Multiparametric curve fitting--VIII: The reliability of dissociation constants estimated by analysis of absorbance-pH curves

The program SPOPT estimates stability constants beta(pqr) and molar absorptivities epsilon(pqr) of all light-absorbing species M(p)L(q)H(r) by analysis of the absorbance-concentration (or absorbance-pH) curve. The program DCMINUIT estimates dissociation constants and molar absorptivities of protonated species. Both programs have been tested and compared with DCLET and LETAGROP-SPEFO for analysis of the overlapping equilibria of a triprotic acid. Computer plots of the residual-square-sum function are used to test the conditioning of parameters. Two approaches are made to formulation of the mathematical model, and several optimization algorithms are tested to find a reliable minimization procedure. The accuracy of ill-conditioned parameters is shown to be dependent on the precision of the absorbance measurements. General rules for investigation of A -pH curves are recommended.     

Computer estimation of dissociation constants. Part V. Regression analysis of extended Debye-Hueckel law

Nonlinear regression program DHMINOPT has been used for an analysis of a set of values expressing the dependence of mixed dissociation constant on ionic strength according to the extended Debye-Hueckel law. Efficiency of program has been examined on simulated data loaded with generated random errors. Goodness-of-fit brings various regression diagnostics enabling to prove a reliability of a regression process and parameter estimates. For five selected sulphonephtalein indicators, i.e. Bromocresol Green, Bromophenol Red, Bromocresol Purple, Bromothymol Blue and Phenol Red, the thermodynamic dissociation constant has been determined at 25°C together with the ion-size parameter and the salting-out coefficient.Previous Part IV.: Mikrochim. Acta1992,108, 227.     

Multiparametric curve fitting-IV Computer-assisted estimation of successive dissociation constants and of molar absorptivities from absorbance-pH curves by the DCLET program

The program DCLET evaluates the dissociation (or protonation) constants and molar absorptivities (HjL) of all light-absorbing species (HjL), (j = 0,..., J) of a polyprotic acid (HjL) by a non linear regression of the function A = f(pH; pK (a), (HjL)), i.e., by multiparametric curve fitting. The three specific subroutines DATADC, UBBEDC, SKRDC described form part of the general program ABLET. The goodness of fit is tested by statistical examination of the residuals. Heuristic or algorithmic strategies of minimization may be used, and experimental or synthetic data may be processed. By examining the effects on the results of varying the density and distribution of points of a synthetic data set, it is possible to improve the planning of experiments, and by introducing parametric weight, to improve the sensitivity of a particular parameter in a model.     

Computer estimation of dissociation constants. Part IV. Precision and accuracy of potentiometric determinations

The protonation constants logK _Hj of the acidH _J are determined by regression analysis of potentiometric titration data whencommon parameters (logK _Hj,j = 1,...,J) andgroup parameters (E ⁰,L ₀,H _T ) are refined. Two kinds of systematic error have been investigated: the error from an uncertainty of group parameters and the error from a computational strategy of the minimization algorithm used. An analysis of variance of logK _Hj matrix was made for 6 reproduced titrations and 7 computational strategies of 6 various regression programs. It was concluded that the influence of the program used is negligible. From two ways of calibration of the glass electrode cell,the internal calibration (performed during titration) was slightly more accurate thanthe external calibration (done separately). Of programs tested, the ESAB and ACBA are most powerful because they permit refinement of group parameters and internal calibration. D-tartaric acid was chosen as model substance.Previous Part III.: Iraqi J. Sci.1981,22, 67.     

Multiparametric curve fitting-IX Simultaneous regression estimation of stoichiometry and stability constants of complexes

A chemical model (i.e., the number of complexes, their stoichiometry and stability constants with molar absorptivities) in solution equilibria may be established by (i) the trial-and-error method in which stability constants are estimated for an assumed set of complexes in the mixture and a fitness test is used to resolve a choice of plausible models to find the true one; (ii) the simultaneous estimation of the stoichiometry and stability constants for species divided into "certain" species for which the parameters beta(pqr), (p, q, r) are known and held constant, and "uncertain" species with unknown parameters which are determined by regression analysis. The interdependence of stability constants and particular sets of stoichiometric indices requires that the computational strategy should be chosen carefully for each particular case. The benefits and limitations of both approaches are compared by means of examples of potentiometric titration data analysis by the POLET(84) program and of spectrophotometric data analysis by the SQUAD(84) program. A strategy for efficient computation is suggested.     

Thermodynamic dissociation constants of isocaine, physostigmine and pilocarpine by regression analysis of potentiometric data

Concentration and mixed dissociation constant(s) of three drug acids, H(J)L, isocaine, physostigmine and pilocarpine, at various ionic strengths, I, in the range 0.03-0.81 and 25 degrees C have been determined with the use of regression analysis of potentiometric titration data when common parameter, pK(a), and group parameters E'(0), L(0), and H(T) are simultaneously refined. Internal calibration of the glass electrode cell in the concentration scale [H(+)] performed during titration was used. The estimate of ill-conditioned group parameters has a great influence on a systematic error in estimated pK(a) and therefore it makes the computational strategy important. As more group parameters are refined and a better fit achieved, a more reliable estimate of dissociation constants results. The thermodynamic dissociation constant, pK(a)(T), an ill-conditioned ion-size parameter, ?, and the salting-out coefficient, C, were estimated by non-linear regression of {pK(a), I} data and an extended Debye-Hückel equation. The goodness-of-fit test based on regression diagnostics is a measure of the reliability of parameters, and proves that reliable estimates for isocaine pK(a)(T)(=)8.96(1), ?=8(3) A and C=0.50(3) at 25 degrees C, for physostigmine pK(a)(T)(=)8.07(3), ?=19(26) A and C=0.64(3) at 25 degrees C, and for pilocarpine pK(a)(T)(=)7.00(1), ?=7(1) A and C=0.53(2) at 25 degrees C were found.     

