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Single turnover mechanism of a trypsin-reactor with high enzyme concentration
Journal of Biotechnology 60 (1998) 81 – 95
Single turnover mechanism of a trypsin-reactor with high enzyme concentration Paola Fermi, Riccardo Biffi, Virna Conti, Roberto Ramoni, Stefano Grolli, Paolo Accornero, Enrico Bignetti * Istituto di Biochimica Veterinaria, Uni6ersita` di Parma, 6ia del Taglio 8, 43100 Parma, Italy Received 15 August 1997; received in revised form 27 November 1997; accepted 28 November 1997
Abstract A small column containing 2 mM CH-Sepharose 4B-immobilized trypsin was connected to a flow injection device equipped for potentiometric measurements (0.01–2 mM protons) and for post-column analysis by spectrophotometry and capillary electrophoresis (CE). The device was engaged with Na-benzoyl-L-arginine pNO2-anilide (BAPNA), b-lactoglobulin (b-Lac) and peptides of V8-protease predigested b-Lac. At a given flow rate, the reaction with BAPNA or b-Lac (below 2 mM) produced about 1 proton per substrate molecule in each sample (linear relation to substrate amount); with peptides (below 22 mM), the reaction did not exceed 0.17 acid equivalents per substrate molecule (hyperbolic dependence). Final experiments demonstrated that the reactor gave a correct estimate of available lysine in peptides of b-Lac modified with 5-nitrosalicylaldehyde. The data could be predicted by a kinetic model describing the reactor performance in ‘single turnover’ conditions. The interplay between resident time and the non-catalytic amount of trypsin prevented each enzyme molecule from recycling as well as each substrate molecule (containing one or more cleavage sites) from encountering the enzyme more than once. In conclusion, both from the experimental and the theoretical point of view, this work permitted the analysis of trypsin behaviour in some extreme working conditions and indicates how to modulate the performance of an endoprotease-based reactor. A brief discussion on potential applications in protein mapping and tagging and in the quantitative analysis of protein bioavailability by means of a biosensorial strategy is also described. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Trypsin reactor; Single turnover reaction; Endoprotease-based biosensor
Abbre6iations: b-Lac, b-lactoglobulin (A and B isomers); BAPNA, Na-benzoyl-L-arginine pNO2-anilide; CE, capillary electrophoresis; CFA, continuous flow apparatus; D, V8 endoprotease digested b-lactoglobulin; FIA, flow injection analysis; M, 5-nitrosalicylaldehyde-modified b-lactoglobulin; MD, V8 protease-digested 5-nitrosalicylaldehyde-modified b-lactoglobulin; N, native b-lactoglobulin; NSA, 5-nitrosalicylaldehyde. * Corresponding author. Tel.: + 39 521 984865; fax: + 39 521 980624; e-mail: [email protected] 0168-1656/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 1 6 5 6 ( 9 7 ) 0 0 1 8 9 - 2
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1. Introduction A potentiometric biosensor based on endoproteases for the assay of amino acid content in proteins was recently proposed by Ramoni et al. (1994). The activity resulting from trypsin coupled to a glass electrode was assayed in a model reaction with Na-benzoyl-L-arginine pNO2-anilide (BAPNA) as a chromogenic substrate analogue. With this system, potentiometric measurements of proton production and spectrophotometric measurements of pNO2-aniline release during trypsincatalyzed hydrolysis of BAPNA were carried out in parallel. It was observed that BAPNA hydrolysis was not significantly affected by enzyme immobilization; however, the investigation did not include natural substrates. In the literature, the steric hindrance effects of solid supports on endoprotease activity have not yet been investigated in depth (Goldstein, 1976; Lilly and Dunnill, 1976). Furthermore, it was noted that direct contact between the biological matrix and the electrochemical sensor did not seem to be a prerequisite for an efficient response from the biosensor. As a matter of fact, it was interesting to observe that potentiometric signals of BAPNA hydrolysis did not depend on the trypsin-matrix whether wrapped in full contact to the glass electrode or dispersed in solution. It appeared worthwhile to study this unexpected result in more detail. Therefore, in these experiments, we tried to increase the capacity of the enzyme-electrode (built-in configuration) in the detection of lysines and arginines present in peptides or proteins. As a model, native and V8-endoprotease digested b-lactogloblulin (b-Lac) was chosen to represent true alimentary substrates. With these samples, however, reaction rates were difficult to interpret because they were too slow when compared to spontaneous acidification and too conditioned by substrate dimensions. This initial failure led to several conclusions: (1) when the enzyme was immobilized in a built-in configuration, it was in catalytic amounts and therefore the related signals were weak; (2) pH 8.7, which seemed to be the optimum for BAPNA hydrolysis (Fritz et al., 1974), was not the correct
working pH with natural substrates because amino groups in peptides exerted a strong buffering effect; and (3) in a built-in configuration, the enzyme matrix posed serious restrictions on the diffusion of peptides through inner enzyme layers, thus reducing dramatically the overall signal (see also point 1). Therefore, the methodology was modified by introducing three crucial changes: (1) the use of CH-Sepharose 4B, a CNBr-activated Sepharose modified by the addition of an eight-carbon arm in order to elongate the distance between trypsin and the matrix itself; (2) the use of an appropriate buffer working at pH 10 in order to reduce the buffering effect of the substrates and their products to a minimum; and (3) redesigning the system and adapting it to a flow-injection analysis (FIA) strategy (Danielsson and Mosbach, 1988). To this end, a continuous flow apparatus (CFA) was developed. The enzyme reactor was located upstream and physically apart from a chamber (flow cell) containing the electrochemical sensor. In point three a FIA system can work when the biological signal at the enzyme-reactor is large and stable and can propagate unperturbed downstream to the sensor. Furthermore, it was highly desirable to obtain a conversion efficiency close to 100% (Ho, 1988). This requirement derived from a need either to counterbalance high detection threshold of the apparatus and to collect enough product for postcolumn analytical purposes, especially when dealing with protein analysis. In the procedure there were several parameters affecting reactor performance and most of them (e.g. physical dispersion) could be easily controlled. Overall, however, the amount of immobilized enzyme played a key role. In conventional biosensors, enzyme immobilization on planar surfaces usually occurs to a limited extent so that, considering the concentration in the total assay volume, the enzyme works in small catalytic amounts and according to classic ‘steady-state kinetics’ (Guilbault, 1976). In CFA, on the contrary, trypsin was immobilized on Sepharose-4B beads and tightly packed in the reactor thus reaching a local concentration comparable to or larger than substrate Km. To a degree, these conditions should have mimicked some assays in solution with high enzyme concentration (Reiner, 1969; Segel, 1975) or fast kinetic experiments carried out in
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continuous- and stopped-flow apparata by ‘rapid mixing techniques’ (Fierke and Hammes, 1995). In our case, not every step of substrate conversion could be followed, however, it was still possible to measure the amount of product released by the reactor at the end of the resident time. Therefore, only amplitudes, rather than rates, were the significant signals reported here. Nevertheless, it was possible to derive a kinetic model to describe the effect of high local enzyme concentration on the performance of a single reactor engaged with different types of substrates at a given flow rate.
2. Materials and methods
2.1. Trypsin immobilization Bovine pancreas trypsin (Boehringer, Germany) was immobilized either on CNBr-activated Sepharose 4B (Pharmacia, Sweden) or on CH-Sepharose 4B (Sigma), following customer indications. In these experiments, 150 ml of swollen CH-Sepharose gel was obtained from 50 mg of dry resin. The coupling yield was : 7 mg of immobilized enzyme per 150 ml of gel. Compared to the protein binding capacity of this resin, immobilized trypsin corresponded to 40 – 50% of resin equivalents. The enzyme gel was packed into a 4 mm diameter column (reactor). Since the molecular fractionation range of CHSepharose 4B gel was between 6×104 and 2× 106 Da, it was assumed that trypsin (a 23 kDa protein) could freely diffuse between gel particles and within gel pores and that it could attach to the resin surface facing outer and inner volume of the gel. By using p-nitro-aniline as a chromophoric tracer, it was observed that this volume almost coincided with the total volume of the gel. Conversely, the void volume V0 of the gel was only 37% of the total. Therefore, enzyme amount Etot $2 mM was calculated by considering the total volume of the cylindrical bed, in accordance with Lilly et al. (1966) and Shan et al. (1993). The void volume was used in calculating the resident time of the mobile phase (see below).
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2.2. Assay buffer All the assays were made in non-degasled aqueous solvents, buffered at pH 10.0 by the addition of NaHCO3 (0.5 mM) and NaOH. At this pH, trypsin was still quite active (Greene and Bartelt, 1977) and spontaneous acidification due to CO2 in the air was prevented long enough to guarantee a stable baseline. At this pH, C-terminal carboxyl groups, which were enzymatically released upon peptide bond cleavage, fully dissociated a proton. On the other hand, N-terminal a-amino groups that were concomitantly released, associated protons to a very low extent. Thus, the undesirable buffering effects of the products were minimized. In this buffer, the signal–noise ratio of the device remained quite satisfactory, as it was sensitive to additions of 10 − 5 M protons.
2.3. Continuous flow apparatus The assay buffer flowed through the trypsin reactor by means of a peristaltic Econo-pump (Biorad) at constant rates (0.1–1 ml min − 1). Substrate samples (200–800 ml) were loaded using a valve and eluted with the assay buffer at the same rates. The outlet of the column was connected to a flow chamber (inner volume of : 1.5 ml) that contained a magnetic stirring bar and a pHC 2406 glass electrode (Radiometer, Denmark). The electrode was connected to a PHM62 Standard pH-meter (Radiometer, Denmark) interfaced with a REC-102 chart recorder (Pharmacia, Sweden). Traces were recorded in mV. After every assay, a pulse (0.4 ml) of NaCl (150 mM) was injected in order to wash the resin. Samples coming out of the flow chamber were fractionated and read in a standard UV-vis spectrophotometer or analyzed by CE. Calibration of the apparatus was carried out by loading and eluting two of the products of trypsincatalyzed reaction with BAPNA: p-nitro-aniline and protons. The aniline derivative, monitored by spectrophotometry, was indicative of CFA elution pattern. Conversely, HCl pulses in the assay buffer determined the potentiometric calibration curve of the device.
