Di-fluoresceinthiocarbamyl-insulin: A Fluorescent Substrate for the Assay of Protein Disulfide Oxidoreductase Activity

ANALYTICAL BIOCHEMISTRY ARTICLE NO.

248, 94–101 (1997)

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Di-fluoresceinthiocarbamyl-insulin: A Fluorescent Substrate for the Assay of Protein Disulfide Oxidoreductase Activity Alejandro P. Heuck and Ricardo A. Wolosiuk Instituto de Investigaciones BioquıB micas (Fundacio´n Campomar, F.C.E.N.-U.B.A, CONICET), Antonio Machado 151, (1405) Buenos Aires, Argentina

Received November 13, 1996

We have developed a novel method for the continuous assay of protein disulfide oxidoreductase activity using as substrate bovine pancreas insulin in which both N-terminal amino groups are chemically modified with fluorescein isothiocyanate. The reduction of intercatenary disulfide bonds of di-fluoresceinthiocarbamyl-insulin with dithiothreitol initially lowers but subsequently enhances the emission intensity. In this biphasic kinetics, the rate of increase is sensitive enough for the estimation of Escherichia coli thioredoxin concentrations from 5 nM (0.06 mg/ml) to 500 nM (6 mg/ml). Neither changes of pH over a range of 6.2 to 8.4 nor neutral salts (K/, Mg2/, and Ca2/) at concentrations lower than 100 mM affect this simple reaction system. Moreover, the fluorometric method is functional for measuring the reductive capacity of Brassica napus protein disulfide isomerase. Hence, a highly reproducible and accurate one-stage assay for protein disulfide oxidoreductase activity not only greatly improves the sensitivity compared to the commonly used turbidimetric assay but also represents a reliable alternative to assays based on accessory enzymes or radiolabeled substrates. q 1997 Academic Press

A growing family of related proteins, named collectively protein disulfide oxidoreductase (PDOR), assists in the cleavage, formation, and reshuffling of disulfide bonds by which target proteins adopt the functional tertiary structure (1–3). The mechanism of action of these catalysts relies on the rapid rate at which cysteine residues in the active site of the PDOR (-Cys-X-YCys-) undergo thiol/disulfide exchange with sulfhydryl groups or disulfide bonds of target proteins. In all living organisms, thioredoxin (Trx) modulates protein structure by reducing cystines via the highly conserved site (-Trp-Cys-Gly-Pro-Cys-) (4). On the other hand, protein disulfide isomerase (PDI) in the endoplasmic reticulum of eukaryotes and DsbA in the bacterial periplasm are

prominent catalysts for the formation of cystines whereby convey target proteins to a stable conformational state. Since the finding of Holmgren (5), the extensively used procedure for the estimation of PDOR activity has relied on the precipitation of insulin B-chain that follows the reduction of intercatenary disulfide bonds. However, the turbidimetric method not only requires high concentrations of insulin but also signals become detectable after a prolonged lag phase. Later, the assay was improved with radioactivelly labeled insulin followed by the analysis of constituent chains by HPLC (6) or the spectrophotometric determination of NADPH oxidation in the presence of NADP-thioredoxin reductase (7). It is well-known, however, that the hazardous handling of radioactive compounds in two-stage procedures is not very convenient for routine analysis of a large number of samples. On the other hand, the sensitivity of auxiliary enzymes (e.g., NADP-thioredoxin reductase) to the composition of the milieu precludes the analysis of heterogeneous crude extracts as well as different experimental conditions (pH, temperature, metabolites). Of particular interest to our laboratory has been the quantification of PDOR activity originated from plant sources (8). Given that the fluorescence emission increases upon the reduction of intercatenary disulfide bonds of di-FTC-insulin (8a), we deemed it desirable to know whether this novel feature is suitable for the estimation of PDOR activity. Data from application to Trx and PDI (9) assessed the feasibility, reproducibility, and validity of the determination of PDOR activity by the fluorometric method. MATERIALS AND METHODS

Materials Bovine pancreas insulin (henceforth insulin), fluorescein isothiocyanate (isomer I), and all biochemicals were purchased from Sigma Chemical Co. (St. Louis,

