PROCESS FOR DETERMINING ENZYMATIC ACTIVITY

Abstract: This invention provides a process for determining the activity of an object enzyme in a chain reaction system consisting of an object enzyme and a conjugate enzyme, which comprises determining the maximum reaction veloc­ ity of the conjugate enzyme (V max; 2 ) and dividing the reac­ tion velocity of the conjugate enzyme (V₂) by the reaction velocity ratio (r₂; reaction velocity of conjugate enzyme/­ reaction velocity of object enzyme) which is determined by substituting (V max; 2 ) in the following equation (6) or diluting the conjugate enzyme to prepare at least two solutions of different concentrations (nothing but the con­ centration ratio is known), determining V₂ at each con­ centration and dividing the resulting V₂ by r₂ determined by plotting. This invention provides a process for determining the activity of an object enzyme accurately to thereby make it possible to prepare a diagnostic determining kit.

Description: PROCESS FOR DETERMINING ENZYMATIC ACTIVITY Detailed Description of the Invention: This invention relates to a process for determining the activity of an object enzyme by using a conjugate enzyme which has a relatively large Michaelis constant (Km) in a chain reaction system. More particularly it relates to a process for calculating the activity of an object enzyme which comprises using a conjugate enzyme which has a relatively large Michaelis constant (Km) in a considerably smaller amount than sufficient to thereby determine V2 in a chain reaction system. In chain enzyme reactions, there are generally at least two enzymes which play a conjugative role to form a chain reaction system. For example, adenosin deaminase and glutamate dehydrogenase form a conjugated enzymatic system in the following chain reaction scheme (12): EMI1.1 <tb> Adenosine <SEP> H2O <SEP> Glutamic <SEP> acid <SEP> r <SEP> NADP+ <tb> <SEP> Adenosinedeaminase <SEP> Glutamate <tb> <SEP> / <SEP> \ <SEP> I <SEP> \ <SEP> dehydrogenase <SEP> (12) <tb> Adenine <SEP> <SEP> NH3 <SEP> / <SEP> 3 <SEP> NADPH <tb> <SEP> a-Ketoglutaric <tb> <SEP> acid <tb> In the present invention, an enzyme of which the activity is to be determined in such a chain reaction system will be called the object enzyme, e.g. adenosine deaminase in the above-mentioned chain reaction scheme, while the other the conjugate enzyme, e.g., glutamate dehydrogenase in this example. There are nuinerous chain reaction systems other than that described above with adenosine deaminase and glutamate dehydrogenase which usually occurs in vivo. For example, it is also possible to couple hexokinase with glucose-6-phosphate dehydrogenase to form a chain reaction system. The following enzymes are also capable of coupling with glutamate dehydrogenase (G1DH) similarly to adenosine deaminase to form a chain reaction system respectively by the reaction as described below: AMD deaminase (EC 3,5,4,6) Adenine deaminase (EC 3,5,4,2) Guanine deaminase (EC 3,5,4,3) Arginine deaminase (EC 3,5,3,6) Urease (EC 3,5,1,5) In the same way, Acetyicholine esterase (AchE) can be measured with acetate kinase (AK) which has a high Km. Acetylcholine + H20 EMI2.1 Choline + acetate Acetate + ATP EMI2.2 Acetylphosphate + ADP ADP + PEP EMI2.3 Pyruvate + ATP Pyruvate + NADH EMI2.4 Lactate + This invention provides a process which is effective in determining the activity of an object enzyme by using a conjugate enzyme in a chain reaction system which has a relatively large Michaelis constant (e.g. Km > 1 mM). It is generally very difficult to determine the activity of an object enzyme by using an enzyme which serves as a conjugate enzyme in a chain reaction system and has a relatively large Michaelis constant as well. Therefore a sufficient amount of the conjugate enzyme must be added in a conventional process, although troubles might often occur in such a case in that cost, solubility or purity of the conjugate enzyme would make it impossible to add a sufficient amount thereof. Heretofore no other means than adding a seemingly sufficient amount of a conjugate enzyme are employed in a conventional process to prepare a diagnostic determining kit by using a chain reaction system involving a conjugate enzyme having a relatively large Michaelis constant. Needless to say, it is necessary to add a