Kinetic analysis of γ-glutamyltransferase reaction process for measuring activity via an integration strategy at low concentrations of γ-glutamyl p-nitroaniline

Kinetic analysis of γ-glutamyltransferase reaction process for measuring activity via an integration strategy at low concentrations of γ-glutamyl p -nitroaniline 1 first-author 1 1 2 1 2 2 1 corresp ‡Corresponding Author ‡Corresponding Author †E-mail:liaofeish@yahoo.comliaofeish@cqmu.edu.cn †E-mail:liaofeish@yahoo.comliaofeish@cqmu.edu.cn liaofeish@yahoo.com Key Laboratory of Medical Laboratory Diagnostics of Ministry of Education, Chongqing Medical University, Chongqing 400016, China Key Laboratory of Medical Laboratory Diagnostics of Ministry of Education, Chongqing Medical University, Chongqing 400016, China Unit for Biotransformation and Protein Biotechnology, Chongqing Key Laboratory of Biochemical and Molecular Pharmacology, Chongqing Medical University, Chongqing 400016, China Unit for Biotransformation and Protein Biotechnology, Chongqing Key Laboratory of Biochemical and Molecular Pharmacology, Chongqing Medical University, Chongqing 400016, China At 0.12 mmol/L γ-glutamyl p -nitroaniline (GGPNA), an improved integrated method was developed for kinetic analysis of γ-glutamyltransferase (GGT) reaction process and the integration with the classical initial rate method to measure serum GGT. For the improved integrated method, an integrated rate equation, which used the predictor variable of reaction time and considered inhibitions by both GGPNA and products, was nonlinearly fit to GGT reaction processes. For the integration strategy, classical initial rates were estimated when GGPNA consumption percentages were below 50%; otherwise, maximal reaction rates of GGT were estimated by the improved integrated method and converted into initial rates according to the differential rate equation at 0.11 mmol/L GGPNA. The integration strategy was validated using optimized GGT kinetic parameters and 10-s intervals to record reaction curves within 8.0 min. By the integration strategy, there was a linear response from 0.9 to 32.0 U/L GGT, coefficients of variation were below 3.5% for GGT from 8.0 to 32.0 U/L ( n =5), and GGT activities in clinical sera responded linearly to their classical initial rates at 2.00 mmol/L GGPNA with an expected slope. Therefore, the integration strategy was successful in measuring GGT at 0.12 mmol/L GGPNA. Integration strategy Chromogenic substrate Data processing γ-Glutamyltransferase Kinetic analysis Serum enzyme assay Introduction 1 Serum enzymes are important in laboratory medicine. The classical initial rate method, which is commonly used to measure serum enzymes, analyzes reaction data before the instantaneous reaction rates show obvious decreases from the average rate at the beginning of reaction. As a result, the classical initial rate method requires substrate concentrations higher than the Michaelis-Menten constant ( K m ) of an enzyme for desirable linear ranges. For automated assays of serum enzymes in clinical laboratories to enhance throughput and reliability, chromogenic substrates are widely used, but such substrates usually tolerate low solubility, inhibition/activation on enzymes, and/or high cost. To avoid such potential disadvantages, chromogenic substrates are always utilized at low concentrations. In these cases, the linear ranges to measure serum enzymes by the classical initial rate method are usually unsatisfactory. As an example, serum γ-glutamyltransferase (GGT; E.C. 2.3.2.2) has important diagnostic roles (Whitfield, 2001 2001 ; Ruttmann et al., 2005 2005 ; Turgut et al., 2006 2006 ; Lim et al., 2007 2007 ; Giral et al., 2008 2008 ; Jo et al., 2009 2009 ). To measure serum GGT, γ-glutamyl p -nitroaniline (GGPNA) is used as a chromogenic substrate (Shaw et al., 1972 1972 ; Fossati et al., 1986 1986 ). However, the K m of GGT for GGPNA is very high, while GGPNA solubility is very low, so that the linear ranges to measure GGT with GGPNA at practical concentrations are inevitably unsatisfactory. Therefore, alternative methods are desired for serum enzyme assays when chromogenic substrates have to be used at low concentrations. Kinetic analysis of enzyme reaction process is an alternative