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MO). Other reagents were of analytical grade. Trx was purified by the method 2 described in (10). Details on the purification of PDI from seeds of Brassica napus (rapeseed) will be given elsewhere. Solutions of DTT were titrated with the Ellman’s reagent using a molar absorptivity at 412 nm of 14,150 M01 cm01 for 2-nitro5-thiobenzoate (11). Preparation of Di-FTC-insulin Purification of di-FTC-insulin was performed according to the procedure of Heuck and Wolosiuk (8a). Briefly, fluorescein isothiocyanate reacted with insulin (molar ratio, 2:1) at pH 9 for 10 h, and di-FTC-insulin1 was purified by successive anion-exchange and reversed-phase chromatography. The purity of the derivatized insulin was estimated at greater than 95% as determined by HPLC and electrophoresis on a 16.5% polyacrylamide gel stained with Coomassie brilliant blue. Determination of PDOR Activity Fluorometric assay. All kinetic experiments were carried out at 227C in plastic spectrofluorometric cuvettes (1 1 1 cm) placed in a Jasco FP-770 spectrofluorometer. In addition to the sample, the assay solution contained (in micromoles): potassium phosphate buffer (pH 7.5), 300; EDTA, 3; and di-FTC-insulin, 0.0002. The reaction was started by adding 0.3 mmoles of DTT (final volume, 3 ml) and measured by following the emission intensity at 519 nm while exciting at 495 nm. The excitation and the emission bandwidth on monochromators were at 5 nm. One unit of PDOR was the amount of enzyme that transforms 1 mmol of di-FTCinsulin per minute. Turbidimetric assay. PDOR activity was assayed at 227C by injecting the sample to be tested into a solution that contained 375 mg of insulin and the following (in micromoles): potassium phosphate buffer (pH 6.6), 50; EDTA, 1; and DTT, 0.165 (final volume, 0.5 ml). The precipitation of insulin B-chain was followed at 650 nm in a Gilford Response II spectrophotometer. Determination of PDI Activity The activity of B. napus PDI was measured by following the reactivation of scrambled RNase according to Hawkins et al. (12). Absorption Spectra Absorption spectra of 2.5 mM di-FTC-insulin were measured in a Gilford Response II spectrophotometer 1 Abbreviations used: di-FTC-insulin, di-fluoresceinthiocarbamylinsulin; DTT, dithiothreitol; EDTA, (ethylenedinitrilo)tetraacetate; PDI, protein disulfide isomerase; PDOR, protein disulfide oxidoreductase; Trx, Escherichia coli thioredoxin.

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(light path, 1 cm). Wavelengths were scanned from 600 to 240 nm (slit, 0.5 nm). Molar absorptivities at 495 nm in 1 M NaOH and 0.1 M potassium phosphate buffer (pH 7.5)/1 mM EDTA were 133,600 M01 cm01 and 94,000 01 M cm01, respectively. Fluorescence Emission Spectra A plastic spectrofluorometric cuvette (1 1 1 cm) contained 0.13 mM di-FTC-insulin dissolved in a solution of 0.1 mM potassium phosphate buffer (pH 7.5) and 1 mM EDTA. Emission spectra were measured at 227C on a Jasco FP770 spectrofluorometer by scanning from 500 to 600 nm (excitation wavelength, 495 nm) with the emission and excitation bandwidths at 5 nm. Other Methods The concentration of di-FTC-insulin solutions was measured by both the molar absorptivities described above and the method of Lowry et al. (13) using insulin as standard. The concentrations of Trx and PDI were determined by the molar absorptivity of 13,700 M01 cm01 at 280 nm for the former (10) and the method of Lowry et al. calibrated with bovine serum albumin for the latter. Mathematical Treatment of the Experimental Data To refine the estimation of rate constants, temporal variations of fluorescence emission were fitted to the kinetic model described in the Appendix. Fittings were performed with a personal computer using the Table Curve program (Jaendel Scientific) for nonlinear regressions. This procedure was performed for each experiment and rates of PDOR activity were calculated from the maximal positive slope of traces. RESULTS

