Mathematical modeling and scale-up of size-exclusion chromatography

Advances in modeling techniques for the production and purification of biomolecules: A comprehensive review

In response to the growing demand for therapeutic biomolecules, there is a need for continuous and cost-effective bio-separation techniques to enhance extraction yield and efficiency. Aqueous biphasic extractive fermentation has emerged as an integrated downstream processing technique, offering selective partitioning, high productivity, and preservation of biomolecule integrity. However, the dynamic nature of this technique requires a comprehensive understanding of the underlying separation mechanisms. Unfortunately, the analysis of parameters influencing this dynamic behavior can be challenging due to limited resources and time. To address this, mathematical modeling approaches can be employed to minimize the tedious trial-and-error experimentation process. This review article presents mathematical modeling approaches for both upstream and downstream processing techniques, focusing on the production of biomolecules which can be used in pharmaceutical industries in a cost-effective manner. By leveraging mathematical models, researchers can optimize the production and purification processes, leading to improved efficiency and processing cost reduction in biomolecule production.

Mechanistic modeling of cation exchange chromatography scale-up considering packing inhomogeneities

In process development and characterization, the scale-up of chromatographic steps is a crucial part and brings a number of challenges. Usually, scale-down models are used to represent the process step, and constant column properties are assumed. The scaling is then typically based on the concept of linear scale-up. In this work, a mechanistic model describing an anti-Langmuirian to Langmuirian elution behavior of a polypeptide, calibrated with a pre-packed 1 ml column, is applied to demonstrate the scalability to larger column volumes up to 28.2 ml. Using individual column parameters for each column size, scaling to similar eluting salt concentrations, peak heights, and shapes is experimentally demonstrated by considering the model's relationship between the normalized gradient slope and the eluting salt concentration. Further scale-up simulations show improved model predictions when radial inhomogeneities in packing quality are considered.

Bovine serum albumin and myoglobin separation by size exclusion SMB

The separation of the proteins Bovine Serum Albumin (BSA) and Myoglobin (Mb) was achieved by Size-Exclusion Simulated Moving Bed (SE-SMB) and performed experimentally in the FlexSMB® unit, an SMB unit designed and built in the Laboratory of Separation and Reaction Engineering. Before accomplishing the separation experiments in the mentioned unit, separation regions were computed by simulation based on a phenomenological mathematical model to determine appropriate operating conditions. The developed model was validated in advance, against fixed-bed dynamic adsorption experimental results, for pure component and binary mixtures. Then the SMB experiments were carried out, and purities of the Mb on the extract and BSA on the raffinate streams were 98% and 96%, respectively. The achieved recoveries were 80% of Mb on the extract and 94% of BSA on the raffinate. Lastly, productivities of 6.4 g_protein⋅l_ads^-1⋅day^-1 for the extract and 28.8 g_protein⋅l_ads^-1⋅day^-1 for the raffinate were obtained.

Development of Novel High-Resolution Size-Guided Turbidimetry-Enabled Particle Purification Liquid Chromatography (PPLC): Extracellular Vesicles and Membraneless Condensates in Focus

Acellular particles (extracellular vesicles and membraneless condensates) have important research, drug discovery, and therapeutic implications. However, their isolation and retrieval have faced enormous challenges, impeding their use. Here, a novel size-guided particle purification liquid chromatography (PPLC) is integrated into a turbidimetry-enabled system for dye-free isolation, online characterization, and retrieval of intact acellular particles from biofluids. The chromatographic separation of particles from different biofluids—semen, blood, urine, milk, and cell culture supernatants—is achieved using a first-in-class gradient size exclusion column (gSEC). Purified particles are collected using a fraction collector. Online UV–Vis monitoring reveals biofluid-dependent particle spectral differences, with semen being the most complex. Turbidimetry provides the accurate physical characterization of seminal particle (Sp) lipid contents, sizes, and concentrations, validated by a nanoparticle tracking analysis, transmission electron microscopy, and naphthopyrene assay. Furthermore, different fractions of purified Sps contain distinct DNA, RNA species, and protein compositions. The integration of Sp physical and compositional properties identifies two archetypal membrane-encased seminal extracellular vesicles (SEV)—notably SEV large (SEV_L), SEV small (SEV_S), and a novel non-archetypal-membraneless Sps, herein named membraneless condensates (MCs). This study demonstrates a comprehensive yet affordable platform for isolating, collecting, and analyzing acellular particles to facilitate extracellular particle research and applications in drug delivery and therapeutics. Ongoing efforts focus on increased resolution by tailoring bead/column chemistry for each biofluid type.

