Selectivity optimization parameter space

We want values of pA"w, pAj, and pK2 that minimize the sum of squares of residuals in cell B12. Select SOLVER from the TOOLS menu. In the SOLVER window, Set Target Cell B12 Equal to Min By Changing Cells B9. B10. Bl 1. Then click Solve and SOLVER finds the best values in cells B9, BIO, and Bll to minimize the sum of squares of residuals in cell B12. Starting with 13.797, 2.35, and 9.78 in cells B9, B10, and Bll gives a sum of squares of residuals equal to 0.110 in cell B12. After SOLVER is executed, cells B9, B10, and Bll become 13.807, 2.312, and 9.625. The sum in cell B12 is reduced to 0.0048. When you use SOLVER to optimize several parameters at once, it is a good idea to try different starting values to see if the same solution is reached. Sometimes a local minimum can be reached that is not as low as might be reached elsewhere in parameter space. 

This criterion may be used during a sequential optimization process (see chapter 5), leading to an acceptable result and to completion of the optimization process once the threshold value has been reached. Alternatively, it may be used to establish ranges of conditions in the parameter space for which the result will be acceptable. This latter approach has been followed by Glajch et al. [415], by Haddad et al. [424] and by Weyland et al. [425] and was referred to as resolution mapping by the former. Within the permitted area(s) secondary criteria are then required to select the optimum conditions. For example, the conditions at which the k value of the last peak (k is minimal while the minimum value for Rsexceeds 1 may be chosen as the optimum. Such a composite criterion can be described as... 

Typically for this kind of optimization, and, indeed, for all procedures used to optimize chromatographic selectivity is that at many different points in the parameter space complete overlap of two components occurs. In figure 5.1 this is the case at all points at which amin = 1. In two-dimensional optimization processes the conditions at which two particular components show complete overlap will form a line rather than a point, and so on. 

In some cases, the results of the initial experiments can be used to reduce the number of parameters considered or to narrow down the limits defined for the selected parameters. In both cases this can result in great simplifications for the optimization process. This will be discussed in section 5.4. After the reduction of the parameter space additional experiments may have to be performed to complete the initial data set. 

Various strategies have been advocated in order to cover the physicochemical parameter space of a series of new compounds as well as possible. Familiar strategies go back to proposals by Topliss and Craig. Both are schemes used for substituent variation at a selected site. The Topliss substitution scheme can be used to optimize aromatic and aliphatic substituents using a fixed set of substituents and rules. A Craig plot is a 2D plot of selected descriptors, for example, Hammett electronic properties) and Hansch 7T values (lipophilicity). Substituents can be selected from each quadrant of this plot such that they vary widely in their properties, for example, lipophilic and hydrophilic, electron-donor and electron-acceptor, and to ensure the two properties are not correlated in the selected set which is preferable for the generation of stable QSAR models. 

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