EP1025443A1 - Method for evaluating an effect characteristic of a biochemically active stimulation means - Google Patents

Method for evaluating an effect characteristic of a biochemically active stimulation means

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Publication number
EP1025443A1
EP1025443A1 EP98951862A EP98951862A EP1025443A1 EP 1025443 A1 EP1025443 A1 EP 1025443A1 EP 98951862 A EP98951862 A EP 98951862A EP 98951862 A EP98951862 A EP 98951862A EP 1025443 A1 EP1025443 A1 EP 1025443A1
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EP
European Patent Office
Prior art keywords
biochemically
amount
stimulation means
biochemically active
active stimulation
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EP98951862A
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German (de)
French (fr)
Inventor
Peter Hedlund
Gabriel Von Euler
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Karolinska Innovations AB
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Karolinska Innovations AB
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Publication of EP1025443A1 publication Critical patent/EP1025443A1/en
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    • C—CHEMISTRY; METALLURGY
    • C12—BIOCHEMISTRY; BEER; SPIRITS; WINE; VINEGAR; MICROBIOLOGY; ENZYMOLOGY; MUTATION OR GENETIC ENGINEERING
    • C12Q—MEASURING OR TESTING PROCESSES INVOLVING ENZYMES, NUCLEIC ACIDS OR MICROORGANISMS; COMPOSITIONS OR TEST PAPERS THEREFOR; PROCESSES OF PREPARING SUCH COMPOSITIONS; CONDITION-RESPONSIVE CONTROL IN MICROBIOLOGICAL OR ENZYMOLOGICAL PROCESSES
    • C12Q1/00—Measuring or testing processes involving enzymes, nucleic acids or microorganisms; Compositions therefor; Processes of preparing such compositions
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/48—Biological material, e.g. blood, urine; Haemocytometers
    • G01N33/50—Chemical analysis of biological material, e.g. blood, urine; Testing involving biospecific ligand binding methods; Immunological testing
    • G01N33/53—Immunoassay; Biospecific binding assay; Materials therefor
    • G01N33/557—Immunoassay; Biospecific binding assay; Materials therefor using kinetic measurement, i.e. time rate of progress of an antigen-antibody interaction

Definitions

  • the present invention relates to methods for evaluating an effect characteristic of a biochemically active stimulation means, including biochemically active com- pounds .
  • the dissociative anaesthetic MK-801 (a dizocilpine maleate developed by Merck, Sharp and Dohme, Inc.) binds to the inside of the channel pore of the N-methyl-D-aspartate (NMDA) receptor complex.
  • NMDA N-methyl-D-aspartate
  • the non-equilibrium binding of tritiated MK-8C1 is regulated by glutamate and glycine in such a way that botn agonists are required to produce an effect.
  • glutamate antagonists or glycine antagonists may prevent the specific binding of subsequently added [ 3 H]MK-801.
  • the basic binding level of [ 3 H]MK-801 i.e. when no agonists are added, is dependent on the residual endogenous levels of glutamate and glycine.
  • the basic binding level of [ 3 H] K-801 can be decreased by extensive v/ashing of the membranes before the incubation.
  • too extensive washing may disintegrate important intramembrane structu- res or wash away other important cofactors.
  • the first bias which will lead to a too low estimation of the true EC59 value, is due to the fact that the added amino acid concentrations do not reflect the true amino concentrations present in the test tube.
  • the second bias which will lead to a too high estimate of the true EC 50 value, will be present if the basic binding levels are included in the calculations, because these levels are higher than the true baseline (i.e. zero binding) and thus, the EC 50 curve is shifted up and to the right.
  • an object of the invention is to provide a method for evaluating an effect characteristic of a bio- chemically active stimulation means, such that a better accommodation of said basic binding levels and the like are obtained.
  • a method for evaluating an effect characteristic of a biochemically active stimulation means comprising the steps of: providing a set of measurement pairs, each consisting of an amount of biochemically active stimulation means applied to a biological material and a value related to a biochemically mediated effect associated therewith; selecting a functional relationship, comprising one or more parameters, between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect, wherein said functional relationship is defined so as to accommodate the existence of a non-zero value of biochemically mediated effect at a zero amount of applied biochemically active stimulation means; adjusting said functional relationship to match said set of measurement pairs by adjusting said parameters; and deriving, based upon said functional relationship, a negative, non-zero value of said amount of biochemically active stimulation means at which said value of biochemi- cally mediated effect becomes essentially zero,
  • a method for evaluating an effect characteristic of a biochemically active stimulation means comprising the steps of: providing a set of measurement pairs, each consisting of a value related to the amount of a biochemically active stimulation means applied to a biological material and a value related to a biochemi- cally mediated effect associated therewith, said set of measurement pairs together indicating a functional relationship between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect; and extrapolating said set of measurement pairs, indicating said functional relationship, to derive a negative, non-zero value of said amount of applied biochemically active stimulation means at which said value of biochemically mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material, thereby explaining the existence of a non-zero biochemically mediated effect at a zero amount of applied bio- logically active stimulation means.