Fluorescent Properties of Di-FTC-insulin The absorption spectra of oxidized and reduced diFTC-insulin showed the maximum at 495 nm, a shoulder around 460 nm, and other maxima at ca. 380, 317, and 283 nm (Fig 1A). Although similar profiles appeared when oxidized di-FTC-insulin was dissolved in 0.1 M potassium phosphate buffer (pH 7.5) containing 1 mM EDTA, the intensity was 31% lower. Apparently, intercatenary disulfide bonds make the substituent available for contact either with external molecules or with side chains of the polypeptide because the reduction of cystines with 10 mM DTT enhanced the intensity without shifting the maxima (Fig. 1B). In line with a quenching of the fluorophore, the emission spectrum of di-FTC-insulin was similar in shape and position, but lower in intensity, to free fluorescein (14). The significant basal fluorescence of di-FTC-insulin (F0) increased 2.8-fold when the pH rose from 6.2 to 8.4

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FIG. 1. (A) Absorption spectrum of di-FTC-insulin (2.5 mM) in 1 M NaOH. (B) Fluorescence emission spectra of di-FTC-insulin (0.13 mM) were recorded prior to (oxidized) and after (reduced) an incubation for 60 min with 10 mM DTT. The excitation wavelength was 495 nm.

(Fig. 2). Similarly, the fluorescence emission of reduced products (Ff) evinced a 2.4-fold enhancement over the same range of pH. At first it appeared that the transition of fluorescein from the monoanion to the dianion form (pKa ca. 6.4) would constrain the use of di-FTCinsulin. However, we found that the reductive process can be conveniently monitored using the fractional intensity associated with F0 , as marker of the oxidized substrate, and Ff , as indicative of reduced products. Plotting normalized intensities vs pH, [(Ff 0 F0)/F0] not only circumvented the use of arbitrary units in fluorescence measurements but also minimized the pH dependence to a slight decrease from 1.1 at pH 6.2 to 0.83 at pH 8.4. In particular, data from experiments carried out at pH 7.5 with different preparations of di-FTCinsulin confirmed that (Ff 0 F0)/F0 was 0.80 { 0.05 over a wide range of di-FTC-insulin concentrations. Congruent with these results, [(Ff 0 F0)/F0] remained invariable when the measurement of emission intensities was performed in the presence of 0.1 to 100 mM of K/, Mg2/, or Ca2/, even though both F0 and the concomitant Ff increased ca. 30% over this range of concentrations. Taken together, these data indicated that the fluorescence enhancement was relatively stable while the composition of the medium abruptly altered the absolute values of emission intensities. In other words, our estimation of di-FTC-insulin reduction was not affected by factors that drastically modified the fluorescence inherent to the fluorescein moiety. Biochemical Reduction of FTC-insulin The above findings prompted us to explore whether the enhancement of emission intensity that accompanies the reduction of di-FTC-insulin could be extended to the analysis of PDOR activity. To undertake this

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study, we chose Trx (12 kDa) as representative of the PDOR family because this ubiquitous protein has the ability to reduce a broad spectrum of disulfide bonds in proteins. Preliminary analysis of reaction products by polyacrylamide gel electrophoresis in the presence of sodium dodecylsulfate made evident that Trx accelerates the cleavage of intercatenary disulfide bonds of di-FTC-insulin by DTT (not shown). In line with the visual inspection, typical temporal variations of fluorescence given in Fig. 3A illustrate that emission intensities of solutions containing 0.7 mM di-FTC-insulin, 0.1 mM DTT, and variable concentrations of Trx comprised three well-defined phases: (i) a variable lag period, (ii) a steady increase in which the higher the concentration of Trx the faster the rate of fluorescence enhancement, and (iii) a final (constant) fluorescence emission [(Ff 0 F0)/F0 Å 0.80]. In order to implement the measurement of PDOR activity, we analyzed time–progress curves with a sequential model in which quantum yields of intermediates were lower than both the oxidized substrate and reduced products. A more rigorous treatment is given in the Appendix. The advantage of the proposed mechanism was that it accounts for all experimental data in the calculation of kinetic parameters, i.e., the decrease, the increase, and the plateau of fluorescence emission. Moreover, the second-order constants provided by this approach were congruent with biochemical reductions (k4 Å k5 Å 3.2 1 104 M01 s01) much faster than chemical reductions (k1 Å k2 Å 7.4 01 01 M s ). We maintained throughout the present study the value of k3 as 1.600 M01 s01 (4). Changing the concentration of Trx from 5 to 500 nM (i) shortened the extension of the lag period while increased the negative intensity of emission and (ii) stimulated the rate of fluorescence enhancement. For the

