Eric von Lieres

A fast and accurate solver for the general rate model of column liquid chromatography

Abstract Practical application of the general rate model is often hindered by computational complexity and by unknown parameter values. Model simplifications and parameter correlations are not always applicable, and repeated model solutions are required for parameter estimation and process optimization. We have hence developed and implemented a fast and accurate solver for the general rate model with various adsorption isotherms. Several state of the art scientific computing techniques have been combined for maximal solver performance: (1) the model equations are spatially discretized with finite volumes and the weighted essentially non-oscillatory (WENO) method. (2) A non-commercial solver with variable stepwidth and order is applied for time integration. (3) The internal linear solver module is replaced by customized code that is based on domain decomposition and can be executed on parallel computers. We demonstrate the speed and accuracy of our solver with numerical examples. The WENO method significantly improves accuracy even on rather coarse grids, and the solver runtime scales linearly with relevant grid sizes and processor numbers. Code parallelization is essential for utilizing the full power of multiprocessor and multicore technology in modern personal computers. The general rate model of a strongly non-linear two component system is solved in few seconds.

Spatiotemporal microbial single-cell analysis using a high-throughput microfluidics cultivation platform

Cell‐to‐cell heterogeneity typically evolves due to a manifold of biological and environmental factors and special phenotypes are often relevant for the fate of the whole population but challenging to detect during conventional analysis. We demonstrate a microfluidic single‐cell cultivation platform that incorporates several hundred growth chambers, in which isogenic bacteria microcolonies growing in cell monolayers are tracked by automated time‐lapse microscopy with spatiotemporal resolution. The device was not explicitly developed for a specific organism, but has a very generic configuration suitable for various different microbial organisms. In the present study, we analyzed Corynebacterium glutamicum microcolonies, thereby generating complete lineage trees and detailed single‐cell data on division behavior and morphology in order to demonstrate the platforms overall capabilities. Furthermore, the occurrence of spontaneously induced stress in individual C. glutamicum cells was investigated by analyzing strains with genetically encoded reporter systems and optically visualizing SOS response. The experiments revealed spontaneous SOS induction in the absence of any external trigger comparable to results obtained by flow cytometry (FC) analyzing cell samples from conventional shake flask cultivation. Our microfluidic setup delivers detailed single‐cell data with spatial and temporal resolution; complementary information to conventional FC results.

Influence of Organic Solvents on Enzymatic Asymmetric Carboligations

The asymmetric mixed carboligation of aldehydes with thiamine diphosphate (ThDP)-dependent enzymes is an excellent example where activity as well as changes in chemo- and stereoselectivity can be followed sensitively. To elucidate the influence of organic additives in enzymatic carboligation reactions of mixed 2-hydroxy ketones, we present a comparative study of six ThDP-dependent enzymes in 13 water-miscible organic solvents under equivalent reaction conditions. The influence of the additives on the stereoselectivity is most pronounced and follows a general trend. If the enzyme stereoselectivity in aqueous buffer is already >99.9% ee, none of the solvents reduces this high selectivity. In contrast, both stereoselectivity and chemoselectivity are strongly influenced if the enzyme is rather unselective in aqueous buffer. For the S-selective enzyme with the largest active site, we were able to prove a general correlation of the solvent-excluded volume of the additives with the effect on selectivity changes: the smaller the organic solvent molecule, the higher the impact of this additive. Further, a correlation to log P of the additives on selectivity was detected if two additives have almost the same solvent-excluded volume. The observed results are discussed in terms of structural, biochemical and energetic effects. This work demonstrates the potential of medium engineering as a powerful additional tool for varying enzyme selectivity and thus engineering the product range of biotransformations. It further demonstrates that the use of cosolvents should be carefully planned, as the solvents may compete with the substrate(s) for binding sites in the enzyme active site.