  • the invention is based upon the accommodation and derivation of an intrinsic or endogenous amount of stimulation means, or an intrinsic representation thereof, present in said biological material and explaining the existence of a non-zero biochemically mediated effect at a zero amount of added biochemically active stimulation means, for example explaining and accommodating basic binding levels discussed above as a result of residual endogenous substance present in the biological material.
  • this intrinsic or endogenous stimulation means is taken into account by letting the concentration-response curves discussed above expand into an area of negative added concentration, correspon- ding to a positive amount of intrinsic concentration.
  • this intrinsic parameter will occasionally be called the z-value. By taking the presence of this z- value into account, more reliable estimations of E max , EC50 and the Hill coefficient is obtained.
  • the invention is preferably performed as a curve- fitting model on a computer and is easily realised by those skilled in the art of curve fitting algorithms using available curve fitting software programs.
  • the z-value is obtained by projecting the response-concentration curve to zero binding (or zero effect) , reading the concentration of added biochemically active compound associated therewith, and changing the sign from minus to plus.
  • sai ⁇ functional relationship is preferably defined as:
  • said amount of biochemically active stimulation means applied to said biological material is reoresented in the form of a concentration of added biochemically active compound, preferably, depending on the application, selected from the group consisting of agonists, antibodies and enzyme substrates.
  • biochemically active compound preferably, depending on the application, selected from the group consisting of agonists, antibodies and enzyme substrates.
  • such compounds may be any molecule or ion that bind to a receptor
  • Agonists may be neurotransmitters, hormones, growth factors and other proteins, enzymes, peptides, nucleotides and nucleic acids, lipids such as arachidonic acid metabolites, metal ions, vitamins, co- enzymes, quinones, cyclitols, steroids, carbohydrates, carotenoids, immunoglubulins, cytokines, folic acid and related compounds, corrinoids, anesthetic compounds, gases such as nitric oxide, and synthesized analogs of these agonists.
  • said amount of biochemically active stimulation means applied to said biological material is an amount of physical stimulation, such as a mechanical or electromagnetical stimulation.
  • Many, but not all, of such other types of stimulation means causes a release of a biochemically active compound which is thereby added to said biological material.
  • said biochemically mediated effect is typically represented as concentration of a chemical substance (which may or may not be the same as the one originating the effect) present in said biological material.
  • said effect may be represented as an amount of cells or individuals which show a specific biological change as a result of said applied biochemically active stimulation means.
  • the biochemically mediated effect may also be represented as an physiological effect, such as respiratory rate, heart rate, or locomotion, or the like.
  • z-analysis An example of where the methods according to the invention, referred to below as z-analysis, is applied is v/hen measuring the binding of the non-competitive NMDA- receptor antagonist MK-801 in response to glutamate, as discussed above, in a membrane preparation of brain tissue.
  • MK-801 binds to the inside of the ion channel pore of the NMDA receptor, and its access is dependent of activation of the glutamate binding site.
  • the binding of MK-801 may reflect the stimulatory action of glutamate.
  • z-analysis of the glutamate concentration-response curve reveal a) the residual, endogenous concentration of glutamate, and b) correct stimulation parameters such as EC 5 0 values, E max values and Hill coefficients, so that the characteristics of glutamate stimulation on NMDA receptors can be compared between different brain areas, in spite of the fact that the respective membrane preparations may contain different concentrations of glutamate.
  • the invention will be useful in many types of academic and commercial biochemical, pharmacological and pharmaceutical research and development for properly evaluating the characteristics of substrates interacting with receptors, enzymes or other recognition sites, as do most pharmaceutical agents currently in use and under development.
  • a clinical example is challenge tests used for individuals being evaluated for possible or manifest metabolic or endocrine diseases. For example, glucose is given in different doses to an individual to measure insulin production. The resulting dose-response curve may be analyzed using z-analysis to yield estimations of the concentration of endogenous glucose and true stimulation parameters such as EC 50 , E nax and Hill slopes.
  • Another example is when thyrotropin-releasing hor- mone is given to an individual, and where serum levels of thyroid-stimulating hormone and thyroid hormone is measured. Endogenous thyrotropin-releasing hormone is released from the hypothalamus and stimulates the release of thyroid-stimulating hormone from the pituitary, which in turn stimulates the formation of thyroid hormones. The resulting dose-response curve may be analyzed using the invention to qud estimations of the concentration of endogenous thyrotropin-releasing hormone and true stimulation parameters such as EC 50 , E max and Hill slopes.
  • Another example is when measuring the activity of a purified enzyme, for example from blood, serum, or tissue taken from an individual, in response to an mducer. The invention is then for example used to reveal true affinity parameters for the mducer by compensating for residual, endogenous amounts of mducer.
  • Yet another example is when measuring the activity of a receptor, for example from blood, serum, or tissue taken from an individual, m response to an agonist.
  • the invention is then for example used to reveal true affinity parameters for the agonist by compensating for residual, endogenous amounts of agonist.
