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lish the link between the gradient status (or time) and the pH scale. Buffer reagents are commercially available and supplied by Sirius analytical Instruments. Data Analysis Two methods can be used:
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AFD : Automated rst derivative TFA : Target factor analysis
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Automated First Derivative. The AFD method calculates the rst derivative of the absorbance against the pH curve and assigns the pKa to the pH where a maximum peak is found. AFD is a simple and quick method to calculate pKa, but it is limited to relatively simple molecules. Typically AFD is well suited for monoprotic molecules (or well-separated pKa s) that generate a good UV signal. From a practical viewpoint it is not recommended to use AFD when OPH is lower than 1. OPH (overall peak height) is a parameter, that describes the amplitude of the absorbance change induced by the ionization: OPH = 1000 Difference between minimum and maximum values of dA dpH . Target Factor Analysis. The TFA method has already been described elsewhere36 and is brie y described below: The absorbance A is linked to the concentration of the species present in the solution. Their absorbance and at each wavelength the Beer-Lambert law applies such that: A = C E, where C and E are, respectively, the concentration of each independent light-absorbing species as a function of pH and the molar absorptivity of each species as a function of pH and wavelength. At the start of the calculation, C and E are guessed values, whereas A is a measured value. During the calculation the A matrix is whereby deconvoluted using target factor analysis whereby values of the concentration and absorptivity are proposed iteratively until A - C E tends to a minimum. At that point, the pKa values required to calculate the distribution of species (C matrix) are assumed to be to correct pKa values.
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potential and limitations
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TFA analysis of the pH/spectra is more time-consuming and requires additional expertise to run the software. It is, however, a more powerful tool that allows one to cope with overlapping pKa s and is able to separate noise from signal by principal component analysis, thus yielding less favorable signal to noise ratios. To some extent TFA is also able to remove signal due to precipitation of the sample, particularly if the number of ionization s is xed by an independent method (i.e., using an in silico method). Practical Considerations for Data Re nement, AFD or TFA Use of AFD. ALL conditions below have to be ful lled:
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Number of peaks equals number of expected pKa s Peaks separated by at least 2 pKa units Symmetrical peaks OPH <1.0
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Use of TFA. TFA is used if ANY of the conditions below applies:
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Overlapping pKa s Number of peaks in AFD not equal to number of expected pKa s OPH <1
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With the currently commercially available technology, a success rate of 60% to 70% can be envisaged with real-life compounds from lead optimization programs. Further improvement could be envisaged if one could circumvent precipitation of samples, for example, by addition of a co-solvent in the buffer reagents. The strength of the technique lies in its speed and degree of automation (samples can be loaded in 96-well plates). However, our experience has shown that successful automated data analysis requires relatively clean data. For this reason we expect improvement in ef ciency once a set of cosolvent buffer reagents becomes available.
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PERMEABILITY DETERMINATIONS
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Permeability pH Pro les: Ionization, Membrane Retention, and Unstirred Layers
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There are a variety of terms used in the literature to express permeability. As experimental permeability can be corrected in a number of ways to
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account for membrane retention, ionization, and unstirred layer effect, the de nitions used in this chapter is given below together with their physicochemical meaning: De nitions Log Pa: Apparent permeability. It is directly calculated from the concentration in the acceptor concentration Log Pe: Effective permeability. This is log Pa corrected by membrane retention (if any). In absence of membrane retention, log Pa = log Pe Log Pm: Membrane permeability. That is log Pe corrected by the unstirred layer effect. Log Po: Intrinsic permeability. That is log Pm corrected by ionization. For neutral compounds log Pm = log Po Membrane permeability depends on the ability of the compound to diffuse through the unstirred layer and the membrane. Intrinsic permeability is linked to membrane partitioning as described below: log Po = log P (mem) + log D , h (15.4)
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where log P(mem) is the partition coef cient between the membrane considered and the incubation medium, D the diffusion coef cient of the compound within the membrane and h the membrane thickness. Effective membrane permeability is related to membrane permeability and unstirred layer permeability as: 1 1 1 = + Pe Pm Pu 1 or 1 Ct Cn 1 = + , Pe Po Pu 1 (15.6) (15.5)
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where Ct/Cn represent the fraction of neutral species. Equation (15.6) can be used to derive log Pm in terms of pH (and log Po) for ionizable compounds with known pKa values. This is illustrated graphically with Diclofenac permeability pH pro le in Figure 15.3. The dynamic range of all permeability assays is limited by the diffusion through the unstirred layers (see Table 15.4). As the thickness of the unstirred layer increases, the dif-
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0 -1 -2 log Po = -1.3
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