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All measurements were carried out at room temperature. It was determined that the reactor could be stored at 4°C for 1 month without significant loss of activity.
2.4. Trypsin substrates 2.4.1. BAPNA The hydrolysis of BAPNA (Boehringer, Germany) could be observed with the spectrophotometer as already reported by Ramoni et al. (1994). Stock solutions were freshly prepared in the assay buffer prior to use (2 mM is the solubility limit). 2.4.2. Nati6e b-lactoglobulin A three-fold crystallized fraction of bovine milk b-Lac (containing A and B isomers) (Sigma) was used as a native protein substrate (N). 2.4.3. Predigested b-lactoglobulin Predigestion of b-Lac into smaller peptides (D) was carried out by incubating a stock solution of N (1 mM) with staphylococcal V8 protease (Sigma; 10 − 7 to 10 − 6 M) at 37°C for 12 h in the presence of phosphate (5 mM) buffered with additions of NaOH to maintain a constant level of pH 7.8. In these conditions, V8 protease cleaved peptides bonds at C-terminal sites of glutammic and aspartic acids (Drapeau, 1976; 1977). Aliquots of the stock solution were kept frozen at − 20°C and were thawed and diluted immediately before use. The molecular weight composition of N (200 ml of 0.5–1 mM) was analyzed in fast protein liquid chromatography apparatus (FPLC) (Pharmacia, Sweden) by running a gel permeation chromatography on a Superdex-75 column (optimal exclusion range: 300–70 000 Da) equilibrated with the assay buffer and calibrated with a mixture of pure bovine serum albumin, ovalbumin and soybean trypsin inhibitor (Sigma). Conversely, the composition of D was determined by analyzing the peptide mixture using CE, in a PACE 5000 (Beckman) controlled by System Gold version 8.1. Runs were performed in phosphate buffer (50 mM) pH 2.7, at constant voltage (25 kV) and at 20°C in a capillary of 50 cm effective length and
75 mm I.D. The electropherograms were monitored at 214 nm with a data collection rate of 5 Hz.
2.4.4. Modified b-lactoglobulin b-Lac (0.5 mM) was incubated with 5-nitrosalicylaldehyde (NSA; 50 mM) (Sigma) in bicarbonate buffer (50 mM) at pH 9.0 at room temperature for 30 min. Then, NaBH4 (3–5 mg ml − 1) was slowly added to the sample under continuous stirring (Means, 1977). After overnight dialysis in the assay buffer at 4°C, the modified protein showed a strong absorbtion at 390 nm that, when divided by the corresponding molar extinction coefficient = 13200 M − 1 cm − 1, resulted in a maximum of 21 blocked primary amino groups out of the 32 present in the protein dimer. The molar extinction coefficient was estimated by carrying out experiments with reversed reagent concentrations (i.e. by keeping the protein in large excess with respect to NSA). Modified b-Lac (M) was also predigested with V8 protease and fragments (MD) were analyzed by means of CE, in the same experimental conditions.
3. Results
3.1. Choice of the apparatus and calibration The sketch of the CFA is reported in Fig. 1 (Roda et al., 1988). Firstly, our device was calibrated with respect to flow dynamics and dispersion. After loading 400 ml of p-nitro-aniline samples (0.25–2 mM) with a flow rate of 0.2 ml min − 1 (for example see Fig. 2A), the front of the dye reached the flow chamber in 5 min. Then, more than 90% of the dye was eluted from it in a further 30 min, approximately, in a total volume of 6 ml with a 15-fold dilution as a mean. Similar results were obtained when calibrating CFA with HCl. Signal bell shapes (Fig. 2B) were not symmetric and showed a large base, mainly reflecting two phenomena: physical dispersion along the path and large dilution into the flow cell. However, they were reproducible at the same
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3.2. ‘Single turno6er’ kinetic model The overall trypsin reaction could be written as the unireactant mechanism:
(1)
Fig. 1. Schematic view of the ‘constant flow apparatus’ (CFA).
flow rate. From the comparison with HCl calibration curves, the amount of protons released by the reactor in the presence of any substrate could be evaluated.
Several enzyme reactors have been described in the literature (Lilly et al., 1966; Goldman et al., 1971; Roda et al., 1988; Cobb and Novotny, 1989; Kumaran and Tran-Minh, 1992; Nashabeh and El Rassi, 1992). In most examples, substrate conversion was never complete, even at very low flow rates. The oldest case was the clear example reported by Lilly et al. (1966) where product concentration was linearly related to the logarithm of the fraction of the remaining substrate. For this model, the appropriate kinetic equation was derived from the integrated form of the classic Henri equation in ‘steady-state’ conditions with
Fig. 2. Calibration of CFA. (A) Spectroscopic (bars) and potentiometric (solid line) signals with pulses (2 mM, 0.4 ml) of p-NO2-aniline and of HCl, respectively, eluted at a constant flow (0.2 ml min − 1). (B) Relationship between potentiometric signals (peak heights) and HCl (open circles) or BAPNA (filled circles), respectively. Samples (0.4 ml) varied from 0.25 to 2 mM and were eluted at constant flow (0.2 ml min − 1) with the assay buffer. The two sets of data could be interpolated by straight dashed lines according to linear regression analysis (r \0.95). Peak areas plotted instead of peak heights gave same results. The solid line referred to BAPNA dependence theoretically expected on the basis of the ‘single-turnover’ kinetic model described in the text.
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substrate in large excess (Henri, 1904). On the contrary, our results could be understood only by keeping in mind that the retention time could be adjusted to block reaction at will. Moreover, the presumed concentration of trypsin Etot in the reactor was very high ( : 2 mM), i.e. it was larger than or comparable to substrate Km (see below and Table 1). Therefore, at any given time, the fraction of enzyme-bound substrate and enzymebound product would be consistent relative to free species; the usual ‘steady-state kinetics’ behaviour with catalytic amounts of enzyme could not be expected. Under such experimental conditions and by defining a single turnover reaction as a single cleavage on each substrate molecule whether it contains one or more cleavage sites, the kinetic model should: (1) avoid the assumption of Stot constant during the reaction, a typical bottleneck in the mathematical treatment posed by ‘stationary conditions’ with catalytic enzyme amounts (Gutfreund and Sturtevant, 1956; Fierke and Hammes, 1995); and (2) give indications on how to modulate sample flow rate in order to limit the reactor to a single turnover during resident time. Data interpretation could be carried out using the model based on ‘steady state kinetics with high enzyme concentrations’ (Reiner, 1969; Segel, 1975) or on the model based on ‘transient kinetics’ (Luisi and Bignetti, 1974; Fierke and Hammes, 1995; Johnson, 1995). In our opinion, only the ‘transient kinetic’ approach could satisfy the expectations created by the second point made above (Appendix A). Briefly, starting from (1), general equation: 1 Ptot = [(Stot + Etot + Km) 2 − (Stot + Etot +Km)2 −4StotEtot] (1−e − kcat(V0/Q))
(A10)
and two simplified forms, respectively for ‘substrate saturation by the enzyme’ and for ‘enzyme saturation by the substrate’: Ptot =
Etot S (1 − e − kcat(V0/Q)) Etot +Km tot
(A11)
Ptot =
Stot Etot(1−e − kcat(V0/Q)) Stot + Km
(A12)
were derived considering Kd(ES) = Km, k2 = kcat, V0 = 0.055 ml and sample flow rate Q expressed in ml min − 1.
3.3. Substrate analysis 3.3.1. BAPNA Firstly, steady-state kinetic parameters of BAPNA hydrolysis were reevaluated at the spectrophotometer by using catalytic amounts of immobilized trypsin in stirred suspensions at pH 10.0. The data, plotted by the Lineweaver–Burk method (not shown), gave Km = 0.2 mM and kcat = 25 min − 1 (see Table 1). Subsequently, the behaviour of CFA with pulses (0.4 ml) of BAPNA (0.25–2 mM) was tested. Flow rate could be adjusted between 0.2 and 0.3 ml min − 1 without significant variations in the response. Experimentally, time scale and profile of the potentiometric traces closely resembled those obtained with the two calibration tests of CFA as reported in Fig. 2A. The linear plot in Fig. 2B was obtained by reporting peak heights (or areas) as a function of BAPNA. By comparison with the proton calibration curve, hydrolyzed BAPNA was 72% in all samples. In reasonable agreement with this result it was observed, using the spectrophotometer, that BAPNA was converted with an efficiency of Ptot/Stot of :80%. With flow rates below 0.1 ml min − 1, the time required for the assay was too long and the baseline was too steep. Conversely, by increasing flow rates above 0.2 ml min − 1, signals tended to assume the form of sharp peaks but conversion efficiency fell dramatically. At a rate of 1 ml min − 1, signals (peak areas) were : 40% lower and this was confirmed by spectrophotometric measurements showing that only 50–60% of BAPNA was hydrolyzed. In these experiments, the relationships Etot ] Stot and Etot Km seemed to be operative (Table 1) thus the kinetic model discussed above and, in particular, Eq. (A11) were used to interpret these data. In fact, a conversion efficiency Ptot/Stot of 89% with Q=0.2 ml min − 1 (see Fig. 2B) and of 67% with Q= 1 ml min − 1 was calculated.