  • a clinical example is to use the invention when measuring the serum concentrations of the hormone prolac- t m response to the ⁇ opamine agonist bromocriptme .
  • the release of prolactm is under pnysiological conditions inhibited by dopam e through activation of dop- amme D 2 receptors.
  • the stimulatory action of the agonist leads to an inhibition of the effect.
  • Bromocriptme is used the clinic to inhibit hypersecretion of prolactm from the pituitary .
  • the maximal effect is determined m order to use z-analysis.
  • the maximal serum concentrations of prolactm is oetermmed by giving a dopamme D 2 receptor antagonist sucn as halo- peridol.
  • concentration-response curves of bromocriptme is analyzed according to the invention to yield a) the endogenous concentration of ⁇ opamine, expressed as bromocriptme equivalents (derived from curve fitting extending to the maximal serum concentration of prolactm) after treatment with a dopamme D 2 receptor antagonist, and b) correct inhibition parameters such as IC 50 values, I max values, and Hill coefficients.
  • concentration-response curves of bromocriptme is analyzed according to the invention to yield a) the endogenous concentration of ⁇ opamine, expressed as bromocriptme equivalents (derived from curve fitting extending to the maximal serum concentration of prolactm) after treatment with a dopamme D 2 receptor antagonist, and b) correct inhibition parameters such as IC 50 values, I max values, and Hill coefficients.
  • Still another example is antibody-antigen assays, where the invention is used for example to determine the concentrations of endogenous antigen or antibody, or to determine true affinity parameters for the antibody- anti
  • the invention is preferably used to compare effect characteristics of one biochemically active stimulation means with other biochemically active stimulation means for the selection of stimulation means for the treatment of diseases.
  • the invention is preferably used when evaluating saturation or stimulation models for enzymatic reactions or receptor binding.
  • the invention should be of value to all kinds of pharmacological and biochemical assays where the presence of an endogenous or intrinsic agonist produces a response baseline above zero but where the addition of an antagonist can block the response completely (at least in theory) .
  • FIG. 1 schematically shows a prior art saturation curve diagram of using a linear-linear representation
  • Fig. 2 schematically shows a prior art stimulation curve diagram of using a logarithmic-linear representation
  • Fig. 3 schematically shows a z-analysis curve diagram according to the invention using a linear-linear representation.
  • the measurement pairs provided in Table I may for example have been obtained by studying the binding levels of [ 3 H]MK-801, as discussed above.
  • the obtained measurement pairs is inputted manually to the program execution using a computer keyboard connected to said computer or automatically via an input interface from, for example, automated detection equipment used to obtain said measurement pairs .
  • Fig. 1 the measurement data were fitted according to a traditional saturation curve model displayed on a linear-linear graph.
  • the traditional saturation curve model of Fig. 1 is defined by the functional relationship (1)
  • Fig. 2 the same measurement data listed in Table I were fitted according to a traditional stimulation curve model displayed on a logarithmic-linear graph.
  • the traditional stimulation curve model of Fig. 2 is defined by the functional relationship (2)
  • x is the concentration of added compound
  • E is the measured binding level
  • E 0 is the basic binding level or effect observed without any added compound
  • E max is the maximum binding level not including said non-specific effect
  • EC 50 is the concentration, as calculated starting from said non-specific effect level.
  • the basic binding level E 0 was found to be 30, the maximal binding level E max , not incorporating the basic binding level, was found to be 81, and the concentration EC 50 of added compound at half the maximal binding level, starting from the basic binding level, was found to be 15 for best curve fitting.
  • the selected and derived relationship will accommodate the actual measurement pairs in indicating a basic binding level of about 30 at zero concentration of added compound.
  • Fig. 3 the same measurement data listed in Table I were fitted according to a z-analysis curve model according to the present invention and displayed on a linear-linear graph.
  • the z-analysis curve model of Fig. 3 according to the invention is defined by the functional relationship (3)
  • the maximal binding level E raax was found to be 110 (very similar to the total value of E max +E 0 of Fig. 2), the intrinsic concentration z was found to be 4.0 and the concentration EC 5 0 of added compound at half the maximal binding level, including said intrinsic concentration, was found to be 10.8 for best possible curve fitting.
  • the selected and derived relationship will accommodate the actual measurement pairs in indicating a basic binding level of about 30 at zero concentration of added compound.
  • the characteristics of the selected functional rela- tionship (3) it is possible to derive said intrinsic representation of an endogenous property.
  • an intrinsic or endogenous concentration value corresponding to said z-para- meter, may be calculated from the fitted relationship of Fig. 2, i.e. after having derived the curve fitted para- meters E max , E 0 and EC 50 , by setting the total sum E of the relationship (2) to be zero and deriving the x-value at which such zero effect will be obtained.
  • E max the curve fitted para- meters
  • E 0 the curve fitted para- meters
  • the z-value obtained according to the invention will provide important information in the evaluation of effect characteristics of different biochemically active stimulation means, as discussed above.
  • biochemically active stimulation is to be interpreted in a broad sense, such as including an enhanced binding between a compound and a biological material, for instance between an antibody and an antigen.