Zonal rate model for stacked membrane chromatography. I: Characterizing solute dispersion under flow-through conditions

Conventional models of both packed-bed and stacked-membrane chromatography typically attribute elution band broadening to non-idealities within the column. However, when the column length to diameter ratio is greatly reduced, as in stacked-membrane chromatography, variations in solute residence times within the feed-distribution (inlet) and eluent-collection (outlet) manifolds can also contribute to band broadening. We report on a new zonal rate model (ZRM) for stacked-membrane chromatography that improves on existing hold-up volume models that rely on one plug-flow reactor and one stirred-tank reactor in series to describe dispersion of solute during transport into and out of the column. The ZRM radially partitions the membrane stack and the hold-up volumes within the inlet and outlet manifolds into zones to better capture non-uniform flow distribution effects associated with the large column diameter to height ratio. Breakthrough curves from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1) under non-binding conditions and used to evaluate the ZRM as well as previous models. The ZRM was shown to be significantly more accurate in describing protein dispersion and breakthrough. The model was then used to decompose breakthrough data, where it was found that variations in solute residence time distributions within the inlet and outlet manifolds make the dominant contribution to solute dispersion over the recommended range of feed flow rates. The ZRM therefore identifies manifold design as a critical contributor to separation quality within stacked-membrane chromatography units.

Mechanistic modeling of ion-exchange process chromatography of charge variants of monoclonal antibody products

Ion-exchange chromatography (IEX) is universally accepted as the optimal method for achieving process scale separation of charge variants of a monoclonal antibody (mAb) therapeutic. These variants are closely related to the product and a baseline separation is rarely achieved. The general practice is to fractionate the eluate from the IEX column, analyze the fractions and then pool the desired fractions to obtain the targeted composition of variants. This is, however, a very cumbersome and time consuming exercise. A mechanistic model that is capable of simulating the peak profile will be a much more elegant and effective way to make a decision on the pooling strategy. This paper proposes a mechanistic model, based on the general rate model, to predict elution peak profile for separation of the main product from its variants. The proposed approach uses inverse fit of process scale chromatogram for estimation of model parameters using the initial values that are obtained from theoretical correlations. The packed bed column has been modeled along with the chromatographic system consisting of the mixer, tubing and detectors as a series of dispersed plug flow and continuous stirred tank reactors. The model uses loading ranges starting at 25% to a maximum of 70% of the loading capacity and hence is applicable to process scale separations. Langmuir model has been extended to include the effects of salt concentration and temperature on the model parameters. The extended Langmuir model that has been proposed uses one less parameter than the SMA model and this results in a significant ease of estimating the model parameters from inverse fitting. The proposed model has been validated with experimental data and has been shown to successfully predict peak profile for a range of load capacities (15-28mg/mL), gradient lengths (10-30CV), bed heights (6-20cm), and for three different resins with good accuracy (as measured by estimation of residuals). The model has been also validated for a two component mixture consisting of the main mAb product and one of its basic charge variants. The proposed model can be used for optimization and control of preparative scale chromatography for separation of charge variants.

Fast and accurate parameter sensitivities for the general rate model of column liquid chromatography

Abstract A fast and accurate solver for the general rate model is extended for computing sensitivities that describe the impact of small parameter changes on the simulated chromatograms. Parameter sensitivities are required by many optimization algorithms and are useful for understanding how chromatograms depend on specific system properties or operating conditions. They are efficiently computed with arbitrary precision by integrating a forward sensitivity DAE system that is derived from the original DAE system. The involved partial derivatives are either manually derived or computed by algorithmic differentiation. This approach is demonstrated to be more robust and faster for realistically sized problems, as compared to the traditional finite difference approach. Sensitivities are computed not only with respect to intrinsic model parameters, such as diffusion coefficients and isotherm parameters, but also with respect to parameters in the boundary concentrations, such as the slope of an elution salt gradient. The extended solver is part of the Chromatography Analysis and Design Toolkit (CADET).

Computational fluid dynamic simulation of axial and radial flow membrane chromatography: mechanisms of non-ideality and validation of the zonal rate model.

