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

pH- and Functionalization-Dependent Host-Guest Interactions Between Fluorescein and Various Poly(amidoamine) Dendrimers

Dendrimers are branched macromolecules that can be functionalized with a large variety of chemical moieties. Dendrimers can therefore be specifically designed to interact with target molecules. Although tailored dendrimers hold promise for targeted drug delivery and wastewater cleanup, these applications require more detailed and systematic studies on how dendrimer-guest interactions depend on environmental conditions. In light of this need, we studied pH-dependent interactions between fluorescein and poly(amidoamine) dendrimers with three different terminal groups. Crucially, both fluorescein and dendrimers have multiple protonation equilibria, which can enable interactions in different pH windows through various possible mechanisms. Such interactions are studied through UV-vis and fluorescence spectroscopies, which reveal a redshift that occurs upon fluorescein-dendrimer binding. The resulting pH-dependent spectra are complex but can be analyzed quantitatively with an open-source mathematical protocol. Consequently, we show that fluorescein binds across four pH units with amine-terminated dendrimers, across two units with hydroxyl-terminated dendrimers and does not interact attractively with carboxyl-terminated dendrimers. These functionalization-dependent host-guest interactions stabilize fluorescein's dianionic form and are predominantly electrostatically driven, with likely auxiliary hydrogen and CH-π bonding. Notably, these auxiliary mechanisms appear too weak to drive dendrimer-fluorescein interactions on their own. Overall, this work yields valuable insights into dendrimer-fluorescein association and provides a readily reproducible framework for studying host-guest interactions.

Determination of acid dissociation constants, enthalpy, entropy and Gibbs free energy of the baricitinib by the UV-metric and pH-metric analysis

Baricitinib is a drug used for the treatment of rheumatoid arthritis. It is a selective and reversible inhibitor of Janus kinases 1 and 2, which play an important role in signalling the pro-inflammatory pathway activated in autoimmune disorders such as rheumatoid arthritis. The pH-spectrophotometric and pH-potentiometric titrations allowed the measurement of three or four successive dissociation constants of Baricitinib. Baricitinib neutral LH₂ molecule was able to protonate into two soluble cations LH₄²⁺, LH₃⁺ and dissociate into two soluble anions LH^- and L^2- in pure water. The graph of molar absorption coefficients of differently protonated species versus wavelength indicated that the spectra ε_L, ε_LH, ε_LH2 were the nearly the same for these species and that the spectra ε_LH4 and ε_LH3 were also similar. In the pH range from 2-13, four pK_a´s of spectra analysis were reliably estimated by REACTLAB at I =0.0020 mol. dm^-3 values pK^T_a1 = 3.07, pK^T_a2 = 3.87, pK^T_a3 = 6.27, pK^T_a4 = 12.78 at 25 °C and pK^T_a1 = 3.00, pK^T_a2 = 3.79, pK^T_a3 = 6.12, pK^T_a4 = 12.75 at 37 °C. Potentiometric pH-titration analysis for a higher concentration of 1 × 10^-3 mol. dm^-3 estimated with ESAB at I =0.0001 mol. dm^-3 values pK^T_a1 = 3.69, pK^T_a2 = 3.81, pK^T_a3 = 4.73 at 25 °C and pK^T_a1 = 3.62, pK^T_a2 = 3.73, pK^T_a3 = 4.43 at 37 °C. Molar enthalpy ΔH°, molar entropy ΔS° and Gibbs free energy ΔG° were calculated from the spectra using a dependence ln K to 1/T.

The dissociation constants of the cytostatic bosutinib by nonlinear least-squares regression of multiwavelength spectrophotometric and potentiometric pH-titration data

Potentiometric and spectrophotometric pH-titration of the multiprotic cytostatics bosutinib for dissociation constants determination were compared. Bosutinib treats patients with positive chronic myeloid leukemia. Bosutinib exhibits four protonatable sites in a pH range from 2 to 11, where two pK are well separated (ΔpK>3), while the other two are near dissociation constants. In the neutral medium, bosutinib occurs in the slightly water soluble form LH that can be protonated to the soluble cation LH4(3+). The molecule LH can be dissociated to still difficultly soluble anion L(-). The set of spectra upon pH from 2 to 11 in the 239.3-375.0nm was divided into two absorption bands: the first one from 239.3 to 290.5nm and the second from 312.3 to 375.0nm, which differ in sensitivity of chromophores to a pH change. Estimates of pK of the entire set of spectra were compared with those of both absorption bands. Due to limited solubility of bosutinib the protonation in a mixed aqueous-methanolic medium was studied. In low methanol content of 3-6% three dissociation constants can be reliably determined with SPECFIT/32 and SQUAD(84) and after extrapolation to zero content of methanol they lead to pKc1=3.43(12), pKc2=4.54(10), pKc3=7.56(07) and pKc4=11.04(05) at 25°C and pKc1=3.44(06), pKc2=5.03(08) pKc3=7.33(05) and pKc4=10.92(06) at 37°C. With an increasing content of methanol in solvent the dissociation of bosutinib is suppressed and the percentage of LH3(2+) decreases and LH prevails. From the potentiometric pH-titration at 25°C the concentration dissociation constants were estimated with ESAB pKc1=3.51(02), pKc2=4.37(02), pKc3=7.97(02) and pKc4=11.05(03) and with HYPERQUAD: pKc1=3.29(12), pKc2=4.24(10), pKc3=7.95(07) and pKc4=11.29(05).