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Abstract

The present invention relates to a method for evaluating an effect characteristic of a biochemically active stimulation means, wherein a set of measurement pairs are provided, each consisting of a value related to the amount of a biochemically active stimulation means applied to a biological material and a value related to a biochemically mediated effect associated therewith, said set of measurement pairs together indicating a functional relationship between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect. According to the invention, said set of measurement pairs, indicating said functional relationship, is extrapolated for deriving a negative, non-zero value of said amount of applied biochemically active stimulation means at which said value of biochemically mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material, thereby explaining the existence of a non-zero biochemically mediated effect at a zero amount of applied biologically active stimulation means.

Description

METHOD FOR EVALUATING AN EFFECT CHARACTERISTIC OF A BIOCHEMICALLY ACTIVE STIMULATION MEANS
Field of Invention
The present invention relates to methods for evaluating an effect characteristic of a biochemically active stimulation means, including biochemically active com- pounds .
Technical Background
In the field of biomedical and biological research and industry, evaluation and analysis of chemical reac- tions between ligands and receptors has for many years been of great importance, and there is an ever present need for improvements of available analysing techniques in many applications. Many of the analysing schemes of today v/ithin the fields of clinical chemistry, clinical immunology and clinical microbiology is based upon the measurement and evaluation of binding reactions.
As an example, the dissociative anaesthetic MK-801 (a dizocilpine maleate developed by Merck, Sharp and Dohme, Inc.) binds to the inside of the channel pore of the N-methyl-D-aspartate (NMDA) receptor complex. The non-equilibrium binding of tritiated MK-8C1 is regulated by glutamate and glycine in such a way that botn agonists are required to produce an effect. Thus, addition of either glutamate antagonists or glycine antagonists may prevent the specific binding of subsequently added [3H]MK-801.
The basic binding level of [3H]MK-801, i.e. when no agonists are added, is dependent on the residual endogenous levels of glutamate and glycine. Hence, the basic binding level of [3H] K-801 can be decreased by extensive v/ashing of the membranes before the incubation. However, it is difficult if not impossible to remove ail glutamate and glycine by this procedure. Furthermore, too extensive washing may disintegrate important intramembrane structu- res or wash away other important cofactors. In any case, the presence of basic binding levels complicates the analysis of agonist concentration-response curves with regard to the determination of Emaχ (maximal attainable response) , EC50 (concentration at which 50% of the maximal response has occurred) and Hill coefficient (curve slope at the E50 point) values.
When trying to fit this data with the use of nonlinear curve-fitting procedures using conventional one or two binding site models, two types of biases will be pro- duced. The first bias, which will lead to a too low estimation of the true EC59 value, is due to the fact that the added amino acid concentrations do not reflect the true amino concentrations present in the test tube. The second bias, which will lead to a too high estimate of the true EC50 value, will be present if the basic binding levels are included in the calculations, because these levels are higher than the true baseline (i.e. zero binding) and thus, the EC50 curve is shifted up and to the right.
Furthermore, conventional curve-fitting models try to construct a hypothetical curve with the greatest slope steepness above the half-maximum binding, associated with a biased estimation also of the Emax value and the Hill coefficient. The bias induced by the residual glutamate and glycine will be relatively less biasing at high con- centrations of added agonist. Hence, prior art methods do not produce reliable estimations of the EC_3 value and Hill coefficient.
Hence, an object of the invention is to provide a method for evaluating an effect characteristic of a bio- chemically active stimulation means, such that a better accommodation of said basic binding levels and the like are obtained. Summary of the invention
According to the present invention, said and other objects are achieved by methods as defined in the accompanying claims. Hence, according to a first aspect of the invention, there is provided a method for evaluating an effect characteristic of a biochemically active stimulation means, comprising the steps of: providing a set of measurement pairs, each consisting of an amount of biochemically active stimulation means applied to a biological material and a value related to a biochemically mediated effect associated therewith; selecting a functional relationship, comprising one or more parameters, between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect, wherein said functional relationship is defined so as to accommodate the existence of a non-zero value of biochemically mediated effect at a zero amount of applied biochemically active stimulation means; adjusting said functional relationship to match said set of measurement pairs by adjusting said parameters; and deriving, based upon said functional relationship, a negative, non-zero value of said amount of biochemically active stimulation means at which said value of biochemi- cally mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material explaining the presence of said non-zero effect at a zero amount of applied biochemically active stimulation means.
According to a second aspect of the invention, there is provided a method for evaluating an effect characteristic of a biochemically active stimulation means, comprising the steps of: providing a set of measurement pairs, each consisting of a value related to the amount of a biochemically active stimulation means applied to a biological material and a value related to a biochemi- cally mediated effect associated therewith, said set of measurement pairs together indicating a functional relationship between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect; and extrapolating said set of measurement pairs, indicating said functional relationship, to derive a negative, non-zero value of said amount of applied biochemically active stimulation means at which said value of biochemically mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material, thereby explaining the existence of a non-zero biochemically mediated effect at a zero amount of applied bio- logically active stimulation means.
