Dilutions linear series

Dilution linearity was evaluated with three serum samples. Dilution was conducted by preparing 2 folds serial dilution series. Expected values of the diluted samples were calculated from the concentrations measured in the undiluted sample. 

A bioequivalence study was conducted in nonhuman primates to assess in vivo equivalence for the two forms of the drug. In preparation for sample analysis, the assays were optimized and standard curves were prepared using each form of the protein in study matrix. In addition, spiked controls were serially diluted and each series was measured in the N-and C-terminus-specific assays. The results for the C-terminus assay were equivalent, as shown in Fig. 9.3, demonstrating acceptable dilutional linearity with either sample type. However, as one can see in Fig. 9.4, the N-terminus assay clearly does not equivalently recognize the two forms of the drug. 

The sensitivity of an immunoassay is typically defined by its LLOQ, which can only be determined when a reference standard is available. Alternatively, a detection limit of qualitative assays is used where a distinction is essentially made between positive and negative results only. Typically, the antibody data are reported as titer, the titer being the reciprocal of the highest dilution of a sample in which the instrument response is greater than the cutoff response [22]. At least two positive control analytes should be used. If a positive control antibody is available, a pseudocalibration curve can be generated by a series of dilutions. However, one should keep in mind that true quantitation is impossible because of the lack of a true reference compound. Determination of the dilutional linearity is not so important when the result is reported as a titer. However, if the determination of positive samples is based on the interpolation from a reference standard curve, it is essential to demonstrate that the QC samples fall within the (limited) linear range of the calibration curve and not on a plateau or a region that may include a hook effect. 

Data Analysis The results were plotted at first glance a linear regression of absorbance versus concentration appeared appropriate. The two dilution series individually yielded the figures of merit given in Table 4.17, bottom. The two regression lines are indistinguishable, have tightly defined slopes. 

The linearity of the detector can be obtained by diluting the analyte stock solution and measuring the associated responses, while the linearity of the analytical method can be determined by making a series of concentrations of the analyte from independent sample preparations (weighing and spiking) [15]. It is also essential that the basic calibration linear curve be obtained by using independent samples, and not by using samples that have been prepared by dilution and injected into HPLC/GC, or spotted on one TLC plate. 

Add an aliquot of the hydrazine-modified protein solution to the p-nitrobenzaldehyde solution and incubate at 37°C for 1 hour or at room temperature for 2 hours. To assure accuracy, determine the linear response range of the test by adding a series of different concentrations of the hydrazine-modified protein solution to the p-nitrobenzaldehyde buffer. This is done by preparing a set of serial dilutions of the protein solution and... 

To evaluate linearity, limits of detection (LOD), limits of quantitation (LOQ), and sensitivity, an experiment assessed the responses for different concentrations of two analytes of interest. The analytes employed were methyl paraben and rhodamine 110 chloride. Consecutive 5.0 /jL injections of a series of serial dilutions (four replicates) of this standard mixture containing the analytes described were carried out via a cartridge packed with C18 stationary phase and per-column dimensions of 0.5 mm circular cross section and 80 mm length. 

Figure 8.5 Transmission infrared spectra of CO adsorbed at room temperature on a series of silica-supported Pd-Ag alloys. CO adsorption on Ag is negligible. The dashed spectra are for higher CO exposures (0.5 Torr), the full spectra for low exposures (0.01 Torr). On pure Pd, CO adsorbs predominantly on multiple sites (frequen-cies below 2000 cm"1). As Pd becomes diluted with Ag, linearly bonded CO becomes dominant, indicating that ensembles of two or more Pd atoms to accommodate multiply bonded CO are no longer present, (from Soma-Noto and Sachtler [18]).

The best way to accomplish this is to prepare standards in the usual way—add increasing volumes of a standard analyte solution to a series of volumetric flasks (include zero added)—but also add a volume of the sample solution to each before diluting to the mark with solvent. Thus you would have a series of standards in which the concentration of analyte added would be known, the smallest concentration added being zero. Exactly how much sample solution is used and what concentration added values would be prepared would be dictated by what concentration levels, with additions, would produce a linear standard curve. In any case, a diluted sample matrix is present in each standard and the matrices are matched. A disadvantage is that it is impossible to prepare a blank with a matched matrix. Thus, a pure solvent blank, or other approximation, must be used. 

