Parameters indicator variables

Regression analysis [388, 389, 571] correlates independent X variables (e.g. physicochemical parameters, indicator variables) with dependent Y variables e.g. biological data) (Figure 30). The dependent variables contain error terms e, while the independent variables are supposed to contain no such error. In reality, this is only an approximation, because the physicochemical parameters of a QSAR equation indeed contain experimental error however, in most cases this error is much smaller than the error in the biological data. Only Free Wilson (indicator) variables are error-free terms. 

The Kd(X) values thus obtained (Table 3) were analyzed by the multivariant technique using such parameters as n, a0, Bt, Ibmch, and Ihb, where Bj is a STERIMOL parameter showing the minimum width of substituents from an axis connecting the a-atom of the substituents and the rest of molecule, and Ibrnch, an indicator variable representing the number of branches in a substituent. 

This is an inverted parabolic relation in terms of ttx (calculated hydrophobic parameter of the substituents), which suggests that activity of these compounds first decreases as the hydrophobicity of substituents increases and after a certain point (inversion point ttx = 0.67), activity begins to increase. This may correspond to an allosteric reaction [54]. The indicator variable I is assigned the value of 1 and 0 for the presence and absence of N(CH3)2 substituent at the X position. Its positive coefficient suggests that the presence of a N(CH3)2 substituent at X position, increases the activity. REC is the relative effective concentration i.e., concentration relative to topotecan, whose value is arbitrarily assumed as 1, that is able to produce the same cleavage on the plasmid DNA in the presence of human topo I. 

The indicator variable I is assigned the value of 1 for the presence of amide derivatives and 0 for the esters. Its negative coefficient suggests that esters would be preferred over amides for this data set. nx is the calculated hydrophobic parameter of the X-substituents. Its positive coefficient suggests that the highly hydrophobic X-substituents would be preferred. 

Dearden,. C., Ghafourian, T. Hydrogen bonding parameters for QSAR comparison of indicator variables, hydrogen bond counts, molecular orbital and other parameters. J. Chem. Inf. Comput. Sci. 1999, 39, 231-235. 

In the above expression the indicator variable I(X) takes the value 0 or 1, depending upon the absence or presence of the substituent X in a particular compound. The overall result of the regression is not significant at the 0.05 level of probability. This may be due to the unfavorable proportion of the number of compounds to the number of parameters in the regression equation (10 to 6). Only the indicator variable for substituent NHj at position W in the tetracycline molecule reaches significance (p = 0.02). This can be confirmed by looking at Table 37.4... 

The formulation of the engineered nonlinear short-term model presented is a variant of an MINLP model described in the dissertation by Schulz [5], In this subsection, all necessary indices, parameters and variables are introduced, and the constraints and the objective function are derived. In the following section, the nonlinear formulation is linearized yielding a MILP model. In order to keep track of the variables used in the MINLP and in the MILP formulation, they are displayed in Figure 7.3 along with some key parameters. 

A classical Hansch approach and an artificial neural networks approach were applied to a training set of 32 substituted phenylpiperazines characterized by their affinity for the 5-HTiA-R and the generic arAR [91]. The study was aimed at evaluating the structural requirements for the 5-HTiA/ai selectivity. Each chemical structure was described by six physicochemical parameters and three indicator variables. As electronic descriptors, the field and resonance constants of Swain and Lupton were used. Furthermore, the vdW volumes were employed as steric parameters. The hydrophobic effects exerted by the ortho- and meta-substituents were measured by using the Hansch 7t-ortho and n-meta constants [91]. The resulting models provided a significant correlation of electronic, steric and hydro-phobic parameters with the biological affinities. Moreover, it was inferred that the... 

Model. These guidelines provided concepts or operating hypotheses on which the synthesis of approximately 120 additional compounds was based. Towards the end of this phase of the project, hereafter referred to as Phase I, our concepts had crystallized to the point where they could be expressed using the discrete quantitative parameters described in Table I. Parameters illustrated in the table bearing the I tag are indicator variables set equal to unity when the indicated feature is present, zero when it is not I[56] = 1 indicates compounds in which the entire dione moiety is... 

