Stochastic Theory Of Chromatography Research Articles

Unraveling peak asymmetry in chromatography through stochastic theory powered Monte Carlo simulations

An overarching theory of chromatography capable of modeling all analyte-stationary phase interactions would enable predictive design of pharmaceutically relevant separations. The stochastic theory of chromatography has been postulated as a suitable basis to achieve this goal. Here, we implement Dondi and Cavazzini's Monte Carlo framework that utilizes experimentally accessible single molecule kinetics and use it to correlate heterogenous adsorption statistics at the stationary phase to shifts in asymmetry. The contributions cannot be captured or modeled through ensemble chemometrics. Simulations reveal that peak asymmetry scales non-linearly with longer analyte-stationary phase interactions and migrates towards symmetry across the column length, even without column overloading.

A mechanistic examination of salting out in protein–polymer membrane interactions

Developing a mechanistic understanding of protein dynamics and conformational changes at polymer interfaces is critical for a range of processes including industrial protein separations. Salting out is one example of a procedure that is ubiquitous in protein separations yet is optimized empirically because there is no mechanistic description of the underlying interactions that would allow predictive modeling. Here, we investigate peak narrowing in a model transferrin-nylon system under salting out conditions using a combination of single-molecule tracking and ensemble separations. Distinct surface transport modes and protein conformational changes at the negatively charged nylon interface are quantified as a function of salt concentration. Single-molecule kinetics relate macroscale improvements in chromatographic peak broadening with microscale distributions of surface interaction mechanisms such as continuous-time random walks and simple adsorption-desorption. Monte Carlo simulations underpinned by the stochastic theory of chromatography are performed using kinetic data extracted from single-molecule observations. Simulations agree with experiment, revealing a decrease in peak broadening as the salt concentration increases. The results suggest that chemical modifications to membranes that decrease the probability of surface random walks could reduce peak broadening in full-scale protein separations. More broadly, this work represents a proof of concept for combining single-molecule experiments and a mechanistic theory to improve costly and time-consuming empirical methods of optimization.

Retention controlling and peak shape simulation in anion chromatography using multiple equilibrium model and stochastic theory

The stochastic theory of chromatography and an equilibrium based approach were used for the prediction of peak shape and retention data of anions. This attempt incorporating the potential advantages of two different chromatographic phenomena for analytical purposes. It is an integrated method to estimate kinetic and thermodynamic properties for the same chromatographic run of ions. The stochastic parameters of eluted anions, such as the residence time of the molecule on the surface of the stationary phase, and the average number of adsorption steps were determined on the basis of a retention database of organic and inorganic anions (formate, chloride, bromide, nitrate, sulphate, oxalate, phosphate) obtained by using carbonate/bicarbonate eluent system at different pHs (9–11) and concentrations (7–13 mM). In the investigated IC system the residence times are much higher and the average number of sorption steps is somewhat smaller than in RP-HPLC. The simultaneous application of the stochastic and the multispecies eluent/analyte model was utilized to peak shape simulation and the retention controlling of various anions under elution conditions of practical importance. The similarities between the measured and the calculated chromatograms indicates the predictive and simulation power of the combined application of the stochastic theory and the multiple species eluent/analyte retention model.

Adsorption behavior of a teicoplanin aglycone bonded stationary phase under harsh overload conditions

Silica-bonded teicoplanin aglycone allows enantioseparation of amino acids by reversed-phase liquid chromatography with a low organic solvent content. However, a reversible change in the adsorption behavior leading to a retention time shift (RTS) was observed when a preparative scale column was treated with harsh preparative chromatography-like conditions between finite-injection HPLC runs conducted under exactly the same conditions. This behavior was observed for all five investigated aliphatic and aromatic amino acids. In all cases, the retention times were prolonged after the overload conditions and the RTS was more pronounced for the later eluting d-enantiomer. We defined a standardized method for measuring the RTS and performed a systematic investigation on the influence of experimental conditions (type and concentration of pH modifier and organic modifier, temperature, pH) on the RTS. In this way a solvent composition – 90/10 50 mM NH 4Ac pH 5.8/MeOH – was identified that yielded no observable shift in retention time after overload conditions for both enantiomers. In order to treat the observed phenomenon on a mechanistic level, we applied band profile analysis based on the stochastic theory of chromatography and identified two different enantioselective sites. When the band profile analysis was performed on elution profiles obtained from runs with prolonged retention time after harsh overload conditions, the retention time shift could be attributed to both differentiable types of adsorption sites. One site was found to make both, enantioselective and non-selective contributions.

The characteristic function method in the stochastic theory of chromatography

The characteristic function method in the stochastic theory of chromatography

On the Stochastic Theory of Chromatography

Chromatography has been represented as a Poisson process and expressions have been derived for the elution curves of various types of chromatographic systems, such as a column with several kinds of sites, and a column with one kind of site but with various realistic input distributions. The previous stochastic treatments of chromatography have solved exactly only the case of a column with one kind of site with a delta-function input distribution. These various cases have been solved by means of the complex-variable theory of Laplace transforms. The exact expressions are usually complicated and of not much numerical utility. A technique is described by means of which any case can be well approximated by a consideration of only the first few central moments. This has proved to be of great practical use since there exists a theorem of mathematical statistics which allows one to determine moments of complex problems when those of simpler problems are known. This makes it possible to derive easily used expressions for the various elution curves.