0–2 0–1 0 – 22
b
Calculated with trypsin-Sepharose in suspension. Depending on different aggregation states. c Depending on dimensions (see Fig. 3). d Calculated on the basis of a ‘single turnover’ kinetic model.
a
10.0 6.6 1.8
25 6 12
BAPNA Native b-Lac Predigested bLac
0.2 0.3 1.1
kcat a (min−1) Km a (mM) E0/Km Explored range (mM)
Substrate
Linear Linear Hyperbolic
Response
1 17 – 68b 53c
0.8 1.1 B1
Cleavable sites per sub- Observed cleavages per strate molecule substrate molecule
0.9 0.8 B1
Predicted cleavages per substrate moleculed
Table 1 Functional and kinetic properties of a trypsin reactor (150 ml) containing 2 mM enzyme with different substrates at constant flow (0.2 ml min−1)
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3.3.2. Nati6e b-lactoglobulin Native b-Lac is a dimer of 18 kDa subunits. The aggregation state and isomer composition of the protein at pH 10 was analyzed by gel permeation chromatography. The result indicated the coexistence of different aggregation states in bLac, mainly: monomers, dimers and tetramers, at a molar ratio of :4:1:1.5. Thus, from now on in the text, the concentration of N corresponds to the sum of the individual concentrations of all the different b-Lac forms present in solution. Using CE, N gave two major peaks according to the presence of A and B isomers (not shown). Steady-state kinetic parameters of N hydrolysis with a known amount of immobilized trypsin was evaluated. Assays were carried out by means of the pH-meter, with the active matrix in stirred suspensions and with catalytic enzyme amounts (not shown). Summarizing the results, it was very difficult to precisely define steady state kinetic parameters with N. As with other endoproteases (unpublished observations), the immobilization negatively affected the access of large substrates to trypsin and caused unspecific interactions with it. In fact large amounts of active resins and long incubation times were needed for mapping of a protein sequence in batch conditions. Moreover, the substrate concentrations were kept at or below 1.3 mM in order to avoid undesirable viscosity and buffering effects. Even though the Lineweaver–Burk plot was affected by a large S.E., apparent Km = 0.3 mM and kcat =6.0 min − 1 were calculated (see Table 1). In principle, inhibition experiments of BAPNA hydrolysis in the presence of variable N should confirm the validity of these parameters. Indeed, BAPNA hydrolysis was inhibited by N additions but in a ‘mixed-type’ mode, a totally different behaviour compared to the typical ‘competitive’ mode observable with the soluble enzyme. A mixed-type inhibition could not be explained per-se, unless it was due to the occurence of reduced active site availability and unspecific protein–resin interaction. Subsequently, N pulses (0.4 ml up to 1.3 mM) were loaded and eluted through CFA at a constant flow (0.2 ml min − 1). The relationship between signals and N concentration is reported in Fig. 4A and in Table 1. The data could be inter-
polated by a straight line applying linear regression analysis. In conformity with the proton calibration curve in Fig. 2B, 1.1 peptide bonds were split in each b-Lac molecule as a mean. After CFA elution, N samples were extensively dialyzed using membranes with a molecular cutoff of 12 kDa, in order to remove large fragments possibly produced by the reactor. Nevertheless, their optical densities at 280 nm were only slightly changed. This was indicative of an almost complete recovery of b-Lac after dialysis, but nothing could be deduced about primary sequence integrity. Therefore, samples passed through CFA were analyzed by CE. The analysis indicated a very low digestion of the major components into few small peaks at longer retention times. This evidence, together with the small CFA signals, suggested that only a few low-dimension peptides at the protein surface were removed. According to kcat, a single b-Lac dimer with 34 cleavage sites would require about six turnovers, i.e. 1 min or more, to be completely digested. However, resident time (16.5 s) did not permit more than one or two cycles. In fact, the degree of digestion corresponded to a stoichiometry of one cleavage per substrate molecule, that is, in terms of substrate ‘molarity’, conversion efficiency was close to 100%. On the basis of the results, the ‘single turnover’ model was reconsidered and Eq. (A11) applied as the most likely to describe a situation close to Etot ] Stot and Etot (Km) The equation gave 80% of substrate conversion, i.e. 0.8 specific bonds cleaved per protein molecule as a mean (see Fig. 4A).
3.3.3. Predigested b-lactoglobulin As confirmed by CE analysis, V8 protease digestion of b-Lac resulted in the detachment of five single amino acids and 24 peptides (see Fig. 3). Two of these peptides, are discarded by trypsin since they contain a lysine donating a carboxyl group to a proline (Laskowski and Sealock, 1971). Therefore, in the text, D concentration is always referred to as the molar concentration of dimeric b-Lac multiplied by 22. Steady-state kinetic assays with D and with immobilized trypsin in stirred suspensions were carried out. Using the glass electrode, the active
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Fig. 3. Primary structure of b-lactoglobulin (A* and B° variants) according to Swiss-Protein Database. Theoretical cleavage sites of trypsin and of V8 endoprotease were shown, respectively, with (n) and (¡). The lysine – proline bond was voluntarily excluded for trypsin specificity reasons.
resin exhibited an apparent Km =1.1 mM and a kcat = 12 min − 1 (see Table 1). By spectrophotometry, inhibition kinetics showed that D played the role of a competitive inhibitor towards BAPNA hydrolysis with an apparent Km =0.83 mM consistent with the corresponding Km mentioned above. The results obtained with CFA are reported in Fig. 4B. Potentiometric signals increased asymptotically with substrate and levelled off at a nominal D concentration of 12 mM. From a comparison with the proton calibration curve in Fig. 2B, it was noted that signal amplitudes at the plateau corresponded to a maximum production of 1.8 mM protons. Interestingly, this concentration coincided almost perfectly with enzyme equivalents in the reactor, as if the enzyme became limiting as substrate tended toward infinity. The reaction did not exceed a single turnover notwithstanding the presence of excess substrate and a resident time allowing more than three enzyme recyclings. It is also worth noting that D had the lowest affinity for the enzyme (Km $Etot) among the substrates used (see Table 1). Therefore, these data could be analyzed only by using the general Eq. (A10). The solid line in Fig. 4B
was the result predicted by the model by assuming signal saturation at 2 mM protons and Kd(ES) = Km = 1.1 mM. A better view of the comparison between experimental data and theoretical expectations is reported in Fig. 4C. The experimental data in Fig. 4B are considered to be the consequence of a simple isotherm of ligand binding to a homogeneous set of specific enzyme sites. These results were linearized in a double reciprocal plot. A linear regression analysis (r\ 0.97) gave an apparent Kd(ES) = 1.9 mM quite in accordance with Km and with the straight line predicted by the model.
3.3.4. Modified b-lactoglobulin Finally, it was tested whether CFA could monitor the reduced availability of b-Lac with chemically modified lysines (M). After an extensive protein treatment with NSA (see Section 2) and considering the presence of two lysine–proline bonds (not attacked by trypsin) and six unmodified arginines in a dimer, we calculated that trypsin cleavable sites in M were reduced to 39– 44% of N. The enzymatic activity of trypsin activity, either in solution or in suspension, was negligible in the presence of this sample. Then M
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Fig. 4.
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was predigested with V8 protease into peptide fragments (MD) and these were loaded into the reactor. A control experiment was carried out with a non-modified predigested sample (D). The device gave signals with MD (not shown) that were about 35% of the signals observed with D and only slightly below the predicted 39 – 44% range. As reported above, the reactor could not recognize M. This evidence might be explained by assuming that all the lysines on the protein surface had been modified blocking trypsin access to the core of the protein where the remaining unmodified sites were located. Qualitatively speaking, the hidden potentiality in M was not revealed giving an erroneous view of its intrinsic bioavailability. In contrast MD gave significant signals. The small difference between experimental and expected availability might be attributed to a possible cross-inhibitory effect of peptides carrying modified lysines on overall trypsin reaction.
4. Discussion Several analytical methods for lysine detection have been proposed so far, but all of them have been able to recognize lysine or its derivatives only when free in solution. Moreover, these methods were often inaccurate because of lysine modifications during sample preparation (Peterson and Warthesen, 1979; Acquistucci et al., 1987; Medina Hernandez and Garcia Alvarez-Coque, 1992). Therefore, the development of a biosensorial strategy for lysine detection in proteins by using an endoprotease represented an interesting alternative worth pursuing. To this end, trypsin was chosen because its activity is strictly specific for the cleavage of peptide bonds involving arginine or lysine and because its structure and function are well established.
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After several trials with different potentiometric devices and trypsin immobilization procedures, it was finally decided to explore the performance of an FIA apparatus connected to a reactor containing the enzyme immobilized on CH-Sepharose 4B resin. This was a new approach that required careful theoretical enzyme kinetic evaluations. Besides the fact that enzymatic proteolysis is generally characterized by small turnover numbers, several parameters had to be considered since the recorded signal was the result of a balance between protons produced by the reactor, physical dispersion of the signal in the carrier stream, assay buffer characteristics, spontaneous acidification in open vessels and buffering effects of reagents and products. Therefore, in order to increase the relative amplitude of the biological signal obtained at the enzyme-reactor level, even with substrates present at concentrations well below their Km, trypsin at high concentration (2 mM) was loaded into the reactor. The results show the effect of this parameter on reactor conversion efficiency at a given flow rate. The main features of our reactor are summarized in Table 1. It should be emphasised that, working with a protease, a certain degree of ambiguity regarding the term ‘conversion efficiency’ may arise depending on whether the concentration of substrate molecules or the concentration of all cleavable sites is considered, since these concentrations always coincide in an analogue substrate but not always in a natural one. In steady state kinetic conditions the splitting of a cleavable site in a natural substrate most probably doubles substrate molecules, at least at the very beginning of the reaction. Moreover, protein digestion produces peptides with a different Km and it cannot be predicted which kind of substrate is going to be processed preferentially at each enzyme cycle. Other problems like steric hindrance, unspecific substrate adhesion, etc. might also arise working with an immobilized enzyme. Thus, it might be
Fig. 4. (A) Relationship (filled squares) between potentiometric signal (peak heights) and molar concentrations of native b-lactoglobulin. (B) Relationship (filled squares) between potentiometric signals and molar concentrations of a b-lactoglobulin peptide mixture. (C) Double reciprocal plot of the data in B (filled squares). Solid lines in (A), (B) and (C) corresponded to theoretical curves obtained by assuming the ‘single turnover’ kinetic model described in the text. Dashed lines in (A) and (C) were interpolations calculated by using linear regression analysis (r\0.97).
