Predicting pKa

Benchmarking In Silico Tools for Cysteine pKa Prediction

Accurate estimation of the pK_a's of cysteine residues in proteins could inform targeted approaches in hit discovery. The pK_a of a targetable cysteine residue in a disease-related protein is an important physiochemical parameter in covalent drug discovery, as it influences the fraction of nucleophilic thiolate amenable to chemical protein modification. Traditional structure-based in silico tools are limited in their predictive accuracy of cysteine pK_a's relative to other titratable residues. Additionally, there are limited comprehensive benchmark assessments for cysteine pK_a predictive tools. This raises the need for extensive assessment and evaluation of methods for cysteine pK_a prediction. Here, we report the performance of several computational pK_a methods, including single-structure and ensemble-based approaches, on a diverse test set of experimental cysteine pK_a's retrieved from the PKAD database. The dataset consisted of 16 wildtype and 10 mutant proteins with experimentally measured cysteine pK_a values. Our results highlight that these methods are varied in their overall predictive accuracies. Among the test set of wildtype proteins evaluated, the best method (MOE) yielded a mean absolute error of 2.3 pK units, highlighting the need for improvement of existing pK_a methods for accurate cysteine pK_a estimation. Given the limited accuracy of these methods, further development is needed before these approaches can be routinely employed to drive design decisions in early drug discovery efforts.

A multiple linear regression approach to the estimation of carboxylic acid ester and lactone alkaline hydrolysis rate constants

Pesticides, pharmaceuticals, and other organic contaminants often undergo hydrolysis when released into the environment; therefore, measured or estimated hydrolysis rates are needed to assess their environmental persistence. An intuitive multiple linear regression (MLR) approach was used to develop robust QSARs for predicting base-catalyzed rate constants of carboxylic acid esters (CAEs) and lactones. We explored various combinations of independent descriptors, resulting in four primary models (two for lactones and two for CAEs), with a total of 15 and 11 parameters included in the CAE and lactone QSAR models, respectively. The most significant descriptors include pKa, electronegativity, charge density, and steric parameters. Model performance is assessed using Drug Theoretics and Cheminformatics Laboratory's DTC-QSAR tool, demonstrating high accuracy for both internal validation (r2 = 0.93 and RMSE = 0.41-0.43 for CAEs; r2 = 0.90-0.93 and RMSE = 0.38-0.46 for lactones) and external validation (r2 = 0.93 and RMSE = 0.43-0.45 for CAEs; r2 = 0.94-0.98 and RMSE = 0.33-0.41 for lactones). The developed models require only low-cost computational resources and have substantially improved performance compared to existing hydrolysis rate prediction models (HYDROWIN and SPARC).

Technology development to evaluate the effectiveness of viscosity reducing excipients

Addition of pharmaceutical excipients is a commonly used approach to decrease the viscosity of highly concentrated protein formulations, which otherwise could not be subcutaneously injected or processed. The variety of protein-protein interactions, which are responsible for increased viscosities, makes a portfolio approach necessary. Screening of several excipients to develop such a portfolio is time and money consuming in industrial settings. Responsible protein-protein interactions were investigated using the interaction parameter k_D obtained from dynamic light scattering measurements in the studies presented herein. Together with in-silico calculated excipient parameter, k_D could be used as a screening tool accelerating screening and formulation development as k_D is suitable to high-throughput formats using small quantities of protein and low concentrations. A qualitative correlation between k_D and high-concentration viscosity behavior could be shown in our case.

A Fast and Interpretable Deep Learning Approach for Accurate Electrostatics-Driven pKa Predictions in Proteins

Existing computational methods for estimating pK_a values in proteins rely on theoretical approximations and lengthy computations. In this work, we use a data set of 6 million theoretically determined pK_a shifts to train deep learning models, which are shown to rival the physics-based predictors. These neural networks managed to infer the electrostatic contributions of different chemical groups and learned the importance of solvent exposure and close interactions, including hydrogen bonds. Although trained only using theoretical data, our pKAI+ model displayed the best accuracy in a test set of ∼750 experimental values. Inference times allow speedups of more than 1000× compared to physics-based methods. By combining speed, accuracy, and a reasonable understanding of the underlying physics, our models provide a game-changing solution for fast estimations of macroscopic pK_a values from ensembles of microscopic values as well as for many downstream applications such as molecular docking and constant-pH molecular dynamics simulations.