method for enzyme assay, but classical methods for kinetic analysis of enzyme reaction process usually yield unreliable results (Atkins and Nimmo, 1973 1973 ; Newman et al., 1974 1974 ; Orsi and Tipton, 1979 1979 ). Recently, an improved integrated method was developed for kinetic analysis of enzyme reaction process, using integrated rate equations with the predictor variable of reaction time to fit experimental reaction curves (Liao et al., 2001 2001 ; 2003 2003 ; 2005 2005 ; 2006 2006 ; 2007 2007 ; Walsh et al., 2010 2010 ). To measure enzymes, this improved integrated method gave a higher upper limit of linear response at substrate concentrations even lower than K m , but it had the disadvantage of low analysis efficiency at lower enzyme activities because, for most enzymes, reaction curves should be monitored until at least a 50% consumption of substrates. Fortunately, there is an integration strategy to solve this problem (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). For this integration strategy, experimental reaction curves are recorded as usual, and the method for analyzing an enzyme reaction curve is switched from the classical initial rate method to the improved integrated method upon satisfaction of a pre-defined cutoff. In detail, a reaction curve is analyzed by the classical initial rate method to derive the classical initial rate as the enzyme activity when the pre-defined switch cutoff is not satisfied; otherwise, the reaction curve is analyzed by the improved integrated rate method to estimate the maximum reaction rate ( V m ) and this V m is subsequently converted into an initial rate, according to the differential rate equation at a preset substrate concentration (PSC), to serve as the enzyme activity. Surely, this switch cutoff should be unique and dependent on enzyme activities. This integration strategy to measure enzyme activity has expanded linear ranges and practical efficiency at substrate concentrations comparable to or lower than K m . Hence, it is desirable to achieve this improved integrated method for an enzyme on a chromogenic substrate, to determine a switch cutoff, and then to optimize kinetic parameters, as well as experimental conditions, to validate the integration strategy for enzyme assay. Measurement of GGT with GGPNA manifests the disadvantages of the classical initial rate method because GGPNA has low solubility, GGT has low affinity for GGPNA, and there are inhibitions of GGT by both substrates and products (London et al., 1976 1976 ; Cook and Peters, 1986 1986 ; Cook et al., 1987 1987 ; Dvorakova et al., 1996 1996 ; Stein et al., 2001 2001 ; Castonguay et al., 2007 2007 ). Diversified reactions of GGT on GGPNA and inhibitions of GGT by GGPNA and products complicate the kinetics of the GGT reaction on GGPNA, which results in difficulty in establishing the improved integrated method for the GGT reaction. In the present study, therefore, we investigated the improved integrated method for the GGT reaction at a GGPNA concentration with no solubility problem but obvious inhibitions on GGT, and then the integration strategy for the assay of serum GGT. Materials and methods 1 Reagents and animals 2 Noniondet P40 and GGPNA were from Sigma-Aldrich (St. Louis, MO, USA). Other reagents of analytical grade were from Chongqing Beibei Chemical Factory, China. Leftover clinical sera were collected in a nearby hospital, stored at 4 °C, and analyzed within 24 h. Mice were from the Experimental Animal Center of our university. Experiments with clinical sera and mice were approved by the Ethics Commissions of Chongqing Medical University, China. Mouse kidneys were homogenized with 100 mmol/L sodium phosphate buffer (PBS) at pH 7.4 plus 0.1% Noniondet P40 at 4 °C, and the supernatant after centrifugation at 4 °C was kept at 4 °C before analyses within 12 h. Monitoring of reaction curves and estimation of classical initial rates 2 In 1.20 ml of reaction mixtures, final glycinylglycine at 75 mmol/L and PBS (pH 7.4) at 100 mmol/L were used. Before GGT was added to initiate a reaction, other components, including GGPNA, were mixed and incubated at (25.0±0.5) °C for 10 min. Fifteen seconds after reaction initiation, absorbance at 405 nm < 1.300 was recorded, at 2-s