Schild regression
The Schild plot is named after Heinz Otto shield graphical method for determining the pharmacological potency of an antagonist ( pA2 value ) using the linear regression ( Schild regression ). The Schild plot here describes the linear relationship between the logarithm of the molar concentration of antagonist (log [ antagonist ]) and the inhibitory effect of the antagonists (represented as log ( r -1)):
Particular importance has the regression line in the Schild plot. Their pitch provides information on the nature of antagonism. The antagonist potency ( pA2 value) corresponds to the abscissa of the regression line.
Practical implementation
To pick up a sign - plots and the consequent calculation of pA2 - value of the antagonist was incubated in separate experiments at different concentrations in a pharmacological test system (eg cell culture or tissue) or administered in animal studies, an experimental animal. The concentration of agonist is then administered by adding or increasing concentrations of an agonist is usually determined, at which a half-maximal effect can be observed ( EC50 ). This value is dependent on the concentration of the antagonist, and increases with increasing antagonist concentration. The ratio of the EC50 in the presence of antagonists, and EC50 in the absence of antagonist is referred to as the concentration ratio ( concentration ratio) R:
The determined for different concentrations of antagonist concentration ratio is entered as log ( r-1 ) against the logarithm of the molar concentration of antagonist in a diagram. The intersection of the abscissa corresponds to the compensation function, in the presence of linearity, and a slope of the regression line of about m = 1, the pA2 value of the antagonist.
Alternatively, a plate -Plot based on the value of any ECX is theoretically possible.
Determination of the pA2 value using the sign - plots: Rising antagonist concentrations lead to a rightward shift of the concentration-response curve and a decrease in the pEC50 value of the agonist. From this shift to the right the concentration ratio r can be calculated, which is entered as log ( r-1 ) against the logarithm of the molar concentration of antagonist in the Schild plot (embedded figure) and used to determine the pA2 value.
Interpretations
In addition to a determination of the pA2 value of the Schild plot also allows statements about the qualitative nature of the antagonism. Thus, a linearity of the compensation function, and a slope of the regression straight line of m = 1 is a good indication of the presence of competitive antagonism. Under these conditions, corresponding to the calculated pA2 value of the affinity constants pK of the antagonist.
Deviation from linearity
Displays the compensation function a nonlinear behavior, so, even if it satisfies all other conditions (particularly caused by the antagonist parallel rightward shift of the concentration-response curve of the agonist ), will no longer speak of a purely competitive antagonism. Assigns the compensation function of two or more linear sections, this points to a competition between agonist and antagonist by two or more binding sites on the receptor.
Deviation of the slope m = 1
Tells in at least approximate linearity of the regression function has a slope of m> 1 on, which means a disproportionate decrease in the effect of the antagonist with decreasing concentration in practice, this points to an inactivation or uptake of antagonists under experimental conditions. This phenomenon occurs also in case of insufficient incubation time of the antagonist.
The frequently observable event that the best-fit line plot of the shield has a slope of m <1, can be returned to, inter alia, uptake or inactivation of the agonist used. Also, a competition of antagonist and agonist at different binding sites with different binding affinities for these ligands can lead to a best-fit line with a slope of m <1.
Alternatives
Alternative methods include, for example, the Gaddum equation by John Gaddum and the Cheng -Prusoff equation.