Method for determining the metabolic capacity of at least one enzyme

Abstract

A method for determining the metabolic capacity of an enzyme includes time-resolved determination of the concentration of a product in exhaled air. The product is created by metabolism of a substrate, previously administered to an individual, by an enzyme of the individual. The product concentration is determined until the maximum product concentration in the exhaled air is reached. A model function is fitted to measured values of the product concentration, obtained by the time-resolved determination of the product concentration between start and end times. The metabolic capacity of the enzyme is determined based on parameters of the model function. Determining the metabolic capacity of the enzyme takes place based on at least two parameters of the model function, wherein the maximum value and time constant of the model function are not selected as parameters at the same time, and the start and/or end times are not selected as parameters.

Claims

1. A method for determining the metabolic capacity of at least one enzyme, comprising the following steps: predetermining a dosage of a substrate to be administered to an individual having the at least one enzyme such that the predetermined dosage provides for determining the metabolic capacity of the at least one enzyme, the predetermined dosage being sufficient for targeted induction of metabolism of the substrate; administering the predetermined dosage of the substrate to the individual, wherein the substrate is available for metabolism within 60 seconds of the administering; collecting air exhaled by the individual that has a product of the metabolized substrate; measuring with a measuring apparatus a property of the product indicative of the concentration of the product in the exhaled air in order to determine the concentration of the product in the exhaled air; using the determined concentration of the product, performing the following: time-resolved determining of the concentration of the product in the air exhaled by the individual, wherein the product has been created by the metabolism of the substrate, previously administered to the individual, by the at least one enzyme of the individual and wherein the product concentration of the product of the metabolized substrate is determined essentially only at the least until the maximum product concentration in the air exhaled by the individual is reached, fitting of a model function to measured values of the product concentration, which were obtained by the time-resolved determination of the product concentration between a start time and an end time, determining the metabolic capacity of the at least one enzyme on the basis of parameters of the model function, which specify the model function, wherein determining the metabolic capacity of the enzyme takes place on the basis of at least two parameters of the model function, with the proviso that the maximum value of the model function and the time constant of the model function are not selected as parameters at the same time, insofar as the model function is a mono-exponential function, and with the further proviso that the start time and/or the end time are not selected as parameters; determining the state of health of the individual concerning specific bodily functions based on the metabolic capacity of the at least one enzyme; and reporting the state of health of the individual.

2. The method according to claim 1, wherein the parameters are selected from the group comprising the maximum value of the model function, the i-th moment of the model function with i=1, 2, 3, 4, . . . , the j-th central moment of the model function with j=1, 2, 3, 4, . . . , the standard deviation of the model function, a time constant of the model function, the centre of gravity of the time constants, the mean deviation of the time constants from the centre of gravity, the variation of the time constants, the distribution of the time constants, the weighting of the time constants, the weighting of the distribution of the time constants, the weighting of the variation of the time constants.

3. The method according to claim 1, wherein the model function is a solution function of a first order differential equation, a solution function of a second order differential equation, a solution function of a third order differential equation, a solution function of a combination of differential equations of various orders or a multi-exponential function as a function of time.

4. The method according to claim 1, comprising flowing the exhaled air through the measuring apparatus, wherein the determination of the concentration of the product takes place with the exhaled air flowing through the measuring apparatus.

5. The method according to claim 4, wherein a flow rate of the exhaled air, flowing through the measuring apparatus which is used for determining the concentration, is determined.

6. The method according to claim 1, wherein to determine the concentration of the product the measuring apparatus has a breathing resistance below 100 mbar.

7. The method according to claim 1, wherein the entire exhaled air of at least one breath of the individual is used as exhaled air.

8. The method according to claim 1, wherein determining the concentration of the product takes place, while the individual is essentially in a resting position selected from a lying position or a sitting position.

9. The method according to claim 1, wherein determining the concentration of the product takes place, while the individual is in a lying or sitting position, in which the position of at least one of the legs and the upper part of the body of the individual is changed by less than 45 degrees, particularly by less than 30 degrees and especially by less than 15 degrees compared with the predetermined position.

10. The method according to claim 1, wherein determining the concentration of the product takes place by at least one of infrared-absorption spectroscopy, mass spectrometry, computer tomography and nuclear magnetic resonance spectroscopy.

