In indirect detection, sample components lacking detectable properties are detected by adding a detectable component to the eluent, a so-called probe that interacts with the analytes to be detected. This study focuses on modeling indirect detection in two principally different cases. In case (1), the analyte component has the same charge as the probe component, so the probe acts as a co-ion of the analyte. In case (2), the analyte component has the opposite charge to the probe, so the probe acts as a counter-ion of the analyte. In the co-ion case (1), the analytes are alkyl sulfonates, and a competitive bi-Langmuir isotherm model was used. In the counter-ion case (2), the analytes are amines, and a modified bi-Langmuir isotherm model, incorporating ion-pairing on the stationary phase surface, was derived and applied for simulating the elution profiles. The chromatographic system comprised an XBridge Phenyl column as the stationary phase and an acetonitrile/phosphate buffer mixture with varying concentrations of sodium 2-naphthalenesulfonate as the eluent. In both cases, the detectable probe component was sodium 2-naphthalenesulfonate. The applied isotherm models successfully predicted system peaks with high agreement in both model cases, with calculated relative errors in retention times typically below 4.72 % and often below 1 %. The models were employed to predict the sensitivity of analytical methods, demonstrating excellent agreement between experimental and calculated sensitivities. These findings confirm the validity of the new adsorption isotherm model under these experimental conditions. 

Short interfering RNA (siRNA) represents a rapidly expanding class of marketed oligonucleotide therapeutics. Due to its double-stranded nature, the characterization of siRNA is twofold: (i) at the single-strand (denaturing) level for impurity profiling and (ii) at the intact (nondenaturing) level to confirm duplex formation and quantify excess single strands (including single strand-derived impurities). While denaturing analysis can be carried out using conventional ion-pair reversed-phase liquid chromatography (IP-RPLC), nondenaturing characterization of siRNA is a significantly less straightforward task. Typical IP-RPLC conditions have an intrinsic denaturing effect on siRNA, thereby limiting the development of viable approaches for the intact duplex analysis. In this study, we demonstrate, through the design of experiments of siRNA melting temperatures and chromatography analyses, that the simple addition of salts, such as phosphate-buffered saline and ammonium acetate, to eluents enhances the suitability of IP-RPLC for the nondenaturing analysis of siRNA during both UV- and mass spectrometry-based analysis. This work represents a milestone in overcoming the challenges associated with nondenaturing analysis of siRNAs by IP-RPLC and offers a fresh angle for exploring IP-RPLC of siRNAs.

The retention of three peptides was studied under analytical and overloaded conditions at different concentrations of trifluoroacetic acid (TFA) and water added to the co-solvent methanol (MeOH). Four columns with different stationary phase properties, i.e., silica, diol, 2-ethylpyridine and cyanopropyl (CN) columns, were evaluated in this investigation. The overall aim was to get a deeper understanding on how column chemistry as well as water and TFA in the co-solvent affect the analytical and overloaded elution profiles using multivariate design of experiments and adsorption measurements of co-solvent components. Multivariate experimental design modeling indicated that water had on average around five times higher effect on the retention than the addition of TFA. The results also showed that the retention increases with the addition of TFA and water to the co-solvent on all columns except the CN column, on which the retention decreased. When examining the effect of adding water to the co-solvent, evidence of a hydrophilic interaction liquid chromatography (HILIC)-like retention mechanism was found on the three other columns with more polar stationary phases. However, on the CN column water acted as an additive, decreasing the retention due to competition with the peptide for available adsorption surface. Adsorption isotherm measurements of the polar solvent MeOH showed that MeOH adsorbs much weaker on the CN column than on the other columns. Addition of TFA and water to the co-solvent substantially sharpened the elution profiles under both overloaded and analytical conditions. Adding a small amount of TFA (from 0 % to 0.05 %) to the co-solvent substantially improved the peak shape of the elution profiles, while further addition (from 0.05 % to 0.15 %) had only a minor effect on the elution profile shape. The reduced retention on the CN column could not be explained by TFA adsorption, which was very weak on all studied columns (retention factor, 0.05–0.15). One could therefore speculate that the ion-pairing complex formed between the peptide and TFA in the mobile phase, reduce the retention due to its reduced polarity. On the other columns displaying HILIC-like properties, the TFA probably just decreased the pH of the mobile phase, thereby promoting the partitioning of the peptide into the water-rich layer. Finally, peak deformation due to diluent–eluent mismatch was observed under overloaded conditions. This was most severe in the cases where MeOH adsorption to the stationary phase was strong and the peptides were only mildly retained. Adding 1,4-dioxan to the diluent resolved this issue. 

