Accurate pK Research Articles

Bridging Machine Learning and Thermodynamics for Accurate pK a Prediction.

Integrating scientific principles into machine learning models to enhance their predictive performance and generalizability is a central challenge in the development of AI for Science. Herein, we introduce Uni-pK a, a novel framework that successfully incorporates thermodynamic principles into machine learning modeling, achieving high-precision predictions of acid dissociation constants (pK a), a crucial task in the rational design of drugs and catalysts, as well as a modeling challenge in computational physical chemistry for small organic molecules. Uni-pK a utilizes a comprehensive free energy model to represent molecular protonation equilibria accurately. It features a structure enumerator that reconstructs molecular configurations from pK a data, coupled with a neural network that functions as a free energy predictor, ensuring high-throughput, data-driven prediction while preserving thermodynamic consistency. Employing a pretraining-finetuning strategy with both predicted and experimental pK a data, Uni-pK a not only achieves state-of-the-art accuracy in chemoinformatics but also shows comparable precision to quantum mechanics-based methods.

Isodesmic reaction for accurate theoretical pKa calculations of amino acids and peptides.

Theoretical and quantitative prediction of pKa values at low computational cost is a current challenge in computational chemistry. We report that the isodesmic reaction scheme provides semi-quantitative predictions (i.e. mean absolute errors of 0.5-1.0 pKa unit) for the pKa1 (α-carboxyl), pKa2 (α-amino) and pKa3 (sidechain groups) of a broad set of amino acids and peptides. This method fills the gaps of thermodynamic cycles for the computational pKa calculation of molecules that are unstable in the gas phase or undergo proton transfer reactions or large conformational changes from solution to the gas phase. We also report the key criteria to choose a reference species to make accurate predictions. This method is computationally inexpensive and makes use of standard density functional theory (DFT) and continuum solvent models. It is also conceptually simple and easy to use for researchers not specialized in theoretical chemistry methods.

SP27-1 Risk pathogens and PK/PD of antibiotics

The aim of this work was to compare the suitability of different pharmacodynamic models for PK–PD modeling of verapamil cardiovascular effects in aortic coarctated rats (ACo), a model of renovascular hypertension.A “shunt” microdialysis probe was inserted in a carotid artery of anaesthetized sham-operated (SO) and ACo rats for determination of verapamil plasma concentrations and their effects on blood pressure and heart rate after intravenous application (1 and 3 mg kg− 1). Correlation between verapamil plasma levels and their cardiovascular effects was established by fitting data to a linear, and a conventional and modified Emax model.No differences in verapamil volume of distribution were observed between experimental groups. Whilst clearance increased with dose in SO rats, no differences were found in verapamil clearance in ACo comparing both dose levels. A good correlation between verapamil plasma unbound concentrations and their hypotensive and chronotropic effects was found in both experimental groups using the tested PK–PD models. Although all pharmacodynamic models allowed a precise estimation of verapamil PK–PD parameters, linear and Emax model did not permit an accurate PK–PD parameter estimation for the hypotensive and chronotropic effect, respectively. Conversely, the modified Emax model allows both a precise and accurate estimation of PK–PD parameters for verapamil effects. Although, absolute verapamil blood pressure lowering effect was greater in ACo rats compared with SO rats, no differences were found in verapamil PK–PD parameters estimated for the hypotensive response.Side-by-side comparison of the tested pharmacodynamic models showed that accuracy of PK–PD parameters estimation by using the linear and classical Emax model depends on the magnitude of concentration–effect curve covered in the study. Conversely, the modified Emax model allowed both a precise and accurate estimation of PK–PD parameters, suggesting that the modified Emax pharmacodynamic model is the most suitable for verapamil PK–PD modeling.

Nano-scale liquid chromatography/mass spectrometry and on-the-fly orthogonal array optimization for quantification of therapeutic monoclonal antibodies and the application in preclinical analysis

