Herein, we used a Bayesian multilevel model of chromatographic retention to compare five reversed-phase high-performance liquid chromatography stationary phases: XBridge Shield RP18, XTerra MS C18, ...XBridge Phenyl, XBridge C8, and Xterra MS C8. For this, we used a large data set of retention times collected using chromatographic techniques coupled with mass spectrometry. The experiments were conducted in gradient mode for an initial mixture of 300 small analytes for a wide range of pH values in methanol and acetonitrile at two temperatures and for three gradient durations. Our analysis was based on a mechanistic model derived from the principles and fundamentals of liquid chromatography and utilized previously reported chromatographic parameters. The data and model were used to characterize the between-column differences in the chromatographic parameters of the neutral, acidic, and basic analytes. The analysis provides an interpretable summary of stationary-phase properties that can be used in decision-making, i.e., finding the best chromatographic conditions using limited experimental data. The proposed approach is an interesting alternative to the existing approaches used to compare chromatographic stationary phases.
It is relatively easy to collect chromatographic measurements for a large number of analytes, especially with gradient chromatographic methods coupled with mass spectrometry detection. Such data ...often have a hierarchical or clustered structure. For example, analytes with similar hydrophobicity and dissociation constant tend to be more alike in their retention than a randomly chosen set of analytes. Multilevel models recognize the existence of such data structures by assigning a model for each parameter, with its parameters also estimated from data. In this work, a multilevel model is proposed to describe retention time data obtained from a series of wide linear organic modifier gradients of different gradient duration and different mobile phase pH for a large set of acids and bases. The multilevel model consists of (1) the same deterministic equation describing the relationship between retention time and analyte-specific and instrument-specific parameters, (2) covariance relationships relating various physicochemical properties of the analyte to chromatographically specific parameters through quantitative structure–retention relationship based equations, and (3) stochastic components of intra-analyte and interanalyte variability. The model was implemented in Stan, which provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods.
Graphical abstract
Relationships between log
k
and MeOH content for acidic, basic, and neutral compounds with different log
P
.
CI
credible interval,
PSA
polar surface area
Quantitative structure–retention relationships (QSRRs) are used in the field of chromatography to model the relationship between an analyte structure and chromatographic retention. Such models are ...typically difficult to build and validate for heterogeneous compounds because of their many descriptors and relatively limited analyte-specific data. In this study, a Bayesian multilevel model is proposed to characterize the isocratic retention time data collected for 1026 heterogeneous analytes. The QSRR considers the effects of the molecular mass and 100 functional groups (substituents) on analyte-specific chromatographic parameters of the Neue model (i.e., the retention factor in water, the retention factor in acetonitrile, and the curvature coefficient). A Bayesian multilevel regression model was used to smooth noisy parameter estimates with too few data and to consider the uncertainties in the model parameters. We discuss the benefits of the Bayesian multilevel model (i) to understand chromatographic data, (ii) to quantify the effect of functional groups on chromatographic retention, and (iii) to predict analyte retention based on various types of preliminary data. The uncertainty of isocratic and gradient predictions was visualized using uncertainty chromatograms and discussed in terms of usefulness in decision making. We think that this method will provide the most benefit in providing a unified scheme for analyzing large chromatographic databases and assessing the impact of functional groups and other descriptors on analyte retention.
Chromatographic retention times are usually modeled considering only one analyte at a time. However, it has certain limitations as no information is shared between the analytes, and consequently the ...model predictions poorly generalize to out-of-sample analytes. In this work, a publicly available dataset was used to illustrate the benefits of pooling the individual data and analyzing them simultaneously utilizing Bayesian hierarchical approach. Statistical analysis was carried out using the Stan program coupled with R, which enables full Bayesian inference with Markov chain Monte Carlo sampling. This methodology allows (i) incorporating prior knowledge about the likely values of model parameters, (ii) considering the between-analyte variability and the correlation between the model parameters, (iii) explaining the between-analyte variability by available predictors, and (iv) sharing information across the analytes. The latter is especially valuable when only limited information is available in the data about certain model parameters. The results are obtained in the form of posterior probability distribution, which quantifies uncertainty about the model parameters and predictions. Posterior probability is also directly relevant for decision-making. In this work, we used the Neue model to describe the relationship between retention factor and acetonitrile content in the mobile phase for 1026 analytes. The model was parametrized in terms of retention factor in 100% water, retention factor in 100% acetonitrile, and curvature coefficient, and considered log
P
and
pK
a
as predictors. From this analysis, we discovered that the analytes formed two clusters with different retention depending on the degree of analyte dissociation. The final model turned out to be well calibrated with the data. It gives insight into the behavior of analytes in the chromatographic column and can be used to make predictions for a structurally diverse set of analytes if their log
P
and
pK
a
values are known.