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hard to assume a simple Michaelian kinetic model of the type shown in Eq. (1) to describe the activity of an immobilized endoprotease. However, it should be noted that transient reactions observed in our reactor were described best by a ‘single turnover’ kinetic model that utilized the steady state kinetic parameters kcat and Km calculated assuming Eq. (1). Considering substrate molarity, it was observed that 100% of BAPNA or b-Lac molecules and only a maximum of 17% of b-Lac peptides did not encounter a trypsin molecule more than once during the resident time. This striking difference was due to the fact that, BAPNA or b-Lac molecules engaged a stoichiometric enzyme amount because the ratio Etot/Km was sufficiently higher than 1; vice versa, the b-Lac peptides reaction exhibited a substrate saturation dependence of the classical Michaelian type because Etot/Km was close to 1. Using this data, an appropriate flow rate by which BAPNA could undergo a complete conversion in all samples was found. At this flow rate, approximately one of the 34 cleavable sites in N was cut by the reactor. Since enzyme concentration was saturating, this event occurred simultaneously on all substrate molecules and, most probably, at the same primary sequence site. A general protocol based on these experimental conditions might offer a good tool to tag protein substrates (e.g. enzymes, antibodies, receptors, etc.) for the study of the relationship between structure and function. To this regard, the reactor response to b-Lac, in comparison to the lack of response to the same protein that was modified at the surface by other means, should be noted. In the case of peptides, conversion efficiency was low. Nevertheless, in terms of absolute concentration this corresponded to 2 mM product under substrate saturating conditions. Such a large product accumulation could not be easily achieved in only a few seconds in any other conventional assay based on catalytic enzyme amounts. This might represent an advantage from a general point of view since large amounts of products are often required for different postcolumn analytical purposes. Moreover, although the reactor analyzed only a small percent of the
total peptides in a sample, it could give a correct estimate of the fraction of lysines that were originally modified in the native protein. Apart from kinetic considerations, essential amino acid detection and quantitation through a biosensorial strategy might supply a parameter for total quality certification in food technology applications. We believe that our results justify a further development of the system. In order to facilitate the analysis of the integrity of protein core amino acids, a reliable predigestion of N with V8-endoprotease was developed. Enzymatic sample treatment prior to a specific instrumental analysis is a useful step already described in the literature (Nashabeh and El Rassi, 1992 and the literature cited therein). We are now trying to improve this procedure by preincubating the sample with a mixture of endoproteases in a microdialyzing device positioned upstream. This step would also help the analysis with realistic samples. A similar experimental approach has never been considered in detail in preceeding enzyme-reactor studies. In general, this work was limited by high enzyme costs and by a low protein coupling efficiency of active planar or round surfaces. Today, trypsin and Sepharose-4B beads are inexpensive and extremely versatile. In particular, this resin exists in various activated forms for high efficiency covalent protein coupling and is easy and safe to handle. Moreover, protein coupling to Sepharose occurs in mild aqueous solvents and involves mostly external primary amino groups, thus preserving native structure and activity of the attached ligand. Finally, Sepharose shows hydrodynamic properties that are adequate for this application and an exclusion range that could be problematic only for the diffusion of very large macromolecules. Gels of this matrix with attached antibodies or proteins for various purposes such as affinity chromatography (Bignetti et al., 1987), selective immunoaffinity isolation of microorganisms (Scolari et al., 1993) and ligand–protein interaction studies (Bussolati et al., 1993) have already been used in our laboratory. Here, it can be concluded that such a matrix, indeed, fulfills all the requirements for the development of an enzyme-reactor.
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Acknowledgements We would like to thank John P. Verville for the critical reading of the manuscript. This work was supported by National Research Council of Italy, special project RAISA, sub-project 4.
Appendix A For simplicity, it has been assumed that the reactor volume V0 (0.055 ml) is a thin working section of exchangeable water which is replaced by another one flowing with constant rate Q (expressed in ml min − 1). The total sample volume passing through the reactor can be considered as the sum of several working sections equal to V0. Looking at the example of chymotrypsin in pre-steady-state experiments in solution (Gutfreund and Sturtevant, 1956) and in steady-state experiments in the crystal (Merli and Rossi, 1986), the steps represented in Eq. (1) may occur in each working section:
(2) Moreover, it has been assumed that: (1) large amounts of the substrate may be tied up rapidly (approximately at t =0) in the binary (ES) complex; (2) the bimolecular process of (ES) formation equilibrates rapidly relative to its decay (k − 1 k2) so that substrate binding can be treated as a kinetically independent process with the equilibrium dissociation constant Kd(ES) =Km; (3) the conversion of (ES) into (EP) represents a simplified step including the transfer of an acyl group from substrate to enzyme, a concomitant amino group liberation and the subsequent intermediate deacylation (the rate determining step); thus, k2 =kcat; and (4) the conversion of (EP) back to (ES) can be neglected for energetic reasons; (5) at the end of a single turnover, a rapid binding equilibrium between (E) and (P) (proton included) in the same concentration range is achieved; therefore, it is conceivable that (EP)
93
accumulates as a dead-end complex ([EP]k3 E][P]k − 3) thus preventing further enzyme recycling (unpublished steady state experiments in the presence of large amounts of products with trypsin in solution confirmed the possibility of product inhibition). According to these assumptions, the product concentration calculated in any working section is equivalent to product concentration in the total sample volume at the end of the overall reaction. In order to calculate it, mass conservation relationships with substrate and enzyme concentrations Stot and Etot before mixing, are posed: Stot = (S)0 + (ES)0
(A2)
Etot = (E)0 + (ES)0
(A3)
and the following quadratic expression is derived: (ES)0 1 = [(Stot + Etot + Km) 2 − (Stot + Etot + Km)2 − 4StotEtot]
(A4)
Then, provided that the resident time limits the reaction extent to no more than a single turnover, (ES)0 is converted to products in a single exponential decay according to rate equation: 6=
d(ES)0 d((EP)t + (P)t ) dPtot =− = (ES)0k2 = dt dt dt
= (ES)0kcat
(A5)
By substituting the quadratic expression Eq. (A4) into Eq. (A5), the form assumed is: 1 6 = kcat[(Stot + Etot + Km) 2 − (Stot + Etot + Km)2 − 4StotEtot]
(A6)
This form can be adopted in general. Nevertheless, in the limiting case that Etot Stot (namely at conditions of ‘saturating substrate with the enzyme’), Eq. (A6) can be simplified according to ‘binomial approximation’ (Reiner, 1969): 6=
Etot S k Etot + Km tot cat
(A7)
On the contrary, when Stot Etot (‘saturating enzyme with the substrate’), the simplified form which is symmetrical to Eq. (A7) is:
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94
6=
Stot EtotKcat Stot + Km
(A8)
Product concentration at resident time t (V0Q − 1) can be calculated by integrating Eq. (A5): Ptot =(EP)t + (P)t = (ES)0 −(ES)t =(ES)0(1− e − kcat(V0/Q))
(A9)
Eqs. (A6), (A7) and (A8) can be integrated respectively as: 1 Ptot = [(Stot + Etot + Km) 2 − (Stot + Etot +Km)2 −4StotEtot] (1−e − kcat(V0/Q))
(A10)
Ptot =
Etot S (1 − e − kcat(V0/Q)) Etot +Km tot
(A11)
Ptot =
Stot E (1 − e − kcat(V0/Q)) Stot +Km tot
(A12)
When Ptot =(ES)0 enzyme molecules are synchronized in a single turnover reaction at each working section renewal.
References Acquistucci, R., Bassotti, G., Cubadda, R., 1987. Valutazione di metodi chimici per la determinazione della lisina disponobile in alimenti ad elevato contenuto in carboidrati. Riv. Soc. Ital. Sci. Aliment. 16, 447–452. Bignetti, E., Damiani, G., De Negri, P., Ramoni, R., Avanzini, F., Ferrari, G., Rossi, G.L., 1987. Specificity of an immunoaffinity column for odorant-binding protein from bovine nasal mucosa. Chem. Senses 12, 601–608. Bussolati, L., Ramoni, R., Grolli, S., Donofrio, G., Bignetti, E., 1993. Preparation of an affinity resin for odorants by coupling odorant binding protein from bovine nasal mucosa to sepharose 4B. J. Biotechnol. 30, 225–230. Cobb, K.A., Novotny, M., 1989. High-sensitivity peptide mapping by capillary zone electrophoresis and microcolumn liquid chromatography, using immobilized trypsin for protein digestion. Anal. Chem. 61, 2226–2231. Danielsson, B., Mosbach, K., 1988. Introduction. Methods Enzymol. 137, 3 – 14. Drapeau, G.R., 1976. Protease from Staphylococcus aureus. Methods Enzymol. 45, 469–475. Drapeau, G.R., 1977. Cleavage at glutamic acid with staphylococcal protease. Methods Enzymol. 47, 189–191. Fierke, C.A., Hammes, G.G., 1995. Transient kinetic approach to enzyme mechanism. Methods Enzymol. 249, 3–37.