Thus, the commonly applied parameters , and Es are explicit representations of lipophilic, electronic and steric properties respectively. Indicator variables, on the contrary, frequently refer to fixed combinations of physico-chemical properties. For example, an indicator variable which denotes the presence of a 4-methoxy-group in general structure 6 refers simultaneously to all physico-chemical properties of this substituent, i.e. to its contribution to the lipophilic ( ), electronic (a), and steric properties (Es) of the system. 

The possibility of describing chemical structures numerically with the aid of physico-chemical parameters and indicator variables puts us in the position to determine similarity or dissimilarity of chemical compounds more objectively. Chemical compounds can be represented as points in an n-dimensional space whose coordinates are formed by the parameters which are used to characterize the compounds. This space is therefore called parameter space. The distance of two... 

This indicates that a general geothermal pattern has been established in the total column and that rapidly circulating warmer water has only local effects on the clay mineralogy. The mineralogy of these different types of semi-permeable rocks corresponds, on a depth-temperature basis, very closely with that found in pelitic shale rocks of other studies. It is likely therefore that high permeability gives a noticeably different set of chemical parameters (intensive variables) to a rock whereas medium to low permeability can be assimilated to a "closed" system where rock and fluid are effectively part of the same physicochemical unit. 

The estimates of Muller et al. (1994) for just three plant species yielded a range of a factor of 12 for the volume fraction of the cellular lipids vcl and a factor of 7 for the cuticular membrane v0 which would indicate that these parameters are variable and that they must be estimated for each plant species or canopy of interest. However, only in one case has an independent measure of the volume fractions been successfully used to fit measured KPA data (Tolls and McLachlan, 1994) in most other cases the volume fractions were deduced from the regression of measured KPA against Kow/Kaw. 

At this point, a considerable amount of theory on Hansch analysis has been presented with almost no examples of practice. The next three Case Studies will hopefully solidify ideas on Hansch analysis that have already been discussed. Each Case Study introduces a different idea. The first is an example of a very simple Hansch equation with a small data set. The second demonstrates the use of squared parameters in Hansch equations. The third and final Case Study shows how indicator variables are used in QSAR studies. If you are unfamiliar with performing linear regressions, be sure to read Appendix B on performing a regression analysis with the LINEST function in almost any common spreadsheet software. A section in the appendix describes in great detail how to derive Equations 12.20 through 12.22 in the first Case Study. 

It is important to have the correct set of variables specified as independent and dependent to meet the modeling objectives. For monitoring objectives observed conditions, including the aforementioned independent variables (FICs, TICs, etc.) and many of the "normally" (for simulation and optimization cases) dependent variables (FIs, TIs, etc.) are specified as independent, while numerous equipment performance parameters are specified as dependent. These equipment performance parameters include heat exchanger heat transfer coefficients, heterogeneous catalyst "activities" (representing the relative number of active sites), distillation column efficiencies, and similar parameters for compressors, gas and steam turbines, resistance-to-flow parameters (indicated by pressure drops), as well as many others. These equipment performance parameters are independent in simulation and optimization model executions. 

Experimental parameters or variables involved included solubility, diffusivity, suspension concentration, release opening radius, declination angle, and number of cells. Experimental results indicated that this device behaved in accordance with the theoretical model. 

Suppose that we wish to make inferences on the parameters 0i,i = 1,g, where 9i represents the logarithm of the ratio of the expression levels of gene i under normal and disease conditions. If the ith gene has no differential expression, then the ratio is 1 and hence 0 = 0. In testing the g hypotheses Ho, 0 = 0, / = 1,..., g, suppose we set R, = 1 if H0, is rejected and Ri = 0 otherwise. Then, for any multiple testing procedure, one could in theory provide a complete description of the joint distribution of the indicator variables R, ..., Rg as a function of 0i,..., 0g in the entire parameter space. This is impractical if g > 2. Different controls of the error rate control different aspects of this joint distribution, with the most popular being weak control of the familywise error rate (FWER), strong control of the familywise error rate, and control of the false discovery rate (FDR). 

QSAR Quantitative structure-activity relationship. Quantitative structure-bio-logical activity model derived using regression analysis and containing as parameters physical-chemical constants, indicator variables, or theoretically calculated values. 

---