Tutorial on a chemical model building by least-squares non-linear regression of multiwavelength spectrophotometric pH-titration data

Although the modern instrumentation enables for the increased amount of data to be delivered in shorter time, computer-assisted spectra analysis is limited by the intelligence and by the programmed logic tool applications. Proposed tutorial covers all the main steps of the data processing which involve the chemical model building, from calculating the concentration profiles and, using spectra regression, fitting the protonation constants of the chemical model to multiwavelength and multivariate data measured. Suggested diagnostics are examined to see whether the chemical model hypothesis can be accepted, as an incorrect model with false stoichiometric indices may lead to slow convergence, cyclization or divergence of the regression process minimization. Diagnostics concern the physical meaning of unknown parameters beta(qr) and epsilon(qr), physical sense of associated species concentrations, parametric correlation coefficients, goodness-of-fit tests, error analyses and spectra deconvolution, and the correct number of light-absorbing species determination. All of the benefits of spectrophotometric data analysis are demonstrated on the protonation constants of the ionizable anticancer drug 7-ethyl-10-hydroxycamptothecine, using data double checked with the SQUAD(84) and SPECFIT/32 regression programs and with factor analysis of the INDICES program. The experimental determination of protonation constants with their computational prediction based on a knowledge of chemical structures of the drug was through the combined MARVIN and PALLAS programs. If the proposed model adequately represents the data, the residuals should form a random pattern with a normal distribution N(0, s2), with the residual mean equal to zero, and the standard deviation of residuals being near to experimental noise. Examination of residual plots may be assisted by a graphical analysis of residuals, and systematic departures from randomness indicate that the model and parameter estimates are not satisfactory.     

The thermodynamic dissociation constants of losartan, paracetamol, phenylephrine and quinine by the regression analysis of spectrophotometric data

The mixed dissociation constants of four drug acids - losartan, paracetamol, phenylephrine and quinine - at various ionic strengths I of range 0.01 and 1.0 and at temperatures of 25 and 37 °C were determined using SPECFIT32 and SQUAD(84) regression analysis of the pH-spectrophotometric titration data. A proposed strategy of efficient experimentation in a dissociation constants determination, followed by a computational strategy for the chemical model with a dissociation constants determination, is presented on the protonation equilibria of losartan. Indices of precise methods predict the correct number of components, and even the presence of minor ones when the data quality is high and the instrumental error is known. Improved identification of the number of species uses the second or third derivative function for some indices, namely when the number of species in the mixture is higher than 3 and when, due to large variations in the indicator values even at logarithmic scale, the indicator curve does not reach an obvious point where the slope changes. The thermodynamic dissociation constant was estimated by nonlinear regression of {pK_a, I} data at 25 and 37 °C: for losartan and 3.57(3), and 4.80(3), for paracetamol and 9.65(1), for phenylephrine and 8.95(1), and 10.22(1), for quinine and 4.12(1), and 8.46(2). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates to be found.     

The thermodynamic dissociation constants of ambroxol, antazoline, naphazoline, oxymetazoline and ranitidine by the regression analysis of spectrophotometric data

The mixed dissociation constants of five drug acids—ambroxol, antazoline, naphazoline, oxymetazoline and ranitidine—at various ionic strengths I of range 0.01 and 1.0 and at temperatures of 25 and 37 °C were determined using SQUAD(84) regression analysis of the pH-spectrophotometric titration data. A proposed strategy of efficient experimentation in a protonation constants determination, followed by a computational strategy for the chemical model with a protonation constants determination, is presented on the protonation equilibria of ambroxol. The thermodynamic dissociation constant pK_a^T was estimated by non-linear regression of {pK_a, I} data at 25 and 37 °C: for ambroxol and 8.25 (4), log  and 11.83 (8), for antazoline and 7.83 (6), and 9.55 (2), for naphazoline and 10.63 (1), for oxymethazoline and 10.77 (7), pK_a,2^T=12.03(3) and 11.82 (4) and for ranitidine and 1.77 (1). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates to be found.     