Fritz, H., Trautschold, I., Werle, E., 1974. Protease inhibitors. In: Bergmeyer, H.U. (Ed.), Methods of Enzymatic Analysis, vol. 2. Academic Press, New York, pp. 1066 – 1080. Goldman, R., Goldstein, L., Katchalski, E., 1971. Water-insoluble enzyme derivatives and artificial enzyme membranes. In: Stark, G.R. (Ed.), Biochemical Aspects of Reactions on Solid Supports. Academic Press, New York, pp. 1 – 78. Goldstein, L., 1976. Kinetic behavior of immobilized enzyme system. Methods Enzymol. 44, 397 – 443. Greene, L.J., Bartelt, D.C., 1977. Specificity hydrolysis by trypsin at alkaline pH. Methods Enzymol. 47, 170 – 174. Guilbault, G.G., 1976. Enzyme electrodes and solid surface fluorescence methods. Methods Enzymol. 44, 579 – 633. Gutfreund, H., Sturtevant, J.M., 1956. The mechanism of the reaction of chymotrypsin with p-nitrophenyl acetate. Biochem. J. 63, 656 – 661. Henri, V., 1904. Recherches physico-chimiques sur les diastases. Arch. Fisiol. 1, 299 – 324. Ho, M.H., 1988. Use of immobilized enzyme reactors in flow-injection analysis. Methods Enzymol. 137, 271 – 287. Johnson, K.A., 1995. Rapid quench kinetic analysis of polymerases, adenosinetriphosphatases, and enzyme intermediates. Methods Enzymol. 249, 38 – 61. Kumaran, S., Tran-Minh, C., 1992. Determination of organophosphorous and carbamate insecticides by flow injection analysis. Anal. Biochem. 200, 187 – 194. Laskowski Jr., M., Sealock, R.W., 1971. Protein proteinase inhibitors — Molecular aspects. In: Boyer, P.D. (Ed.), The Emzymes, vol. 3. Academic Press, New York, pp. 375 – 473. Lilly, M.D., Hornby, W.E., Crook, E.M., 1966. The kinetics of carboxymethylcellulose-ficin in packed beds. Biochem. J. 100, 718 – 723. Lilly, M.D., Dunnill, P., 1976. Immobilized-enzyme reactors. Methods Enzymol. 44, 717 – 738. Luisi, P.L., Bignetti, E., 1974. The half-of-the-sites reactivity of horse liver alcohol dehydrogenase in the presence of alcohol substrates. J. Mol. Biol. 88, 653 – 670. Means, G.E., 1977. Reductive alkylation of amino groups. Methods Enzymol. 47, 469 – 478. Medina Hernandez, M.J., Garcia Alvarez-Coque, M.C., 1992. Available lysine in protein, assay using o-phthalaldehyde/ N-acetyl-L-cysteine spectrophotometric method. J. Food Sci. 57, 503 – 505. Merli, A., Rossi, G.L., 1986. Deacylation kinetic of g-chymotripsin in solution and in the crystal. FEBS Lett. 199, 179 – 181. Nashabeh, W., El Rassi, Z., 1992. Enzymophoresis of nucleic acids by tandem capillary enzyme reactor-capillary zone electrophoresis. J. Chromatogr. 596, 251 – 264. Peterson, W.R., Warthesen, J.J., 1979. Total and available lysine determinations using high-pressure liquid chromatography. J. Food Sci. 44, 994 – 997. Ramoni, R., Fermi, P., Bussolati, L., Grolli, S., Donofrio, G., Bignetti, E., 1994. Application of endoproteases to biosensor technology. Life Chem. Rep. 11, 357 – 362.
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95 Reiner, J.M., 1969. Behavior of Enzyme Systems, 2nd ed. Van Nostrand Reinhold, New York. Roda, A., Girotti, S., Ghini, S., Carrea, G., 1988. Continousflow assay with nylon tube-immobilized bioluminescent enzymes. Methods Enzymol. 137, 161–171. Scolari, G.L., Vescovo, M., Cappa, F., Bottazzi, V., Bussolati, L., Bignetti, E., 1993. Immuno-based strategy for Clostrid-
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ium tyrobutyricum specific recognition. Biotechnol. Tech. 7, 43 – 46. Segel, I.H., 1975. Enzyme Kinetics. Wiley, New York. Shan, Y., McKelvie, I.D., Hart, B.T., 1993. Characterization of immobilized Escherichia coli alkaline phosphatase reactors in flow injection analysis. Anal. Chem. 65, 3053 – 3060.
Single turnover mechanism of a trypsin-reactor with high enzyme concentration Paola Fermi, Riccardo Biffi, Virna Conti, Roberto Ramoni, Stefano Grolli, Paolo Accornero, Enrico Bignetti * Istituto di Biochimica Veterinaria, Uni6ersita` di Parma, 6ia del Taglio 8, 43100 Parma, Italy Received 15 August 1997; received in revised form 27 November 1997; accepted 28 November 1997
Abstract A small column containing 2 mM CH-Sepharose 4B-immobilized trypsin was connected to a flow injection device equipped for potentiometric measurements (0.01–2 mM protons) and for post-column analysis by spectrophotometry and capillary electrophoresis (CE). The device was engaged with Na-benzoyl-L-arginine pNO2-anilide (BAPNA), b-lactoglobulin (b-Lac) and peptides of V8-protease predigested b-Lac. At a given flow rate, the reaction with BAPNA or b-Lac (below 2 mM) produced about 1 proton per substrate molecule in each sample (linear relation to substrate amount); with peptides (below 22 mM), the reaction did not exceed 0.17 acid equivalents per substrate molecule (hyperbolic dependence). Final experiments demonstrated that the reactor gave a correct estimate of available lysine in peptides of b-Lac modified with 5-nitrosalicylaldehyde. The data could be predicted by a kinetic model describing the reactor performance in ‘single turnover’ conditions. The interplay between resident time and the non-catalytic amount of trypsin prevented each enzyme molecule from recycling as well as each substrate molecule (containing one or more cleavage sites) from encountering the enzyme more than once. In conclusion, both from the experimental and the theoretical point of view, this work permitted the analysis of trypsin behaviour in some extreme working conditions and indicates how to modulate the performance of an endoprotease-based reactor. A brief discussion on potential applications in protein mapping and tagging and in the quantitative analysis of protein bioavailability by means of a biosensorial strategy is also described. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Trypsin reactor; Single turnover reaction; Endoprotease-based biosensor
Abbre6iations: b-Lac, b-lactoglobulin (A and B isomers); BAPNA, Na-benzoyl-L-arginine pNO2-anilide; CE, capillary electrophoresis; CFA, continuous flow apparatus; D, V8 endoprotease digested b-lactoglobulin; FIA, flow injection analysis; M, 5-nitrosalicylaldehyde-modified b-lactoglobulin; MD, V8 protease-digested 5-nitrosalicylaldehyde-modified b-lactoglobulin; N, native b-lactoglobulin; NSA, 5-nitrosalicylaldehyde. * Corresponding author. Tel.: + 39 521 984865; fax: + 39 521 980624; e-mail: [email protected] 0168-1656/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 1 6 5 6 ( 9 7 ) 0 0 1 8 9 - 2
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1. Introduction A potentiometric biosensor based on endoproteases for the assay of amino acid content in proteins was recently proposed by Ramoni et al. (1994). The activity resulting from trypsin coupled to a glass electrode was assayed in a model reaction with Na-benzoyl-L-arginine pNO2-anilide (BAPNA) as a chromogenic substrate analogue. With this system, potentiometric measurements of proton production and spectrophotometric measurements of pNO2-aniline release during trypsincatalyzed hydrolysis of BAPNA were carried out in parallel. It was observed that BAPNA hydrolysis was not significantly affected by enzyme immobilization; however, the investigation did not include natural substrates. In the literature, the steric hindrance effects of solid supports on endoprotease activity have not yet been investigated in depth (Goldstein, 1976; Lilly and Dunnill, 1976). Furthermore, it was noted that direct contact between the biological matrix and the electrochemical sensor did not seem to be a prerequisite for an efficient response from the biosensor. As a matter of fact, it was interesting to observe that potentiometric signals of BAPNA hydrolysis did not depend on the trypsin-matrix whether wrapped in full contact to the glass electrode or dispersed in solution. It appeared worthwhile to study this unexpected result in more detail. Therefore, in these experiments, we tried to increase the capacity of the enzyme-electrode (built-in configuration) in the detection of lysines and arginines present in peptides or proteins. As a model, native and V8-endoprotease digested b-lactogloblulin (b-Lac) was chosen to represent true alimentary substrates. With these samples, however, reaction rates were difficult to interpret because they were too slow when compared to spontaneous acidification and too conditioned by substrate dimensions. This initial failure led to several conclusions: (1) when the enzyme was immobilized in a built-in configuration, it was in catalytic amounts and therefore the related signals were weak; (2) pH 8.7, which seemed to be the optimum for BAPNA hydrolysis (Fritz et al., 1974), was not the correct
working pH with natural substrates because amino groups in peptides exerted a strong buffering effect; and (3) in a built-in configuration, the enzyme matrix posed serious restrictions on the diffusion of peptides through inner enzyme layers, thus reducing dramatically the overall signal (see also point 1). Therefore, the methodology was modified by introducing three crucial changes: (1) the use of CH-Sepharose 4B, a CNBr-activated Sepharose modified by the addition of an eight-carbon arm in order to elongate the distance between trypsin and the matrix itself; (2) the use of an appropriate buffer working at pH 10 in order to reduce the buffering effect of the substrates and their products to a minimum; and (3) redesigning the system and adapting it to a flow-injection analysis (FIA) strategy (Danielsson and Mosbach, 1988). To this end, a continuous flow apparatus (CFA) was developed. The enzyme reactor was located upstream and physically apart from a chamber (flow cell) containing the electrochemical sensor. In point three a FIA system can work when the biological signal at the enzyme-reactor is large and stable and can propagate unperturbed downstream to the sensor. Furthermore, it was highly desirable to obtain a conversion efficiency close to 100% (Ho, 1988). This requirement derived from a need either to counterbalance high detection threshold of the apparatus and to collect enough product for postcolumn analytical purposes, especially when dealing with protein analysis. In the procedure there were several parameters affecting reactor performance and most of them (e.g. physical dispersion) could be easily controlled. Overall, however, the amount of immobilized enzyme played a key role. In conventional biosensors, enzyme immobilization on planar surfaces usually occurs to a limited extent so that, considering the concentration in the total assay volume, the enzyme works in small catalytic amounts and according to classic ‘steady-state kinetics’ (Guilbault, 1976). In CFA, on the contrary, trypsin was immobilized on Sepharose-4B beads and tightly packed in the reactor thus reaching a local concentration comparable to or larger than substrate Km. To a degree, these conditions should have mimicked some assays in solution with high enzyme concentration (Reiner, 1969; Segel, 1975) or fast kinetic experiments carried out in
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continuous- and stopped-flow apparata by ‘rapid mixing techniques’ (Fierke and Hammes, 1995). In our case, not every step of substrate conversion could be followed, however, it was still possible to measure the amount of product released by the reactor at the end of the resident time. Therefore, only amplitudes, rather than rates, were the significant signals reported here. Nevertheless, it was possible to derive a kinetic model to describe the effect of high local enzyme concentration on the performance of a single reactor engaged with different types of substrates at a given flow rate.