In this study, overloaded elution profiles under ultra-high-pressure liquid chromatographic (UHPLC) conditions and accounting for the severe pressure and temperature gradients generated, are compared with experimental data. The model system consisted of an C18 column packed with 1.7-µm particles (i.e., a UHPLC column) and the solute was 1,3,5-tri‑tert-butylbenzene eluted with a mobile phase composed of 85/15 (v/v) acetonitrile/water. Two thermal modes were considered, and the solute was eluted at the very high inlet pressures necessary to achieve a highly efficient and rapid chromatographic process, as provided by using columns packed with small particles. However, the high inlet pressure and high linear velocity of the mobile phase caused the production of a significant amount of heat, and consequently, the formation of axial and radial temperature gradients. Due to these gradients, the retention and the mobile phase velocity were no longer constant. Thus, simple mathematical models consisting only of the mass balance equations are unsuitable to properly model the elution profiles. Here, the elution concentration profiles were predicted using a combined two-dimensional heat and mass transfer model, also including the calculation of the mobile phase velocity distribution. The isotherm adsorption model was the bi-Langmuir isotherm model with Henry constants that depended on the local temperature and pressure in the column. These adjustments allowed us to precisely account for changes in the shape and retention of the overloaded concentration profiles in the mobile phase. The proposed model provided accurate predictions of the overloaded concentration profiles, demonstrating good agreement with experimental profiles eluted under severe pressure and temperature gradients in the column even in the most extreme cases where the pressure drops reached 846 bar and the temperature gradients equaled 0.15 K mm−1 and 0.95 K mm−1 in the axial and the radial directions, respectively. In such cases 36 % decrease of the retention factor was observed along the column and 2 % increase in radial direction. These changes, combined with the velocity distribution, shifted the overloaded elution profile’s shock towards the center of the column, advancing approximately 3 mm from its initial position close to the column wall. Ultimately, this resulted in the broadening of the elution band. 

The adsorption and desorption behavior of volatile nitrogen-containing compounds in vapor phase by solid-phase microextraction Arrow (SPME-Arrow) and in-tube extraction (ITEX) sampling systems, were investigated experimentally using gas chromatography-mass spectrometry. Three different SPME-Arrow coating materials, DVB/PDMS, MCM-41, and MCM-41-TP and two ITEX adsorbents, TENAX-GR and MCM-41-TP were compared to clarify the selectivity of the sorbents towards nitrogen-containing compounds. In addition, saturated vapor pressures for these compounds were estimated, both experimentally and theoretically. In this study, the adsorption of nitrogen-containing compounds on various adsorbents fol-lowed the Elovich model well, while a pseudo-first-order kinetics model best described the desorption kinetics. Pore volume and pore sizes of the coating sorbents were essential parameters for the deter-mination of the adsorption performance for the SPME-Arrow sampling system. MCM-41-TP coating with the smallest pore size gave the slowest adsorption rate compared to that of DVB/PDMS and MCM-41 in the SPME-Arrow sampling system. Both adsorbent and adsorbate properties, such as hydrophobicity and basicity, affected the adsorption and desorption kinetics in SPME-Arrow system. The adsorption and desorption rates of studied C6H15N isomers in the MCM-41 and MCM-41-TP sorbent materials of SPME-Arrow system were higher for dipropylamine and triethylamine (branched amines) than for hexylamine (linear chain amines). DVB/PDMS-SPME-Arrow gave fast adsorption rates for the aromatic-ringed pyridine and o-toluidine. All studied nitrogen-containing compounds demonstrated high desorption rates with DVB/PDMS-SPME-Arrow. Chemisorption and physisorption were the sorption mechanisms in MCM-41-and MCM-41-TP-SPME-Arrow, but additional experiments are needed to confirm this. An active sampling technique ITEX gave comparable adsorption and desorption rates on the selective MCM-41-TP and univer-sal TENAX-GR sorbent materials for all the compounds studied. Vapor pressures of nitrogen-containing compounds were experimentally estimated by using retention index approach and these values were compared with the theoretical ones, calculated using the COnductor-like Screening MOdel for Real Sol-vent (COSMO-RS) model. Both values agreed well with those found in the literature proving that these methods can be successfully used in predicting VOC's vapor pressures, e.g. for the formation of secondary organic aerosols.