Hence, the invention is based upon the accommodation and derivation of an intrinsic or endogenous amount of stimulation means, or an intrinsic representation thereof, present in said biological material and explaining the existence of a non-zero biochemically mediated effect at a zero amount of added biochemically active stimulation means, for example explaining and accommodating basic binding levels discussed above as a result of residual endogenous substance present in the biological material.
According to the invention, this intrinsic or endogenous stimulation means is taken into account by letting the concentration-response curves discussed above expand into an area of negative added concentration, correspon- ding to a positive amount of intrinsic concentration. In the following, this intrinsic parameter will occasionally be called the z-value. By taking the presence of this z- value into account, more reliable estimations of Emax, EC50 and the Hill coefficient is obtained. The invention is preferably performed as a curve- fitting model on a computer and is easily realised by those skilled in the art of curve fitting algorithms using available curve fitting software programs.
As discussed above, the z-value is obtained by projecting the response-concentration curve to zero binding (or zero effect) , reading the concentration of added biochemically active compound associated therewith, and changing the sign from minus to plus.
According to a preferred emooαiment of said aspects according to the invention, there is provided a new algorithm for accommodating the presence of said intrinsic or endogenous amount of stimulation means. Hence, saiα functional relationship is preferably defined as:
wherein: x is said amount (generally a concentration) of applied biochemically active stimulation means; y is said value related to a biochemically mediated effect at said amount x of applied biochemically active stimulation means; Ema< is the maximum value of said biochemically mediated effect; z is said intrinsic amount of biochemically active stimulation means; EC50-Z is an amount of applied biochemically active stimulation reans corresponding to half said maximum biochemically rrediated effect; and n is the Hill coefficient. Even thougn the invention is of course not limited to this new relationship, the incorporation of said z-value, both accommodating for a non-zero response at a zero amount of adαed stimulation means and representing said intrinsic behaviour, results m a more accurate and reliable relationsmp and thus m the derivation of more reliable and correct binding constant parameters, such as Emax, EC50, K-, ana the like. According to a typical embodiment of the invention, said amount of biochemically active stimulation means applied to said biological material is reoresented in the form of a concentration of added biochemically active compound, preferably, depending on the application, selected from the group consisting of agonists, antibodies and enzyme substrates. Generally, such compounds may be any molecule or ion that bind to a receptor
(agonists), antigen (antibody), or other recognition site eliciting an effect. Agonists may be neurotransmitters, hormones, growth factors and other proteins, enzymes, peptides, nucleotides and nucleic acids, lipids such as arachidonic acid metabolites, metal ions, vitamins, co- enzymes, quinones, cyclitols, steroids, carbohydrates, carotenoids, immunoglubulins, cytokines, folic acid and related compounds, corrinoids, anesthetic compounds, gases such as nitric oxide, and synthesized analogs of these agonists.
However, in other embodiments, said amount of biochemically active stimulation means applied to said biological material is an amount of physical stimulation, such as a mechanical or electromagnetical stimulation. Many, but not all, of such other types of stimulation means causes a release of a biochemically active compound which is thereby added to said biological material.
Also, said biochemically mediated effect is typically represented as concentration of a chemical substance (which may or may not be the same as the one originating the effect) present in said biological material. In other applications, said effect may be represented as an amount of cells or individuals which show a specific biological change as a result of said applied biochemically active stimulation means. The biochemically mediated effect may also be represented as an physiological effect, such as respiratory rate, heart rate, or locomotion, or the like.
An example of where the methods according to the invention, referred to below as z-analysis, is applied is v/hen measuring the binding of the non-competitive NMDA- receptor antagonist MK-801 in response to glutamate, as discussed above, in a membrane preparation of brain tissue. MK-801 binds to the inside of the ion channel pore of the NMDA receptor, and its access is dependent of activation of the glutamate binding site. Thus, under non-equilibrium conditions, the binding of MK-801 may reflect the stimulatory action of glutamate. z-analysis of the glutamate concentration-response curve reveal a) the residual, endogenous concentration of glutamate, and b) correct stimulation parameters such as EC50 values, Emax values and Hill coefficients, so that the characteristics of glutamate stimulation on NMDA receptors can be compared between different brain areas, in spite of the fact that the respective membrane preparations may contain different concentrations of glutamate.
As the example above indicates, the invention will be useful in many types of academic and commercial biochemical, pharmacological and pharmaceutical research and development for properly evaluating the characteristics of substrates interacting with receptors, enzymes or other recognition sites, as do most pharmaceutical agents currently in use and under development.
A clinical example is challenge tests used for individuals being evaluated for possible or manifest metabolic or endocrine diseases. For example, glucose is given in different doses to an individual to measure insulin production. The resulting dose-response curve may be analyzed using z-analysis to yield estimations of the concentration of endogenous glucose and true stimulation parameters such as EC50, Enax and Hill slopes.