Modulating physicochemical properties of tetrahydropyridine-2-amine BACE1 inhibitors with electron-withdrawing groups: A systematic study

A common challenge for medicinal chemists is to reduce the pK_a of strongly basic groups' conjugate acids into a range that preserves the desired effects, usually potency and/or solubility, but avoids undesired effects like high volume of distribution (V_d), limited membrane permeation, and off-target binding to, notably, the hERG channel and monoamine receptors. We faced this challenge with a 3,4,5,6-tetrahydropyridine-2-amine scaffold harboring an amidine, a key structural component of potential inhibitors of BACE1, the rate-limiting enzyme in the production of Aβ species that make up amyloid plaques in Alzheimer's disease. In our endeavor to balance potency with desirable properties to achieve brain penetration, we introduced a diverse set of groups in beta position of the amidine that modulate logD, PSA and pK_a. Given the synthetic challenge to prepare these highly functionalized warheads, we first developed a design flow including predicted physicochemical parameters which allowed us to select only the most promising candidates for synthesis. For this we evaluated a set of commercial packages to predict physicochemical properties, which can guide medicinal chemists in their endeavors to modulate pK_a values of amidine and amine bases.

Predicting pKa Values of Quinols and Related Aromatic Compounds with Multiple OH Groups

Quinonoid compounds play central roles as redox-active agents in photosynthesis and respiration and are also promising replacements for inorganic materials currently used in batteries. To design new quinonoid compounds and predict their state of protonation and redox behavior under various conditions, their pK_a values must be known. Methods that can predict the pK_a values of simple phenols cannot reliably handle complex analogues in which multiple OH groups are present and may form intramolecular hydrogen bonds. We have therefore developed a straightforward method based on a linear relationship between experimental pK_a values and calculated differences in energy between quinols and their deprotonated forms. Simple adjustments allow reliable predictions of pK_a values when intramolecular hydrogen bonds are present. Our approach has been validated by showing that predicted and experimental values for over 100 quinols and related compounds differ by an average of only 0.3 units. This accuracy makes it possible to select proper pK_a values when experimental data vary, predict the acidity of quinols and related compounds before they are made, and determine the sites and orders of deprotonation in complex structures with multiple OH groups.

DFT-Machine Learning Approach for Accurate Prediction of pKa

In this study, we propose a novel method of pK_a prediction in a diverse set of acids, which combines density functional theory (DFT) method with machine learning (ML) methods. First, the DFT method with B3LYP/6-31++G**/SM8 is used to predict pK_a, yielding a mean absolute error of 1.85 pK_a units. Subsequently, such pK_a values predicted from the DFT method are employed as one of 10 molecular descriptors for developing ML models trained on experimental data. Kernel Ridge Regression (KRR), Gaussian Process Regression, and Artificial Neural Network are optimized using three Pipelines: Pipeline 1 involving only hyperparameter optimization (HPO), Pipeline 2 involving HPO followed by a relative contribution analysis (RCA) and recursive feature elimination (RFE), and Pipeline 3 involving HPO followed by RCA and RFE on an expanded set of composite features. Finally, it is demonstrated that KRR with Pipeline 3 yields optimal pK_a prediction at an MAE of 0.60 log units. This algorithm was then utilized to predict the pK_a of 37 novel acids. The two most important features were determined to be the number of hydrogen atoms in the molecule and the degree of oxidation of the acid. The predicted pK_a values were documented for future reference.

Computing Protein pKas Using the TABI Poisson–Boltzmann Solver

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson–Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site–site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work, we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. The pKa computing procedure is enclosed in a convenient Python wrapper which is publicly available at the corresponding author’s website. Predicted results are compared with experimental pKas for several proteins. Among ongoing efforts to improve protein pKa calculations, the advantage of TABI is that it reduces the numerical errors in the electrostatic calculations so that attention can be focused on modeling assumptions.

On the Accuracy of the Direct Method to Calculate pKa from Electronic Structure Calculations

The direct method (HA_(soln) ⇌ A_(soln)^– + H_(soln)⁺) for calculating pK_a of monoprotic acids is as efficient as thermodynamic cycles. A selective adjustment of proton free energy in solution was used with experimental pK_a data. The procedure was analyzed at different levels of theory. The solvent was described by the solvation model density (SMD) model, including or not explicit water molecules, and three training sets were tested. The best performance under any condition was obtained by the G4CEP method with a mean absolute error close to 0.5 units of pK_a and an uncertainty around ±1 unit of pK_a for any training set including or excluding explicit solvent molecules. PM6 and AM1 performed very well with average absolute errors below 0.75 units of pK_a but with uncertainties up to ±2 units of pK_a, using only the SMD solvent model. Density functional theory (DFT) results were highly dependent on the basis functions and explicit water molecules. The best performance was observed for the local spin density approximation (LSDA) functional in almost all calculations and under certain conditions, as high as those obtained by G4CEP. Basis set complexity and explicit solvent molecules were important factors to control DFT calculations. The training set molecules should consider the diversity of compounds.