Membrane chromatography (MC) is increasingly being used as a purification platform for large biomolecules due to higher operational flow rates. The zonal rate model (ZRM) has previously been applied to accurately characterize the hydrodynamic behavior in commercial MC capsules at different configurations and scales. Explorations of capsule size, geometry and operating conditions using the model and experiment were used to identify possible causes of inhomogeneous flow and their contributions to band broadening. In the present study, the hydrodynamics within membrane chromatography capsules are more rigorously investigated by computational fluid dynamics (CFD). The CFD models are defined according to precisely measured capsule geometries in order to avoid the estimation of geometry related model parameters. In addition to validating the assumptions and hypotheses regarding non-ideal flow mechanisms encoded in the ZRM, we show that CFD simulations can be used to mechanistically understand and predict non-binding breakthrough curves without need for estimation of any parameters. When applied to a small-scale axial flow MC capsules, CFD simulations identify non-ideal flows in the distribution (hold-up) volumes upstream and downstream of the membrane stack as the major source of band broadening. For the large-scale radial flow capsule, the CFD model quantitatively predicts breakthrough data using binding parameters independently determined using the small-scale axial flow capsule, identifying structural irregularities within the membrane pleats as an important source of band broadening. The modeling and parameter determination scheme described here therefore facilitates a holistic mechanistic-based method for model based scale-up, obviating the need of performing expensive large-scale experiments under binding conditions. As the CFD model described provides a rich mechanistic analysis of membrane chromatography systems and the ability to explore operational space, but requires detailed knowledge of internal capsule geometries and has much greater computational requirements, it is complementary to the previously described strengths and uses of the ZRM for process analysis and design.

Effects of uncertainties in experimental conditions on the estimation of adsorption model parameters in preparative chromatography

Model-based process design is increasingly popular when designing pharmaceutical purification processes. The effect of uncertainties in concentration measurements on the estimation of model parameters is analyzed for two cases of non-isocratic adsorption chromatography. A model, calibrated to experiments, is used to generate data by adding a Monte Carlo sampled error in the inlet concentrations. New model parameters are estimated by minimizing the deviation between the synthetic data and the model. The first case is a separation of rare earth elements by ion-exchange chromatography and the second case is a purification of insulin from a product-related impurity by reversed-phase chromatography. It is shown that normally distributed errors in the concentrations result in deviations in the UV-signal that are not normally distributed. With the applied method, known concentration distributions can be translated into probability distributions of the model parameters, which can be taken into account in the model-based process design

Zonal rate model for axial and radial flow membrane chromatography. Part I: Knowledge transfer across operating conditions and scales

The zonal rate model (ZRM) has previously been applied for analyzing the performance of axial flow membrane chromatography capsules by independently determining the impacts of flow and binding related non‐idealities on measured breakthrough curves. In the present study, the ZRM is extended to radial flow configurations, which are commonly used at larger scales. The axial flow XT5 capsule and the radial flow XT140 capsule from Pall are rigorously analyzed under binding and non‐binding conditions with bovine serum albumin (BSA) as test molecule. The binding data of this molecule is much better reproduced by the spreading model, which hypothesizes different binding orientations, than by the well‐known Langmuir model. Moreover, a revised cleaning protocol with NaCl instead of NaOH and minimizing the storage time has been identified as most critical for quantitatively reproducing the measured breakthrough curves. The internal geometry of both capsules is visualized by magnetic resonance imaging (MRI). The flow in the external hold‐up volumes of the XT140 capsule was found to be more homogeneous as in the previously studied XT5 capsule. An attempt for model‐based scale‐up was apparently impeded by irregular pleat structures in the used XT140 capsule, which might lead to local variations in the linear velocity through the membrane stack. However, the presented approach is universal and can be applied to different capsules. The ZRM is shown to potentially help save valuable material and time, as the experiments required for model calibration are much cheaper than the predicted large‐scale experiment at binding conditions. Biotechnol. Bioeng. 2013; 110: 1129–1141.

The effect of composition on Diffusion of macromolecules in a crowded environment

We study diffusion of macromolecules in a crowded cytoplasm-like environment, focusing on its dependence on composition and its crossover to the anomalous subdiffusion. The crossover and the diffusion itself depend on both the volume fraction and the relative concentration of macromolecules. In accordance with previous theoretical and experimental studies, diffusion slows down when the volume fraction increases. Contrary to expectations, however, the diffusion is also strongly dependent on the molecular composition. The crossover time decreases and diffusion slows down when the smaller macromolecules start to dominate. Interestingly, diffusion is faster in a cytoplasm-like (more polydisperse) system than it is in a two-component system, at comparable packing fractions, or even when the cytoplasm packing fraction is larger.