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

Growth and shrinkage of pluronic micelles by uptake and release of flurbiprofen: variation of pH

The micellization of Pluronic triblock copolymers (P103, P123, and L43) in the presence of flurbiprofen at different pH was studied by small-angle neutron scattering (SANS), pulsed-field gradient stimulated-echo nuclear magnetic resonance (PFGSE-NMR), and surface tension measurements. Addition of flurbiprofen to the Pluronic at low pH leads to an increase in the fraction of micellization, aggregation number, and the core radius of the micelles. However, changing the pH to above the pKa of flurbiprofen in an ethanol/water mixture (∼6.5) reduces the fraction of micellization and results in a weaker interaction between the drug and micelles due to the increased drug solubility in aqueous solution.

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.

Comparison of nine programs predicting pK(a) values of pharmaceutical substances

Knowledge of the possible ionization states of a pharmaceutical substance, embodied in the pK(a) values (logarithm of the acid dissociation constant), is vital for understanding many properties essential to drug development. We compare nine commercially available or free programs for predicting ionization constants. Eight of these programs are based on empirical methods: ACD/pK(a) DB 12.0, ADME Boxes 4.9, ADMET Predictor 3.0, Epik 1.6, Marvin 5.1.4, Pallas pKalc Net 2.0, Pipeline Pilot 5.0, and SPARC 4.2; one program is based on a quantum chemical method: Jaguar 7.5. We compared their performances by applying them to 197 pharmaceutical substances with 261 carefully determined and highly reliable experimental pK(a) values from a literature source. The programs ADME Boxes 4.9, ACD/pK(a) DB 12.0, and SPARC 4.2 ranked as the top three with mean absolute deviations of 0.389, 0.478, and 0.651 and r(2) values of 0.944, 0.908, and 0.894, respectively. ACD/pK(a) DB 12.0 predicted all sites, whereas ADME Boxes 4.9 and SPARC 4.2 failed to predict 5 and 18 sites, respectively. The performance of the quantum chemical-based program Jaguar 7.5 was not as expected, with a mean absolute deviation of 1.283 and an r(2) value of 0.579, indicating the potential for further development of this type of approach to pK(a) prediction.

Accurate potentiometric determination of lipid membrane-water partition coefficients and apparent dissociation constants of ionizable drugs: electrostatic corrections

PURPOSE

Potentiometric lipid membrane-water partition coefficient studies neglect electrostatic interactions to date; this leads to incorrect results. We herein show how to account properly for such interactions in potentiometric data analysis.

MATERIALS AND METHODS

We conducted potentiometric titration experiments to determine lipid membrane-water partition coefficients of four illustrative drugs, bupivacaine, diclofenac, ketoprofen and terbinafine. We then analyzed the results conventionally and with an improved analytical approach that considers Coulombic electrostatic interactions.

RESULTS

The new analytical approach delivers robust partition coefficient values. In contrast, the conventional data analysis yields apparent partition coefficients of the ionized drug forms that depend on experimental conditions (mainly the lipid-drug ratio and the bulk ionic strength). This is due to changing electrostatic effects originating either from bound drug and/or lipid charges. A membrane comprising 10 mol-% mono-charged molecules in a 150 mM (monovalent) electrolyte solution yields results that differ by a factor of 4 from uncharged membranes results.

CONCLUSION

Allowance for the Coulombic electrostatic interactions is a prerequisite for accurate and reliable determination of lipid membrane-water partition coefficients of ionizable drugs from potentiometric titration data. The same conclusion applies to all analytical methods involving drug binding to a surface.

Prediction of drug distribution within blood

Drug distribution in blood, defined as drug blood-to-plasma concentration ratio (R(b)), is a fundamental pharmacokinetic parameter. It relates the plasma clearance to the blood clearance, enabling the physiological interpretation of this parameter. Although easily experimentally determined, R(b) values are lacking for the vast majority of drugs. We present a systematic approach using mechanistic, partial least squares (PLS) regression and artificial neural network (ANN) models to relate various in vitro and in silico molecular descriptors to a dataset of 93 drug R(b) values collected in the literature. The ANN model resulted in the best overall approach, with r(2)=0.927 and r(2)=0.871 for the train and the test sets, respectively. PLS regression presented r(2)=0.557 for the train and r(2)=0.656 for the test set. The mechanistic model provided the worst results, with r(2)=0.342 and, additionally, is limited to drugs with a basic ionised group with pKa<7. The ANN model for drug distribution in blood can be a valuable tool in clinical pharmacokinetics as well as in new drug design, providing predictions of R(b) with a percentage of correct values within a 1.25-fold error of 86%, 84% and 87% in the train, test and validation set of data.