intervals and within 10 min unless otherwise stated, on a spectrophotometer linked to a computer (Liao et al., 2009 2009 ). One unit of GGT was deemed to be the amount able to produce 1 µmol p -nitroaniline per min. The classical initial rate was the average rate from 50 to 160 s after reaction initiation. For the integration strategy, the final GGPNA was 0.12 mmol/L and no more than 150 μl of mouse kidney homogenate or 100 μl of clinical serum was included in the reaction mixture. In order to check the validity of the integration strategy, GGT activities in clinical sera were determined by both the classical initial rate method at 2.00 mmol/L GGPNA and the integration strategy at 0.12 mmol/L GGPNA. Regression analyses of GGT activities in clinical sera by the integration strategy at 0.12 mmol/L GGPNA and the classical initial rate method at 2.00 mmol/L GGPNA both yielded a slope. The consistency of the slope with the ratios of converting factors (CFs) at the aforementioned two GGPNA concentrations, calculated via Eq. ( 2 2 ) as described below, supports the validity of the integration strategy. Estimation of initial rate by the improved integrated method 2 There was a negligible change of absorbance due to nonenzymatic reaction within 10 min. Assigning the instantaneous absorbance in a reaction curve under analysis to A , the maximal absorbance to A m , the absorptivity of p -nitroaniline to ε , glycinylglycine concentration to c A , GGT K m for GGPNA to K m D , and the competitive inhibition constant of glycinylglycine on GGT to K i A , the differential rate equation for GGT reaction was integrated into Eq. ( 1 1 ) (see Appendix) (London et al., 1976 1976 ): $${C_5} \times \ln \left( {{\text{ }}{c_{\text{A}}} + {C_1} \times \frac{{A_{\text{m}} - A}}{\varepsilon }} \right) + \frac{{C_3}}{{C_1}} \times \frac{{A_{\text{m}} - A}}{\varepsilon } + \left( {K_{\text{m}}^{\text{D}} + \frac{{K_{\text{m}}^{\text{D}}}}{{K_{\text{i}}^{\text{A}}}} \times {c_{\text{A}}}} \right) \times \ln \frac{{A_{\text{m}} - A}}{\varepsilon } = a - {V_{\text{m}}} \times t$$ . In Eq. ( 1 1 ), a was a constant to account for the lag time for steady-state reaction. With A m as a nonlinear parameter adjusted at the step of 0.001 for data transformation according to the left part in Eq. ( 1 1 ), nonlinear fitting of Eq. ( 1 1 ) to an experimental reaction curve gave the slope to index V m . Based on the preset GGPNA and glycinylglycine concentrations, C 1 was below 1 and C 1 ×( A m − A )/ ε was below 0.12 mmol/L, while c A was over 74 mmol/L. Hence, ln( c A + C 1 ×( A m − A )/ ε ) is a constant, but ln(( A m − A )/ ε ) has much larger changes during GGT reaction. Consequently, K m D and K i A potentially had great effects on V m and required optimizations while other kinetic parameters were those for hog kidney GGT (London et al., 1976 1976 ). After V m was estimated, the PSC was fixed at 0.11 mmol/L to calculate the initial rate ( V i ) from V m by multiplying V m with the CF defined in Eq. ( 2 2 ). In Eq. ( 2 2 ), the concentration of glycinylglycine as acceptor was taken as a constant at 75 mmol/L, and other kinetic parameters except K m D and K i A were those as reported by London et al. ( 1976 1976 ). $${\text{CF}} = \frac{{0.027 \times {\text{PS}}{{\text{C}}^2} + {\text{PSC}}}}{X}{\text{, }}X = 0.167 \times {\text{PSC}^2} + (2.0 \times K_\text{m}^{\text{D}}/K_\text{i}^\text{A} + 0.027 \times K_\text{m}^\text{D} + 1.332) \times \text{PSC} + (75 \times K_\text{m}^{\text{D}}/K_\text{i}^\text{A} + K_\text{m}^\text{D})$$ . Integration strategy 2 The switch cutoff should be defined for the integration strategy. For reliable V m , the improved integrated method required at least 50% consumption of GGPNA. Clinical sera in reaction mixtures had different absorbances at 405 nm. Forty-five seconds after reaction initiation, the increase of absorbance due to the release of p -nitroaniline from GGPNA was usually below 0.050 with most sera. Therefore, for the integration strategy, the cutoff to switch from the classical initial rate method to the improved integrated method for analyzing reaction data was the increase of absorbance over 0.560 within the stated reaction duration, which corresponded to slightly more than 50% consumption