11. The method according to claim 1, wherein the model function can be expressed by the following formula:
MetPow=cal*[F(product,t)f(product,t).sub.nat]*g(P)*h(n)*L(n/M)*(n/M.sup.2)*V(n/M), wherein MetPow denotes the metabolic capacity, cal is a constant taking into account corrections, F(product,t) is a function expressing the dynamics of exhaled product, f(product,t).sub.nat is a function expressing the natural abundance of the product in the air exhaled by the individual prior to substrate administration, g(P) is a function expressing the dependence of the product production rate P of the individual on the activity status of the individual, h(n) is a function expressing the number of product molecules generated per substrate molecule, L(n/M) is a function expressing a non-linear behaviour of the metabolic capacity dependent on the number of administered substrate molecules n, wherein M denotes the bodyweight of the individual, and V(n/M) is a function expressing dependencies due to different administration procedures of the substrate.

12. The method according to claim 11, wherein g(P)=P and/or h(n)=1 and/or V(n/M)=1.

13. The Method according to claim 1, wherein the model function can be expressed by the following formula:
MetPow=cal*[F(.sup.13CO.sub.2,.sup.12CO.sub.2,t)f(.sup.13CO.sub.2,.sup.12CO.sub.2,t).sub.nat]*g(P.sub.CO2)*h(n)*L(n/M)*(n/M.sup.2)*V(n/M) wherein MetPow denotes the metabolic capacity, cal is a constant taking into account corrections, F(.sup.13CO.sub.2, .sup.12CO.sub.2,t) is a function expressing the dynamics of exhaled .sup.13CO.sub.2 as product or expressing the dynamics of exhaled ratio of .sup.13CO.sub.2/.sup.12CO.sub.2, f(.sup.13CO.sub.2,.sup.12CO.sub.2,t).sub.nat is a function expressing the natural abundance of .sup.13CO.sub.2 and .sup.12CO.sub.2 in the air exhaled by the individual prior to substrate administration, g(P.sub.CO2) is a function expressing the dependence of the CO.sub.2 production rate P.sub.CO2 of the individual on the activity status of the individual, h(n) is a function expressing the number of CO.sub.2 molecules generated per substrate molecule, L(n/M) is a function expressing a non-linear behaviour of the metabolic capacity dependent on the number of administered substrate molecules n, wherein M denotes the bodyweight of the individual, and V(n/M) is a function expressing dependencies due to different administration procedures of the substrate.

14. The method according to claim 13, wherein g(P.sub.CO2)=P.sub.CO2 and/or h(n)=1 and/or V(n/M)=1.

15. The method according to claim 1, wherein at least one of methacetin, phenacetin, aminopyrine, caffeine, erythromycin and ethoxycoumarin, in each case .sup.13C-labeled, is used as the substrate.

16. The method according to claim 1, wherein an aqueous solution of .sup.13C-methacetin and a solubilizer is used as the substrate.

17. The method according to claim 16, wherein the concentration of the solubilizer is 10 to 100 mg/ml and the concentration of the .sup.13C-methacetin is 0.2 to 0.6% weight by weight.

18. The method according to claim 16, wherein the concentration of the .sup.13C-methacetin is more than 3% weight by weight.

19. A method for determining the metabolic capacity of at least one enzyme to determine a state of health of an individual, comprising the following steps: time-resolved determining of the concentration of a product in the air exhaled by an individual, wherein the product has been created by a metabolism of a substrate, previously administered to the individual, by the at least one enzyme of the individual and wherein the product concentration is determined essentially only until the maximum product concentration in the air exhaled by the individual is reached, fitting of a model function to measured values of the product concentration, which were obtained by the time-resolved determination of the product concentration between a start time and an end time, determining the metabolic capacity of the enzyme on the basis of parameters of the model function, which specify the model function, wherein determining the metabolic capacity of the enzyme takes place on the basis of at least two parameters of the model function, with the proviso that the maximum value of the model function and the time constant of the model function are not selected as parameters at the same time, insofar as the model function is a mono-exponential function, and with the further proviso that the start time and/or the end time are not selected as parameters; determining the state of health of the individual concerning specific bodily functions based on the metabolic capacity of the at least one enzyme and reporting the state of health of the individual.

