Tables 2 and 3). Thus, specifically the k_cat/K_m values (but not all the Michaelis–Menten parameters in general) reported for thioredoxin in previous studies (see for example^13,32) could still be used in modeling thioredoxin-dependent networks or in the kinetic analysis of related reactions such as peroxiredoxin reduction. A second contribution from our work is that this study provides the first experimental support for the computational and theoretical modeling studies that have already used the redox couple approach to develop the kinetic models of the thioredoxin system in the Jurkat-T,³⁰ E. coli,²⁹ and red blood cells.³¹ This work therefore serves as a reference point for the further adoption of systems biology approaches in the study of thioredoxin and other redoxin systems.

Disclaimer statements

Contributors LP and CSP performed the modeling analysis. LP performed the experimental work and drafted the paper while CSP edited the paper.

Funding This work is based on the research supported in part by the National Research Foundation (NRF) of South Africa. Any opinion, finding and conclusion or recommendation expressed in this material is that of the author(s) and the NRF does not accept any liability in this regard. LP is a recipient of an NRF Scarce Skills Scholarship.

Conflicts of interest The authors declare no conflict of interest.

Ethics approval Ethical approval was not required for this study.

Supplementary material

Supplementary material for this article can be found at: www.maneyonline.com/doi/suppl/10.1179/1351000215Y.0000000024.

Acknowledgments

The authors wish to thank Professor Johann M. Rohwer (Stellenbosch University) for generously providing the modeling scripts used in this study and for critical comments on the revised manuscript.