FIG. 2. pH dependence of the fluorescence emission of di-FTC-insulin prior to (F0) and after (Ff) the reaction with DTT. Di-FTC-insulin (32.4 mM) was incubated for 90 min at 377C in 0.1 ml of 100 mM Tris–HCl buffer (pH 7.9) containing 20 mM DTT and aliquots (0.01 ml) were withdrawn and injected into 3 ml of 50 mM Tris/50 mM potassium phosphate adjusted to the desired pH with either HCl or KOH. Excitation and emission wavelengths were 495 and 519 nm, respectively.

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FIG. 3. Effect of Trx on the biochemical reduction of di-FTC-insulin. Continuous lines were theoretical profiles calculated from the model described in the Appendix with parameters given in the text. (A) Time course of fluorescence. Symbols represent experimental values of emission intensity periodically measured (excitation. 495 nm; emission. 519 nm) in 2 ml of 100 mM potassium phosphate buffer (pH 7.5), 3 mM EDTA, 0.7 mM di-FTC-insulin, 0.1 mM DTT, and Trx, as indicated. (B) PDOR activity. Symbols represent maximum rates of fluorescence enhancement and errors were within 7%.

model described in the Appendix almost all of fluorescent changes in the lag phase express the formation of transient species, whereas the positive slope of fluorescence enhancement vs time 0(1/0.80)r(F2 0 F1)/ F0r[di-FTC-ins]00 represents the amount of di-FTCinsulin reduced in the period t2 –t1 . On this basis, these measurable rates provided a linear correlation between PDOR activity and concentrations of Trx lower than 200 nM (Fig. 3B); beyond this concentration, the causal link remained but departed from linearity. Cleavage of disulfide bonds in di-FTC-insulin is due primarily to Trx. However, some of di-FTC-insulin reduction and the maintenance of Trx in the reduced state are linked to the direct action of DTT (cf. Scheme I). To estimate the contribution of the reductant to the fluorescence measurement, we followed the progression of emission intensities of a solution containing 0.7 mM di-FTC-insulin, 70 nM Trx, and variable concentrations of DTT (Fig. 4A). Based on the previous model, typical theoretical curves accurately described the three

SCHEME I. Mechanism of di-FTC-insulin reduction.

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phases that constitute the temporal variation of emission intensity. Using these experimental data, second order constants were k1 Å 0.9 M01 s01, k2 Å 0.4 M01 s01, k4 Å 5.5 1 104 M01 s01, and k5 Å 6.2 1 104 M01 s01. Most significantly, the sequential model predicted the biphasic dependence of the rate of fluorescence enhancement on the concentration of DTT (Fig. 4B). Throughout the present study, solutions of di-FTCinsulin provided a linear dependence of fluorescence enhancement on substrate concentration up to 1 mM. Unfortunately, the pronounced inner filter effect hindered measurements at higher concentrations of diFTC-insulin. Comparison of the Fluorometric Assay with the Turbidimetric Method An important issue in our studies was whether the fluorometric method constitutes an advantage over the most used assay of PDOR activity, i.e., the quantification of light attenuation caused by the aggregation of insulin B-chain when intercatenary disulfide bonds are reduced (5). This technique has been used successfully many times because it relies on a readily available substrate and a common spectrophotometer. However, a disregarded aspect of this methodology is that the slowness and the low sensitivity of coalescence and precipitation give rise to a prolonged lag phase whose length depends on both pH and the concentrations of insulin and Trx. Therefore, a comparison of turbidimetry with fluorometry was performed and typical results are shown in Fig. 5. It can be seen that 1 mM (12 mg/ml) Trx elicited an immediate enhancement of fluorescence with 0.07 mM di-FTC-insulin, whereas a 30-min lag preceded the measurement of light attenuation with 130 mM insulin. Moreover, the fluorometric procedure was reliable with concentrations of Trx lower than 100 nM, whereas the turbidimetric assay lacked sensitivity.