considerably large amount of a conjugate enzyme if it has a relatively large Michaelis constant. A process for determining the activity of an object enzyme has been known in which the object enzyme is subjected to a chain reaction with one or more conjugate enzymes and the determined reaction velocity of the final conjugate enzyme is regarded as the activity of the object enzyme. However, this determining process is effective only under such conditions that the conjugate enzyme has a small Michaelis constant and is present in a sufficient amount. That is to say, this process has such disadvantages that a considerably higher enzyme concentration will be necessary with an increase in the Michaelis constant and the reaction velocity of the conjugate enzyme will not approach to that of the object enzyme during the determination. As the result of our researches for determining the activity of an object enzyme by using a small amount of a conjugate enzyme, we have succeeded in calculating the reaction velocity of the object enzyme by determining the maximum reaction velocity of a conjugate enzyme accurately, calculating r2 by equation (6) and determining the reaction velocity of the conjugate enzyme (V2), or by diluting the conjugate enzyme to prepare at least two solutions of different concentrations, determining V2 at each concentration of E2 and determining the activity ratio r2 by plotting. Thus this invention provides a process for determining the activity of an object enzyme in a chain reaction system consisting of an object enzyme and a conjugate enzyme, which comprises determining the maximum reaction velocity of the conjugate enzyme (Vmax;2) and dividing the reaction velocity of the conjugate enzyme (V2) by the reaction velocity ratio (r2, reaction velocity of conjugate enzyme/reaction velocity of object enzyme) which is determined by substituting (Vmax;2) in the following equation (6), EMI5.1 or diluting the conjugate enzyme to prepare at least two solutions of different concentrations (nothing but the concentration ratio is known), determining V2 at each concentration of E2 and dividing the resulting V2 by r2 determined by plotting. According to the process of the present invention for determining the activity of an object enzyme by using a small amount of a conjugate enzyme, it is possible to prepare an excellent diagnostic determining kit economically and efficiently. Brief Description of the Drawings: Fig. 1 shows a relationship among r2, n2 and F2. Fig. 2 shows a relationship between r2b/r2a (= V2b/V2a) and r2a, in which A, B, C and D represent a case where Vl t/2 x Km;2 equals to 0, 0.01, 0.02 and 0.05 respectively. Fig. 3 shows curves which respectively indicate a relationship between V2b/V2a and r2a as Vmax;2b/Vmax;2a is changed, wherein (1 - k) x V1 x t/Km;2 = 0. Fig. 4 shows an example of adenosine deaminase determination under activity-controlled conditions, in which V1 represents the reaction velocity of ADA determined I min and 10 sec to 1 min and 50 sec after the initiation of the reaction by using a sufficient amount of GlDH (17,000 pM/min), V1/2 represents an activity equal to one-half V}, X represents V2 determined 10 min and 10 sec to 10 min and 50 sec after the initiation of the reaction. by using 235j & /min of G1DH activity and Y represents V2 determined 10 min and 10 sec to 10 min and 50 sec after the initiation of the reaction, by using 94 M/min of GIDH activity. Background of the Invention: In a binary chain reaction system scheme (I), we shall generally assume that I) the reaction velocity (activity) V1 of an object enzyme E1 is constant; and 2) the reaction of a conjugate enzyme E2 obeys Michaelis-Menten equation. EMI7.1 where S: substrate P: final product E: enzyme V: velocity. The above-mentioned scheme (1) leads to the following equation (2), which in turn leads to equation (3). d[S2]/dt = V1 - Vmax;2/(1+Km;2/[S2]) ... (2) t = -{Km;2/(V1-Vmax;2)}{V2/(V2-Vmax;2)} +{Vmax; ; 2/(V1-V 2) )Rn(Vmax;2(V2-V1) /V1 (V2-Vmax;2)} .............. (3) where V1: reaction velocity of E1 (M/min) V2: reaction velocity of E2 (M/min) Vmax;2: maximum reaction velocity of E2 (M/min) Km;2: Michaelis constant (M) of E2 with regard to t: time (min). Equation (3) is transformed into equation (4) by defining Vmax;2/V1 = and V2/V1 = r2. EMI8.1 Then equation (5) is defined as follows and substituted into equation (4) to thereby lead euqation (6). EMI8.2 F (n2, r2) represents a function of n2 and r2. Two separate reaction systems in which n2 and r2 are identical respectively have the same F2. Fig. 1 shows a relationship among r2, n2 and F2, indicating a relationship between n2 and F2 at various r2 from 0.1 to 0.999, i.e. V2/V1 = 0.10 - 0.999. If r2 is constant, F2 is substantially constant when n2 > 5. In other words, when n2 is greater than 5 and Vmax; 2 is known, it is possible to determine r2. Then it is also possible to determine V1 by dividing the determined V2 by r2. This process will be referred to as Process 1. However, it is more troublesome than expected to determine Vmax;2 In addition, Vmax;2 should be determined each time when E2 would not be so stable. It can not be ensured that E2 might not be inactivated during storage, particularly in the case of preparing a kit or the like. The following Process 2 makes it possible to determine r2 when Vmax; 2 is not known accurately. Then it is also possible to determine V1 by dividing the determined V2 by the resulting r2. First, E2 concentration, although unknown, is defined as Vmax;2a. Then the E2 is diluted accurately to a concentration of Vmax;2b. The known dilution, i.e. Vmax12b/Vmax;2a1 is defined as k, and V2 values determined by adding E2 in an amount of Vmax;2a and Vmax;2b are defined as V2a and V2b respectively. r2a and r2b are defined as V2a/V and V2b/Vl respectively to define F2 thereof as F2a and F2b respectively. Thus equation (6) is transformed into equations (7) and (8) and these equations lead to equation (9), which in turn leads to equation (10). Vmax;2a = F2axKm;2/t+V1 ............... (7) V = F2bxKm;2/t+V1 ............... (8) EMI10.1 F2b = kxF2a-(1-k)xV1xt/Km;2 ........... (10) Theoretically, k may take any value within the range of 0 to 1. When k = 0.5 (i.e. two-fold dilution), equation (10) may be transformed into the following equation (11). F2b = 0.5F2a- 0.5 V1 X t/Km;2 (11) When n is greater than 5, F2a corresponding to r2a of 0.1 to 0.999 may be determined by Fig. I. Then the resulting F2a is substituted into equation (11) to determine F2b, by which the corresponding r2b may be determined. Fig. 2 can be obtained by plotting r2bZr2a (= V2b/V2a) against r2a when the second term of the right side of equation (11), i.e. V1 t/2 x Km;2, is 0, 0.01, 0.02 and 0.05. Curves A, B, C and D represent the individual case as described above. When the determination range of V1 is set to 0 to 10 pM/min, it is necessary that 10 x 10-6 x t/2 x Km;2 - 0.01, that is to say, t/Km;2 # 2 x 10 to render the above-mentioned second term smaller than 0.01. For example, when using E2 having Km;2 = 5 x 10 3 M, it is necessary to determine V2a and V2b within 10 min after the initiation of the reaction, i.e. t < 10. In this case, error of r 2a is represented by the transverse distance between curves A and B. Accordingly it is shown by determining r2a by using curve E which is obtained by connecting midpoints of the transverse distances between curves A and B that a Vmax 2 concentration which makes V2b/V2a higher than 0.56, 0.58 and 0.60 respectively must be selected to render the error lower than 10%, 5% and 3% when the determination range of V1 is 0 to 10 pM/min. When V2 is determined one min after the initiation of the reaction in the determination range of V1 of 0 to 10 pM by using the same E2 (Km;2 = 5 x 10 3 M) as described above, the second term of the right side of equation (11) approximately equals to zero and the relationship between V2b/V2a and r2a is approximated by curve A. Consequently determination with little error may be carried out by using curve A. As a matter of course, a larger amount of E2 (i.e. higher Vmax;2) should be added in such a case than with the case in which determination is carried out 10 min after the initiation of the reaction. The second term of the right side of equation (11) will become smaller with an increase in Km;2, resulting in a higher accuracy of the determination. When identical determination accuracy is expected, the period from the initiation of the reaction to the determination will be prolonged with an increase in Cm;2, i.e. a smaller amount of E2 may be used. It is also possible to change the determination accuracy