Inductive effects in amino acids and peptides: Ionization constants and tryptophan fluorescence

Although inductive effects in organic compounds are known to influence chemical properties such as ionization constants, their specific contribution to the properties/behavior of amino acids and functional groups in peptides remains largely unexplored. In this study we developed a computationally economical algorithm for ab initio calculation of the magnitude of inductive effects for non-aromatic molecules. The value obtained by the algorithm is called the Inductive Index and we observed a high correlation (R² = 0.9427) between our calculations and the pK_a values of the alpha-amino groups of amino acids with non-aromatic side-chains. Using a series of modified amino acids, we also found similarly high correlations (R² > 0.9600) between Inductive Indexes and two wholly independent chemical properties: i) the pK_a values of ionizable side-chains and, ii) the fluorescence response of the indole group of tryptophan. After assessing the applicability of the method of calculation at the amino acid level, we extended our study to tryptophan-containing peptides and established that inductive contributions of neighboring side-chains are transmitted through peptide bonds. We discuss possible contributions to the study of proteins.

Standard state free energies, not pKas, are ideal for describing small molecule protonation and tautomeric states

The pK_a is the standard measure used to describe the aqueous proton affinity of a compound, indicating the proton concentration (pH) at which two protonation states (e.g. A^- and AH) have equal free energy. However, compounds can have additional protonation states (e.g. AH₂⁺), and may assume multiple tautomeric forms, with the protons in different positions (microstates). Macroscopic pK_as give the pH where the molecule changes its total number of protons, while microscopic pK_as identify the tautomeric states involved. As tautomers have the same number of protons, the free energy difference between them and their relative probability is pH independent so there is no pK_a connecting them. The question arises: What is the best way to describe protonation equilibria of a complex molecule in any pH range? Knowing the number of protons and the relative free energy of all microstates at a single pH, ∆G°, provides all the information needed to determine the free energy, and thus the probability of each microstate at each pH. Microstate probabilities as a function of pH generate titration curves that highlight the low energy, observable microstates, which can then be compared with experiment. A network description connecting microstates as nodes makes it straightforward to test thermodynamic consistency of microstate free energies. The utility of this analysis is illustrated by a description of one molecule from the SAMPL6 Blind pK_a Prediction Challenge. Analysis of microstate ∆G°s also makes a more compact way to archive and compare the pH dependent behavior of compounds with multiple protonatable sites.

Open-source QSAR models for pKa prediction using multiple machine learning approaches

BACKGROUND

The logarithmic acid dissociation constant pKa reflects the ionization of a chemical, which affects lipophilicity, solubility, protein binding, and ability to pass through the plasma membrane. Thus, pKa affects chemical absorption, distribution, metabolism, excretion, and toxicity properties. Multiple proprietary software packages exist for the prediction of pKa, but to the best of our knowledge no free and open-source programs exist for this purpose. Using a freely available data set and three machine learning approaches, we developed open-source models for pKa prediction.

METHODS

The experimental strongest acidic and strongest basic pKa values in water for 7912 chemicals were obtained from DataWarrior, a freely available software package. Chemical structures were curated and standardized for quantitative structure-activity relationship (QSAR) modeling using KNIME, and a subset comprising 79% of the initial set was used for modeling. To evaluate different approaches to modeling, several datasets were constructed based on different processing of chemical structures with acidic and/or basic pKas. Continuous molecular descriptors, binary fingerprints, and fragment counts were generated using PaDEL, and pKa prediction models were created using three machine learning methods, (1) support vector machines (SVM) combined with k-nearest neighbors (kNN), (2) extreme gradient boosting (XGB) and (3) deep neural networks (DNN).

RESULTS

The three methods delivered comparable performances on the training and test sets with a root-mean-squared error (RMSE) around 1.5 and a coefficient of determination (R2) around 0.80. Two commercial pKa predictors from ACD/Labs and ChemAxon were used to benchmark the three best models developed in this work, and performance of our models compared favorably to the commercial products.