of GGPNA. This switch cutoff corresponded to an initial rate of about 10 U/L GGT. In the integration strategy, the classical initial rate was estimated when GGPNA consumption did not reach the preset cutoff, while the improved integrated method was used to estimate the initial rate when GGPNA consumption reached the preset cutoff. Absorptivity of p -nitroaniline was fixed at 9.87 [(mmol/L)·cm] −1 (London et al., 1976 1976 ). Programming and statistic analyses 2 The software written in Visual Basic 6.0 was used. A subprogram for the improved integrated method with GGT reaction was added and K m D and K i A were adjusted manually. By the improved integrated method, the detection limit was the initial rate with deviation within 3% from that estimated with data of 80% GGPNA consumption (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). The lower and upper limits of the linear response were those exhibiting deviations below twice the standard error of estimate ( s ) from the linear plot if the lower limit was over the detection limit; otherwise, the lower limit was the detection limit itself. Results were expressed as mean±standard deviation and compared by Student’s t -test at P < 0.05 with functions in Microsoft Excel. Results and discussion 1 Optimizations of GGT kinetic parameters 2 To realize the integration strategy, two linear response plots, by the classical initial rate method and the improved integrated method, should become one continuous linear plot covering expanded ranges. Hence, there should be consistent slopes of linear response and an overlapped region of initial rates measurable with consistent results by the two individual methods (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). Of hog kidney GGT, K m D was 1.87 mmol/L and K i A was 0.28 mmol/L (London et al., 1976 1976 ). Using this combination of K m D and K i A , the improved integrated method was feasible to measure GGT activities. However, the integration strategy was non-valid with these two kinetic parameters because the two linear plots by the two individual methods were separated (Fig. 1 1 ). For the consistency in both slopes of the linear response and initial rates within an overlapped region, K m D and K i A in Eq. ( 1 1 ), as well as PSC in Eq. ( 2 2 ), should be optimized. By the integration strategy with other one-enzyme reactions, the optimized PSC was about 93% of the initial substrate concentrations (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). GGT from different sources showed different kinetic parameters (London et al., 1976 1976 ; Cook and Peters, 1986 1986 ; Cook et al., 1987 1987 ; Dvorakova et al., 1996 1996 ; Stein et al., 2001 2001 ; Castonguay et al., 2007 2007 ). Hence, using 2-s intervals to monitor GGT reaction curves within 10 min to enhance confidence in achieving an overlapped region of initial rates measurable by the two individual methods, K m D and K i A were optimized firstly with PSC fixed at 93% of the initial GGPNA concentration. V i : initial rate; x : amount of GGT from kidney homogenate Using different combinations of K m D and K i A , both within 2.50 mmol/L, for kinetic analyses of GGT reaction curves, consistent slopes of the linear response and overlapped regions of initial rates measurable by the two individual methods were observed. However, there were still no consistent initial rates within the overlapped regions. A higher K m D yielded a larger V m , but a smaller CF defined in Eq. ( 2 2 ), and a higher K i A yielded a smaller V m , but a higher CF (Fig. 2 2 ). Hence, K m D and K i A had opposite effects on initial rates estimated by the improved integrated method; K i A for a preset K m D , or vice versa, should be optimized for kinetic analyses of GGT reaction curves to estimate initial rates so that the integration strategy can be validated. For any preset K m D , which varied from 0.80 to 2.00 mmol/L, there was always an optimal K i A to produce consistent slopes for the linear responses and negligible differences in initial rates within the aforementioned overlapped regions measurable by the two individual methods (Fig. 3 3 ). More importantly, there was a linear response of this optimal K i A for the consistent initial rates within the overlapped