Thermodynamic protonation constants of vardenafil by the nonlinear regression of multiwavelength pH-spectrophotometric titration data

pH-spectrophotometric titration data were used to determine protonation constants of vardenafil at different ionic strengths I and temperatures of 25°C and 37°C. The use of two different multiwavelength and the multivariate treatment of spectral data, SPECFIT32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis is presented. The reliability of the protonation constants of the drug was proven with goodness-of-fit tests of the pH-spectra. The thermodynamic protonation constants log K Ti were estimated by a nonlinear regression of (log K, I) data using the Debye-Hückel equation, yielding log K 4T = 3.59(1) and 3.26(1), log K 3T = 5.64(1) and 5.81(1), log K 2T = 9.41(1) and 8.59(2), log K 1T = 10.92(2) and 10.05(1) at 25°C and 37°C, where the figure in brackets is the standard deviation in last significant digit. Concurrently, the experimental determination of four thermodynamic protonation constants was combined with the computational prediction of the MARVIN program based on knowledge of the chemical structures of the drug and was in good agreement with its experimental value. The factor analysis of spectra in the INDICES program predicts the correct number of light-absorbing components when the instrument error is known and when the signal-to-error ratio SER is higher than 10.

Thermodynamic dissociation constants of risedronate using spectrophotometric and potentiometric pH-titration

Risedronate inhibits bone resorption in diseases like osteoporosis, Paget’s disease, tumor bone diseases or the malfunction of phosphocalcium metabolism. The acid-base properties of risedronate in an aqueous solution have been studied in a pH range from 2 to 12 and can be described in terms of four dissociation steps: pK a,2, pK a,4, pK a,5 (related to the dissociation of POH groups) and pK a,3 related to the dissociation of protonated amino group NH3+. The mixed dissociation constants were determined at different ionic strengths I = 0.02 to 0.20 mol dm−3 KCl and of 25°C and 37°C using pH-spectrophotometric and pH-potentiometric titration methods. Determination of group parameters L 0, H T might lead to false estimates of common parameters p K a;therefore, the computational strategy employed is important. A comparison between the two programs ESAB and HYPERQUAD demonstrated that the ESAB program provides a better fit of potentiometric titration curve. The thermodynamic dissociation constants pK aT were estimated by a nonlinear regression of (pK a, I) data and a Debye-Hückel equation at 25°C and 37°C, pK a,2T = 2.37(1) and 2.44(1), pK a,3T = 6.29(3) and 6.26(1), pK a,4T = 7.48(1) and 7.46(2) and pK a,5T = 9.31(7) and 8.70(3) at 25°C and 37°C using pH-spectroscopic data and pK a,2T = 2.48(3) and 2.43(1), pK a,3T= 6.12(2) and 6.10(2), pK a,4T = 7.25(2) and 7.23(1) and pK a,5T = 12.04(5) and 11.81(2) at 25°C and 37°C. The ascertained estimates of three dissociation constants pK a,3, pK a,4, pK a,5 are in agreement with the predicted values obtained using PALLAS

Reliability of dissociation constants and resolution capability of SQUAD(84) and SPECFIT/32 in the regression of multiwavelength spectrophotometric pH-titration data

The resolving power of multicomponent spectral analysis and the computation reliability of the stability constants and molar absorptivities determined for five variously protonated anions of physostigmine salicylate by the SQUAD(84) and SPECFIT/32 programs has been examined with the use of simulated and experimental spectra containing overlapping spectral bands. The reliability of the dissociation constants of drug was proven with goodness-of-fit tests and by examining the influence of pre-selected noise level s(inst)(A) in synthetic spectra regarding the precision s(pK) and also accuracy of the estimated dissociation constants. Precision was examined as the linear regression model s(pK)=β(0)+β(1)s(inst)(A). In all cases the intercept β(0) was statistically insignificant. When an instrumental error s(inst)(A) is small and less than 0.5 mAU, the parameters' estimates are nearly the same as the bias ΔpK=pK(a,calc)-pK(a,true) is quite negligible. In all four dissociation constants the bias seems to be quite small even though for pK(a4) it is a little bit higher, i.e., +0.05 for s(inst)(A) about 1.0 mAU. In the interval of s(inst)(A) from 0.1 to 1.0 mAU all four dissociation constants pK(i) are accurate enough. Of the various regression diagnostics considered, the goodness-of-fit is the most efficient criterion of whether the parameters found adequately represent the data. The magnitude of instrumental error s(inst)(A) only slightly affects the shape of a Cattel's scree graph s(k)(A)=f(k) to determine the true number of light-absorbing species in the equilibrium mixture.

