The thermodynamic dissociation constants of the anticancer drugs camptothecine, 7-ethyl-10-hydroxycamptothecine, 10-hydroxycamptothecine and 7-ethylcamptothecine by the least-squares nonlinear regression of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of four anticancer drugs - camptothecine, 7-ethyl-10-hydroxycamptothecine, 10-hydroxycamptothecine and 7-ethylcamptothecine, including diprotic and triprotic molecules at various ionic strengths I of range 0.01 and 0.4, and at temperatures of 25 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. A proposed strategy for dissociation constants determination is presented on the acid-base equilibria of camptothecine. Indices of precise modifications of the factor analysis in the program INDICES 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. The thermodynamic dissociation constant was estimated by nonlinear regression of {pK_a, I} data at 25 and 37 °C: for camptothecine and 3.02(8), and 10.23(8); for 7-ethyl-10-hydroxycamptothecine, and 2.46(6), and 8.74(3), and 9.47(8); for 10-hydroxycamptothecine and 2.84(5), and 8.92(2), and 9.98(4); and for 7-ethylcamptothecine and 3.30(16), and 10.98(18). Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates found to be proven. Pallas and Marvin predict pK_a being based on the structural formulae of drug compounds in agreement with the experimental value.     

A novel computational strategy for the pKa estimation of drugs by non‐linear regression of multiwavelength spectrophotometric pH‐titration data exhibiting small spectral changes

A new computational procedure for the protonation model building of a multiwavelength and multivariate spectra treatment is proposed for the special case of small changes in spectra. The absorbance change Δ_i for the ith spectrum divided with the instrumental standard deviation s_inst(A) represents the signal‐to‐error ratio SER of the spectra studied. The determination of the number of chemical components in a mixture is the first important step for further quantitative analysis in all forms of spectral data treatment. Most index‐based methods of the factor analysis can always predict the correct number of components, and even the presence of a minor one, when the SER is higher than 10. The Wernimont–Kankare procedure in the program INDICES performs reliable determinations of the instrumental standard deviation of the spectrophotometer used s_inst(A), correctly predicts the number of light‐absorbing components present, and also solves ill‐defined problems with severe collinearity in spectra or very small changes in spectra. The mixed dissociation constants of three drugs, haemanthamine, lisuride, and losartan, including diprotic molecules at ionic strengths of I = 0.5 and 0.01 and at 25°C were determined using two different multiwavelength and multivariate treatments of the spectral data, SPECFIT32 and SQUAD(84) non‐linear regression analyses and INDICES factor analysis, even in the case of small absorbance changes in spectra. The dissociation constant pK_a was estimated by non‐linear regression of {pK_a, I} data at 25°C: for haemanthamine pK_a = 7.28(1) at I = 0.50, for lisuride pK_a = 7.86(1) and for losartan pK_a,1 = 3.60(1), pK_a,2 = 4.73(1) at I = 0.01. Goodness‐of‐fit tests for the various regression diagnostics enabled the reliability of the parameter estimates found to be proven. PALLAS and MARVIN predict pK_a being based on the structural formulae of the drug compounds in agreement with the experimental value. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.