Isobologram

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An isobologram or isobole diagram is a representation of the effectiveness of different combinations of two active ingredients (drugs, poisons, pesticides, herbicides, etc.) used in pharmacology and toxicology in the form of a two-dimensional nomogram with Cartesian coordinates. The doses or concentrations of the two active ingredients are plotted on the axes. A line in this system that connects those dose or concentration pairs that have identical biological effects is called isoboles . Specific interrelationships between active ingredients (e.g. in the sense of a synergism or antagonism ) can be derived from the course of the isoboles .

background

For a single active ingredient, the relationship between the two parameters dosage and biological response can be shown in a classic, two-dimensional dose-effect curve . If, on the other hand, two active substances are to be examined in combination, the number of parameters increases to three (dose of the first active substance, dose of the second active substance, strength of the biological response), so that a three-dimensional representation (with a surface instead of a curve) would have to be changed . In order to avoid this complex type of representation, the strength of the biological response is eliminated as a parameter by adding a certain (basically freely selectable) value (in pharmacology, for example, the minimum effective dose or the ED 50 or ED 90 value in which Toxicology about the lethal dose LD 50 or LD 100 ) is fixed. This leaves only the concentrations of the active ingredients as variables, and a two-dimensional representation becomes possible. Several isoboles for the same active ingredient pair can be displayed next to each other in a diagram, which relate to different biological effects.

Historical development and areas of application

The representation of isoboles was originally introduced in pharmacology by Siegfried Walter Loewe and H. Muischnek in order to be able to draw conclusions about the mechanism of action of the active ingredients from the course of the isoboles. In their first work on this topic, they did not use any experimental data, but instead constructed various theoretically conceivable isobole courses based solely on the prediction of different mechanistic interactions between the investigated active ingredients. The background of this work was to unify the then inconsistent terminology of the interactions between active ingredients, which often used terms such as “synergism”, “antagonism”, “addition” and “potentiation” without defining them more precisely, and at the same time to use a tool to provide their destination.

As a practical application, there is not only the distinction between different types of interaction for the investigated active ingredients, but also, in the case of synergism, the determination of an optimal dosage ratio of the two active ingredients, in which the greatest effect can be achieved with the least amount of substance. In the 1960s, the use of isobolograms was transferred to agrochemicals in order to optimize the dosage of pesticides . Here, too, the idea of ​​reducing the use of substances while maximizing the effect (and the associated cost optimization) was an important incentive.

Examples

  • When two active substances produce an effect on their own, but do not influence the effect of the other at all: The isobole is like a right-angled curve, which in the isobologram forms a rectangle with the axes, the corners of which are marked by the points (0; 0), (Y; 0), (0; X) and (Y; X) are described (where Y and X represent the respective effective doses for the individual active ingredient). The isobole runs from (Y; 0) via (Y; X) to (0; X).
  • If two active ingredients have an ideal additivity of the effects: The isobole runs as a straight line from (Y; 0) to (0; X), i.e. divides the rectangle described above diagonally from top left to bottom right into two triangles.
  • When two active ingredients synergistically influence each other: The isobole runs within the lower triangle from (Y; 0) to (0; X). It is similar to an anti-proportional function graph (hyperbola), but in contrast to this it reaches the respective axes and does not necessarily have to have symmetrical branches.
  • When two active substances influence each other subadditively: The isobole runs within the upper triangle from (Y; 0) to (0; X). It resembles a hyperbola mirrored on the diagonal from the previous example.
  • If two active substances influence each other antagonistically: The isobole runs outside the rectangle described in the first example from (Y; 0) to (0; X).
  • If a substance strengthens the effect of an active substance, but does not have any effect of its own: The isobole is again similar to the hyperbola-like curve from the synergism example, but it does not reach the axis on which the concentration of the strengthening substance is plotted, but runs parallel to this axis in the area of ​​high concentrations of the reinforcing substance.

With the terminology used above to characterize the interactions (synergism, antagonism, additive or subadditive or reinforcing effect), it should be noted that these terms are not used uniformly in the literature to this day. For example, some authors do not identify any area of ​​subadditive effects, but instead refer to this as antagonism.

Difficulties, criticism, simplifications

A difficulty in the construction of isobolograms arises from the fact that the biological reactions examined as target variables (examples: the ED or LD values) represent statistical variables that cannot be determined from a single experiment. Therefore, the underlying dose-response curves for the individual substances and their mixtures are usually determined over the entire range of action and the value intended for use in the isobologram is interpolated. However, since dose-effect relationships mostly do not run linearly over the entire investigation area, but often assume an S-shaped appearance, the experimentally determined values ​​cannot simply be subjected to a linear regression in order to determine the course. Instead, a mathematical transformation using a logit or probit method is required in order to arrive at linearized dose-effect relationships. The effort required for this is seen as a disadvantage of the representation.

A simplified method for the construction of isobolograms in the field of herbicides assumes that dose-effect relationships in the range of the IC 50 dose (the dose that inhibits the growth of the target organism by 50%) are usually linear, so that - with a corresponding Selection of the experimentally determined data points - again a linear regression is sufficient to be able to interpolate the IC 50 value. Only one isobole (for the IC 50 value) then has to be constructed from a corresponding data set, but the effort for the mathematical analysis of the data is reduced.

An even further simplified method dispenses with the construction of the isoboles, but only starts from the determination of the necessary dose for the active ingredients to be combined in pure form, which are required to achieve the biological response of interest. A mixture containing 50% of this dose of both substances is then tested for its effectiveness: If no effect is observed, the substances have an antagonistic effect, if the effect of interest is reached, the effects are additive and if the effect is intensified, there is synergism in front. A rough distinction is therefore made here as to whether the effect of this combination is above, below or on the additive diagonal of a (theoretical) isobologram.

Individual evidence

  1. ↑ FX Reichl: Pocket Atlas of Toxicology. Thieme, Stuttgart, 2nd edition, 2002, pp. 8–9.
  2. ↑ S. Loewe, H. Muischnek: About combination effects . In: Naunyn-Schmiedebergs archive. Volume 313, 1926, pp. 313-326.
  3. ↑ HF Zipf: Practical aspects for combination experiments with 2 substances. In: drug research. Volume 3, 1953, pp. 398-403.
  4. ^ VS Rao: Principles of Weed Science. CRC Press, Boca Raton, 2009, pp. 349-354.
  5. ↑ PML Tammes: Isoboles, a graphic representation of synergism in pesticides. In: Netherlands Journal of Plant Pathology. Volume 70, 1964, pp. 73-80.
  6. ^ CI Bliss: The method of probits. In: Science. Volume 79, 1937, pp. 38-39.
  7. ↑ IO Akobundu, RD Sweet, WB Duke: A Method of Evaluating Herbicide Combinations and Determining Herbicide Synergism. In: Weed Science. Volume 23 (1), 1975, pp. 20-25.
  8. ^ JH Gaddum: Pharmacology. Steinkopff, Darmstadt, 3rd edition, 1952, pp. 350–351.