Another example is when thyrotropin-releasing hor- mone is given to an individual, and where serum levels of thyroid-stimulating hormone and thyroid hormone is measured. Endogenous thyrotropin-releasing hormone is released from the hypothalamus and stimulates the release of thyroid-stimulating hormone from the pituitary, which in turn stimulates the formation of thyroid hormones. The resulting dose-response curve may be analyzed using the invention to vield estimations of the concentration of endogenous thyrotropin-releasing hormone and true stimulation parameters such as EC50, Emax and Hill slopes. Another example is when measuring the activity of a purified enzyme, for example from blood, serum, or tissue taken from an individual, in response to an mducer. The invention is then for example used to reveal true affinity parameters for the mducer by compensating for residual, endogenous amounts of mducer.
Yet another example is when measuring the activity of a receptor, for example from blood, serum, or tissue taken from an individual, m response to an agonist. The invention is then for example used to reveal true affinity parameters for the agonist by compensating for residual, endogenous amounts of agonist. A clinical example is to use the invention when measuring the serum concentrations of the hormone prolac- t m response to the αopamine agonist bromocriptme . The release of prolactm is under pnysiological conditions inhibited by dopam e through activation of dop- amme D2 receptors. Thus, in this case, the stimulatory action of the agonist leads to an inhibition of the effect. Bromocriptme is used the clinic to inhibit hypersecretion of prolactm from the pituitary . When analysing inhibitory effects, the maximal effect is determined m order to use z-analysis. In this case, the maximal serum concentrations of prolactm is oetermmed by giving a dopamme D2 receptor antagonist sucn as halo- peridol. Once the maximal serum concentration of prolactm has been determined, concentration-response curves of bromocriptme is analyzed according to the invention to yield a) the endogenous concentration of αopamine, expressed as bromocriptme equivalents (derived from curve fitting extending to the maximal serum concentration of prolactm) after treatment with a dopamme D2 receptor antagonist, and b) correct inhibition parameters such as IC50 values, Imax values, and Hill coefficients. Still another example is antibody-antigen assays, where the invention is used for example to determine the concentrations of endogenous antigen or antibody, or to determine true affinity parameters for the antibody- antigen coupling.
The invention is preferably used to compare effect characteristics of one biochemically active stimulation means with other biochemically active stimulation means for the selection of stimulation means for the treatment of diseases.
Also, the invention is preferably used when evaluating saturation or stimulation models for enzymatic reactions or receptor binding.
This way of calculating agonist concentration and binding parameters is suggested to produce better estimates than prior art schemes. The invention should be of value to all kinds of pharmacological and biochemical assays where the presence of an endogenous or intrinsic agonist produces a response baseline above zero but where the addition of an antagonist can block the response completely (at least in theory) .
Further aspects and features of the invention will be more fully understood from the following description of an exemplifying embodiment thereof.
Brief Description of the drawings
An exemplifying embodiment of the invention will now be described with reference to the accompanying drawings, in which: Fig. 1 schematically shows a prior art saturation curve diagram of using a linear-linear representation;
Fig. 2 schematically shows a prior art stimulation curve diagram of using a logarithmic-linear representation; and Fig. 3 schematically shows a z-analysis curve diagram according to the invention using a linear-linear representation. Detailed Description of a Preferred Embodiment
In the following three examples shown in Fig. 1, 2, and 3, three different types of analysis were used to evaluate the same set of measurement pairs, said set of measurement pairs being given in Table I below.
Table I
The measurement pairs provided in Table I may for example have been obtained by studying the binding levels of [3H]MK-801, as discussed above.
Having obtained the measurement pairs listed in Table I in some way or the other, these are provided to a computer for the execution of a curve fitting software procedure. For example, the obtained measurement pairs is inputted manually to the program execution using a computer keyboard connected to said computer or automatically via an input interface from, for example, automated detection equipment used to obtain said measurement pairs .
With regard to curve fitting procedures, reference can be made to, for instance, MARQUARDT , D.W. (1963). An algorithm for least-squares estimation of non-linear parameters. J. Soc. Indust . Appl.Math. , 11, 431-441 and LEVENBERG, K. (1944) . A method for the solution of certain non-linear problems in least squares. Q. Appl.Math. ,2, 164-168.
As well as providing said measurement pairs to said execution of the curve fitting procedure, one must also select a functional relationship which the curve fitting procedure, using computerised iterative procedures, is to bring to match said measurement pairs.
In Fig. 1, the measurement data were fitted according to a traditional saturation curve model displayed on a linear-linear graph. The traditional saturation curve model of Fig. 1 is defined by the functional relationship (1)
wherein x is the concentration of added compound, E is the measured binding level, Emax is the maximum binding level and EC50 is the concentration required to reach half the maximal binding level. Note that in this example, as well as in the examples shown in Fig. 2 and 3, the Hill coefficient n is assumed to be essentially equal to one. In Fig. 1, having performed the curve fitting procedure using the functional relationship (1) above, the parameter Emax, i.e. the maximal binding level, was found to be 94 and the parameter EC50, i.e. the concentration of added compound at half the maximal binding level, was found to be 3.5 for attaining best possible curve fitting. Note, in Fig. 1, that even though the actual measurement pairs seem to indicate a basic binding level of about 30 at zero concentration of added compound, the derived relationship will not allow such a relation, because of the characteristics of the selected functional relationship (1) above, and hence the produced fitted curve will force a display of a zero binding level at zero concentration of added compound. Also, note that the derived maximum binding level Emax of 94 is actually lower than the highest binding level point given by said set of measurement pairs .