20. The method of claim 19, further comprising determining a subsequent examination of the individual based on previously determined state of the health of the individual concerning specific bodily functions based on the metabolic capacity of the at least one enzyme.

21. The method of claim 1, further comprising determining a subsequent examination of the individual based on previously determined state of the health of the individual concerning specific bodily functions based on the metabolic capacity of the at least one enzyme.

22. The method of claim 1, further comprising providing the previously determined state of health of the individual to the individual.

23. The method of claim 21, further comprising providing the previously determined subsequent examination to the individual.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Further details of aspects of the invention presently claimed will be further explained with the help of figures of exemplary embodiments.

(2) FIG. 1 shows a graphic representation of the kinetics of the concentration of a metabolized product over the measurement period and

(3) FIG. 2 shows a graphic representation of the non-linearity of the metabolic power of the liver determined according to an embodiment.

DETAILED DESCRIPTION

(4) FIG. 1 shows a graphic representation of the measured product concentration in the air exhaled by an individual as a function of time. As substrate, .sup.13C-labeled methacetin at a dose of 2 mg per kilogram bodyweight of the individual was administered to the individual, wherein the release period was shorter than 60 seconds. In the body of the individual the .sup.13C-labeled methacetin was metabolized in the liver to paracetamol and .sup.13C-labeled CO.sub.2. The latter was detected as product in the air exhaled by the individual.

(5) The diagram of FIG. 1 shows a rise in the .sup.13CO.sub.2-concentration in the form of the delta-over-baseline-value (DOB-value) in the exhaled air. 1 DOB here refers to a change of the .sup.13CO.sub.2-to-.sup.12CO.sub.2-ratio by a thousandth above the natural ratio. The obtained measured values, illustrated in FIG. 1, are subsequently fitted with a suitable model function. This is not yet illustrated in FIG. 1. From this model functionwith a function equation familiar as suchdifferent parameters can now be derived which specify the function. From these parameters conclusions can be drawn about the metabolic capacity of the examined enzyme system.

(6) The time point of maximum methacetine metabolism (t.sub.max, approximately at 6.5 minutes) and the time point of half-maximum methacetine metabolism (t.sub.1/2, approximately at 1.5 minutes) are indicated in FIG. 1.

(7) As methacetin is almost solely metabolized in the liver, with the specified metabolism dynamics it is possible to directly and immediately trace the metabolism of the administered substrate by the enzymes existing in the liver. In this way, the administered methacetin is demethylated by the enzyme CYP450 1A2 in the liver. By interpreting the rise kinetics of the administered methacetin and the parameters derived thereof it is now possible to directly determine the liver function. Here, for instance the value of the maximum product concentration in the exhaled air P.sub.max allows a statement to be made about the number of the healthy liver cells and the liver volume which is thus available for metabolism; whereas the rise in the form of the time constant(s) of the model function, fitted to the measured values, allows statements to be made about the entrance velocity of the substrate into the liver cells. The time constant(s) of the model function thus allows statements to be made about whether the liver is at all capable to absorb substrates. From the scattering of the time constants conclusions can be drawn about intercellular differences regarding a substrate susceptibility of the liver cells.

(8) FIG. 2 shows the non-linearity of the metabolic power of the liver determined by methacetin metabolism. The metabolic power was determined according to the formulae indicated above for different methacetin metabolisms observed after methacetin administration in different dosages. Specifically, 1 mg .sup.13C-labeled methacetin per kg bodyweight, 2 mg/kg, 4 mg/kg and 8 mg/kg were administered.

(9) 1 mg .sup.13C-labeled methacetin per kg body weight M as well as 2 mg/kg show a linear dependence in the measured signals. Increase of administration to 4 mg/kg shows 10% deviation from the linear behaviour and administration of 8 mg/kg shows more than 20% deviation from the linear behaviour.

(10) This non-linearity is expressed by the function L(n/M), wherein n denotes the number of substrate molecules, i.e. methacetin molecules, and M denotes the bodyweight in kg. This function L(n/M) forms part of the fitting curve represented in FIG. 2 by the interpolation curve between the single measurement points. The straight curve indicates a hypothetical interpolation curve if a linear dependence of the metabolic power on the dosage of the substrate was assumed and no non-linear effects were regarded.