by using a proper curve in Fig. 2. For example, when V2 is determined 10 min after the initiation of the reaction by using E2 (kin;2 = 5 x 10 M), accurate V1 may be determined by using curve B if V1 is approximately 10 ijM/min. As described above, Fig. 2 may be drawn depending on E2 concentration ratio, Cm;2, t and desired range of V1 determination. Fig. 3 is obtained by determining k as 0.1 to 0.9 and the second term of the right side as zero in equation (10). In practice, V2b/V2a is determined by V2a and V2b which are determined by the addition of E2 of V and V respectively, and r2 is determined by the curve obtained by plotting V2b/V2a against r2a. Activity determinations of a series of samples are carried out by using E2 of Vmax;2a. Then V1 of each sample may be determined by dividing the resulting V2 by r2a. Process 2 as described above may be applied to a ternary chain reaction system and so on. For example, it may be considered that V2 =. V3 and V1 . V2 respectively, when E3 having small Km is added in a greater amount than that of E2 having large Km, or contrary to this E3 having large Km;3 is added in a smaller amount than that of E2 having small Km Therefore the theory in a binary chain reaction system may be applied as such. In the following examples are described several embodiments to illustrate the present invention. Example 1 Process 1 (a process for determining V1 by an accu rate determination of may V The activity of adenosine deaminase (ADA) was determined by using glutamate dehydrogenase (G1DH) obtained from yeast in the chain reaction system of scheme (12). EMI13.1 <tb> <SEP> Glutamic <SEP> acid <tb> Adenosineg <SEP> H20 <SEP> 9 <SEP> NADP+ <tb> <SEP> ADA <SEP> ..... <SEP> (12) <tb> AdenineNH <SEP> NADPH <tb> <SEP> 3 <tb> <SEP> a-Ketoglutaric <SEP> acid <tb> First, K of GlDH with regard to ammonia, which m was used as a conjugate enzyme, was determined. The reaction velocity was determined in the presence of an 80 mM potassium phosphate buffer solution (pH 7.4), 5 mM of a-ketoglutaric acid (a-KG) and 0.2 mM of NADPH while varying the concentration of ammonium acetate. Then the K was determined m to be 3.4 x 10 M from a Lineweaver-Burk plot of the determined values. Subsequently Vmax;2 (in Fig. 1, F = 0.69 when n > 10) which made V2 to become 50% of V1 when t = 10 (min) was found to be 235 pM/min (0.235 U/ml) by calculating with the resulting K and equation (6). Then a different amount of ADA (i.e. different V1) from E2 of Vmax; 2 = 235 pM/min (determined at 300C, pH 7.4) was added to 0.7 mM (approximately 20 times as much as Km) of adenosine, 5 mM of a-KG, 0.25 mM of NADPH and a 50 mM potassium phosphate buffer solution to determine GlDH activity 10 min after the initiation of the reaction at 300C (curve X in Fig. 1). V2 was also determined under the same conditions except for reducing the amount of G1DH to 1/2.5 (94 pM/min) (curve Y in Fig. 4). A sufficient amount of G1DH (17,000 pM/min) was added to determine V1 in the period of 1 min and 10 sec to I min and 50 sec after the initiation of the reaction (curve V1 in Fig. 4). Comparing the dotted line which shows one-half V1 (V1/2 in Fig. 4) with curve A, it was found that ADA activity can be determined with an error less than 2% by doubling the determined activity of G1DH within a range of ADA activity of 0 to 16 pM/min. That is to say, accurate V1 can be determined by dividing V2 by 0.5 when V2 is within a range of 0 to 8 pM/min. On the other hand, when V1 = 40 pM/min, the theoretical value of V2 was 89% of (V1)/2 while the determined value thereof was 78% of (V1)/2. Further deviation of a determined V1 from a theoretical one was observed when V1 was still higher. Such a phenomenon seemed to result from an experimentally lower value of V2 because the NADPH concentration when carrying out the determination had become too low when V1 was too high, as the former had been adjusted to 0.25 mM to put the absorbance of the reaction liquor at 340 nm within the range determinable by a spectrometer in setting the determination conditions (Km of G1DH with regard to NADPH was 1.3 x 10-4 M). In a determination by using 94 pM/min of G1DH (curve B), the determinable range of V2 in proportion to V1 would be broadened to 0 to 30 iiM/min, as a matter of course. The ratio r2 of V2 to V1 in this case