regions to preset K m D (Fig. 4 4 ); the optimal K i A was 1.90 mmol/L for K m D preset at 1.87 mmol/L. Therefore, it was feasible to validate the integration strategy with GGT by optimizing kinetic parameters as long as both reaction duration and intervals to monitor reaction curves were optimized; K i A at 1.90 mmol/L and K m D at 1.87 mmol/L were used throughout for kinetic analyses of GGT reaction curves, unless otherwise stated. Optimizations of reaction duration and intervals to monitor reaction curves 2 In general, experimental conditions that simultaneously produce higher values of the upper limit of the linear response by the classical initial rate method and lower values of the detection limit by the improved integrated method are preferred, so that there are wider overlapped regions of the initial rates measurable by the two individual methods (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). The improved integrated method with GGT requires reaction data of over 50% substrate consumption (data not shown); this requirement restricts the initial GGPNA concentrations to be below 0.26 mmol/L because 50% consumption of GGPNA will give an absorbance of about 1.300 as the threshold measurable on common spectrophotometers. Shorter intervals to record reaction curves increase the upper limits of the linear response by the classical initial rate method and longer reaction duration reduces the detection limits by the improved integrated method (Liao et al., 2009 2009 ; Liu et al., 2009 2009 ). Hence, shorter intervals and longer duration to monitor reactions are preferred by the integration strategy as long as the analysis efficiency is practical. The use of regular intervals over 20 s to monitor reactions reduced the upper limit of the linear response of GGT measured by the classical initial rate method, whereas this little affected the upper or lower limit measured by the improved integrated method. By monitoring reaction curves within 6 min at 20-s intervals, there was no overlapped region of GGT initial rates measurable by the two individual methods, and hence the integration strategy was non-valid. When the duration to monitor reaction at 20-s intervals was prolonged to 8 min or the regular intervals for monitoring reaction curves within 6 min were shortened to 10 s, there were consistent slopes of the linear response and a narrow overlapped region of GGT initial rates measurable with consistent results by the two individual methods (Table 1 1 ). Hence, GGT reaction curves were monitored within 8.0 min at 10-s intervals for enhanced confidence in validating the integration strategy. The same series of reaction curves were analyzed after adjusting the regular intervals and/or the reaction duration. All linear response equations gave R 2 > 0.99 indicated the detection limit was higher than the lower limit and hence the detection limit itself was used as the lower limit RD: reaction duration; d t : regular interval; V i : initial rate; x : amount of GGT from kidney homogenate Condition Method Equation Upper limit (U/L) Lower limit (U/L) 3 RD = 6 min d t =10 s Classical initial rate method V i =0.217 x +0.879, s < 0.15 11.0 0.45 Improved integrated method V i =0.215 x +0.889, s < 0.21 32.0 ~9.0 * * Integration strategy V i =0.216 x +0.788, s < 0.29 32.0 0.87 5 3 RD=6 min d t =20 s Classical initial rate method V i =0.214 x +0.920, s < 0.17 10.0 0.51 Improved integrated method V i =0.213 x +0.933, s< 0.21 32.0 ~10.0 * * Integration strategy Not available 5 3 RD=8 min d t =10 s Classical initial rate method V i =0.217 x +0.879, s < 0.16 11.0 0.48 Improved integrated method V i =0.215 x +0.852, s< 0.20 32.0 ~9.0 * * Integration strategy V i =0.215 x +0.738, s< 0.20 32.0 0.93 5 3 RD=8 min d t =20 s Classical initial rate method V i =0.211 x +1.120, s< 0.17 10.0 0.51 Improved integrated method V i =0.213 x +0.939, s< 0.23 32.0 ~9.0 * * Integration strategy V i =0.214 x +0.930, s< 0.30 32.0 0.90 5 3 RD=8 min d t =30 s Classical initial rate method V i =0.208 x +1.080, s< 0.21 9.0 0.63 Improved integrated method V i =0.204 x +1.470, s< 0.24 32.0 ~10.0 * * Integration strategy Not available By the integration strategy under conditions as optimized above, initial rates from 0.9 to 32.0 U/L