Toxicity of β-blockers is one of the most common causes of poison-induced cardiogenic shock throughout the world. Therefore, methodologies for in vivo removal of the drugs from the body have been under investigation. Intralipid emulsion (ILE) is a common commercial lipid emulsion used for parenteral nutrition, but it has also been administered to patients suffering from drug toxicities. In this work, a set of β-blockers of different hydrophobicity’s (log KD values ranging from 0.16 to 3.8) were investigated. The relative strength of the interactions between these compounds and the ILE was quantitatively assessed by means of binding constants and adsorption constants of the formed β-blocker-ILE complexes. The binding constants were determined by capillary electrokinetic chromatography and the adsorption constants were calculated based on different adsorption isotherms. Expectedly, the binding constants were strongly related to the log KD values of the β-blockers. The binding and adsorption constants also show that less hydrophobic β-blockers interact with ILE, suggesting that this emulsion could be useful for capturing such compounds in cases of their overdoses. Thus, the use of ILE for treatment of toxicities caused by a larger range of β-blockers is worth further investigation. 

Preparative chromatography is the best generic method currently available for purifying small drugs and valuable chemical components at the 10-kg level. Progress in computer technology, the development of new non-chiral/chiral stationary phases, and numerous improvements in reliability and economic performance have considerably increased the interest in modeling in academia and industry. This chapter introduces the modeling of preparative liquid chromatography in order to improve the purification process for valuable chemical components such as drugs and chiral components. We review the most important column and adsorption models and the methods for determining the essential thermodynamic adsorption data for both column characterization and process improvement. We also cover important operational modes (e.g., separation in gradient mode), cases involving additives or ion-pair reagents, and operational conditions sometimes neglected in the modeling process, for example, involving the impact of injection profiles. 

Ion-pair chromatography is the de facto standard for separating oligonucleotides and related impurities, particularly for analysis but also often for small-scale purification. Currently, there is limited understanding of the quantitative modeling of both analytical and overloaded elution profiles obtained during gradient elution in ion-pair chromatography. Here we will investigate a recently introduced gradient mode, the so-called ion-pairing reagent gradient mode, for both analytical and overloaded separations of oligonucleotides. The first part of the study demonstrates how the electrostatic theory of ion-pair chromatography can be applied for modeling gradient elution of oligonucleotides. When the ion-pair gradient mode is used in a region where the electrostatic surface potential can be linearized, a closed-form expression of retention time can be derived. A unified retention model was then derived, applicable for both ion-pair reagent gradient mode as well as co-solvent gradient mode. The model was verified for two different experimental systems and homo- and heteromeric oligonucleotides of different lengths. Quantitative modeling of overloaded chromatography using the ion-pairing reagent gradient mode was also investigated. Firstly, a unified adsorption isotherm model was developed for both gradient modes. Then, adsorption isotherms parameter of a model oligonucleotide and two major synthetic impurities were estimated using the inverse method. Secondly, the parameters of the adsorption isotherm were then used to investigate how the productivity of oligonucleotide varies with injection volume, gradient slope, and initial retention factor. Here, the productivity increased when using a shallow gradient slope combined with a low initial retention factor. Finally, experiments were conducted to confirming some of the model predictions. Comparison with the conventional co-solvent gradient mode showed that the ion-pairing reagent gradient leads to both higher yield and productivity while consuming less co-solvent.