Thermodynamic dissociation constants of silychristin, silybin, silydianin and mycophenolate by the regression analysis of spectrophotometric data

Mixed dissociation constants of four drug acids, i.e. silychristin, silybinin, silydianin and mycophenolate at various ionic strengths I of range 0.01 and 0.30 and at temperatures of 25 and 37 °C were determined using the SQUAD(84) regression analysis program applied to pH-spectrophotometric titration data. The proposed strategy of an efficient experimentation in a protonation constants determination, followed by a computational strategy for the chemical model with a protonation constants determination, is presented on the protonation equilibria of silychristin. The thermodynamic dissociation constant pK_a^T was estimated by non-linear regression of {pK_a, I} data at 25 and 37 °C: for silychristin pK_a,1^T=6.52(16) and 6.62(1), pK_a,2^T=7.22(13) and 7.41(5), pK_a,3^T=8.96(9) and 8.94(9), pK_a,4^T=10.17(7) and 10.03(8), pK_a,5^T=11.89(4) and 11.63(7); for silybin pK_a,1^T=7.00(4) and 6.86(5), pK_a,2^T=8.77(11) and 8.77(3), pK_a,3^T=9.57(8) and 9.62(1), pK_a,4^T=11.66(3) and 11.38(1); for silydianin pK_a,1^T=6.64(7) and 7.10(6), pK_a,2^T=7.78(5) and 8.93(1), pK_a,3^T=9.66(9) and 10.06(11), pK_a,4^T=10.71(7) and 10.77(7), pK_a,5^T=12.26(5) and 12.14(5); for mycophenolate pK_a^T=8.32(1) and 8.14(1). Goodness-of-fit tests for various regression diagnostics enabled the reliability of parameter estimates to be found.     

The thermodynamic dissociation constants of methotrexate by the nonlinear regression and factor analysis of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of methotrexate — chemically (2S)-2-[(4-{[(2,4-diamino-7,8-dihydropteridin-6-yl)methyl] (methyl)amino}phenyl)formamido]pentanedioic acid (the cas number 59-05-2) at various ionic strengths I of range 0.01–0.4, and at temperatures of 25°C and 37°C, were determined with the use of two different multiwavelength and multivariate treatments of spectral data, SPECFIT32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis according to a general rule of first, determining the number of components, and then calculating the spectral responses and concentrations of the components. Concurrently, the experimental determination of the thermodynamic dissociation constants was in agreement with its computational prediction of the PALLAS programme based on knowledge of the chemical structures of the drug. The factor analysis in the INDICES programme predicts the correct number of light-absorbing components when the data quality is high and the instrumental error is known. Three thermodynamic dissociation constants were estimated by nonlinear regression of {pK _a , I} data: for methotrexate pK_a1^T= 2.895(13), pK_a2^T= 4.410(14), pK_a3^T= 5.726(15) at 25°C and pK_a1^T= 3.089(15), pK_a2^T= 4.392(12), pK_a3^T= 5.585(11) at 37°C, where the figure in brackets is the standard deviation in last significant digits. The reliability of the dissociation constants of the drug were proven by conducting goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data.      

Reliability and uncertainty in the estimation of p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> by least squares nonlinear regression analysis of multiwavelength spectrophotometric pH titration data

When drugs are poorly soluble then, instead of the potentiometric determination of dissociation constants, pH-spectrophotometric titration can be used along with nonlinear regression of the absorbance response surface data. Generally, regression models are extremely useful for extracting the essential features from a multiwavelength set of data. Regression diagnostics represent procedures for examining the regression triplet (data, model, method) in order to check (a) the data quality for a proposed model; (b) the model quality for a given set of data; and (c) that all of the assumptions used for least squares hold. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high leverages, that cause many problems when regression fitting the absorbance response hyperplane. All graphically oriented techniques are suitable for the rapid estimation of influential points. The reliability of the dissociation constants for the acid drug silybin may be proven with goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data. The uncertainty in the measurement of the pK _a of a weak acid obtained by the least squares nonlinear regression analysis of absorption spectra is calculated. The procedure takes into account the drift in pH measurement, the drift in spectral measurement, and all of the drifts in analytical operations, as well as the relative importance of each source of uncertainty. The most important source of uncertainty in the experimental set-up for the example is the uncertainty in the pH measurement. The influences of various sources of uncertainty on the accuracy and precision are discussed using the example of the mixed dissociation constants of silybin, obtained using the SQUAD(84) and SPECFIT/32 regression programs.