CONCLUSIONS

This work provides multiple QSAR models to predict the strongest acidic and strongest basic pKas of chemicals, built using publicly available data, and provided as free and open-source software on GitHub.

A Way towards Reliable Predictive Methods for the Prediction of Physicochemical Properties of Chemicals Using the Group Contribution and other Methods

Physicochemical properties of chemicals as referred to in this review include, for example, thermodynamic properties such as heat of formation, boiling point, toxicity of molecules and the fate of molecules whenever undergoing or accelerating (catalytic) a chemical reaction and therewith about chemical equilibrium, that is, the equilibrium in chemical reactions. All such properties have been predicted in literature by a variety of methods. However, for the experimental scientist for whom such predictions are of relevance, the accuracies are often far from sufficient for reliable application We discuss current practices and suggest how one could arrive at better, that is sufficiently accurate and reliable, predictive methods. Some recently published examples have shown this to be possible in practical cases. In summary, this review focuses on methodologies to obtain the required accuracies for the chemical practitioner and process technologist designing chemical processes. Finally, something almost never explicitly mentioned is the fact that whereas for some practical cases very accurate predictions are required, for other cases a qualitatively correct picture with relatively low correlation coefficients can be sufficient as a valuable predictive tool. Requirements for acceptable predictive methods can therefore be significantly different depending on the actual application, which are illustrated using real-life examples, primarily with industrial relevance. Furthermore, for specific properties such as the octanol-water partition coefficient more close collaboration between research groups using different methods would greatly facilitate progress in the field of predictive modelling.

Aqueous Drug Solubility: What Do We Measure, Calculate and QSPR Predict?

Detailed critical analysis of publications devoted to QSPR of aqueous solubility is presented in the review with discussion of four types of aqueous solubility (three different thermodynamic solubilities with unknown solute structure, intrinsic solubility, solubility in physiological media at pH=7.4 and kinetic solubility), variety of molecular descriptors (from topological to quantum chemical), traditional statistical and machine learning methods as well as original QSPR models.

Modeling caspase-1 inhibition: Implications for catalytic mechanism and drug design

The metabolic product of caspase-1, IL-1β, is an important mediator in inflammation and pyroptosis cell death process. Alzheimer's disease, septic shock and rheumatoid arthritis are IL-1β mediated diseases, making the caspase-1 an interesting target of pharmacological value. Many inhibitors have been developed until now, most of them are peptidomimetic with improved potency. In the present study, all-atom molecular dynamics simulations and the MM/GBSA method were employed to reproduce and interpret the results obtained by in vitro experiments for a series of inhibitors. The analysis shows that the tautomeric state of the catalytic His237 impact significantly the performance of the prediction protocol, providing evidence for a His237 tautomeric state different to the proposed in the putative mechanism. Additionally, analysis of inhibitor-enzyme interactions indicates that the differences in the inhibitory potency of the tested ligands can be explained mainly by the interaction of the inhibitors with the S2-S4 protein region. These results provide guidelines for subsequent studies of caspase-1 catalytic reaction mechanism and for the design of novel inhibitors.

An explicit-solvent hybrid QM and MM approach for predicting pKa of small molecules in SAMPL6 challenge

In this work we have developed a hybrid QM and MM approach to predict pKa of small drug-like molecules in explicit solvent. The gas phase free energy of deprotonation is calculated using the M06-2X density functional theory level with Pople basis sets. The solvation free energy difference of the acid and its conjugate base is calculated at MD level using thermodynamic integration. We applied this method to the 24 drug-like molecules in the SAMPL6 blind pKa prediction challenge. We achieved an overall RMSE of 2.4 pKa units in our prediction. Our results show that further optimization of the protocol needs to be done before this method can be used as an alternative approach to the well established approaches of a full quantum level or empirical pKa prediction methods.