was calculated to be 0.25 theoretically, which was approximately equal to VI determined by dividing the resulting V2 by 0.25. Example 2 Process 2 (a process for determining the activity ratio r2a (= V2a/Vl) by diluting E2 to prepare at least two solutions of different concentrations (nothing but concentration ratio is known) and determining V2 at each E2 concentration (determined value; V2a ' V2b ...)) Determination was carried out in the same reaction system as in Example 1 by using 5 mM of a-KG, 0.25 mM of NADPH, a 50 mM potassium phosphate buffer solution (pH 7.4), ADA (E1) and G1DH (E2) solutions of various concentrations. E2 solutions of two concentrations (Vmax;2a = 250 and 208 'LM/ min) were prepared and each was further diluted to 1/2, 2/5 and 1/3. Each E2 solution was added to the reaction liquor and a decrease in NADPH concentration was observed for a period of 10 min and 10 sec to 10 min and 50 sec after the initiation of the reaction to determine V2. V2's determined by using E2 solution, 1/2 E2 solution, 2/5 E2 solution and 1/3 E2 solution will be referred to as 2a' V2b1, V2b2 and V2b3 respectively. V1 was determined by determining r2a corresponding to the activity ratio of each combination (V2bl/V2b, V2b2/ V2a and v2b3/v2a) from V2b/V2a vs. r2a curve (Fig. 3) and dividing V2a by the resulting r2a. Results are shown in the following table. Table 1 V1 = 10.0 pM/min Vmax; 2a = 250 M/min EMI17.1 <SEP> Vz <SEP> ¯V2b/V2ar2a <SEP> v,(= <SEP> V2aza <tb> Vmax <SEP> ; <tb> Vmax;2a/2 <SEP> V2bl2 <SEP> 98 <SEP> 0.594 <SEP> 0.530 <SEP> 9.47 <tb> Vmax;2a/2.5 <SEP> 2b22.43 <SEP> 0.485 <SEP> 0.515 <SEP> 9.73 <tb> 2.43 <tb> <SEP> V <SEP> 0 <SEP> 412 <SEP> 0.485 <SEP> 10.35 <tb> Vmax;2a/3 <SEP> V2b32 <SEP> 07 <SEP> 0.412 <SEP> 0.485 <tb> Vmax;2a = 208 pM/min EMI18.1 <tb> Vmax;2 <SEP> L <SEP> V2 <SEP> V2b/V2a <SEP> <SEP> r2a <SEP> <SEP> V1(= <SEP> V2a/r2a) <SEP> <tb> Vmax;2a <SEP> V2a <SEP> 4.42 <tb> Vmax;2a/2 <SEP> V2b12.52 <SEP> 0.569 <SEP> 0.440 <SEP> 10.04 <tb> <SEP> Vmax; ;2a/2.5 <SEP> V2b22.07 <SEP> 0.468 <SEP> 0.450 <SEP> 9.85 <SEP> <tb> I <SEP> V <tb> Vmax;2a/3 <SEP> V2b31 <SEP> 73 <SEP> 0.391 <SEP> 0.430 <SEP> 10.27 <tb> A part from this, V1 was determined by a conventional process. That is to say, a sufficient amount (17 mM/min) of E2 was added to a reaction liquor. Then V2 was determined one min after the initiation of the reaction and the resulting value was regarded as an approximation of V1 (V1 = 10.0 uM/min). The value of V2a/r2a was approximately equal to V1 (10 pM/min) in either case of Vmax;2a = 250 pM/min or 208 M/min. These results suggest that it is possible to determine V1 by calculating V2/r2 with the addition of a considerably smaller amount of a conjugate enzyme having a relatively large Km than the case of a conventional process under adequate conditions. It further suggests that the activity of an object enzyme can be determined with an appreciable accuracy by diluting the conjugate enzyme to prepare two solutions of different concentrations and determining V2 at each concentration, so long as the concentration (dilution ratio) of the added conjugate enzyme was known, without the knowledge of the activity of the added conjugate enzyme accurately. The resulting V1 and the substrate concentra tion K are substituted in Michaelis-Menten m;l equation to thereby determine Vmax from which unit (U) of E1 may be determined.

Claims: Claim A process for determining the activity of an object enzyme in a chain reaction system consisting of an object enzyme and a conjugate enzyme, which comprises determining the maximum reaction velocity of the conjugate enzyme (V and dividing the reaction velocity of the conjugate enzyme (V2) by the reaction velocity ratio (r2; reaction velocity of conjugate enzyme/reaction velocity of object enzyme) which is determined by substituting (V in the following equation (6), EMI20.1 or diluting the conjugate enzyme to prepare at least two solutions of different concentrations (nothing but the concentration ratio is known), determining V2 at each concentration and dividing the resulting V2 by r2a determined by plotting.

Inventors: FUJII, KATSUMI, HORIO, TAKEKAZU, TAKAGAHARA, ISAMU, YAMASHITA, JINPEI, YAMAUTI, JUNITI
Applicants: ORIENTAL YEAST CO., LTD.
Application year: 1984
Main classification: C12Q1
IPC codes: C12Q1