Concentration-response data

The IC50 can thus be accurately determined by fitting the concentration-response data to Equation (5.1) through nonlinear curve-fitting methods. Some investigators prefer to plot data in terms of % inhibition rather than fractional activity. Using the mass-balance relationships discussed above, we can easily recast Equation (5.1) as follows ... 

The second common cause of a low Hill coefficient is a partitioning of the inhibitor into an inactive, less potent, or inaccessible form at higher concentrations. This can result from compound aggregation or insolubility. As the concentration of compound increases, the equilibrium between the accessible and inaccessible forms may increase, leading to a less than expected % inhibition at the higher concentrations. This will tend to skew the concentration-response data, resulting in a poorer... 

In this case, fitting the concentration-response data to Equation (5.4) would yield a smooth curve that appears to ht well but with a Hill coefficient much less than unity. 

Graphing and fitting of the inhibtor concentration-response data to obtain the IC50 is typically the primary mechanism for assessing the relative potency of lead compounds and lead compound analogues (see below). The IC50 can be determined by... 

Figure 5.7 Comparison of four-parameter fy-maxi mum, v-minimum. IC50, and h) and two-parameter (IC50 and h) fits of non-ideal concentration-response data. In panels A and B the data indicate a nonzero plateau at low inhibitor concentration that might reflect a low-amplitude, high-affinity second binding interaction. In panels C and D the data indicate a plateau at high inhibitor concentration that does not achieve full inhibition of the enzyme. There could be multiple causes of behavior such as that seen in panels C and D. One common cause is low compound solubility at the higher concentrations used to construct the concentration-response plot. Note that the discordance between the experimental data and the expected behavior is most immediately apparent in the plots that are fitted by the two-parameter equation.

Table 5.2 Example of a tabular report of concentration-response data for five lead compounds against a common target enzyme...

To continue to optimize compounds and quantitatively assess improvements in affinity requires specialized methods and/or special mathematical handling of concentration-response data. 

Effects of Tight Binding Inhibition on Concentration-Response Data 179... 

EFFECTS OF TIGHT BINDING INHIBITION ON CONCENTRATION-RESPONSE DATA... 

Morrison s Quadratic Equation for Fitting Concentration-Response Data 185... 

MORRISON S QUADRATIC EQUATION FOR FITTING CONCENTRATION-RESPONSE DATA FOR TIGHT BINDING INHIBITORS... 

A better method for analyzing concentration-response data for tight binding inhibitors was developed by Morrison and coworkers (Morrison, 1969 Williams and Morrison, 1979). This treatment is based on defining the Kt value of an inhibitor, or... 

These practical approaches are by no means mutually exclusive, and attempts should be made to combine as many of these as possible to improve ones ability to experimentally measure the K-pp of tight binding inhibitors. Thus one should always work at the lowest enzyme concentration possible, and drive the substrate concentration as high as possible, when dealing with competitive inhibitors. A long preincubation step should be used before activity measurements, or the progress curves should be fitted to Equation (6.2) so that accurate determinations of the steady state velocity at each inhibitor concentration can be obtained. Finally, the concentration-response data should be fitted to Morrison s quadratic equation to obtain good estimates of the value of Arfpp. 

These features are important if the sponsor intends to use the results to support a conclusion that no dosage adjustment is required for patients with impaired hepatic fxmction. Pharmacodynamic assessments may be useful in studies designed to assess the effect of altered liver fxmction, especially if concentration-response data are not available or if there is a concern that an altered hepatic function could alter the PD response. 

Concentration response data are analyzed by a nonlinear regression logistic dose response model. Each of the crude extracts are fractionated into 10-15 subfractions. For each crude extract and the associated subfractions, ICsos and IC90S are determined as outlined above. All crude and subfractions of a particular marine organism are assayed simultaneously (within one assay) and include ribavirin as reference drugs using only A/WY/03/2003 virus. 

Predictive modellinkagesbasedon quantitative concentration-response data... 

Because the Phase I assay portfolio used predominantly human-derived cells, cell lines, and proteins, whereas the in vivo results for anchoring these HTS data were based on in vivo studies in rats, mice, and rabbits, we need to consider in vitro concentration-response data with internal dose-response kinetics for the pregnant dam (28, 69). 

Sigmoidal curves of the concentration-response data are presented in Figure 1, and their probit transformations in Figure 2, where a log-normal model is assumed. Here, the log-concentration transformation (pT-scale) is paired with the probit parameter, which is indicative of the proportion of percentage inhibition . 

Data are recorded using e.g. TIDA software (HEKA Electronics, Lambrecht, Germany) and the results are typically expressed as fraction of baseline current. Concentration-response data can be fitted to an equation of the following form 1/10 = 1/(1 + flcom-poundl/ICso)) such that the IC50 can be calculated with a sigmoidal dose-response curve model. 

Walter et al. (2002) assessed the effect of a mixture of 11 aquatic priority pollutants on algal reproduction. The chemicals were selected for structural diversity by using chemometric methods. In this study, statistical estimates of effect concentrations down to effect levels of 1% were derived by regression analysis of concentration-response data. Based on these estimates of low effects, IA yielded quite accurate predictions of mixture toxicity. 

Gennings C, Carter WH. 1995. Utilizing concentration-response data from individual components to detect statistically significant departures from additivity in chemical mixtures. Biometrics 51 1264—1277. 

The graphic and regression methods are a means of estimating the concentration-response curve. Hypothesis testing is an alternative to the analysis of the concentration-response data. 

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