•A workflow for robustness evaluation in metabolic fingerprinting studies was developed.•Three statistical approaches for robustness assessment were compared.•Critical steps of sample preparation ...procedure for untargeted metabolomics can be identified.•Differences in metabolic profiles resulting from small fluctuations in sample preparation may be explained.•Functionality of analytical method for untargeted metabolomics might be evaluated.
Gas chromatography coupled with mass spectrometry (GC-MS) is considered as a reliable and effective technique for metabolomics analysis of human tissues and body fluids. However, sample preparation procedure for GC-MS is multi-stage, long-lasting and error-prone. That is why Design of Experiments approach is often used to assess the performance of commonly applied sample preparation procedures. In this work, Plackett-Burman design with 5 center points was used to evaluate the impact of 10 variables on the extraction and derivatization of metabolites from human urine samples. The obtained data was subjected to statistical analysis. In the first approach, the principal component analysis was performed to simplify the data matrix. The first two components (explaining the highest percent of the variability) were selected as response variables. They were regressed with parameters to assess the effects of the applied changes. The obtained PCA-based models suggest that alterations applied in input parameters settings may contribute to significant changes in the obtained responses, e.g. altered overnight incubation time influences the obtained metabolic profiles. In the second approach, the whole dataset was simplified by calculating the average signal intensity across metabolites. Those values, subjected to linear regression also pointed the overnight incubation time as the factor affecting sample preparation process the most. Finally, hierarchical linear modeling was applied in order to provide detailed evaluation of the applied changes. Such an approach enables the selection of variables influencing sample's metabolic profiles and each metabolite individually, providing also robustness to outliers. Ultimately, 12 experiments enabled to identify critical stages of the applied sample preparation procedure in terms of metabolic profile (abundances of specific metabolites). Furthermore, the obtained results might also suggest the direction for optimization of GC-MS method for targeted analysis of urine metabolites of different physico-chemical properties and allow to propose some minor modifications that might be beneficial for quality and repeatability of non-targeted experiments.
Display omitted
In this work, we proposed and investigated a Bayesian inference procedure to find the desired chromatographic conditions based on known analyte properties (lipophilicity, pK a, and polar surface ...area) using one preliminary experiment. A previously developed nonlinear mixed effect model was used to specify the prior information about a new analyte with known physicochemical properties. Further, the prior (no preliminary data) and posterior predictive distribution (prior + one experiment) were determined sequentially to search towards the desired separation. The following isocratic high-performance reversed-phase liquid chromatographic conditions were sought: (1) retention time of a single analyte within the range of 4–6 min and (2) baseline separation of two analytes with retention times within the range of 4–10 min. The empirical posterior Bayesian distribution of parameters was estimated using the “slice sampling” Markov Chain Monte Carlo (MCMC) algorithm implemented in Matlab. The simulations with artificial analytes and experimental data of ketoprofen and papaverine were used to test the proposed methodology. The simulation experiment showed that for a single and two randomly selected analytes, there is 97% and 74% probability of obtaining a successful chromatogram using none or one preliminary experiment. The desired separation for ketoprofen and papaverine was established based on a single experiment. It was confirmed that the search for a desired separation rarely requires a large number of chromatographic analyses at least for a simple optimization problem. The proposed Bayesian-based optimization scheme is a powerful method of finding a desired chromatographic separation based on a small number of preliminary experiments.
We present a review of the available literature concerning pKa values and methods for the determination of selected anticancer drugs as well as the most up-to-date knowledge on their different ionic ...forms depending on solution pH. Additionally, to clarify the existing state of knowledge we have presented an overview on the obtained pKa values with the use of experimental and computational methods. As a result, we have demonstrated and proposed acid-base equilibria of cyclophosphamide (CF), ifosfamide (IF), 5-fluorouracil (5-FU), methotrexate (MTX), and imatinib (IMT) in an aqueous solution, and their species distribution curves as a function of pH calculated on the basis of the acid dissociation constants, which are as follows:
CF pKa1 2.3, pKa2 11.1 CF-H2L+/CF-HL/CF-L−
IF pKa1 < 2.5, pKa2 9.1 IF-H2L+/IF-HL/IF-L−
5-FU pKa1 7.5, pKa2 9.0 5-FU-H2L/5-FU-HL−/5-FU-L2−
MTX pKa1 2.9, pKa2 4.6, pKa3 6.6 MTX-H3L+/MTX-H2L/MTX-HL−/MTX-L2−
IMT pKa1 2.5, pKa2 4.0, pKa3 8.3 IMT-H3L3+/IMT-H2L2+/IMT-HL+/MTX-L.