Catalytic mechanism of type C sialidase from Streptococcus pneumoniae: from covalent intermediate to final product

Streptococcus pneumoniae is a Gram-positive human pathogenic bacterium, which is the main cause of pneumonia and meningitis in children and the elderly. Three sialidases (or neuraminidases) encoded from Streptococcus pneumoniae could catalyze the cleavage of sialic acid linkages. This mechanism is directly connected with infection, apoptosis, and signaling, and usually considered to be one of the critical virulence factors. Type C neuraminidase (NanC) is unique because its primary product of Neu5Ac2en is considered to be an inhibitor to the other two sialidases. Experimentally, there are two different pathways for the formation mechanism of Neu5Ac2en catalyzed by NanC. In this work, a combined quantum mechanical and molecular mechanical approach was employed in all calculations. Starting from the covalent sialylated intermediate, we first examined the reaction to Neu5Ac2en and found the reaction prefers a direct proton abstraction mechanism rather than the water mediated proton abstraction mechanism. Free energy profiles can confirm that Neu5Ac2en is the major product of NanC. Functional roles of some important residues were also investigated, e.g., D315 acts as the proton acceptor during the formation of Neu5Ac2en, while the general base for the hydrolytic reaction to Neu5Ac. This study can facilitate the understanding of the catalytic mechanism of NanC and has the potential to aid in future inhibitor design studies.

Absolute and relative pKa predictions via a DFT approach applied to the SAMPL6 blind challenge

In this work, quantum mechanical methods were used to predict the microscopic and macroscopic pK_a values for a set of 24 molecules as a part of the SAMPL6 blind challenge. The SMD solvation model was employed with M06-2X and different basis sets to evaluate three pK_a calculation schemes (direct, vertical, and adiabatic). The adiabatic scheme is the most accurate approach (RMSE = 1.40 pK_a units) and has high correlation (R² = 0.93), with respect to experiment. This approach can be improved by applying a linear correction to yield an RMSE of 0.73 pK_a units. Additionally, we consider including explicit solvent representation and multiple lower-energy conformations to improve the predictions for outliers. Adding three water molecules explicitly can reduce the error by 2-4 pK_a units, with respect to experiment, whereas including multiple local minima conformations does not necessarily improve the pK_a prediction.

SAMPL6: calculation of macroscopic pKa values from ab initio quantum mechanical free energies

Macroscopic pK_a values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pK_a values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pK_as with a maximum likelihood estimator and appropriately summed to yield macroscopic pK_a values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pK_as: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pK_a. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pK_a units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pK_a values for novel compounds with reasonable accuracy.

Automated techniques in pKa determination: Low, medium and high-throughput screening methods

Drug discovery programs that generate hundreds of new molecular entities need efficient methodologies for physicochemical profiling. Several high-throughput methods for pK_a screening have been developed in the last 15 years to determine this key physicochemical parameter. Separation techniques such as HPLC-MS or capillary electrophoresis are particularly well-suited due to their high throughput and capacity to deal with impure or complex samples. In addition, potentiometric and (mostly) UV-metric-based methods (plate-based and automated systems), find their place as very precise methodologies for pK_a determination despite of somewhat lower throughput. Finally, pK_a prediction software packages are useful estimator tools but, to date, they cannot replace experimental measurements when accurate pK_a values are required.

Opioid receptor signaling, analgesic and side effects induced by a computationally designed pH-dependent agonist

Novel pain killers without adverse effects are urgently needed. Opioids induce central and intestinal side effects such as respiratory depression, sedation, addiction, and constipation. We have recently shown that a newly designed agonist with a reduced acid dissociation constant (pK_a) abolished pain by selectively activating peripheral μ-opioid receptors (MOR) in inflamed (acidic) tissues without eliciting side effects. Here, we extended this concept in that pK_a reduction to 7.22 was achieved by placing a fluorine atom at the ethylidene bridge in the parental molecule fentanyl. The new compound (FF3) showed pH-sensitive MOR affinity, [³⁵S]-GTPγS binding, and G protein dissociation by fluorescence resonance energy transfer. It produced injury-restricted analgesia in rat models of inflammatory, postoperative, abdominal, and neuropathic pain. At high dosages, FF3 induced sedation, motor disturbance, reward, constipation, and respiratory depression. These results support our hypothesis that a ligand’s pK_a should be close to the pH of injured tissue to obtain analgesia without side effects.