A detailed investigation of the polymerization of this monomer in a series of solvents has shown, however, that the auto-accelerated character of the reaction is not related to the precipitation of the polymer. Thus, linear conversion curves and atactic polymers are obtained if the monomer is diluted in such nonassociating solvents as toluene, n-hexane, carbon tetrachloride and chloroform, in spite of the precipitation of the polymer, whereas, both auto-acceleration and syndiotacticity persist for fairly high dilutions in water, methanol and dioxane even under conditions where the reaction medium turns homogeneous (4). 

Concentrations in the region of 0.1 mol 1 1 are often convenient but it obviously depends upon such factors as the amount of substance available, the cost, the solubility, etc. From this stock solution, a series of accurate dilutions are prepared using volumetric glassware and the absorbance of each dilution measured in a 1-cm cuvette at the wavelength of maximum absorbance for the compound. A plot of absorbance against concentration will give an indication of the validity of the Beer-Lambert relationship for the compound and a value for the molar absorption coefficient may be calculated from these individual measurements or from the slope of the linear portion of the graph ... 

Since van t Hoff s law is valid only for infinitely diluted solutions, one develops Iloj/c in power law series (break after the linear term in c)... 

Dose-response curves are generated from the two sets of data ( + S9 and — S9) by running two series of plates prepared from a range of serial dilutions (duplicate or triplicate plates for each dilution) of the original sample. The slope of the ideally linear portion of this curve is the specific activity of a pure chemical and is expressed in units of revertants per microgram (rev pg 1) or revertants per nanomole (rev nmob1). 

Wada 109, 110) pioneered studies of polypeptide conformation by the dielectric method. He found 110) a linear dependence of (ft2)1 2 on Mw for a series of PBLG samples (ranging from 7 x 104 to 18 x 104 in Mw) in EDC at 25° C and obtained 3.5 D for gh, where D stands for debye units. He computed (ft2) by the use of an approximate equation derived by himself 109) for rigid-rod molecules, which for very dilute solutions may be written... 

To obtain a useful approximate solution of the PB equation (S8.6-4), we consider the dilute limit in which the electric potential O is weak compared with the ambient thermal energy kT. In this limit, the Boltzmann exponential can be linearized by retaining only the leading term in the power series expansion... 

Stepwise hydrolysis is much more feasible in the case of dialkoxydi-alkyl- or dialkoxydiarylsilanes, for one reason because these may be hydrolyzed in the presence of only catalytic amounts of acidic or alkline reagents. The simplest examples of this class were recently described by Lasocki (37) who hydrolyzed dimethyldimethoxysilane, using 0.75 mole of water per mole of Me2Si(OMe)2 and dilute alcoholic methanol as the solvent, to obtain members of the series, MeO(SiMe20)nMe (n = 2-10). Some cyclic poly(dimethylsiloxanes) were formed simultaneously. The ratio of linear to cyclic products varied with the proportion of water to methoxysilane and with the amount of base used as catalyst. Similar observations were made by Matsui (39). 

Kcto cnol tautomerization reactions usually exhibit general acid and general base catalysis (section General Acid and General Base Catalysis ). The rate coefficients for general acid catalysis, kHA, determined from a series of buffer dilution plots (Fig. 4) tend to obey a linear log-log relationship to the acidity... 

In a long series of papers on the master equation, Pritchard and his coworkers elucidated for the first time the effects of rotational and vibrational disequilibrium on the dissociation and recombination of a dilute diatomic gas. Ultrasonic dispersion in a diatomic gas was analyzed by similar computational experiments, and the first example of the breakdown of the linear mixture rule in chemical kinetics was demonstrated. A major difficulty in these calculations is that the eigenvalue of the reaction matrix (corresponding to the rate constant) differs from the zero eigenvalue (required by species conservation) by less than... 

For a binary Ising lattice, we introduced a nonrandom factor that was observed from simulation to have a linear relation with composition. The characteristic parameter of the linear relation was found by combining a series expansion and the infinite dilution properties. On this basis, an accurate expression for the Helmholtz energy of mixing... 

This type of test is called parallel-line assay and is based on the comparison of a sample response with that of a reference standard (Finney, 1978). In general, it determines the response - at least by duplicates - of a series of dilutions of each preparation (sample and standard) while plotting the means of their corresponding doses on a logarithmic scale. As this test requires analysis of a linear portion of the curves, at least three points of each curve belonging to such a portion should be selected. The more selected points, the better the comparison. 

Dose-response curves from dilution series of samples taken at March 24 from the three mesocosms showed a linear relationship between 10 and 70% lysis. For the whole data set the activity at 4°C was approximately half the activity measured at 15°C (value at 4°C = 0.44 x [value at 15°C] + 3.24, n = 21, r2 = 0.963, P, Fig. 6). 

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