•Review on the literature pKa of five of cytostatics and methods for their determination.•Overview on the determined pKa values by experimental and computational methods.•Presentation of acid-base equilibria of five selected anticancer drugs in an aqueous solution.
Background and Objective
The risk of thrombotic complications in critical patients with COVID-19 remains extremely high, and multicenter trials failed to prove a survival benefit of escalated doses ...of low-molecular-weight heparins (nadroparin calcium) in this group. The aim of this study was to develop a pharmacokinetic model of nadroparin according to different stages of COVID-19 severity.
Methods
Blood samples were obtained from 43 patients with COVID-19 who received nadroparin and were treated with conventional oxygen therapy, mechanical ventilation, and extracorporeal membrane oxygenation. We recorded clinical, biochemical, and hemodynamic variables during 72 h of treatment. The analyzed data comprised 782 serum nadroparin concentrations and 219 anti-Xa levels. We conducted population nonlinear mixed-effects modeling (NONMEM) and performed Monte Carlo simulations of the probability of target attainment for reaching 0.2–0.5 IU/mL anti-Xa levels in study groups.
Results
We successfully developed a one-compartment model to describe the population pharmacokinetics of nadroparin in different stages of COVID-19. The absorption rate constant of nadroparin was 3.8 and 3.2 times lower, concentration clearance was 2.22 and 2.93 times higher, and anti-Xa clearance was 0.87 and 1.1 times higher in mechanically ventilated patients and the extracorporeal membrane oxygenation group compared with patients treated with conventional oxygen, respectively. The newly developed model indicated that 5.900 IU of nadroparin given subcutaneously twice daily in the mechanically ventilated patients led to a similar probability of target attainment of 90% as 5.900 IU of subcutaneous nadroparin given once daily in the group supplemented with conventional oxygen.
Conclusions
Different nadroparin dosing is required for patients undergoing mechanical ventilation and extracorporeal membrane oxygenation to achieve the same targets as those for non-critically ill patients.
Clinical Trial Registration
ClinicalTrials.gov identifier no. NCT05621915.
In this work, various sequential Bayesian‐based method development procedures associated with a search of isocratic chromatographic conditions ensuring baseline separation of one, two, and three ...analytes within the pre‐specified retention time window were evaluated. The accuracy and total analysis time of tested procedures were experimentally and theoretically verified and compared with the usual approaches utilizing one or two preliminary organic modifier gradients. The possession of strong and weakly informative priors about analytes was considered. The overall success rate of tested procedures was high with a small number of mistakes. It was shown that for simple problems considered here one is able to use a sequence of isocratic conditions to find the desired chromatogram. The use of one preliminary gradient was shown to be of similar accuracy and time requirements. Interestingly, the use of two preliminary gradients almost always required more time than procedures involving no or one preliminary gradient. Prior knowledge of analytes considerably shortened method development times for procedures involving no or one preliminary gradient. The sequential Bayesian‐based method development allows us to achieve a desired chromatographic separation by proper weighting of information available to the analyst at each stage of the method development process.
The aim of this work was to develop mathematical models relating the hydrophobicity and dissociation constant of an analyte with its structure, which would be useful in predicting analyte retention ...times in reversed-phase liquid chromatography. For that purpose a large and diverse group of 115 drugs was used to build three QSRR models combining retention-related parameters (logkw—chromatographic measure of hydrophobicity, S—slope factor from Snyder-Soczewinski equation, and pKa) with structural descriptors calculated by means of molecular modeling for both dissociated and nondissociated forms of analytes. Lasso, Stepwise and PLS regressions were used to build statistical models. Moreover a simple QSRR equations based on lipophilicity and dissociation constant parameters calculated in the ACD/Labs software were proposed and compared with quantum chemistry-based QSRR equations. The obtained relationships were further used to predict chromatographic retention times. The predictive performances of the obtained models were assessed using 10-fold cross-validation and external validation. The QSRR equations developed were simple and were characterized by satisfactory predictive performance. Application of quantum chemistry-based and ACD-based descriptors leads to similar accuracy of retention times’ prediction.
PDF