Therapeutic monoclonal antibodies (mAbs) constitute a group of highly effective agents for treating various refractory diseases. Nonetheless it is challenging to achieve selective and accurate quantification of mAb in pharmaceutical matrices, which is required by PK studies. Liquid chromatography/mass spectrometry under selected reaction monitoring mode (LC/SRM-MS) is emerging as an attractive alternative to immunoassays because of the high specificity and multiplexing capacity it provides, but may fall short in terms of sensitivity, reliability and quantitative accuracy. Moreover, the strategy for optimization of the MS conditions for many candidates of signature peptides (SP) and the selection of the optimal SP for quantification remains elusive. In this study, we employed a suite of technical advances to overcome these difficulties, which include: (i) a nano-LC/SRM-MS approach to achieve high analytical sensitivity, (ii) a high-resolution nano-LC/LTQ/Orbitrap for confident identification of candidate peptides, (iii) an on-the-fly orthogonal array optimization (OAO) method for the high-throughput, accurate and reproducible optimization for numerous candidate peptides in a single LC/MS run without using synthesized peptides, (iv) a comprehensive evaluation of stability of candidates in matrix using the optimized SRM parameters, (v) the use of two unique SP for quantification of one mAb to gauge possible degradation/modification in biological system and thus enhancing data reliability (e.g. rejection of data if the deviation between the two SP is greater than 25%) and (vi) the utilization of purified target protein as the calibrator to eliminate the risk of severe negative biases that could occur when a synthesized peptide is used as calibrator. To show a proof of concept, this strategy is applied in the quantification of cT84.66, a chimeric, anti-CEA antibody, in preclinical mouse models. A low detection limit of the mAb down to 3.2ng/mL was achieved, which is substantially more sensitive than established immunoassay methods for anti-CEA antibodies. The quantitative method showed good linearity (within the range of 12.9ng/mL to 32.3μg/mL in plasma), accuracy and precision. Additionally, the ultra-low sample consumption (2μL plasma per preparation) permits the acquisition of an entire set of time course data from the same mouse, which represents a prominent advantage for PK study using small-animal models. The developed method enabled an accurate PK investigation of cT84.66 in mice following intravenous and subcutaneous administrations at relatively low doses over an extended period of time. The strategy employed in this study can be easily adapted to the sensitive and accurate analysis of other mAb and therapeutic proteins.

Modeling Temperature Dependency of Amine Basicity Using PCM and SM8T Implicit Solvation Models

PCM and SM8T continuum solvation models are used to study the temperature dependency of a set of amines in the temperature range 273-393 K using density functional theoretical calculations. Gaseous phase calculations are done using B3LYP and M06 functionals at the 6-311++G(d,p) basis set level. pK(a) values calculated computationally are compared with experimental values in the given temperature region using both continuum solvation models. The continuum solvation models predict the temperature trends of pK(a) compared to experimental trends very nicely. Accurate pK(a) values at 298 K are however required as input to the model. The absolute values of pK(a) values are not reproduced well by these continuum solvation models, and a correction term is therefore introduced. A set of 10 amines, which have potential for CO(2) capture, and where also a large experimental data set of temperature dependent pK(a) values is available, were studied in this work. The temperature dependency of pK(a) values of amines provides a basis for selection for optimum solvents for postcombustion CO(2) capture processes.

Toward accurate prediction of pKa values for internal protein residues: The importance of conformational relaxation and desolvation energy

Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pK(a) prediction informs about proton pathways, thereby revealing detailed acid-base mechanisms. Physics-based methods in the framework of molecular dynamics simulations not only offer pK(a) predictions but also inform about the physical origins of pK(a) shifts and provide details of ionization-induced conformational relaxation and large-scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pK(a) prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pK(a) values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root-mean-square deviation of 1.69 pK units from experiment, and there were only two pK(a)'s with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side-chains in the context of the errors of calculated pK(a) values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pK(a) predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit-solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit-solvent representation may offer improvement of accuracy.

A pH-Dilution Method for Estimation of Biorelevant Drug Solubility along the Gastrointestinal Tract: Application to Physiologically Based Pharmacokinetic Modeling

Physiologically based pharmacokinetic (PBPK) modeling tools have become an integral part of the modern drug discovery-development process. However, accurate PK prediction of enabling formulations of poorly soluble compounds by applying PBPK modeling has been very limited. This is because current PBPK models rely only on thermodynamic drug solubility inputs (e.g., pH-solubility profile) and give little consideration to the dynamic changes in apparent drug solubility (e.g., supersaturation) that occur during gastrointestinal (GI) transit of an enabling formulation of a water insoluble drug. Moreover, biorepresentative and predictive in vitro tools to measure formulation dependent solubility changes during GI transit remain underdeveloped. In this work, we have developed an in vitro dual pH-dilution method based on rat physiology to estimate the apparent drug concentration in solution along the GI tract during release from solubility enabling formulations. This simple dual pH-dilution method was evaluated using various solubility enabling formulations (i.e., cosolvent solution, amorphous solid dispersions) made using a model early development drug candidate with poor aqueous solubility. The in vitro drug concentration-time profiles from the enabling formulations were used as solubility inputs for PBPK modeling using GastroPlus software. This resulted in excellent predictions of the in vivo oral plasma concentration-time profiles, as compared to using the traditional inputs of thermodynamic pH-solubility profiles. In summary, this work describes a novel in vitro method for facile estimation of formulation dependent GI drug concentration-time profiles and demonstrates the utility of PBPK modeling for oral PK prediction of enabling formulations of poorly soluble drugs.