2. Materials and methods
2.1. Trypsin immobilization Bovine pancreas trypsin (Boehringer, Germany) was immobilized either on CNBr-activated Sepharose 4B (Pharmacia, Sweden) or on CH-Sepharose 4B (Sigma), following customer indications. In these experiments, 150 ml of swollen CH-Sepharose gel was obtained from 50 mg of dry resin. The coupling yield was : 7 mg of immobilized enzyme per 150 ml of gel. Compared to the protein binding capacity of this resin, immobilized trypsin corresponded to 40 – 50% of resin equivalents. The enzyme gel was packed into a 4 mm diameter column (reactor). Since the molecular fractionation range of CHSepharose 4B gel was between 6×104 and 2× 106 Da, it was assumed that trypsin (a 23 kDa protein) could freely diffuse between gel particles and within gel pores and that it could attach to the resin surface facing outer and inner volume of the gel. By using p-nitro-aniline as a chromophoric tracer, it was observed that this volume almost coincided with the total volume of the gel. Conversely, the void volume V0 of the gel was only 37% of the total. Therefore, enzyme amount Etot $2 mM was calculated by considering the total volume of the cylindrical bed, in accordance with Lilly et al. (1966) and Shan et al. (1993). The void volume was used in calculating the resident time of the mobile phase (see below).
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2.2. Assay buffer All the assays were made in non-degasled aqueous solvents, buffered at pH 10.0 by the addition of NaHCO3 (0.5 mM) and NaOH. At this pH, trypsin was still quite active (Greene and Bartelt, 1977) and spontaneous acidification due to CO2 in the air was prevented long enough to guarantee a stable baseline. At this pH, C-terminal carboxyl groups, which were enzymatically released upon peptide bond cleavage, fully dissociated a proton. On the other hand, N-terminal a-amino groups that were concomitantly released, associated protons to a very low extent. Thus, the undesirable buffering effects of the products were minimized. In this buffer, the signal–noise ratio of the device remained quite satisfactory, as it was sensitive to additions of 10 − 5 M protons.
2.3. Continuous flow apparatus The assay buffer flowed through the trypsin reactor by means of a peristaltic Econo-pump (Biorad) at constant rates (0.1–1 ml min − 1). Substrate samples (200–800 ml) were loaded using a valve and eluted with the assay buffer at the same rates. The outlet of the column was connected to a flow chamber (inner volume of : 1.5 ml) that contained a magnetic stirring bar and a pHC 2406 glass electrode (Radiometer, Denmark). The electrode was connected to a PHM62 Standard pH-meter (Radiometer, Denmark) interfaced with a REC-102 chart recorder (Pharmacia, Sweden). Traces were recorded in mV. After every assay, a pulse (0.4 ml) of NaCl (150 mM) was injected in order to wash the resin. Samples coming out of the flow chamber were fractionated and read in a standard UV-vis spectrophotometer or analyzed by CE. Calibration of the apparatus was carried out by loading and eluting two of the products of trypsincatalyzed reaction with BAPNA: p-nitro-aniline and protons. The aniline derivative, monitored by spectrophotometry, was indicative of CFA elution pattern. Conversely, HCl pulses in the assay buffer determined the potentiometric calibration curve of the device.
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All measurements were carried out at room temperature. It was determined that the reactor could be stored at 4°C for 1 month without significant loss of activity.
2.4. Trypsin substrates 2.4.1. BAPNA The hydrolysis of BAPNA (Boehringer, Germany) could be observed with the spectrophotometer as already reported by Ramoni et al. (1994). Stock solutions were freshly prepared in the assay buffer prior to use (2 mM is the solubility limit). 2.4.2. Nati6e b-lactoglobulin A three-fold crystallized fraction of bovine milk b-Lac (containing A and B isomers) (Sigma) was used as a native protein substrate (N). 2.4.3. Predigested b-lactoglobulin Predigestion of b-Lac into smaller peptides (D) was carried out by incubating a stock solution of N (1 mM) with staphylococcal V8 protease (Sigma; 10 − 7 to 10 − 6 M) at 37°C for 12 h in the presence of phosphate (5 mM) buffered with additions of NaOH to maintain a constant level of pH 7.8. In these conditions, V8 protease cleaved peptides bonds at C-terminal sites of glutammic and aspartic acids (Drapeau, 1976; 1977). Aliquots of the stock solution were kept frozen at − 20°C and were thawed and diluted immediately before use. The molecular weight composition of N (200 ml of 0.5–1 mM) was analyzed in fast protein liquid chromatography apparatus (FPLC) (Pharmacia, Sweden) by running a gel permeation chromatography on a Superdex-75 column (optimal exclusion range: 300–70 000 Da) equilibrated with the assay buffer and calibrated with a mixture of pure bovine serum albumin, ovalbumin and soybean trypsin inhibitor (Sigma). Conversely, the composition of D was determined by analyzing the peptide mixture using CE, in a PACE 5000 (Beckman) controlled by System Gold version 8.1. Runs were performed in phosphate buffer (50 mM) pH 2.7, at constant voltage (25 kV) and at 20°C in a capillary of 50 cm effective length and
75 mm I.D. The electropherograms were monitored at 214 nm with a data collection rate of 5 Hz.
2.4.4. Modified b-lactoglobulin b-Lac (0.5 mM) was incubated with 5-nitrosalicylaldehyde (NSA; 50 mM) (Sigma) in bicarbonate buffer (50 mM) at pH 9.0 at room temperature for 30 min. Then, NaBH4 (3–5 mg ml − 1) was slowly added to the sample under continuous stirring (Means, 1977). After overnight dialysis in the assay buffer at 4°C, the modified protein showed a strong absorbtion at 390 nm that, when divided by the corresponding molar extinction coefficient = 13200 M − 1 cm − 1, resulted in a maximum of 21 blocked primary amino groups out of the 32 present in the protein dimer. The molar extinction coefficient was estimated by carrying out experiments with reversed reagent concentrations (i.e. by keeping the protein in large excess with respect to NSA). Modified b-Lac (M) was also predigested with V8 protease and fragments (MD) were analyzed by means of CE, in the same experimental conditions.
3. Results
3.1. Choice of the apparatus and calibration The sketch of the CFA is reported in Fig. 1 (Roda et al., 1988). Firstly, our device was calibrated with respect to flow dynamics and dispersion. After loading 400 ml of p-nitro-aniline samples (0.25–2 mM) with a flow rate of 0.2 ml min − 1 (for example see Fig. 2A), the front of the dye reached the flow chamber in 5 min. Then, more than 90% of the dye was eluted from it in a further 30 min, approximately, in a total volume of 6 ml with a 15-fold dilution as a mean. Similar results were obtained when calibrating CFA with HCl. Signal bell shapes (Fig. 2B) were not symmetric and showed a large base, mainly reflecting two phenomena: physical dispersion along the path and large dilution into the flow cell. However, they were reproducible at the same
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3.2. ‘Single turno6er’ kinetic model The overall trypsin reaction could be written as the unireactant mechanism:
(1)
Fig. 1. Schematic view of the ‘constant flow apparatus’ (CFA).
flow rate. From the comparison with HCl calibration curves, the amount of protons released by the reactor in the presence of any substrate could be evaluated.
Several enzyme reactors have been described in the literature (Lilly et al., 1966; Goldman et al., 1971; Roda et al., 1988; Cobb and Novotny, 1989; Kumaran and Tran-Minh, 1992; Nashabeh and El Rassi, 1992). In most examples, substrate conversion was never complete, even at very low flow rates. The oldest case was the clear example reported by Lilly et al. (1966) where product concentration was linearly related to the logarithm of the fraction of the remaining substrate. For this model, the appropriate kinetic equation was derived from the integrated form of the classic Henri equation in ‘steady-state’ conditions with
Fig. 2. Calibration of CFA. (A) Spectroscopic (bars) and potentiometric (solid line) signals with pulses (2 mM, 0.4 ml) of p-NO2-aniline and of HCl, respectively, eluted at a constant flow (0.2 ml min − 1). (B) Relationship between potentiometric signals (peak heights) and HCl (open circles) or BAPNA (filled circles), respectively. Samples (0.4 ml) varied from 0.25 to 2 mM and were eluted at constant flow (0.2 ml min − 1) with the assay buffer. The two sets of data could be interpolated by straight dashed lines according to linear regression analysis (r \0.95). Peak areas plotted instead of peak heights gave same results. The solid line referred to BAPNA dependence theoretically expected on the basis of the ‘single-turnover’ kinetic model described in the text.
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86
substrate in large excess (Henri, 1904). On the contrary, our results could be understood only by keeping in mind that the retention time could be adjusted to block reaction at will. Moreover, the presumed concentration of trypsin Etot in the reactor was very high ( : 2 mM), i.e. it was larger than or comparable to substrate Km (see below and Table 1). Therefore, at any given time, the fraction of enzyme-bound substrate and enzymebound product would be consistent relative to free species; the usual ‘steady-state kinetics’ behaviour with catalytic amounts of enzyme could not be expected. Under such experimental conditions and by defining a single turnover reaction as a single cleavage on each substrate molecule whether it contains one or more cleavage sites, the kinetic model should: (1) avoid the assumption of Stot constant during the reaction, a typical bottleneck in the mathematical treatment posed by ‘stationary conditions’ with catalytic enzyme amounts (Gutfreund and Sturtevant, 1956; Fierke and Hammes, 1995); and (2) give indications on how to modulate sample flow rate in order to limit the reactor to a single turnover during resident time. Data interpretation could be carried out using the model based on ‘steady state kinetics with high enzyme concentrations’ (Reiner, 1969; Segel, 1975) or on the model based on ‘transient kinetics’ (Luisi and Bignetti, 1974; Fierke and Hammes, 1995; Johnson, 1995). In our opinion, only the ‘transient kinetic’ approach could satisfy the expectations created by the second point made above (Appendix A). Briefly, starting from (1), general equation: 1 Ptot = [(Stot + Etot + Km) 2 − (Stot + Etot +Km)2 −4StotEtot] (1−e − kcat(V0/Q))
(A10)
and two simplified forms, respectively for ‘substrate saturation by the enzyme’ and for ‘enzyme saturation by the substrate’: Ptot =
Etot S (1 − e − kcat(V0/Q)) Etot +Km tot
(A11)
Ptot =
Stot Etot(1−e − kcat(V0/Q)) Stot + Km
(A12)
were derived considering Kd(ES) = Km, k2 = kcat, V0 = 0.055 ml and sample flow rate Q expressed in ml min − 1.