The Utility of Calculated Proton Affinities in Drug Design: A DFT Study

Computer-aided drug design comprises several predictive tools, which can calculate various properties of the candidates under development. Proton affinity (PA) is related to pKa (the negative log of the acid dissociation constant (Ka)) one of the fundamental physical properties of drug candidates, determining their water solubility and thus their pharmacokinetic profile. The following questions therefore emerged: to what extent are PA predictions useful in drug design, and can they be reliably used to derive pKa values? Using density functional theory (DFT), it was established that for violuric acid, with three ionisation groups, the PAs correlate well with the measured pKas (R2 = 0.990). Furthermore, an excellent correlation within the amiloride compound family was achieved (R2 = 0.922). In order to obtain correlations for larger compound collections (n = 210), division into chemical families was necessary: carboxylic acids (R2 = 0.665), phenols (R2 = 0.871), and nitrogen-containing molecules (R2 = 0.742). These linear relationships were used to predict pKa values of 90 drug molecules with known pKas. A total of 48 % of the calculated values were within 1 logarithmic unit of the experimental number, but mainstream empirically based methods easily outperform this approach. The conclusion can therefore be reached that PA values cannot be reliably used for predicting pKa values globally but are useful within chemical families and in the event where a specific tautomer of a drug needs to be identified.

Proton dissociation properties of arylphosphonates: Determination of accurate Hammett equation parameters

Determination of the proton dissociation constants of several arylphosphonic acid derivatives was carried out to investigate the accuracy of the Hammett equations available for this family of compounds. For the measurement of the pK_a values modern, accurate methods, such as the differential potentiometric titration and NMR-pH titration were used. We found our results significantly different from the pK_a values reported before (pK_a1: MAE = 0.16 pK_a2: MAE=0.59). Based on our recently measured pK_a values, refined Hammett equations were determined that might be used for predicting highly accurate ionization constants of newly synthesized compounds (pK_a1=1.70-0.894σ, pK_a2=6.92-0.934σ).

Six global and local QSPR models of aqueous solubility at pH = 7.4 based on structural similarity and physicochemical descriptors

Aqueous solubility at pH = 7.4 is a very important property for medicinal chemists because this is the pH value of physiological media. The present work describes the application of three different methods (support vector machine (SVM), random forest (RF) and multiple linear regression (MLR)) and three local quantitative structure-property relationship (QSPR) models (regression corrected by nearest neighbours (RCNN), arithmetic mean property (AMP) and local regression property (LoReP)) to construct stable QSPRs with clear mechanistic interpretation. Our data set contained experimental values of aqueous solubility at pH = 7.4 of 387 chemicals (349 in the training set and 38 in the test set including 16 own measurements). The initial descriptor pool contained 210 physicochemical descriptors, calculated from the HYBOT, DRAGON, SYBYL and VolSurf+ programs. Six QSPRs with good statistics based on fundamentals of aqueous solubility and optimization of descriptor space were obtained. Those models have an RMSE close to experimental error (0.70), and are amenable to physical interpretation. The QSPR models developed in this study may be useful for medicinal chemists. Global MLR, RF and SVM models may be valuable for consideration of common factors that influence solubility. The RCNN, AMP and LoReP local models may be helpful for the optimization of aqueous solubility in small sets of related chemicals.

Determination of acid dissociation constants (pKa) of cephalosporin antibiotics: Computational and experimental approaches

Cefapirin (CEPA) and ceftiofur (CEF) are two examples of widely used veterinarian cephalosporins presenting multiple ionization centers. However, the acid dissociation constants (pK_a) of CEF are missing and experimental data about CEPA are rare. The same is true for many cephalosporins, where available data are either incomplete or even wrong. Environmentally relevant biotic and abiotic processes depend primordially on the antibiotic pH-dependent speciation. Consequently, this physicochemical parameter should be reliable, including the correct ionization center identification. In this direction, two experimental techniques, potentiometry and spectrophotometry, along with two well-known pK_a predictors, Marvin and ACD/Percepta, were used to study the macro dissociation constants of CEPA and CEF. Additionally, the experimental dissociation constants of 14 cephalosporins available in the literature were revised, compiled and compared with data obtained in silico. Only one value was determined experimentally for CEF (2.68 ± 0.05), which was associated to the carboxylic acid group deprotonation. For CEPA two values were obtained experimentally: 2.74 ± 0.01 for the carboxylic acid deprotonation and 5.13 ± 0.01 for the pyridinium ring deprotonation. In general, experimentally obtained values agree with the in silico predicted data (ACD/Percepta RMSE: 0.552 and Marvin RMSE: 0.706, n = 88). However, for cephalosporins having imine and aminothiazole groups structurally close, Marvin presented problems in pK_a predictions. For the biological and environmental fate and effect discussion, it is important to recognize that CEPA and CEF, as well as many other cephalosporins, are present as anionic species in the biologic and environmentally relevant pH values of 6-7.5.