Improved pKa prediction: Combining empirical and semimicroscopic methods

Using three different methods we tried to compute 171 experimentally known pK(a) values of ionizable residues from 15 different proteins and compared the accuracies of computed pK(a) values in terms of the root mean square deviation (RMSD) from experiment. One method is based on a continuum electrostatic model of the protein including conformational flexibility (KBPLUS). The others are empirical approaches with PROPKA deploying physically motivated energy terms with adjustable parameters and PKAcal using an empirical function with no physical basis. PROPKA reproduced the pK(a) values with highest overall accuracy. Differentiating the data set into weakly and strongly shifted experimental pK(a) values, however, we found that PROPKA's accuracy is better if the pK(a) values are weakly shifted but on equal footing with that of KBPLUS for more strongly shifted values. On the other hand, PKAcal reproduces strongly shifted pK(a) values badly but weakly shifted values with the same accuracy as PROPKA. We tested different consensus approaches combining data from all three methods to find a general procedure for most accurate pK(a) predictions. In most of the cases we found that the consensus approach reproduced experimental data with better accuracy than any of the individual methods alone.

Comparison of different pharmacodynamic models for PK–PD modeling of verapamil in renovascular hypertension

Introduction The aim of this work was to compare the suitability of different pharmacodynamic models for PK–PD modeling of verapamil cardiovascular effects in aortic coarctated rats (ACo), a model of renovascular hypertension. Methods A “shunt” microdialysis probe was inserted in a carotid artery of anaesthetized sham-operated (SO) and ACo rats for determination of verapamil plasma concentrations and their effects on blood pressure and heart rate after intravenous application (1 and 3 mg kg − 1 ). Correlation between verapamil plasma levels and their cardiovascular effects was established by fitting data to a linear, and a conventional and modified E max model. Results No differences in verapamil volume of distribution were observed between experimental groups. Whilst clearance increased with dose in SO rats, no differences were found in verapamil clearance in ACo comparing both dose levels. A good correlation between verapamil plasma unbound concentrations and their hypotensive and chronotropic effects was found in both experimental groups using the tested PK–PD models. Although all pharmacodynamic models allowed a precise estimation of verapamil PK–PD parameters, linear and E max model did not permit an accurate PK–PD parameter estimation for the hypotensive and chronotropic effect, respectively. Conversely, the modified E max model allows both a precise and accurate estimation of PK–PD parameters for verapamil effects. Although, absolute verapamil blood pressure lowering effect was greater in ACo rats compared with SO rats, no differences were found in verapamil PK–PD parameters estimated for the hypotensive response. Discussion Side-by-side comparison of the tested pharmacodynamic models showed that accuracy of PK–PD parameters estimation by using the linear and classical E max model depends on the magnitude of concentration–effect curve covered in the study. Conversely, the modified E max model allowed both a precise and accurate estimation of PK–PD parameters, suggesting that the modified E max pharmacodynamic model is the most suitable for verapamil PK–PD modeling.

Accurate pKa Determination for a Heterogeneous Group of Organic Molecules

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.

Protonation Studies of Modified Adenine and Adenine Nucleotides by Theoretical Calculations and 15N NMR

The acid/base character of nucleobases affects phenomena such as self-association, interaction with metal ions, molecular recognition by proteins, and nucleic acid base-pairing. Therefore, the investigation of proton-transfer equilibria of natural and synthetic nucleos(t)ides is of great importance to obtain a deeper understanding of these phenomena. For this purpose, a set of ATP prototypes was investigated using (15)N NMR spectroscopy, and the corresponding adenine bases were investigated by theoretical calculations. (15)N NMR measurements provided not only acidity constants but also information on the protonation site(s) on the adenine ring and regarding the ratio of the singly protonated species in equilibrium. Substituents of different nature and position on the adenine ring did not change the preferred protonation site, which remained N1. However, for 2-thioether-ATP derivatives a mixed population of N1 and N7 singly protonated species was observed. Reduction of basicity of 0.4-1 pK(a) units relative to ATP was also observed for all evaluated ATP derivatives, except for 2-Cl-ATP, for which K(a) was ca. 10,000-fold lower. To explain the substitution-dependent variations in the experimental pK(a) values of the ATP analogues, gas-phase proton affinities (PA), Delta Delta G(hyd), and pK(a) values of the corresponding adenine bases were calculated using quantum mechanical methods. The computed PA and Delta Delta G(hyd) values successfully explained the experimental pK(a) values. A computational procedure for the prediction of accurate pK(a) values was developed using density functional theory and polarizable continuum model calculations. In this procedure, we developed a set of parameters for the polarizable continuum model that was fitted to reproduce experimental pK(a) values of nitrogen heterocycles. This method is proposed for the prediction of pK(a) values and protonation site(s) of purine analogues that have not been synthesized or analyzed.

