Deconvolution Approaches

The course of systemic exposure to a drug is studied by comparing intravenous (IV) administration shidies using deconvolution approach, in which r(f) is the systemic concentration produced from IV adminisfrafion (also called bolus function) and /(f) is the systemic input rate (in units such as g/min) from fhe noninfravenous (non-lV) route ... 

Such a treatment, within its mechanistic restrictions, is general across the full range of experimental techniques. This convolution-deconvolution approach is the basis of the E G G Condecon system. 

As proof of principle, Lehn and coworkers individually synthesized all acyl hydrazone combinations from the 13 DCL building blocks and measured their inhibition of acetylthiocholine hydrolysis by ACE in a standard assay. They then established a dynamic deconvolution approach whereby the pre-equilibrated DCL containing all members is prepared, frozen, and assayed. Thirteen sublibraries were then prepared containing all components minus one hydrazide or aldehyde component, and assayed. Active components in the DCL were quickly identified by an increase in ACE activity, observed in sublibraries missing either hydrazide 7 or dialdehyde i, pointing to the bis-acyl hydrazone 7-i-7 as the most likely active constituent. This was in line with the individual assay data recorded earlier resynthesis of this compound characterized it as a low nanomolar inhibitor of the enzyme. 

When we are solving for an unknown spectrum, each data point contains some information about the component spectral lines. A data point far from the center of a given line would be expected to contain very little information about that line. A hypothetical model of the spectrum could incorporate widely varying estimates of the amplitude of that line without influencing the fit to the data point in question. Three data points moderately distributed near the line center—say, spanning the interval between the half-maximum points—affix the parameters of the line more reliably. Instead of taking equally spaced samples of a trial solution as independent unknowns (the deconvolution approach), we can express the sought-after true spectrum in terms of its spectral-line parameters—amplitudes, half-widths, positions, and so on—provided that we can assume such a model with some confidence. 

Schriemer, D. C. Hindsgaul, 0.1998. Deconvolution approaches in screening compound mixtures. Comb. Chem. High Throughput Screen, 1, 155-170. 

The structure of the bioactive members of a combinatorial library prepared by split synthesis can be determined by several methods including bioactivity/deconvolution, microanalytical methods and encoding. In a generalized example of the biorecognition/ deconvolution approach, the final sublibraries are not pooled but tested as mixtures. The most active sublibrary then defines the synthon used in the last synthetic step. The synthesis is then repeated to the penultimate step these sublibraries are not mixed, but each is separately reacted with the preferred last-step synthon. These resulting sublibraries are tested the most active then defines the preferred synthon in the penultimate step, and hence the last two synthons present in the most active member of the family are defined. 

The spectral information obtained by using appropriate deconvolution approaches, particularly the resolved pure CD spectrum of the intermediate, is the essential starting point, unobtainable by other methods, for deducing the secondary structure of the intermediate. 

Various procedures have been proposed for solving this equation. For example the pore size distribution may be assumed to be of log-normal form (Seaton et al., 1989), or alternatively integration may be replaced by summation and a numerical deconvolution approach adopted (Olivier et al., 1994). 

Isotope ratio measurements were employed for the quantification of analytical data using the isotope dilution strategy. For example, isotope dilution analysis was developed by Sanz-Medel s group for the determination of selenomethionine in Se enriched yeast material by HPLC-ICP-MS using a Se-enriched selenomethionine spike obtained by growing yeast on a Se rich culture medium. For Cr(III)/Cr(VI) determination in yeast, Caruso et al employed the double spike species specific isotope dilution technique measured by HPLC-ICP-MS. The isotope pattern deconvolution approach applied in this work delivers a more intuitive and elegant solution to an otherwise complex data analysis without the need for iterative calculations as widely practised in double spike isotope dilution. The results are in exact agreement with the conventional isotope dilution calculations. ... 

Finally, libraries aimed to chiral resolution of racemates will be covered here in particular, the use of chiral stationary phases (CSPs) has recently been reported for the identification of materials to be used for chiral separation of racemates by HPLC. The group of Frechet reported the selection of two macroporous poly methacrylate-supported 4-aryl-1,4-dihydropyrimidines (DHPs) as CSPs for the separation of amino acid, anti-inflammatory drugs, and DHP racemates from an 140-member discrete DHP library (214,215) as well as a deconvolutive approach for the identification of the best selector phase from a 36-member pool library of macroporous polymethacrylate-grafted amino acid anilides (216,217). Welch and co-workers (218,219) reported the selection of the best CSP for the separation of a racemic amino acid amide from a 50-member discrete dipeptide iV-3,5-dinitrobenzoyl amide hbrary and the follow-up, focused 71-member library (220). Wang and Li (221) reported the synthesis and the Circular Dichroism- (CD) based screening of a 16-member library of CSPs for the HPLC resolution of a leucine ester. Welch et al. recentiy reviewed the field of combinatorial libraries for the discovery of novel CSPs (222). Dyer et al. (223) reported an automated synthetic and screening procedure based on Differential Scanning Calorimetry (DSC) for the selection of chiral diastereomeric salts to resolve racemic mixtures by crystallization. Clark Still rejxrrted another example which is discussed in detail in Section 9.5.4. 

The algorithms in the software must embody certain tentative assumptions in order to analyze the peak envelope, such as, the peaks are Gaussian in form or are described by some other specific distribution function and are symmetric. Furthermore, it must also assume that all the peaks can be described by the same function (/.e., the efficiency of all the peaks is the same), which, as has already been discussed, is also not always true. Nevertheless, providing the composite peak is not too complex, deconvolution can be reasonably successful. If resolution is partial and the components are present in equal quantities, then the deconvolution approach can be very successful. An example of the convolution of two partially resolved peaks of equal size is shown in figure 2. 

Rubtsov DV, Waterman C, Currie RA, Waterfield C, Salazar JD, Wright J, Griffin JL (2010) Application of a Bayesian deconvolution approach for high-resolution (1 )H NMR spectra to assessing the metabolic effects of acute phenobarbital exposure in liver tissue. Anal Chem 82(ll) 4479-4485... 

For a dicussion of the effectiveness of deconvolution approaches in finding the most active component and problems with cumulative activity see Freier el al. 480-482... 

Sarkar, S. Dutta, P.K. Roy, N.C. (1998). A bHnd-deconvolution approach for chromatographic and spectroscopic peak restoration, IEEE transactions on instrumentation and measurement, W61.47, No.4 (August 1998), pp. 941-947, ISSN 0018-9456... 

In the blind deconvolution approach, the object and the PSF are assumed to be unknown and are estimated throughout the iterative process [34-36]. The algorithm uses the standard MLE algorithm described above, together with a PSF estimation for each iteration. The object is computed, using the MLE estimation, as follows ... 

The deconvolution approach for anhydrous portland cement can be easily extended to hydrated portland cements and portland cement-SCM blends. For the latter systems, deconvolved subspectra for the SCMs, e.g. slags, metakaolin and natural pozzolans, can be established and incorporated in the optimisation routine. As an example. Figure 6.28 illustrates the deconvolution of the Si MAS NMR spectrum for a white portland cement hydrated for 2 weeks. The model used for this deconvolution includes subspectra of belite and Mm alite as well as single peaks for the Q Q (lAl) and resonances of the C-S-H phase. For the C-S-H phase. 

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