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FIG. 4. Effect of DTT on the biochemical reduction of di-FTC-insulin. Continuous lines were obtained as indicated in the legend to Fig. 3. (A) Time course of fluorescence. Symbols represent experimental values of emission intensity measured as described in the legend to Fig. 3, except that concentrations of Trx and DTT were 70 nM and the indicated, respectively. (B) PDOR activity. Symbols represent maximum rates of fluorescence enhancement and errors were within 4%.

Estimation of the PDOR Activity of PDI with the Fluorometric Assay The cleavage, formation, and rearrangement of disulfide bonds involve the participation of distinct members of the PDOR superfamily. For PDI, it has been recognized that the reshuffling of disulfide bonds implies the reduction of cystines followed by an equivalent oxidation of different sulfhydryl groups; in other words, two successive thiol/disulfide exchanges maintain the initial redox status of the target protein (8). Hence, the question arose whether di-FTC-insulin would be a substrate for unraveling the underlying reductase activity of PDI. We obtained a homogeneous protein from B. napus seeds (homodimer; subunit molecular mass. 58 kDa) that was functional in the usual assay of PDI activity; i.e., the stimulation of the catalytic capacity of scrambled RNase (12). At pH 7.9, the rate of di-FTC-insulin reduction catalyzed by 6 mg/ml of B. napus PDI (1.5 units min01) was slower than 0.1 mg/ml of Trx (48 units min01) but, at pH 6.5, the former became more active (4.8 units min01),

whereas the latter lost 75% of the activity (12.9 units min01). Whether the enhancement of PDI activity at slightly acidic pHs is restricted to the B. napus enzyme or it was disregarded in previous studies is under investigation. However, these results clearly show that the fluorometric assay can be advantageously exploited for studying the reductase activity inherent to PDI over a wide range of experimental conditions. DISCUSSION

The PDOR activity has been studied extensively by following the precipitation of the insulin B-chain upon the reduction of intercatenary disulfide bonds. However, kinetic features that can be gathered by turbidimetry are somewhat limited as detectable signals appear after a prolonged lag phase and are extremely sensitive to the composition of the reaction milieu. The estimation of NADPH oxidation, in the biochemical reduction of Trx catalyzed by NADP-thioredoxin reductase, constitutes a sensitive measurement, but, unfortunately, endogenous metabolites and the composition of bio-

FIG. 5. Time course of Trx activity. (A) Fluorometric assay, (B) Turbidimetric assay.

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chemical media compromise the activity of the accessory enzyme. On the other hand, a large number of measurements rely on the separation of 125I-insulin from labeled free chains by HPLC. However, two shortcomings preclude the use of this two-stage assay for routine work: the risk associated to the extensive handling of radioactive materials during the separation of products from the unreacted substrate and, more critical, the lack of real-time measurement. The experiments described in this report show that, in the presence of DTT as reductant, di-FTC-insulin is a convenient oxidant not only for the rapid and sensitive quantification of Trx but also for other related PDOR (e.g., PDI). Apart from the absence of accessory enzymes, other features made this novel assay attractive. First, measurements of PDOR activity can normally be made quite reliably because both excitation and emission wavelengths lie in the visible region of the spectrum, thereby circumventing the interference of near UV absorbing molecules (e.g. oxidized glutathione). Second, emission intensities of di-FTC-insulin are sensitive to the composition of the medium, but the slight variation of normalized fluorescence enhancement over a wide range of pH and in the presence of various modulators minimizes experimental variations when handling a large number of samples and conditions. Finally, the fluorometric assay allows the use of DTT, GSH, 2-mercaptoethanol, and ascorbate as alternative substrates for GSH-dependent PDOR’s whose activity are commonly assayed by following NAPDH oxidation in the presence of glutathione reductase. One complication in the present assay is the initial period whose intensity (y-axis) and extension (x-axis) depends on the pH and the concentration of both the reductant and the catalyst. As described in the Appendix, the appearance of intermediates whose collective quantum yields are lower than the oxidized substrate precedes the formation of reduced products whose quantum yields are higher than both transient species and the oxidized substrate. Hence, the former process may be responsible for the anomalous initial drop of fluorescence, whereas the latter accounts for the subsequent increase. The fluorescence emission of reduced products finally reaches constant value when the reductive process exhausts both the oxidized substrate and intermediates. Supporting this view, emission spectra of the oxidized substrate, transient species, and reduced products have similar profiles but different intensities. While rarely stated explicitly, tacit assumptions are made in this treatment. First, we considered that individual steps of the reductive process are irreversible. This is a reasonable assumption because the reassociation of free insulin polypeptides is highly improbable at the concentrations of DTT used in the assay. Nevertheless, it is clearly not valid when the consumption of the reductant leads to a range of off-pathway reactions.