In Fig. 2, the same measurement data listed in Table I were fitted according to a traditional stimulation curve model displayed on a logarithmic-linear graph. The traditional stimulation curve model of Fig. 2 is defined by the functional relationship (2)
wherein x is the concentration of added compound, E is the measured binding level, E0 is the basic binding level or effect observed without any added compound, Emax is the maximum binding level not including said non-specific effect, and EC50 is the concentration, as calculated starting from said non-specific effect level.
In Fig. 2, having performed the curve fitting procedure using the functional relationship (2) above, the basic binding level E0 was found to be 30, the maximal binding level Emax, not incorporating the basic binding level, was found to be 81, and the concentration EC50 of added compound at half the maximal binding level, starting from the basic binding level, was found to be 15 for best curve fitting. Note, in Fig. 2, that in this case the selected and derived relationship will accommodate the actual measurement pairs in indicating a basic binding level of about 30 at zero concentration of added compound. However, it is important to note that the value Emax in this case does not equal the total attainable effect (which is actually given by Emax plus Eo (81+30=111)), and that EC50 correspondingly does not equal the actual half total effect point. Also note that, because of the use of a logarithmic-linear graph, which is very often selected due to the logarithmic differences in the concentrations of added compound used in many types of analysis of the kind mentioned above, it becomes impossible to display negative concentrations of added compound.
In Fig. 3, the same measurement data listed in Table I were fitted according to a z-analysis curve model according to the present invention and displayed on a linear-linear graph. The z-analysis curve model of Fig. 3 according to the invention is defined by the functional relationship (3)
y = // PrEmaX\ \ (3)
((( .) ♦ ')
In Fig. 3, having performed the curve fitting procedure using the functional relationship (3) above, the maximal binding level Eraax was found to be 110 (very similar to the total value of Emax+E0 of Fig. 2), the intrinsic concentration z was found to be 4.0 and the concentration EC50 of added compound at half the maximal binding level, including said intrinsic concentration, was found to be 10.8 for best possible curve fitting. Note, in Fig. 3, that in this case the selected and derived relationship will accommodate the actual measurement pairs in indicating a basic binding level of about 30 at zero concentration of added compound. Also, because of the characteristics of the selected functional rela- tionship (3), it is possible to derive said intrinsic representation of an endogenous property.
It shall also be noted that an intrinsic or endogenous concentration value, corresponding to said z-para- meter, may be calculated from the fitted relationship of Fig. 2, i.e. after having derived the curve fitted para- meters Emax, E0 and EC50, by setting the total sum E of the relationship (2) to be zero and deriving the x-value at which such zero effect will be obtained. However, it is still not possible to visually identify such a point using a logarithmic-linear representation as in Fig. 2.
It is understood that the z-value obtained according to the invention will provide important information in the evaluation of effect characteristics of different biochemically active stimulation means, as discussed above.
Also, even though the invention has been described in relation to an exemplifying embodiment thereof, it is understood that many different alterations and modifications of the different procedure steps may be made within the scope of the invention, as is defined by the accompanying claims. For instance, instead of a biological material, the material could be an artificial material exhibiting similar properties.
Also, the wording "biochemically active stimulation" is to be interpreted in a broad sense, such as including an enhanced binding between a compound and a biological material, for instance between an antibody and an antigen.

Claims

1. Method for evaluating an effect characteristic of a biochemically active stimulation means, comprising the steps of: taking a set of measurement pairs, each consisting of an amount of biochemically active stimulation means applied to a biological material and a value related to a biochemically mediated effect associated therewith; selecting a functional relationship, comprising one or more parameters, between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect, wherein said functional relationship is defined so as to accom- m.odate the existence of a non-zero value of biochemically mediated effect at a zero amount of applied biochemically active stimulation means; adjusting said functional relationship to match said set of measurement pairs by adjusting said parameters; and deriving, based upon said functional relationship, a negative, non-zero value of said amount cf biochemically active stimulation means at which said value of biochemically mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material explaining the presence cf said non-zero effect at a zero amount of applied biochemically active stimulation means.
2. Method as claimed in claim 1, wherein said functional relationship is defined as:
wherein: x is said amount of applied biochemically active stimulation means; y is said value related to a biochemically mediated effect at said amount x of applied biochemically active stimulation means;
Emax is a maximum value of said biochemically mediated effect; z is said intrinsic amount of biochemically active stimulation means;
EC50-Z is an amount of applied biochemically active stimulation means corresponding to half said maximum biochemically mediated effect; and n is the Hill coefficient.
