Logit—log plot

Linear transformation of competition data is usefully carried out using the logit-log plot, also referred to as the indirect Hill plot ... 

Competition curves for displacement of a radiolabelled ligand by a competitive inhibitor, (a) Typical displacement curves for two inhibitors having IC50 values of 10 nM and 1 xM. (b) Indirect logit-log plots of the data in (c) showing how IC50 values may be estimated (see O Section 2.5)... 

Response variables can be plotted in a number of ways. The statistical analysis of data derived from radioligand-antibody interactions and the added information that can be derived from logit-log plots has been considered in detail. ... 

Equations of Ekins et ol,(i96e) logit-log plot of Rodbord et aUi968 ... 

Deviations from the linearized logit-log plot in the low- and high-concentration regions may indicate that improper background corrections have been... 

Assuming linearity of a non-linear plot - e.g., a logit-log plot... 

Fig. 5 SBC cetlibration curve of parous silica (Vydac TP 9) ron a logit-log plot of IC versus R of polystyraie sanples chronatografiied in THF.

Specifically, the responses increased over a wide range of concentrations, and logit/log (Hill) plots yielded slopes of less than 0.8 (not shown). We adopted the minimal model of 1 1 stoichiometry for ligand/receptor interaction, and foresaw three possible contributory causes of shallow response curves (1) multiple receptors with graded affinities but additive effects (2) metabolic inactivation of the peptides during the course of two or three hour assays, and (3) desensitization (down-regulation) during the course of the assays. 

During methods evaluation, standard curves should be plotted in several ways, since different plots reveal different reaction characteristics. For example, the bound/free versus concentration plot is very steep at the low concentration end, and may be used to calculate the detection limit of the assay. The sigmoidal plots of bound/total against log concentration clearly show regions of insensitivity (low and high concentration ends) that might not be clearly apparent in the logit-log curve. 

Principle. In a typical RIA procedure for measuring insulin, T-labeled insulin competes with insulin in a patient sample for binding to an insuhn-specific antibody immobilized on the walls of a polypropylene tube. The supernatant is decanted, and the bound determined in a gamma counter. The amount of insulin in the sample is established by comparison with a calibration curve obtained by plotting on logit-log graph paper the percent of total radioactivity bound (B/T%) against the concentration of the calibrators. Various commercial kits for insulin measurement are now available. 

Alternatively, plotting the dose-response curve on logit-log paper is convenient for the direct estimation of D. Probits are not used... 

Homogeneous EIA lend themselves better to dose-response curve linearization than solid-phase EIA. This type of EIA is generally used for the determination of concentrations of small molecules (haptens, drugs). The major supplier of this type of EIA kits (Syva Co.) recommends the plotting of the response variable ( EMIT Units ) vs the log of the concentration or the presentation of the results on special non-linear graph paper provided by them, which is, in fact, logit-log paper. 

This latter transform is used to linearize the usual sigmoid curve produced in plotting B/Bq vs log dose. This transform may be accomplished by using a computer, logit paper or a table of logit values. 

Hence, the Hill plot can be regarded as a plot of logit (p) against the logarithm of concentration (though it is more usual to employ logs to base 10 than to base e). 

Fig. 2. Log-logit plot of inhibition of HyHE1 5 binding to HEL by mutant lysozymes. The profile of cloned wild-type lysozyme (WT HEL) was not significantly different from that of native wild-type HEL. The reactivity of the R68K mutant was reduced by over 3 log units, similar to that seen previously with bobwhite quail lysozyme [T. B. Lavoie, L. N. W. Kam-Morgan, A. B. Hartman, C. P. Mallett, S. Sheriff, D. A. Saroff, C. R. Mainhart, P. A. Hamel, J. F. Kirsch, A. C. Wilson, and S. J. Smith-Gill, in The Immune Response to Structurally Defined Proteins The Lysozyme Model (S. Smith-Gill and E. Sercarz, eds.), p. 151. Adenine Press, Schenectady, New York, 1989], whereas R45K reduced reactivity by approximately 100-fold.

Values obtained for logit(y) are then plotted against log analyte], and a linear plot is obtained as shown in Figure 16.5. 

IC50 = antilog of X - intercept of logit(5/5o)vs. log(concentration) plot... 

Figure 12 Log-logit plot of the data for caffeine from the experiment described in Fig. 11.

Data Reduction and Analysis For inhibition profiles, the means of triplicate data points (at individual inhibitor concentrations) were plotted. IC50 values were determined using either a log-logit or four parameter fit. (Correlation coefficients were determined from the best fit of these data.) Error bars representing standard deviations (SD) are only presented in selected inhibition profiles. Paraoxon equivalence (%), PE, was determined using the following relationship ... 

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