Window, tolerance

One of the problems with the current version of the program is due to the fact that the comparison of the Rf values requires an exact match. Experimental values will always have some random error. We should therefore compare the Rf values with tolerance. We thus need a rule to decide whether two Rf values are sufficiently close to be considered as equal. This rule, which we will call rfmatch should check whether the value of A is within a tolerance window of 2 Tol centered at the value of B. 

To implement such a rule we need to do some arithmetics to determine the position of the limits of the tolerance window. PROLOG is not an arithmetic language. Thus handling of numerical calculations is somewhat clumsy. The standard arithmetic operators are part of the language. However, they are interpreted as specifying a relation between numbers rather than as commands to perform a calculation. In particular, the operator = signifies equality, but does not trigger the evaluation of an arithmetic expression. 

With the existing version of the PROLOG program the predicate hrf allows for retrieving the Rf values for the compounds in the data base. Backtracking supplies this information for other TLC systems. The same predicate used with the variable for the Rf value instantiated returns the names of compounds with Rf values within the range specified by the tolerance window. The predicate sep checks whether there is a TLC system that separates the two compounds specified. 

If the abundances of the entire ethanol contracted spectrum are lowered — keeping their relative heights the same as in the reference spectrum — a point is reached where none of the unknown ions is of lower abundance than the corresponding ethanol peaks. In the example shown in Figure 7, this occurs when the mass 46 ions become the same height. If a measurement reproducibility of 20% is assumed, two other ions (m/e 43 and 45) are found to agree with the abundances required by the ethanol reference spectrum because they fall within the prescribed tolerance window. In this example, the mixture was about 50% ethanol the excess intensities at m/e 31 and 32 were due to methanol and the excess intensity at m/e 44 was due to the additional presence of CO2. 

If the laboratory protocol requires three ions to be within a tolerance window to identify a substance, it is not permissible to collect additional ions and select those ion ratios that are within tolerance and ignore others that would not result in meeting identification criteria without valid explanation. 

Table 1 Maximum tolerance windows for relative ion intensities to ensure appropriate uncertainty in identification (adapted from the WADA Laboratory International Standard)...

The high-resolving power of the MSI system described here and the capability to extract m/z ratios with narrow tolerance windows allows us to see in color-coded manner that peptides with similar m/z ratios can be localized to different areas of the tissue. This is exemplified for three different peptides with monoisotopic (singly charged) w/z ratios of 1,010.590 (green), 1,010.472 (blue), 1,011.410 (red) in Fig. 25.8 seelSiotc 8). 

The algorithm isotopic pattern filter is based on the accurate m/z of ions, where the m/z differences of selected isotopic ion-pairs (e.g. M-t 1 M and M+2 M, where M is the monoisotopic peak and M -h 1 and M+2 are the first and the second isotopic peak) must fall into the pre-assigned accurate mass tolerance window (e.g. 5 ppm), so satisfying the predefined relative abundance criteria. These filters are based on the isotopic pattern deviation between the empirically measured spectrum and the theoretical spectrum. The application of carbon, chlorine, bromine or sulfur filters also allows reduction of the number of proposed elemental compositions that would fit for a certain mass-accuracy window, as their presence in the molecule produces a characteristic isotopic distribution. The additional information obtained from the isotopic signature reduces dramatically the number of proposed calculated empirical formulae to a number typically below 5. The reduced number of elemental compositions can be searched in databases using elemental composition as the search criterion (e.g. Merck Index, Chemindex, catalogues of standards manufacturer, and Google). 

Biuckner, T. Schellnhuber, H.J., 1999 Climate Change Protection The Tolerable Windows Approach , IPTS Report, 34 6. 

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