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Keywords: sigmaplot, xp, sigmaplot, xp, sigmaplot, for xp, sigmaplot
Global Analysis of Concentration-Response Curves
Using SigmaPlot to perform global curve fitting is described in the enzyme kinetics article. This approach uses an index variable and index values placed in a column in the worksheet. Also, the different data sets
are column concatenated. This may not be desirable in some cases and is not necessary. This application uses a slightly different approach that does not require data column concatenation. Wiener and Thalody describe
the contraction of rabbit aorta to methaxomine and subsequent relaxation to dibenamine. Families of concentration-response curves were measured for varying concentrations of both methaxomine and dibenamine. The
family of data sets was then globally fit to data using the following operational model of agonism where E is the measured response, A is the agonist concentration. The curve fit parameters are Em, KA, n and t. Em, KA and n are global parameters that are fit using all data; t is a local parameter that will be different for each data set; i.e., for two data sets, there will be two parameters t1 and t2.
The SigmaPlot worksheet shows two data sets. The control data set (no dibenamine) is in columns 1 and 2. The data set with dibenamine is in columns 3 and 4. This data is not concatenated.
The curve fit equations for global analysis of this data are
[Variables]
A = {col(1), col(3)} 'methoxamine concentration
Y = {col(2), col(4)} 'contractile response
[Parameters]
K = 5e-5 ' initial estimate for Ka
E = 8.0 ' initial estimate for Em {{previous: 7.98348}}
T1 = 12 ' initial estimate for tau before dibenamine alkylation
T2 = 1 ' initial estimate for tau after dibenamine alkylation
n = 2 ' initial estimate for slope factor
[Equation]
i1 = data(1, 1, size(col(1))) 'index values for T1
i2 = data(2, 2, size(col(3))) 'index values for T2
I={i1, i2} 'concatenated index values
Ti = {T1,T2}[I] 'vector of two T parameters
F = E*(Ti^n)*(A^n)/((K+A)^n + (Ti^n)*(A^n)) 'concentration-response equation
fit F to Y
The data A and Y is concatenated in the [Variables] section using the curly brackets. This replaces the need to concatenate the data in the worksheet.
Then the index variable required for global analysis is defined in the first three lines of the [Equation] section. The square bracket notation ([I]) is used to
define a two-component parameter vector Ti. The concentration-response equation F is actually two equations since it depends on the parameter vector Ti.
In the Regression Wizard select From Code for the data format.
This will use the concatenated columns defined in the [Variables] section. A transform generated the fit lines shown in the following graph.
The relaxation effect of dibenamine is shown, and the global curve fit (solid lines) is excellent.
Download the self-extracting file Global_Fit_to_Concentration-Response.exe and double-click on it to obtain the SigmaPlot notebook with this example, the global curve fit equations and the fit line transform.
1. Weiner, H.L. and Thalody, G.P. Differential attenuation of the responses to Adenosie and Methoxamine in isolated rabbit aorta. J. Pharm. Exp. Therap. 267 (1993) 828-837.
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