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Second, throughout the present study, k3 was the constant determined by Holmgren because it is unlikely that di-FTC-insulin affects the reduction of Trx with DTT (4). In this context, further studies are necessary to characterize the molecular structure of intermediates because their formation is probably more complex than a two-stage process, and additional species might be populated between the oxidized substrate and reduced products. Fluorescent data are completely in agreement with theoretical curves in which quantum yields of participants hold the relationship q3 ú q1 ú q2 . Moreover, the consistency of experimental data with the model gives basis for the calculation of rate constants underlying the chemical and the biochemical reduction of di-FTCinsulin. It is of interest that, notwithstanding we are analyzing a chemically modified insulin, k1 and k2 are similar to the second order constant for the chemical reduction of insulin by DTT (k Å 5 M01 s01) and k4 and k5 resemble those for the reduction of insulin by reduced Trx (k Å 1 1 105 M01 s01) (cf. Table 1 in Ref. 4). More important, the fluorometric assay constitutes an alternative for the quantification of the reductive process. If 0 and 0.80 are the normalized fluorescence enhancement for the oxidized substrate and totally reduced products, respectively, then (1/0.80)r(F 0 F0)/ F0r[di-FTC-ins]0 represents the amount of di-FTC-insulin transformed. Given that oxidized di-FTC-insulin decreases monotonically, the rate of product formation should be estimated when the contribution of reduced products to the total fluorescence supersedes that of transient species. Using the kinetic constants described above, closer inspection of the temporal variation of participants in the reductive process revealed that the maximal rate of fluorescence enhancement correlates with the maximal rate of product formation. On this basis, the activity of Trx arises from the positive slope in the time-progress curves; i.e., d{(1/0.80)r(F2 0 F1)/F0r[di-FTC-ins]0}/dt. Present studies demonstrate that Trx can be estimated very precisely at concentrations lower than 500 nM (6 mg/ml). Although this level of quantification is similar to spectrophotometric and radioactive methods, the fluorometric assay does not have the constrains described above. In this context, the comparison of fluorometry with turbidimetry deserves further comment. Although kinetic heterogeneity has been observed in both, the former is 10-fold more sensitive and requires shorter experimentation times than the latter. More than that, the fluorometric assay has potential utility in studies where turbidimetry becomes unreliable, i.e., crude extracts and multiple experimental conditions. When all data were taken together, we concluded that the one-stage method developed for quantifying Trx and PDI is sufficiently accurate and reproducible to use in studies of the reductive process catalyzed by PDORs. As a complement, Ruddock et al.