In recent decades, there has been a trend toward using larger biological molecules as new active pharmaceutical ingredients (APIs) instead of the classical small organic API molecules. More recently, this trend has shifted from very large biomolecules toward intermediate-sized APIs, such as oligonucleotide therapeutics. Because of their fundamental role in gene regulation, therapeutic oligonucleotides can be directed against their specific ribonucleic acid (RNA) targets, representing a promising customized approach for the treatment of hitherto incurable diseases. There are several FDA-approved oligonucleotide-based therapeutics and many more are awaiting approval. The complicated synthesis and degradation pathways of oligonucleotides, involving sophisticated new chemical modifications, generate hundreds of impurities, in contrast to classical small APIs, which typically contain only around three to five well-defined impurities (Fig. 1). Therefore, this new class of putative drugs entails challenging separation tasks: for example, a small mass change such as 1 Da must be distinguished in a 10,000 Da parent molecule for purposes of both quantification and purification and at extremely high resolution. All therapeutic oligonucleotides must be chemically modified before entering the body. One such modification is the phosphorothioate (PS) modification, which generates diastereomers: for a 20-nucleotide-long PS oligonucleotide, this exceeds half a million diastereomers. In this review, we will examine recently published ion-pair liquid chromatographic separation strategies to meet current challenges in oligonucleotide separations. Ion-exchange chromatography will be briefly discussed based on its merits for large-scale purification. The review focuses on studies combining theory and practice and aiming at the analysis and preparative separation necessary for performing reliable quality control as well as purification. All relevant aspects of the separation systems will be discussed, including the stationary phase, pore size, mobile phase, and ion-pairing reagents. We will also discuss how the properties of the oligonucleotide and its impurities can be exploited to increase separation selectivity. A particular focus will be on the adsorption of ion-pairing reagent and the electrostatic surface potential it generates, allowing for interaction with the highly charged oligonucleotides. Furthermore, the effects of various gradient modes to decrease the electrostatic potential and thereby elute oligonucleotides will be covered. 

Due to their potential for gene regulation, oligonucleotides have moved into focus as one of the preferred modalities modulating currently undruggable disease-associated targets. In the course of synthesis and storage of oligonucleotides a significant number of compound-related impurities can be generated. Purification protocols and analytical methods have become crucial for the therapeutic application of any oligonucleotides, be they antisense oligonucleotides (ASOs), small interfering ribonucleic acids (siRNAs) or conjugates. Ion-pair chromatography is currently the standard method for separating and analyzing therapeutic oligonucleotides. Although mathematical modeling can improve the accuracy and efficiency of ion-pair chromatography, its application remains challenging. Simple models may not be suitable to treat advanced single molecules, while complex models are still inefficient for industrial oligonucleotide optimization processes. Therefore, fundamental research to improve the accuracy and simplicity of mathematical models in ion-pair chromatography is still a necessity. In this study, we predict overloaded concentration profiles of oligonucleotides in ion-pair chromatography and compare relatively simple and more advanced predictive models. The experimental system consists of a traditional C18 column using (dibutyl)amine as the ion-pair reagent and acetonitrile as organic modifier. The models were built and tested based on three crude 16-mer oligonucleotides with varying degrees of phosphorothioation, as well as their respective n – 1 and (P = O)1 impurities. In short, the proposed models were suitable to predict the overloaded concentration profiles for different slopes of the organic modifier gradient and column load.