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 a1T= 2.895(13), pK a2T= 4.410(14), pK a3T= 5.726(15) at 25°C and pK a1T= 3.089(15), pK a2T= 4.392(12), pK a3T= 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.

Multi-wavelength spectrophotometric determination of acidity constant of some newly synthesized Schiff bases and their QSPR study

The acidity constants of some newly synthesized Schiff base derivatives were determined by hard-model based multivariate data analysis of the spectrophotometric data in the course of pH-metric titration in 50% (v/v) methanol-water binary solvent. The employed data analysis method was also able to extract the pure spectra and pH-dependent concentration profiles of the acid-base species. The molecules that possess different substituents (both electron donating and withdrawing) on the ortho-, meta- and para-positions of one of the phenyl ring showed variable acidity constants ranging from 8.77 to 11.07 whereas the parent molecule had an acidity constant of 10.25. To investigate the quantitative effects of changing of substitution pattern on the acidity constant, a quantitative structure-property relation analysis was conducted using substituent constants and molecular descriptor. Some models with high statistical quality (measured by cross-validation Q(2)) were obtained. It was found that the acidity constant of the studied molecules in the methanol-water mixed solvent not only is affected by electronic features of the solutes but also by the lipophilic interaction between methanol part of solvent and the deprotonated solutes.

Experimental correlation between the pKa value of sulfonphthaleins with the nature of the substituents groups

This work presents the results obtained from a spectrophotometry study performed on some indicators of the sulfonphtaleins like phenol red (PR), thymol blue (TB), bromothymol blue (BTB), xylenol orange (XO) and methylthymol blue (MTB). During the first stage the acidity constants of some of the indicators were determined using the data from spectrophotometry, potentiometry and with the use of the software SQUAD. These were as follows: for the equilibrium 2H+BTB<-->H(2)BTB, log beta(2)=15.069+/-0.046 and for H+BTB<-->HBTB, log beta(1)=8.311+/-0.044. For the XO and the MTB five values were calculated for each, namely, for MTB: log beta(5)=42.035, log beta(4)=38.567+/-0.058, log beta(3)=32.257+/-0.057, log beta(2)=23.785+/-0.057, and log beta(1)=12.974+/-0.045 while for XO: log beta(5)=40.120+/-0.102, log beta(4)=35.158+/-0.062, log beta(3)=29.102+/-0.053, log beta(2)=21.237+/-0.044, and log beta(1)=11.682+/-0.044. During the second stage, a study was conducted on the effect of the substituents present in the indicators to determine the effect of different functional groups on the pK(a) value corresponding to the last indicator's dissociation.

The thermodynamic dissociation constants of four non-steroidal anti-inflammatory drugs by the least-squares nonlinear regression of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of four non-steroidal anti-inflammatory drugs (NSAIDs) ibuprofen, diclofenac sodium, flurbiprofen and ketoprofen at various ionic strengths I of range 0.003-0.155, and at temperatures of 25 degrees C and 37 degrees C, were determined with the use of two different multiwavelength and multivariate treatments of spectral data, SPECFIT/32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis. The factor analysis in the INDICES program predicts 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 pK(a)(T) was estimated by nonlinear regression of (pK(a), I) data at 25 degrees C and 37 degrees C. Goodness-of-fit tests for various regression diagnostics enabled the reliability of the parameter estimates found to be proven. PALLAS, MARVIN, SPARC, ACD/pK(a) and Pharma Algorithms predict pK(a) being based on the structural formulae of drug compounds in agreement with the experimental value. The best agreement seems to be between the ACD/pK(a) program and experimentally found values and with SPARC. PALLAS and MARVIN predicted pK(a,pred) values with larger bias errors in comparison with the experimental value for all four drugs.

Characterization of acid–base properties of unstable drugs using a continuous-flow system with UV–vis spectrophotometric detection

In this paper, we propose a continuous-flow system for the study of the acid-base characteristics of unstable drugs. 5-Azacytidine has been selected as a first model of unstable compound, which progressively decomposes in aqueous solutions. Besides, other compounds undergoing hydrolysis and oxidation side reactions have been also analyzed to explore the performance of the method. In comparison with conventional batch titrations, the drug decomposition can be minimized by the continuous renewal of the analyte solution. The composition of the buffer mixture is varied on-line during the process from successive changes in the flow rates of acid and basic stock solutions. As a result, the pH value of the test solution is varied in a controlled manner in the range of 1-13. Multivariate curve resolution based on alternating least squares has been used to extract relevant information concerning the acid-base properties of analytes. Results from the continuous-flow system have been compared with those obtained, using batch spectrophotometric titrations, and in the case of fast degradations, the performance of the proposed procedure has been superior.

Reliability and uncertainty in the estimation of pKa 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.