3.3. Substrate analysis 3.3.1. BAPNA Firstly, steady-state kinetic parameters of BAPNA hydrolysis were reevaluated at the spectrophotometer by using catalytic amounts of immobilized trypsin in stirred suspensions at pH 10.0. The data, plotted by the Lineweaver–Burk method (not shown), gave Km = 0.2 mM and kcat = 25 min − 1 (see Table 1). Subsequently, the behaviour of CFA with pulses (0.4 ml) of BAPNA (0.25–2 mM) was tested. Flow rate could be adjusted between 0.2 and 0.3 ml min − 1 without significant variations in the response. Experimentally, time scale and profile of the potentiometric traces closely resembled those obtained with the two calibration tests of CFA as reported in Fig. 2A. The linear plot in Fig. 2B was obtained by reporting peak heights (or areas) as a function of BAPNA. By comparison with the proton calibration curve, hydrolyzed BAPNA was 72% in all samples. In reasonable agreement with this result it was observed, using the spectrophotometer, that BAPNA was converted with an efficiency of Ptot/Stot of :80%. With flow rates below 0.1 ml min − 1, the time required for the assay was too long and the baseline was too steep. Conversely, by increasing flow rates above 0.2 ml min − 1, signals tended to assume the form of sharp peaks but conversion efficiency fell dramatically. At a rate of 1 ml min − 1, signals (peak areas) were : 40% lower and this was confirmed by spectrophotometric measurements showing that only 50–60% of BAPNA was hydrolyzed. In these experiments, the relationships Etot ] Stot and Etot Km seemed to be operative (Table 1) thus the kinetic model discussed above and, in particular, Eq. (A11) were used to interpret these data. In fact, a conversion efficiency Ptot/Stot of 89% with Q=0.2 ml min − 1 (see Fig. 2B) and of 67% with Q= 1 ml min − 1 was calculated.
0–2 0–1 0 – 22
b
Calculated with trypsin-Sepharose in suspension. Depending on different aggregation states. c Depending on dimensions (see Fig. 3). d Calculated on the basis of a ‘single turnover’ kinetic model.
a
10.0 6.6 1.8
25 6 12
BAPNA Native b-Lac Predigested bLac
0.2 0.3 1.1
kcat a (min−1) Km a (mM) E0/Km Explored range (mM)
Substrate
Linear Linear Hyperbolic
Response
1 17 – 68b 53c
0.8 1.1 B1
Cleavable sites per sub- Observed cleavages per strate molecule substrate molecule
0.9 0.8 B1
Predicted cleavages per substrate moleculed
Table 1 Functional and kinetic properties of a trypsin reactor (150 ml) containing 2 mM enzyme with different substrates at constant flow (0.2 ml min−1)
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P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
3.3.2. Nati6e b-lactoglobulin Native b-Lac is a dimer of 18 kDa subunits. The aggregation state and isomer composition of the protein at pH 10 was analyzed by gel permeation chromatography. The result indicated the coexistence of different aggregation states in bLac, mainly: monomers, dimers and tetramers, at a molar ratio of :4:1:1.5. Thus, from now on in the text, the concentration of N corresponds to the sum of the individual concentrations of all the different b-Lac forms present in solution. Using CE, N gave two major peaks according to the presence of A and B isomers (not shown). Steady-state kinetic parameters of N hydrolysis with a known amount of immobilized trypsin was evaluated. Assays were carried out by means of the pH-meter, with the active matrix in stirred suspensions and with catalytic enzyme amounts (not shown). Summarizing the results, it was very difficult to precisely define steady state kinetic parameters with N. As with other endoproteases (unpublished observations), the immobilization negatively affected the access of large substrates to trypsin and caused unspecific interactions with it. In fact large amounts of active resins and long incubation times were needed for mapping of a protein sequence in batch conditions. Moreover, the substrate concentrations were kept at or below 1.3 mM in order to avoid undesirable viscosity and buffering effects. Even though the Lineweaver–Burk plot was affected by a large S.E., apparent Km = 0.3 mM and kcat =6.0 min − 1 were calculated (see Table 1). In principle, inhibition experiments of BAPNA hydrolysis in the presence of variable N should confirm the validity of these parameters. Indeed, BAPNA hydrolysis was inhibited by N additions but in a ‘mixed-type’ mode, a totally different behaviour compared to the typical ‘competitive’ mode observable with the soluble enzyme. A mixed-type inhibition could not be explained per-se, unless it was due to the occurence of reduced active site availability and unspecific protein–resin interaction. Subsequently, N pulses (0.4 ml up to 1.3 mM) were loaded and eluted through CFA at a constant flow (0.2 ml min − 1). The relationship between signals and N concentration is reported in Fig. 4A and in Table 1. The data could be inter-
polated by a straight line applying linear regression analysis. In conformity with the proton calibration curve in Fig. 2B, 1.1 peptide bonds were split in each b-Lac molecule as a mean. After CFA elution, N samples were extensively dialyzed using membranes with a molecular cutoff of 12 kDa, in order to remove large fragments possibly produced by the reactor. Nevertheless, their optical densities at 280 nm were only slightly changed. This was indicative of an almost complete recovery of b-Lac after dialysis, but nothing could be deduced about primary sequence integrity. Therefore, samples passed through CFA were analyzed by CE. The analysis indicated a very low digestion of the major components into few small peaks at longer retention times. This evidence, together with the small CFA signals, suggested that only a few low-dimension peptides at the protein surface were removed. According to kcat, a single b-Lac dimer with 34 cleavage sites would require about six turnovers, i.e. 1 min or more, to be completely digested. However, resident time (16.5 s) did not permit more than one or two cycles. In fact, the degree of digestion corresponded to a stoichiometry of one cleavage per substrate molecule, that is, in terms of substrate ‘molarity’, conversion efficiency was close to 100%. On the basis of the results, the ‘single turnover’ model was reconsidered and Eq. (A11) applied as the most likely to describe a situation close to Etot ] Stot and Etot (Km) The equation gave 80% of substrate conversion, i.e. 0.8 specific bonds cleaved per protein molecule as a mean (see Fig. 4A).
3.3.3. Predigested b-lactoglobulin As confirmed by CE analysis, V8 protease digestion of b-Lac resulted in the detachment of five single amino acids and 24 peptides (see Fig. 3). Two of these peptides, are discarded by trypsin since they contain a lysine donating a carboxyl group to a proline (Laskowski and Sealock, 1971). Therefore, in the text, D concentration is always referred to as the molar concentration of dimeric b-Lac multiplied by 22. Steady-state kinetic assays with D and with immobilized trypsin in stirred suspensions were carried out. Using the glass electrode, the active
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
89
Fig. 3. Primary structure of b-lactoglobulin (A* and B° variants) according to Swiss-Protein Database. Theoretical cleavage sites of trypsin and of V8 endoprotease were shown, respectively, with (n) and (¡). The lysine – proline bond was voluntarily excluded for trypsin specificity reasons.
resin exhibited an apparent Km =1.1 mM and a kcat = 12 min − 1 (see Table 1). By spectrophotometry, inhibition kinetics showed that D played the role of a competitive inhibitor towards BAPNA hydrolysis with an apparent Km =0.83 mM consistent with the corresponding Km mentioned above. The results obtained with CFA are reported in Fig. 4B. Potentiometric signals increased asymptotically with substrate and levelled off at a nominal D concentration of 12 mM. From a comparison with the proton calibration curve in Fig. 2B, it was noted that signal amplitudes at the plateau corresponded to a maximum production of 1.8 mM protons. Interestingly, this concentration coincided almost perfectly with enzyme equivalents in the reactor, as if the enzyme became limiting as substrate tended toward infinity. The reaction did not exceed a single turnover notwithstanding the presence of excess substrate and a resident time allowing more than three enzyme recyclings. It is also worth noting that D had the lowest affinity for the enzyme (Km $Etot) among the substrates used (see Table 1). Therefore, these data could be analyzed only by using the general Eq. (A10). The solid line in Fig. 4B
was the result predicted by the model by assuming signal saturation at 2 mM protons and Kd(ES) = Km = 1.1 mM. A better view of the comparison between experimental data and theoretical expectations is reported in Fig. 4C. The experimental data in Fig. 4B are considered to be the consequence of a simple isotherm of ligand binding to a homogeneous set of specific enzyme sites. These results were linearized in a double reciprocal plot. A linear regression analysis (r\ 0.97) gave an apparent Kd(ES) = 1.9 mM quite in accordance with Km and with the straight line predicted by the model.
3.3.4. Modified b-lactoglobulin Finally, it was tested whether CFA could monitor the reduced availability of b-Lac with chemically modified lysines (M). After an extensive protein treatment with NSA (see Section 2) and considering the presence of two lysine–proline bonds (not attacked by trypsin) and six unmodified arginines in a dimer, we calculated that trypsin cleavable sites in M were reduced to 39– 44% of N. The enzymatic activity of trypsin activity, either in solution or in suspension, was negligible in the presence of this sample. Then M
90
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
Fig. 4.
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
was predigested with V8 protease into peptide fragments (MD) and these were loaded into the reactor. A control experiment was carried out with a non-modified predigested sample (D). The device gave signals with MD (not shown) that were about 35% of the signals observed with D and only slightly below the predicted 39 – 44% range. As reported above, the reactor could not recognize M. This evidence might be explained by assuming that all the lysines on the protein surface had been modified blocking trypsin access to the core of the protein where the remaining unmodified sites were located. Qualitatively speaking, the hidden potentiality in M was not revealed giving an erroneous view of its intrinsic bioavailability. In contrast MD gave significant signals. The small difference between experimental and expected availability might be attributed to a possible cross-inhibitory effect of peptides carrying modified lysines on overall trypsin reaction.
4. Discussion Several analytical methods for lysine detection have been proposed so far, but all of them have been able to recognize lysine or its derivatives only when free in solution. Moreover, these methods were often inaccurate because of lysine modifications during sample preparation (Peterson and Warthesen, 1979; Acquistucci et al., 1987; Medina Hernandez and Garcia Alvarez-Coque, 1992). Therefore, the development of a biosensorial strategy for lysine detection in proteins by using an endoprotease represented an interesting alternative worth pursuing. To this end, trypsin was chosen because its activity is strictly specific for the cleavage of peptide bonds involving arginine or lysine and because its structure and function are well established.