A pH-dependent computational approach to the effect of mutations on protein stability

This article describes a novel software implementation for high-throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian-chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state-of-the-art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper-stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.

Prediction of the Fate of Organic Compounds in the Environment From Their Molecular Properties: A Review

A comprehensive review of quantitative structure-activity relationships (QSAR) allowing the prediction of the fate of organic compounds in the environment from their molecular properties was done. The considered processes were water dissolution, dissociation, volatilization, retention on soils and sediments (mainly adsorption and desorption), degradation (biotic and abiotic), and absorption by plants. A total of 790 equations involving 686 structural molecular descriptors are reported to estimate 90 environmental parameters related to these processes. A significant number of equations was found for dissociation process (pKa), water dissolution or hydrophobic behavior (especially through the KOW parameter), adsorption to soils and biodegradation. A lack of QSAR was observed to estimate desorption or potential of transfer to water. Among the 686 molecular descriptors, five were found to be dominant in the 790 collected equations and the most generic ones: four quantum-chemical descriptors, the energy of the highest occupied molecular orbital (EHOMO) and the energy of the lowest unoccupied molecular orbital (ELUMO), polarizability (α) and dipole moment (μ), and one constitutional descriptor, the molecular weight. Keeping in mind that the combination of descriptors belonging to different categories (constitutional, topological, quantum-chemical) led to improve QSAR performances, these descriptors should be considered for the development of new QSAR, for further predictions of environmental parameters. This review also allows finding of the relevant QSAR equations to predict the fate of a wide diversity of compounds in the environment.

How Does the Methodology of 3D Structure Preparation Influence the Quality of pKa Prediction?

The acid dissociation constant is an important molecular property, and it can be successfully predicted by Quantitative Structure-Property Relationship (QSPR) models, even for in silico designed molecules. We analyzed how the methodology of in silico 3D structure preparation influences the quality of QSPR models. Specifically, we evaluated and compared QSPR models based on six different 3D structure sources (DTP NCI, Pubchem, Balloon, Frog2, OpenBabel, and RDKit) combined with four different types of optimization. These analyses were performed for three classes of molecules (phenols, carboxylic acids, anilines), and the QSPR model descriptors were quantum mechanical (QM) and empirical partial atomic charges. Specifically, we developed 516 QSPR models and afterward systematically analyzed the influence of the 3D structure source and other factors on their quality. Our results confirmed that QSPR models based on partial atomic charges are able to predict pKa with high accuracy. We also confirmed that ab initio and semiempirical QM charges provide very accurate QSPR models and using empirical charges based on electronegativity equalization is also acceptable, as well as advantageous, because their calculation is very fast. On the other hand, Gasteiger-Marsili empirical charges are not applicable for pKa prediction. We later found that QSPR models for some classes of molecules (carboxylic acids) are less accurate. In this context, we compared the influence of different 3D structure sources. We found that an appropriate selection of 3D structure source and optimization method is essential for the successful QSPR modeling of pKa. Specifically, the 3D structures from the DTP NCI and Pubchem databases performed the best, as they provided very accurate QSPR models for all the tested molecular classes and charge calculation approaches, and they do not require optimization. Also, Frog2 performed very well. Other 3D structure sources can also be used but are not so robust, and an unfortunate combination of molecular class and charge calculation approach can produce weak QSPR models. Additionally, these 3D structures generally need optimization in order to produce good quality QSPR models.

Photometric method for determination of acidity constants through integral spectra analysis

An express method for determination of acidity constants of organic acids, based on the analysis of the integral transmittance vs. pH dependence is developed. The integral value is registered as a photocurrent of photometric device simultaneously with potentiometric titration. The proposed method allows to obtain pKa using only simple and low-cost instrumentation. The optical part of the experimental setup has been optimized through the exclusion of the monochromator device. Thus it only takes 10-15 min to obtain one pKa value with the absolute error of less than 0.15 pH units. Application limitations and reliability of the method have been tested for a series of organic acids of various nature.

