Data interpretation from functions

The objective functions for both k-means clustering and the F-nearest neighbor heuristic given by Eqs. (20) and (21) use information only from the inputs. Because of this capacity to cluster data, local methods are particularly useful for data interpretation when the clusters can be assigned labels. 

The knowledge required to implement Bayes formula is daunting in that a priori as well as class conditional probabilities must be known. Some reduction in requirements can be accomplished by using joint probability distributions in place of the a priori and class conditional probabilities. Even with this simplification, few interpretation problems are so well posed that the information needed is available. It is possible to employ the Bayesian approach by estimating the unknown probabilities and probability density functions from exemplar patterns that are believed to be representative of the problem under investigation. This approach, however, implies supervised learning where the correct class label for each exemplar is known. The ability to perform data interpretation is determined by the quality of the estimates of the underlying probability distributions. 

The identities and roles of many of the drug transporters are discussed in other chapters in this volume, and are not extensively reintroduced here. A goal is to develop a comprehensive panel of cells expressing individual, functional transporters as research reagents. To simplify data interpretation, the set of transporters should be expressed in the same host cell line and the abundance of functional proteins in the cell line should be known relative to the corresponding in vivo values. However, useful mechanistic data can be obtained from less comprehensive systems. 

In the absence of detailed structural information about GPCRs, much of the efforts to interpret experimental results in a structural context has focused on creating molecular representations of these proteins that can incorporate directly and consistently the many types of function-related information (for a recent review, see ref. [5]). In turn, such molecular models serve as hypotheses-generators for experimental probing of functional inferences, and are continuously refined by the data obtained from such experiments. Listed below are some of the main advantages of such an iterative approach, as illustrated in this chapter ... 

The quantity measured in the experimental work on the methane derivatives was the rotation of the Na D-line in ethanol solution (sometimes it was necessary to use another solvent, in which case a correction was applied). The sum (5), as well as its separate terms, was evaluated for 13 different choices of the set of ligands a,b,c,d,x. For eleven of these, the observed sum was less in absolute value than its statistical average calculated from the absolute values of the separate terms. For the other two (as well as for some of the eleven), the mixture contained molecules for which one would expect large deviations from T,rsymmetry, and/or dimerization. For those mixtures for which the sum (5) was small, a least-square fit was made to the data with a function of the form (2). This best fit was interpreted as the T -component, the remainder as the result of deviation from T -symmetry for each molecule. A fit was also made with functions of the form (1), with less quantitative success. 

Data from in vitro activity assays with these purified recombinant proteins can typically be interpreted much more easily than data obtained from experiments with crude or partially purified protein extracts, because (1) there will be no competing proteins with similar activity present in the assay, and (2) there will no enzymes present that convert the product generated by the enzyme of interest, and hence reduce the effective product concentration. A potential downside of the use of recombinant protein over crude extracts is the fact that critical co-factors that will ensure proper activity may not be present in the purified protein fraction. If that is the case, the researcher will have to empirically determine which co-factor and at what concentration needs to be included in the assay. Another consideration is that the native protein may have undergone post-translational processing, such as acetylation, glycosylation, myristoylation, etc. These modifications may not occur or may not occur properly when the protein is expressed in bacterial, fungal or insect cells. Assuming that these potential problems do not occur or can be dealt with, the availability of pure recombinant protein will enable the determination of substrate specificity, as well as kinetic experiments in which the rate of conversion is measured as a function of time and/or substrate concentration. 

The overall conclusion from the analysis of equation 18 over the complete domain of a is that, in principle, information about the shape of the particle size distribution can be obtained directly from turbidity, or in general, from scattering measurements. However, the discriminating power of the measurements in terms of the particle size distribution depends upon the wavelength range selected for the analysis. The major difficulty in the interpretation of the data arises from the behavior of the extinction itself as function of the size parameter which causes the measurements "see" a different average at every wavelength. 

Fig. 17 Energy as a function of a T-T distance and b T-T-T angle used in the simulation procedure (calculated as smoothing spline fits to Boltzmann equilibrium interpretations of the histogrammed data taken from 32 representative zeolite crystal structures). Only the central portions are shown, c The contribution to the energy sum for the merging of two symmetry-related atoms merging is only permitted when the two atoms are at less than a defined minimum distance [84], Reproduced with the kind permission of the Nature Publishing Group (http //www.nature.com/)...

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