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recently reported that a novel decapeptide constitutes an excellent tool for the estimation of the oxidative process because a significant change in the fluorescence emission of a tryptophane residue located close to one of two cysteine residues accompanies the formation of the disulfide bridge (15).

two orders of magnitude higher than the other two components and, as a consequence, the concentration of reduced Trx remains in steady state. On this basis, Scheme I can be visualized as two consecutive pseudo first-order reactions ka

kb

SrIrP

APPENDIX

In this Appendix we present a model, with the accompanying procedure, for the determination of rate constants in a system that exhibits biphasic time–progress curves. The analysis of reductive process relies on consecutive second-order reactions where oxidized diFTC-insulin (S) is first transformed to partially reduced intermediates (I) which in turn are converted to totally reduced products (P) (Scheme I). As usual in most of the thiol/disulfide exchanges catalyzed by PDOR, DTT modifies disulfide bonds of both S and I either directly or mediated by Trx. The complexity of the pathway for the simultaneous operation of the chemical and the biochemical reduction rules out an analytical solution for reaction kinetics so that either steady-state solution or numerical methods must be used. To accomplish a significant simplification in the analysis, we consider collectively all transient species whereby k1 , k2 , k4 , and k5 are composite rate constants. The rate of disappearance of the oxidized substrate S is described by

Temporal concentrations of each species are [S]t Å [S]0r[exp(0kart)] 1 [exp(0kbrt) 0 exp(0kart)]

[9]

[P]t Å [S]0r{1 / [ka 0 kb]01 1 [kbrexp(0kart) 0 karexp(0kbrt)]}

[10]

because at any moment t, [S]0 Å [S]t / [I]t / [P]t . Given that emission intensities of S and chemically reduced P are linear functions of the concentration of oxidized di-FTC-insulin, then the initial (F0) and transient (F) emission intensities are

[1]

which turns to

[8]

[I]t Å [S]0r[ka/(kb 0 ka)]

F0 Å q1r[S]0 0d[S]/dt Å k1r[DTT]r[S] / k4r[Trx]r[S],

[7]

[11]

F Å q1r[S]t / q2r[I]t / q3r[P]t .

[12]

0d[S]/dt Å kar[S]

[2]

where q1 , q2 , and q3 are the proportionality constants that link the concentration of S, I, and P, respectively, to fluorescence measurements. The combination of Eqs. [8] to [12] leads to

ka Å k1r[DTT] / k4r[Trx].

[3]

(F 0 F0)/F0 Å [exp(0kart)]

when

/ [q2/q1]r[ka/(kb 0 ka)]r[exp(0kart) 0 exp(0kbrt)] On the other hand, the formation of P may be obtained taking k2 and k5 as second-order rate constants for the respective chemical and biochemical reduction of I: d[P]/dt Å k2r[DTT]r[I] / k5r[Trx]r[I]

[4]

turns to d[P]/dt Å kbr[I]

[5]

kb Å k2r[DTT] / k5r[Trx].

[6]

when

In our studies, this reduction of the reaction order is plausible because the concentration of DTT is at least

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/ [q3/q1]r{1 / [ka0 kb]01r[kbrexp(0kart) 0 karexp(0kbrt)]} 0 1, [13] which provides the relationship that exists at any time between normalized emission intensities and rate constants of the reductive process depicted in Eq. [7]. Our particular interest lies on a model where q3 ú q1 ú q2 , but the mechanism can be extended to situations in which q2 ú q3 ú q1 or even q2 Å q1 , whereby the temporal variation of fluorescence emission will show an initial burst or a classical lag phase, respectively. We used a nonlinear least-square technique (16) to fit experimental data to the theoretical curve described by Eq. [13]. This procedure is very useful in determining the magnitude of pseudo-first-order constants ka and kb , whose dependence on the concentration of DTT

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and Trx (cf. Eqs. [3] and [6]) leads to estimate k1 , k2 , k4 , and k5 . As corollary, Eq. [13] also describes not only the initial fall but also the subsequent increase of emission intensity from which the positive slope represents the rate of the reductive process. ACKNOWLEDGMENTS This work was supported by a contract with the European Economic Community (CT 92-0070) and grants from Universidad de Buenos Aires and Comisio´n de Investigaciones para el Agro (CIPAGRO). We are grateful to Dr. M. A. BallıB cora for helpful suggestions on the model described in the Appendix. A.P.H. is recipient of a fellowship from Consejo Nacional de Investigaciones CientıB ficas y Te´cnicas (CONICET), and R.A.W. is a Research Member of the same institution.

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