Prediction of the pharmacokinetics and tissue distribution of levofloxacin in humans based on an extrapolated PBPK model

This study developed a physiologically based pharmacokinetic (PBPK) model in intraabdominally infected rats and extrapolated it to humans to predict the levofloxacin pharmacokinetics and penetration into tissues. Twelve male rats with intraabdominal infections induced by Escherichia coli received a single dose of 50 mg/kg body weight of levofloxacin. Blood plasma was collected at 5, 10, 20, 30, 60, 120, 240, 480 and 1440 min after injection, respectively. A PBPK model was developed in rats and extrapolated to humans using GastroPlus software. The predictions were assessed by comparing predictions and observations. In the plasma concentration-versus-time profile of levofloxacin in rats, C max was 23.570 μg/ml at 5 min after intravenous injection, and t1/2 was 2.38 h. The plasma concentration and kinetics in humans were predicted and validated by the observed data. Levofloxacin penetrated and accumulated with high concentrations in the heart, liver, kidney, spleen, muscle and skin tissues in humans. The predicted tissue-to-plasma concentration ratios in abdominal viscera were between 1.9 and 2.3. When rat plasma concentrations were known, extrapolation of a PBPK model was a method to predict the drug pharmacokinetics and penetration in humans. Levofloxacin had good penetration into the liver, kidney and spleen as well as other tissues in humans. This pathological model extrapolation may provide a reference for the study of antiinfective PK/PD. In our study, levofloxacin penetrated well into abdominal organs. Also ADR monitoring should be implemented when using levofloxacin.

Prediction of Pharmacokinetics and Penetration of Moxifloxacin in Human with Intra-Abdominal Infection Based on Extrapolated PBPK Model

The aim of this study is to develop a physiologically based pharmacokinetic (PBPK) model in intra-abdominal infected rats, and extrapolate it to human to predict moxifloxacin pharmacokinetics profiles in various tissues in intra-abdominal infected human. 12 male rats with intra-abdominal infections, induced by Escherichia coli, received a single dose of 40 mg/kg body weight of moxifloxacin. Blood plasma was collected at 5, 10, 20, 30, 60, 120, 240, 480, 1440 min after drug injection. A PBPK model was developed in rats and extrapolated to human using GastroPlus software. The predictions were assessed by comparing predictions and observations. In the plasma concentration versus time profile of moxifloxcinin rats, C_max was 11.151 µg/mL at 5 min after the intravenous injection and t_1/2 was 2.936 h. Plasma concentration and kinetics in human were predicted and compared with observed datas. Moxifloxacin penetrated and accumulated with high concentrations in redmarrow, lung, skin, heart, liver, kidney, spleen, muscle tissues in human with intra-abdominal infection. The predicted tissue to plasma concentration ratios in abdominal viscera were between 1.1 and 2.2. When rat plasma concentrations were known, extrapolation of a PBPK model was a method to predict drug pharmacokinetics and penetration in human. Moxifloxacin has a good penetration into liver, kidney, spleen, as well as other tissues in intra-abdominal infected human. Close monitoring are necessary when using moxifloxacin due to its high concentration distribution. This pathological model extrapolation may provide reference to the PK/PD study of antibacterial agents.

Linear free-energy relationships between a single gas-phase ab initio equilibrium bond length and experimental pKa values in aqueous solution

Remarkably simple yet effective linear free energy relationships were discovered between a single ab initio computed bond length in the gas phase and experimental pKa values in aqueous solution. The formation of these relationships is driven by chemical features such as functional groups, meta/para substitution and tautomerism. The high structural content of the ab initio bond length makes a given data set essentially divide itself into high correlation subsets (HCSs). Surprisingly, all molecules in a given high correlation subset share the same conformation in the gas phase. Here we show that accurate pKa values can be predicted from such HCSs. This is achieved within an accuracy of 0.2 pKa units for 5 drug molecules.

Enantioselective synthesis and physicochemical properties of libraries of 3-amino- and 3-amidofluoropiperidines

The enantioselective syntheses of 3-amino-5-fluoropiperidines and 3-amino-5,5-difluoropiperidines were developed using the ring enlargement of prolinols to access libraries of 3-amino- and 3-amidofluoropiperidines. The study of the physicochemical properties revealed that fluorine atom(s) decrease(s) the pKa and modulate(s) the lipophilicity of 3-aminopiperidines. The relative stereochemistry of the fluorine atoms with the amino groups at C3 on the piperidine core has a small effect on the pKa due to conformationnal modifications induced by fluorine atom(s). In the protonated forms, the C-F bond is in an axial position due to a dipole-dipole interaction between the N-H(+) and C-F bonds. Predictions of the physicochemical properties using common software appeared to be limited to determine correct values of pKa and/or differences of pKa between cis- and trans-3-amino-5-fluoropiperidines.