Free-Wilson technique

Table 6.8 Activity contributions for substituents as determined by the Free-Wilson technique (from Waisser et al. 1993 with kind permission)...

A key advantage of the Free-Wilson method over standard descriptors-based QSAR techniques is the estimation of activity contribution for individual R-group structures that are readily interpretable to medicinal chemists. 

In organic chemistry, decomposition of molecules into substituents and molecular frameworks is a natural way to characterize molecular structures. In QSAR, both the Hansch-Fujita " and the Free-Wilson classical approaches are based on this decomposition, but only the second one explicitly accounts for the presence or the absence of substituent(s) attached to molecular framework at a certain position. While the multiple linear regression technique was associated with the Free-Wilson method, recent modifications of this approach involve more sophisticated statistical and machine-learning approaches, such as the principal component analysis and neural networks. ... 

These special cases of multiple linear regression analysis have been developed for the determination of the impact of individual molecular substructures (independent variables) on one dependent variable. Both techniques are similar yet, the Free-Wilson method considers the retention of the unsubstituted analyte as base, while Fujita-Ban analysis uses the less substituted molecule as reference. These procedures have not been frequently employed in chromatography only their application in QSRR studies in RP TLC and HPLC have been reported. 

The most well-known approaches based on substituent descriptors are the Hansch analysis and - Free-Wilson analysis in the latter technique, the substituents are defined by - indicator variables representing their presence/absence in the substitution sites of the parent molecule. 

An interesting technique which dates from the early days of modem QSAR, known as the Free-Wilson method (Free and Wilson 1964) represents an extreme case of the use of indicator variables, since regression equations are generated which contain no physicochemical parameters. This technique relies on the following assumptions. 

One of the disadvantages of the Free-Wilson method is that— unlike regression equations based on physicochemical parameters— it cannot be used to make predictions for substituents not included in the original analysis. The technique may break down when there are linear dependencies between the structural descriptors, for example, when two substituents at two positions always occur together, or where interactions between substituents occur. Advantages of the technique include its ability to handle data sets with a small number of substituents at a large number of positions, a situation not well handled by other analytical methods, and its ability to describe quite unusual substituents since it does not require substituent constant data. A number of variations and improvements have... 

Consideration of the inhibitor concentration markedly improves the quality of the correlations. Figure 9-51 shows the relationship between experimental and estimated inhibition efficiencies of pyrimidine derivatives (Lukovits et al., 1997) obtained by assuming the Langmuir adsorption. A similar technique can be used for the Free - Wilson variables (Lukovits et al., 1995), again yielding much better results than those obtained using a fixed concentration approach (Dupin et al., 1982). 

In principle, the parameters can be evaluated from minimal experimental data. If vapor-liquid equilibrium data at a series of compositions are available, the parameters in a given excess-free-energy model can be found by numerical regression techniques. The goodness of fit in each case depends on the suitability of the form of the equation. If a plot of GE/X X2RT versus X is nearly linear, use the Margules equation (see Section 3). If a plot of Xi X2RT/GE is linear, then use the Van Laar equation. If neither plot approaches linearity, apply the Wilson equation or some other model with more than two parameters. 

The above techniques have been used in numerous calculations of solute free energy profiles. Wilson and Pohorille [52] and Benjamin[53] have determined the free energy profiles for small ions at the water liquid/vapor interface and compared the results to predictions of continuum electrostatic models. The transfer of small ions to the interface involves a monotonic increase in the free energy which is in qualitative agreement with the continuum model. This behavior is consistent with the increase in the surface tension of water with the increase in the concentration of a very dilute salt solution, and it represents the fact that small ions are repelled from the liquid/vapor interface. On the other hand, calculations of the free energy profile at the water liquid/vapor interface of hydrophobic molecules, such as phenol[54] and pentyl phenol[57] and even molecules such as ethanol [58], show that these molecules are attracted to the surface region and lower the surface tension of water. In addition, the adsorption free energy of solutes at liquid/liquid interfaces[59,60] and at water/metal interfaces[61-64] have been reported. 

A Fortran IV computer program developed by Redifer and Wilson (10) was used to predict thermodynamic equilibrium compositions for 400-700°K and 1 atm total pressure. The calculations are based on a procedure presented by Meissner, Kusik, and Dalzell (11) in which the set of simultaneous reactions is simplified to a set of series-consecutive reactions. Each reaction is carried out in turn on the reactant mixture as though a set of ideal batch equilibrium reactors were aligned in series in which the products from one equilibrium stage become reactants for the next reactor. After all the reactions have been completed, products from the last reactor are recycled to the first reactor, and the reaction sequence is repeated. Equilibrium of all components is complete when the product compositions at the end of two consecutive cycles are identical. The method compares favorably with the free energy minimization technique and is useful for changing conditions or input parameters. 

Copper is detectable histochemically using rubianic acid, which reacts with the metal to yield a black precipitate. Such techniques have shown that the copper accumulates in the hepatic cell first leaving the Kupffer cell free of copper. In the hepatic cell, at first the metal is diffused throughout the cytoplasm, but later it accumulates to form a metallic halo around the nucleus. Copper accumulation in the liver cell precedes the development of cirrhosis. The copper is widely distributed among the brain cells, but the largest concentration of metal is usually found in the basal ganglia. The type of nerve cell involved in copper accumulation in Wilson s disease has not been unequivocally identified. 

Wilson s disease is often attributed to a hereditary deficiency of ceruloplasmin. Ceruloplasmin deficiency can be demonstrated by direct colorimetry of the blue protein, by determination of phenylenediamine oxidase activity, and by immunological techniques. The role of ceruloplasmin in copper metabolism is not known, but it is assumed to serve as an acceptor of the free copper in the plasma. The changes in cerulo-... 

From kinetic theory it can be shown that, in general, larger gas molecules have a lower thermal conductivity. The influence of molecular weight of the gas on the thermal conductivi of fibrous insulations has been adequately covered by Wilson for standard temperatures and pressures and by Verschoor and Greebler for low pressures. However, this technique is limited to an improvement in conductivity approximately equivalent to the difference in free gas conductivity between the high molecular weight gas and air. This paper evaluates an alternate technique for improving the thermal performance of fibrous insulation, i.e., the partial removal (evacuation) of the environmental air. 

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