91
After several trials with different potentiometric devices and trypsin immobilization procedures, it was finally decided to explore the performance of an FIA apparatus connected to a reactor containing the enzyme immobilized on CH-Sepharose 4B resin. This was a new approach that required careful theoretical enzyme kinetic evaluations. Besides the fact that enzymatic proteolysis is generally characterized by small turnover numbers, several parameters had to be considered since the recorded signal was the result of a balance between protons produced by the reactor, physical dispersion of the signal in the carrier stream, assay buffer characteristics, spontaneous acidification in open vessels and buffering effects of reagents and products. Therefore, in order to increase the relative amplitude of the biological signal obtained at the enzyme-reactor level, even with substrates present at concentrations well below their Km, trypsin at high concentration (2 mM) was loaded into the reactor. The results show the effect of this parameter on reactor conversion efficiency at a given flow rate. The main features of our reactor are summarized in Table 1. It should be emphasised that, working with a protease, a certain degree of ambiguity regarding the term ‘conversion efficiency’ may arise depending on whether the concentration of substrate molecules or the concentration of all cleavable sites is considered, since these concentrations always coincide in an analogue substrate but not always in a natural one. In steady state kinetic conditions the splitting of a cleavable site in a natural substrate most probably doubles substrate molecules, at least at the very beginning of the reaction. Moreover, protein digestion produces peptides with a different Km and it cannot be predicted which kind of substrate is going to be processed preferentially at each enzyme cycle. Other problems like steric hindrance, unspecific substrate adhesion, etc. might also arise working with an immobilized enzyme. Thus, it might be
Fig. 4. (A) Relationship (filled squares) between potentiometric signal (peak heights) and molar concentrations of native b-lactoglobulin. (B) Relationship (filled squares) between potentiometric signals and molar concentrations of a b-lactoglobulin peptide mixture. (C) Double reciprocal plot of the data in B (filled squares). Solid lines in (A), (B) and (C) corresponded to theoretical curves obtained by assuming the ‘single turnover’ kinetic model described in the text. Dashed lines in (A) and (C) were interpolations calculated by using linear regression analysis (r\0.97).
92
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
hard to assume a simple Michaelian kinetic model of the type shown in Eq. (1) to describe the activity of an immobilized endoprotease. However, it should be noted that transient reactions observed in our reactor were described best by a ‘single turnover’ kinetic model that utilized the steady state kinetic parameters kcat and Km calculated assuming Eq. (1). Considering substrate molarity, it was observed that 100% of BAPNA or b-Lac molecules and only a maximum of 17% of b-Lac peptides did not encounter a trypsin molecule more than once during the resident time. This striking difference was due to the fact that, BAPNA or b-Lac molecules engaged a stoichiometric enzyme amount because the ratio Etot/Km was sufficiently higher than 1; vice versa, the b-Lac peptides reaction exhibited a substrate saturation dependence of the classical Michaelian type because Etot/Km was close to 1. Using this data, an appropriate flow rate by which BAPNA could undergo a complete conversion in all samples was found. At this flow rate, approximately one of the 34 cleavable sites in N was cut by the reactor. Since enzyme concentration was saturating, this event occurred simultaneously on all substrate molecules and, most probably, at the same primary sequence site. A general protocol based on these experimental conditions might offer a good tool to tag protein substrates (e.g. enzymes, antibodies, receptors, etc.) for the study of the relationship between structure and function. To this regard, the reactor response to b-Lac, in comparison to the lack of response to the same protein that was modified at the surface by other means, should be noted. In the case of peptides, conversion efficiency was low. Nevertheless, in terms of absolute concentration this corresponded to 2 mM product under substrate saturating conditions. Such a large product accumulation could not be easily achieved in only a few seconds in any other conventional assay based on catalytic enzyme amounts. This might represent an advantage from a general point of view since large amounts of products are often required for different postcolumn analytical purposes. Moreover, although the reactor analyzed only a small percent of the
total peptides in a sample, it could give a correct estimate of the fraction of lysines that were originally modified in the native protein. Apart from kinetic considerations, essential amino acid detection and quantitation through a biosensorial strategy might supply a parameter for total quality certification in food technology applications. We believe that our results justify a further development of the system. In order to facilitate the analysis of the integrity of protein core amino acids, a reliable predigestion of N with V8-endoprotease was developed. Enzymatic sample treatment prior to a specific instrumental analysis is a useful step already described in the literature (Nashabeh and El Rassi, 1992 and the literature cited therein). We are now trying to improve this procedure by preincubating the sample with a mixture of endoproteases in a microdialyzing device positioned upstream. This step would also help the analysis with realistic samples. A similar experimental approach has never been considered in detail in preceeding enzyme-reactor studies. In general, this work was limited by high enzyme costs and by a low protein coupling efficiency of active planar or round surfaces. Today, trypsin and Sepharose-4B beads are inexpensive and extremely versatile. In particular, this resin exists in various activated forms for high efficiency covalent protein coupling and is easy and safe to handle. Moreover, protein coupling to Sepharose occurs in mild aqueous solvents and involves mostly external primary amino groups, thus preserving native structure and activity of the attached ligand. Finally, Sepharose shows hydrodynamic properties that are adequate for this application and an exclusion range that could be problematic only for the diffusion of very large macromolecules. Gels of this matrix with attached antibodies or proteins for various purposes such as affinity chromatography (Bignetti et al., 1987), selective immunoaffinity isolation of microorganisms (Scolari et al., 1993) and ligand–protein interaction studies (Bussolati et al., 1993) have already been used in our laboratory. Here, it can be concluded that such a matrix, indeed, fulfills all the requirements for the development of an enzyme-reactor.
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
Acknowledgements We would like to thank John P. Verville for the critical reading of the manuscript. This work was supported by National Research Council of Italy, special project RAISA, sub-project 4.
Appendix A For simplicity, it has been assumed that the reactor volume V0 (0.055 ml) is a thin working section of exchangeable water which is replaced by another one flowing with constant rate Q (expressed in ml min − 1). The total sample volume passing through the reactor can be considered as the sum of several working sections equal to V0. Looking at the example of chymotrypsin in pre-steady-state experiments in solution (Gutfreund and Sturtevant, 1956) and in steady-state experiments in the crystal (Merli and Rossi, 1986), the steps represented in Eq. (1) may occur in each working section:
(2) Moreover, it has been assumed that: (1) large amounts of the substrate may be tied up rapidly (approximately at t =0) in the binary (ES) complex; (2) the bimolecular process of (ES) formation equilibrates rapidly relative to its decay (k − 1 k2) so that substrate binding can be treated as a kinetically independent process with the equilibrium dissociation constant Kd(ES) =Km; (3) the conversion of (ES) into (EP) represents a simplified step including the transfer of an acyl group from substrate to enzyme, a concomitant amino group liberation and the subsequent intermediate deacylation (the rate determining step); thus, k2 =kcat; and (4) the conversion of (EP) back to (ES) can be neglected for energetic reasons; (5) at the end of a single turnover, a rapid binding equilibrium between (E) and (P) (proton included) in the same concentration range is achieved; therefore, it is conceivable that (EP)
93
accumulates as a dead-end complex ([EP]k3 E][P]k − 3) thus preventing further enzyme recycling (unpublished steady state experiments in the presence of large amounts of products with trypsin in solution confirmed the possibility of product inhibition). According to these assumptions, the product concentration calculated in any working section is equivalent to product concentration in the total sample volume at the end of the overall reaction. In order to calculate it, mass conservation relationships with substrate and enzyme concentrations Stot and Etot before mixing, are posed: Stot = (S)0 + (ES)0
(A2)
Etot = (E)0 + (ES)0
(A3)
and the following quadratic expression is derived: (ES)0 1 = [(Stot + Etot + Km) 2 − (Stot + Etot + Km)2 − 4StotEtot]
(A4)
Then, provided that the resident time limits the reaction extent to no more than a single turnover, (ES)0 is converted to products in a single exponential decay according to rate equation: 6=
d(ES)0 d((EP)t + (P)t ) dPtot =− = (ES)0k2 = dt dt dt
= (ES)0kcat
(A5)
By substituting the quadratic expression Eq. (A4) into Eq. (A5), the form assumed is: 1 6 = kcat[(Stot + Etot + Km) 2 − (Stot + Etot + Km)2 − 4StotEtot]
(A6)
This form can be adopted in general. Nevertheless, in the limiting case that Etot Stot (namely at conditions of ‘saturating substrate with the enzyme’), Eq. (A6) can be simplified according to ‘binomial approximation’ (Reiner, 1969): 6=
Etot S k Etot + Km tot cat
(A7)
On the contrary, when Stot Etot (‘saturating enzyme with the substrate’), the simplified form which is symmetrical to Eq. (A7) is:
P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95
94
6=
Stot EtotKcat Stot + Km
(A8)
Product concentration at resident time t (V0Q − 1) can be calculated by integrating Eq. (A5): Ptot =(EP)t + (P)t = (ES)0 −(ES)t =(ES)0(1− e − kcat(V0/Q))
(A9)
Eqs. (A6), (A7) and (A8) can be integrated respectively as: 1 Ptot = [(Stot + Etot + Km) 2 − (Stot + Etot +Km)2 −4StotEtot] (1−e − kcat(V0/Q))
(A10)
Ptot =
Etot S (1 − e − kcat(V0/Q)) Etot +Km tot
(A11)
Ptot =
Stot E (1 − e − kcat(V0/Q)) Stot +Km tot
(A12)
When Ptot =(ES)0 enzyme molecules are synchronized in a single turnover reaction at each working section renewal.
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P. Fermi et al. / Journal of Biotechnology 60 (1998) 81–95 Reiner, J.M., 1969. Behavior of Enzyme Systems, 2nd ed. Van Nostrand Reinhold, New York. Roda, A., Girotti, S., Ghini, S., Carrea, G., 1988. Continousflow assay with nylon tube-immobilized bioluminescent enzymes. Methods Enzymol. 137, 161–171. Scolari, G.L., Vescovo, M., Cappa, F., Bottazzi, V., Bussolati, L., Bignetti, E., 1993. Immuno-based strategy for Clostrid-
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