responded linearly to amounts of GGT from mouse kidney (Fig. 5 5 ), whose upper limit was increased by nearly three-fold and the lower limit was comparable to that by the classical initial rate method alone at the same GGPNA level. The within-run coefficients of variation (CVs) were below 3.5% for GGT varying from 8.0 to 32.0 U/L ( n =5 for each sample). Therefore, the integration strategy was effective to GGT on GGPNA and was potentially applicable to measure GGT in clinical sera. Preliminary application of the integration strategy to clinical sera 2 Optimal K m D and K i A were tested with three clinical sera whose GGT activities were measurable by the two individual methods. Using an optimized K i A according to the relationship in Fig. 4 4 for a K m D varying from 0.80 to 2.00 mmol/L, there were still consistent initial rates measurable by the two individual methods. Hence, K m D and K i A , optimized above, were potentially effective for clinical sera. It is putative that the same amount of an enzyme should have the same V m independent of concentrations of a chromogenic substrate. Thirty-one clinic sera with the widest distribution of classical initial rates of GGT at 2.00 mmol/L GGPNA were selected after screening of a pool of over 150 clinical sera to check the validity of the integration strategy. Of these 31 clinical sera, initial rates of GGT by the integration strategy responded linearly to classical initial rates at 2.00 mmol/L GGPNA with a slope of 0.109 (Fig. 6 6 ). Calculated via Eq. ( 2 2 ), the ratio between CF at 0.12 mmol/L GGPNA and that at 2.0 mmol/L GGPNA was 0.110, which was consistent with the aforementioned slope. The consistency of this slope with expectations strongly supports the validity of the integration strategy. Lipids, bilirubin, and hemoglobin in clinical sera had negligible interference with GGT assay by the integration strategy when the background absorbance was below 0.650; otherwise, background absorbance should be corrected to monitor reaction curves with more than 50% consumption of GGPNA. V i1 : initial rate of the integration strategy at 0.12 mmol/L GGPNA; V i2 : initial rate of the classical initial rate method at 2.00 mmol/L GGPNA Further discussion 2 To measure enzymes, the improved integrated method prefers substrate concentrations close to K m , supporting that GGPNA is unfavorable for GGT assay due to high K m . At 0.12 mmol/L GGPNA, however, the integration strategy effectively expanded the linear range at practical analysis efficiency, and the use of 10-s intervals to monitor reactions enabled operation of multiple sera in parallel on autoanalyzers to enhance the throughput. Therefore, the integration strategy was successful in measuring GGT at GGPNA concentrations much lower than K m . By the classical initial rate method, no chromogenic substrates for serum lipase assay are satisfactory due to their low solubility (Tsao et al., 2007 2007 ; Yamada and Fujita, 2007 2007 ); chromogenic maltotrioside substrates for direct assay of serum α-amylase are also unsatisfactory due to the cost (Winn-Deen et al., 1988 1988 ; Gella et al., 1997 1997 ). Taken together, when concentrations of chromogenic substrates are limited by their solubility, cost, substrate inhibition/activation, and/or measurable ranges on instruments, the integration strategy is an effective and general alternative to measure serum enzymes with expanded linear ranges and practical efficiency, and the optimizations of reaction duration and regular intervals to monitor reaction curves can be general guidelines to validate the integration strategy at low concentrations of chromogenic substrates. References GL Atkins , IA Nimmo . 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New procedure for the measurement of pancreatic lipase activity in human serum using a thioester substrate 10.1631/jzus.B1000171 Project supported by the National Natural Science Foundation of China (No. 30200266) and the Program for New Century Excellent Talents in University of Ministry of Education of China (No. NCET-09-928) 2010-05-10 2011-01-25 2010-07-23 2022-01-05 Copyright © Zhejiang University and Springer-Verlag Berlin Heidelberg 2011 2011 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 03 12