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods.

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.

Simultaneous Determination of Ionization Constants and Isoelectric Points of 12 Hydroxy-s-Triazines by Capillary Zone Electrophoresis and Capillary Isoelectric Focusing

Capillary zone electrophoresis (CZE) was used to separate and determine simultaneously the pK(1), pK(2), and pI values of 12 environmentally relevant hydroxytriazines (hydroxymetabolites of atrazine, terbuthylazine, simazine, and propazine and four (arylamino)-s-triazines) and observe the effects of the alkylamino and arylamino substituents on the measured values. Capillary isoelectric focusing (CIEF) methods were developed to measure the pI of these compounds and compare those values with the CZE-measured pI's. CZE and CIEF can provide accurate pK and pI values reasonably fast, and pI values measured by the two techniques agree. Knowledge of the pK and pI values of hydroxytriazines is important for an understanding of the binding mechanisms of these molecules in environmental matrices. Because the hydroxytriazines may exist as a myriad of species [Formula: see text] neutral, charged, zwitterionic, and keto-enol tautomeric [Formula: see text] depending on structure and pH, we briefly addressed the existence of these species relative to their electrophoretic analysis.

Proton/product time course ratios: a new approach to transient-state kinetic analysis.

The usefulness of the indicator dye method for the detection of transient enzyme-product intermediates has been very limited due to the near impossibility of resolving the apparent single exponential time courses resulting from sequences of steps linked by rather similar rate constants. We propose here a novel approach, the proton-product time course method, a procedure which can extract a great deal of the mechanistic information which remains buried in conventional proton release-time course measurements. The method involves nothing more than measuring the ratio, r, of the moles of H+ released to the moles of product formed as a function of time. We derive the theory relating this r function to mechanisms of varying complexity, explore the theoretical behavior of the function in various possible mechanistic situations, and employ the new approach in an experimental system. We demonstrate the fact that the proton/product time course ratio method can provide evidence of the existence of hidden steps in transient state kinetic studies, that it can determine accurate thermodynamic pK values of the intermediate complexes involved in those steps, and that it can produce time courses of individual intermediates which are obscure to conventional kinetic methods.

The evaluation of Δ C° p for acid-base equilibria from pK measurement

The use of the temperature variation of the dissociation constant for evaluating changes in Δ C° p is reviewed with a view to establishing the degree of reliability of such values. Δ C° p values obtained from dissociation constant measurements are compared, where possible, with the calorimetrically determined values. Significant differences are apparent, suggesting serious shortcomings in the indirect methods of evaluation used so far. The related question of the appropriate form of the pK( T) equation is also discussed. When the “most appropriate” form of pK( t), viz a five-constants equation is used with the accurate data of Ives for the dissociation of cyano-acetic acid, according to the method of Clarke and Glew, the results still retain large uncertainties on Δ C° p . Model exact pK data can be calculated from known assumed Δ G°, Δ H°, Δ C° p , first and second temperature derivatives of Δ C° p at a chosen reference temperature. By introducing variations of various magnitudes and signs on these model values, very accurate “experimental-like” pK values can be generated. When these accurate pK values are analysed on the computer, using the method of Clarke and Glew, and the results are compared, it becomes apparent that over the normal experimental range (O°−50°C or 60°C) even very small errors ( ca 0·00025 pK units) can lead to very large uncertainties on Δ C° p (especially at the two extremes of the temperature range) exceeding in some cases 20 cal. The identification of the true Δ C° p ( T) becomes impossible. It is concluded that the dissociation constant method is not capable as yet of furnishing reliable Δ C° p values; the extension of the temperature range to the neighborhood of 100°C and an increase in the degrees of freedom ( eg by measurements at 5° intervals) could combine to furnish fairly reliable Δ C° p values.