Multiwavelength spectrophotometric determination of acid dissociation constants Part IV. Water-insoluble pyridine derivatives

A multiwavelength spectrophotometric (WApH) titration method for determination of acid dissociation constants (pK(a) values) of ionizable compounds developed previously was applied in the case of pyridine derivatives of pharmaceutical interest. Specifically, UV absorption spectra of the drug solution are acquired in the course of a pH-metric titration using an optical device based on a fibre optics dip probe, a light source and a diode array detector. Target factor analysis was applied to deduce the pK(a) values from the spectral data recorded at different pH. Using this technique, the pK(a) values of six pyridine derivatives were determined successfully. It was demonstrated that the WApH technique in this case outperforms conventional pH-metric methods with respect to the measurement of pK(a) values of the sparingly water soluble samples reported in this study.     

Computation in kinetics, II. Simultaneous regression estimation of rate constants and initial concentrations

The general regression program KILET was used for simultaneous estimation of rate constants and initial concentrations. The method can be used either to improve the quality of fit calculating the possible analytical errors of some initial concentrations of a kinetic experiment or for analytical purposes, i.e. for the determination of analytes, while any side reactions can be taken into account.

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KILET - . - - , - , , .

     

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.      

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 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.     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part I. Theory

Measured additive properties of polyprotic acids and bases as functions of the pH of the solution can be used for the determination of the dissociation constants. A rigorous general equation is derived in this paper for this purpose. The equation relates the additive property of the acid or base to the dissociation constants, the limiting values and activity coefficients of the solute species, and to the pH of the solution. The equation is used to obtain the dissociation constants by fitting it to the experimental data in a nonlinear least-square fitting procedure. Overlapping dissociation constants pose no problem in this method. Applications to spectrophotometry and reversed-phase high performance liquid chromatography are presented in a following paper (Part II of this series).     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part II. Applications

Dissociation constants of some polyprotic acids and bases are determined from spectrophotometric and reversed-phase high performance liquid chromatographic data. A general equation relating additive properties of acids and bases to the pH of the solution is used for this purpose. The method is tested by applying it to the calculation of overlapping pK_as without the prerequisite of measuring the limiting values of the property for the individual species that result from the dissociation of the solute. The possibility of applying the same method to hyperpolarizability measurements is pointed out, and a procedure, based on the general equation, for obtaining the activity coefficients of the ionic species as a function of the ionic strength is also suggested.     

The reactions of diphenylcarbazide and diphenylcarbazone with cations : Part V. Extraction dissociation constants of the carbazone complexes

Extraction experiments in the system water-toluene on the diphenylcarbazone complexes of Mn(II), Fe(II) and (III). Co(II), Ni(II), Cu(ll), Zn(ll), Cd(II), Hg(I) and (II), Sn(II) and Pb(II) are described. Only uncharged complexes are formed, the formulae of which are for mercury HgD, Hg(HD)₂, Hg₂D and Hg₂(HD)₂ and for the other ions mentioned M(HD)_n, depending on the valence _n of the cation. The extraction dissociation constants, the molar extinction coefficients and the partition coefficients of the complexes funned by the cations studied were obtained, The complexes prove to be far less stable than the corresponding dithizone compounds so that diphenylcarbazone is less suitable for general analytical use than its sulphur analogue.     

Ab initio computation of force constants: Part VI. Applications of the force relaxation method for geometry optimization

Techniques to improve the computational efficiency of the force relaxation method are discussed. Force constants for fragments in previously computed smaller molecules can be transferred to construct a guess force constant matrix. Additional force constants that may be needed can be computed by a procedure which uses only one additional force calculation per diagonal force constant required. A scaling technique to improve convergence on the optimized geometry is discussed.     

Electrophoretic mobility and dissociation constants of tripeptides evaluated by isotachophoresis.

Ionic mobilities and dissociation constants of twenty peptides (seventeen tripeptides and a few oligoglycines) were evaluated on the basis of the observed isotachophoretic qualitative indices RE in the pH range 8.1-9.5 by the use of a least-squares method. Good correlation was obtained among the mobilities of amino acids, dipeptides and tripeptides when the clay ball model and the conventional formula weight were adopted.     

Fluorimetric determination of dissociation constants and ph-controlled fluorescence analysis of purines and pyrimidines

Fluorimetrically determined pH-titration curves have been obtained for twelve purines and pyrimidines at room temperature, in aqueous solution. The pK(a) values for these compounds have been determined fluorimetrically and potentiometrically. Except for 6-mercaptopurine and uric acid, there is close agreement between the two sets of pK(a) values, but a large difference for the corresponding excited singlet-state values, pK(S1)(a), which were calculated previously. This indicates that the excited singlet-state proton-transfer rate is much slower than the fluorescence-decay rate of purines and pyrimidines in our experimental conditions. A direct, simple, pH-controlled fluorimetric method is proposed for the determination of purines and pyrimidines. The limits of detection vary between 60 ng ml and 5.4 mug ml .