3. Method as claimed in claim 2, wherein said deriving step comprises deriving one or more parameters selected from the group consisting of the value z, the value EC50, the value Emax and the Hill coefficient.
4. Method as claimed in claim 1, 2, or 3, v/herein said amount of biochemically active stimulation means applied to said biological material is an amount of a biochemically active compound added to said biological material.
5. Method as claimed in claim 4, wherein said amount of added biochemically active compound is represented in the form of a concentration of added biochemically active compound.
6. Method as claimed in claim 4 or 5, wherein said biochemically active compound is a compound selected from the group consisting of agonists, antibodies and enzyme substrates.
7. Method as claimed in any one of the preceding claims, wherein said amount of biochemically active stimulation means applied to said biological material is an amount of physical stimulation, such as a mechanical or electromagnetical stimulation.
8. Method as claimed in claim 7, wherein said physical stimulation causes a release of a biochemically active compound which is thereby added to said biological material .
9. Method as claimed in any one of the preceding claims, wherein said biochemically mediated effect is represented as an amount of a chemical substance present in said biological material.
10. Method as claimed in any one of the preceding claims, wherein said biochemically mediated effect is represented as an amount of cells or individuals which show a specific biological change as a result of said applied biochemically active stimulation means.
11. Method as claimed in any one of the preceding claims, wherein said biochemically mediated effect is represented as an physiological effect, such as respiratory rate, heart rate, or locomotion.
12. Method as claimed in any one of the preceding claims, wherein said derived information as to an interaction characteristic of said biochemically active stimulation means is used to compare the characteristics of said biochemically active stimulation means with other biochemically active stimulation means for the selection of stimulation means for the treatment of diseases.
13. Method as claimed in any one of the preceding claims, wherein said method is used when evaluating saturation or stimulation models for enzymatic reactions or receptor binding.
14. Method for evaluating an effect characteristic of a biochemically active stimulation means, comprising the steps of: taking a set of measurement pairs, each consisting of a value related to the amount of a biochemically active stimulation means applied to a biological material and a value related to a biochemically mediated effect associated therewith, said set of measurement pairs together indicating a functional relationship between said amount of biochemically active stimulation means applied to said biological material and said biochemically mediated effect; and extrapolating said set of measurement pairs, indicating said functional relationship, to derive a negative, non-zero value of said amount of applied biochemically active stimulation means at which said value of biochemically mediated effect becomes essentially zero, said negative, non-zero value representing an intrinsic amount of biochemically active stimulation means in said biological material, thereby explaining the existence of a non-zero biochemically mediated effect at a zero amount of applied biologically active stimulation means.
15. Method as claimed in claim 14, wherein said indicated functional relationship is defined as:
wherein: x is said amount of applied biochemically active stimulation means; y is said value related to a biochemically mediated effect at said amount x of applied biochemically active stimulation means;
Emax is a maximum value of said biochemically mediated effect; z is said intrinsic amount of biochemically active stimulation means;
EC50-z is an amount of applied biochemically active stimulation means corresponding to half said maximum biochemically mediated effect; and n is the Hill coefficient.
16. Method as claimed in claim 15, comprising deriving one or more parameters selected from the group consisting of the value z, the value EC50, the value Emax and the Hill coefficient.
17. Method as claimed in claim 14, 15, or 16, wherein said amount of biochemically active stimulation means applied to said biological material is an amount of a biochemically active compound added to said biological material.
18. Method as claimed in claim 17, wherein said amount of added biochemically active compound is represented in the form of a concentration of added biochemically active compound.
19. Method as claimed in claim 17 or 18, wherein said biochemically active compound is a compound selected from the group consisting of agonists, antibodies and enzyme substrates.
20. Method as claimed in any one of claims 14 to 19, wherein said amount of biochemically active stimulation means applied to said biological material is an amount of physical stimulation, such as a mechanical or electro- magnetical stimulation.
21. Method as claimed in claim 20, wherein said physical stimulation causes a release of a biochemically active compound which is thereby added to said biological material .
22. Method as claimed in any one of claims 14 to 21, wherein said biochemically mediated effect is represented as an amount of a chemical substance present in said biological material.
23. Method as claimed in any one of claims 14 to 22, wherein said biochemically mediated effect is represented as an amount of cells or individuals which show a specific biological change as a result of said applied biochemically active stimulation means.
24. Method as claimed in any one of claims 14 to 23, wherein said biochemically mediated effect is represented as an physiological effect, such as respiratory rate, heart rate, or locomotion.
25. Method as claimed in any one of claims 14 to 24, wherein said derived information as to an interaction characteristic of said biochemically active stimulation means is used to compare the characteristics of said biochemically active stimulation means with other biochemically active stimulation means for the selection of stimulation means for the treatment of diseases.
26. Method as claimed in any one of claims 14 to 25, wherein said method is used when evaluating saturation or - stimulation models for enzymatic reactions or receptor binding.
EP98951862A 1997-10-24 1998-10-23 Method for evaluating an effect characteristic of a biochemically active stimulation means Withdrawn EP1025443A1 (en)

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