VERSE model

Extension of the VERSE Model to Nonlinear Gradient Elution Chromatography 724... 

The VERSE model includes the following equations, reported in dimensionless form [65]. 

To allow for a wide variety of aggregation reactions, the VERSE model [65] uses the following set of basic reactions from which more complex sequences may be built if necessary. 

Only numerical solutions of the VERSE model can be obtained [65]. The partial differential equations are discretized by application of the method of orthogonal collocation on fixed finite elements. Equation 16.59 is divided into 50 or 60 elements, each with four interior collocation points. Legendre polynomials are used for each element. For Eq. 16.62, only one element is required. It is described by a Jacobi polynomial with two interior collocation points. The resulting set of ordinary differential equations, with their initial and boundary conditions and the chemical equations, are solved using a differential algebraic system solver (DASSL) [65,66]. 

Experimental data on the aggregation of myoglobin and j3-lactoglobulin A previously obtained were used to verify the validity of the VERSE model. The first set... 

The second set of experimental data used for verification of the VERSE model was the experimental data of jS-lactoglobulin A reported by Karger and Blanco... 

Figure 16.26 shows that the calculated results closely match the relative peak area ratio and the retention times reported by Karger and Blanco [67]. These authors had also shown that, at higher concentrations, the formation of the octamer and the dodecamer is favored over that of the tetramer and that their corresponding peaks are more pronounced. This behavior is well predicted by the VERSE model (see Figure 16.26)... 

As expected, a lot of work, estimation and guessing goes into model development. In this estimation the developer should rely on the help and advice of both a chemist knowledgeable about similar mechanisms, and a statistician versed in the appropriate mathematics. 

Figure 26 shows plots of this constriction factor verses porosity for various values of L. As observed in Figure 21 for the Michaels model of diffusion in such a cell, the percolation limits are seen where the constriction factor goes to zero at = L/(l + L). 

The model compound anilinostearamide 78, labelled in the aliphatic chain only, prepared subsequently by the reduction of linoleic precursor 79 with hydrogen or deuterium (equation 30), exhibited a chromatographic isotope effect of similar magnitude. The labelled compound elutes on the re versed-phase HPLC prior to the unlabelled one. 

There are a number of ways to model calibration data by regression. Host researchers have attempted to describe data with a linear function. Others ( 4,5 ) have chosen a higher order or a polynomial method. One report ( 6 ) compared the error in the interpolation using linear segments over a curved region verses using a curvilinear regression. Still others ( 7,8 ) chose empirical or spline functions. Mixed model descriptions have also been used ( 4,7 ). 

Amount Transformation. Step 2. The amount transformation was performed in a way similar to that of response by use of a power series but for a different reason. In this case linearity was desired in order to use a simple linear regression model. This transformation therefore required a test for satisfactory conformity. One can use a variety of criteria including the correlation coefficient or visual examination of the plot of rgsiduals verses amount. We chose the F test for lack of fit,... 

However, there are prices to pay for the advantages above. Most empirical modeling techniques need to be fed large amounts of good data. Furthermore, empirical models can only be safely applied to conditions that were represented in the data used to build the model (i.e., extrapolation of such models is very dangerous). In addition, the availability of multiple response variables for building a model results in the temptation to overfit models, in order to obtain artificially optimistic results. Finally, multivariate models are usually much more difficult to explain to others, especially those not well versed in math and statistics. 

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Polymers have also been used for the coating of alumina. Thus, maleic acid adsorbed onto the alumina surface was, in situ, polymerized with 1-octadecene and cross-linked with 1,4-divinylbenzene. It was assumed that the polymer forms a monolayer on the alumina, forming a re versed-phase surface. This assumption was substantiated by results showing that the retention order of model compounds was the same as on an ODS column. The lower separation capacity of the new stationary phase was tentatively explained by the lower surface porosity of alumina. Principal component analysis was employed for the elucidation of the relationship... 

Most RP-HPLC separations are done in the iso-cratic mode (i.e., where the composition of the mobile phase is held constant during the analysis). This approach is suitable when the sample consists of analytes having similar properties or where their hydrophobic-ities encompass a small or moderate range. Under these conditions, all solutes in the sample will be eluted over a reasonable time span (i.e., not too short to prevent resolution of individual analytes and not too long to result in an inconvenient analysis period). Therefore, proper selection of the mobile-phase composition is essential in the development of any re-versed-phase separation method. Fortunately, due to the decades of long practice of RP-HPLC, there exists in the literature and from commercial sources, a wealth of information on suitable mobile-phase compositions for particular types of sample, especially for the Cig stationary phase. In addition, the retention of solutes on hydrophobic phases has been modeled mathematically and there exist computer programs for assisting in the optimization of mobile-phase composition in the solution of various separation problems. 

The VERSE method was extended to describe the consequences of protein denat-uration on breakthrough curves in frontal analysis and on elution band profiles in nonlinear isocratic and gradient elution chromatography [69]. These authors assumed that a unimolecular and irreversible reaction taking place in the adsorbed phase accoimts properly for the denaturation. The choice of this reaction was based on numerous literature observations of the irreversible adsorption of proteins on hydrophobic surfaces [70]. This model (VERSE-LC) was verified using... 

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