Development and modeling of two-dimensional fast protein liquid chromatography for producing nonstructural protein-free food-and-mouth diseases virus vaccine

Concerns for the use of non-purified or incompletely purified inactivated foot-and-mouth disease (FMD) vaccine, like difficulties for differentiation vaccinated from infected animals, can be a motivation in order to develop methods based on size exclusion chromatography (SEC). In this study, a two dimensional size exclusion chromatography (2D-SEC) system was successfully constructed using two different SEC column media to achieve a high-throughput purification system for the cell culture-derived foot and mouth diseases virus (FMDV). A mathematical model was also utilized to predict and to get a better insight into the separation process. Column and the packing particles characteristics such as column void volume, total column volume, particle porosity and accessible particle porosity was acquired experimentally. Retention times and elution profile of two different molecules, blue dextran and bovine serum albumin, were used for evaluating the capability of SEC media for separating two critical impurities (residual DNA (rDNA) and non-structural protein (NSP)) from active ingredient of vaccine (FMDV particle). Experiments were carried out with two different commercial columns (XK 26/60) and (XK 16/100) and with four different packing media superdex 200 prep grade, sephacryl S-500 HR, Sephacryl S-400 HR and Sephacryl S-300HR. The mathematical model was first validated by experimental chromatographic data of different SEC media and was then used to propose the best 2D-SEC system for downstream processing of the FMDV vaccine. The loading capacity of the constructed 2D-SEC sample was increased to 12.5% of total column volume and the purity of the final product was more than 90%. The entire purification process was performed with 77% FMDV recovery and 79.1% virus yield. Based on the high-performance size exclusion chromatography (HPSEC), the purity of the final NSP-free FMDV was about 90% and over 94.6% of host cell DNA was removed. Analyses of the purified FMDV by HPSEC, transmission electron microscopy (TEM) and dynamic light scattering (DLS) indicated that the final product had spherical shape with mean size about 30 nm and their structure remained intact.

Toward a New Brewing Control Chart for the 21st Century

This paper describes new results from a base model of brewing from a bed of packed coffee grains. The model solves for the diffusion of soluble species out of a distribution of particles into the flow through the bed pore space. It requires a limited set of input parameters. It gives a simple picture of the basic physics of coffee brewing and sets out a set of reduced variables for this process. The importance of bed extraction efficiency is elucidated. A coffee brewing control chart has been widely used to describe the region of ideal coffee brewing for some 50 years. A new chart is needed, however, one that connects actual brewing conditions (weight, flow rate, brew time, grind, etc.) to the yield and strength of brews. The paper shows a new approach to brewing control charts, including brew time and bed extraction efficiency as control parameters. Using the base model, an example chart will be given for a particular grind ratio of coarse to fine particles, and an "espresso regime" will be picked out. From such a chart yield, volume and strength of a brew can be read off at will.

Transport properties and size exclusion effects in wide-pore superficially porous particles

The effects of hydrodynamic radius on the transport of solute molecules in packed beds of wide-pore superficially porous particles (SPP) are studied using pore-scale simulation. The free molecular diffusion rate varies with radius through the Stokes-Einstein relation. Lattice Boltzmann and Langevin methods are used to model fluid motion and the transport of an ensemble of solute molecules in the fluid, providing statistics on solute concentration, flux, molecule age and residence time, as a function of depth in the SPP. Intraparticle effective diffusion and bed dispersion coefficients are calculated and correlated with the hydrodynamic radius and accessible porosity. The relative importance of convection and diffusion are found to depend on the molecule (tracer) size through the diffusion rate, and convection effects are more significant for larger, slower-diffusing molecules. When larger molecules are utilized, the intraparticle concentration is reduced in proportion to the local particle porosity, leading to a natural definition of the accessible porosity used in size exclusion chromatography (SEC). Although the pore shape is complex, the SEC constant K can be calculated directly from simulation. Simulation demonstrates that the effective diffusion coefficient is elevated near the particle hull, which is largely open to interstitial flow, and decreases with depth into the particle. All molecules studied here have transport access to the entire particle depth, although the accessible volume at a given depth depends on their size. The first passage time into the particle is well predicted by the diffusion rate, but residence time is influenced by convection, shortening the average visit duration. These results are of interest in "perfusion" chromatography where convection is thought to increase separation efficiency for large biomolecules.

Biophysical analysis of BMV virions purified using a novel method

Brome mosaic virus (BMV) has been successfully loaded with different types of nanoparticles. However, studies concerning its application as a nanoparticle carrier demand high-purity virions in large amounts. Existing BMV purification protocols rely on multiple differential ultracentrifugation runs of the initially purified viral preparation. Herein, we describe an alternative method for BMV purification based on ion-exchange chromatography and size-exclusion chromatography (SEC) yielding 0.2mg of virus from 1g of plant tissue. Our method is of similar efficiency to previously described protocols and can easily be scaled up. The method results in high-quality BMV preparations as confirmed by biophysical analyses, including cryogenic transmission electron microscopy (cryo-TEM), dynamic light scattering (DLS), static light scattering (SLS), and circular dichroism (CD) measurements and attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) spectroscopy. Our results revealed that purified BMV capsids are stable and monodisperse and can be used for further downstream applications. In this work, we also characterize secondary structure and size fluctuations of the BMV virion at different pH values.

Kinetic size-exclusion chromatography with mass spectrometry detection: an approach for solution-based label-free kinetic analysis of protein-small molecule interactions

Studying the kinetics of reversible protein-small molecule binding is a major challenge. The available approaches require that either the small molecule or the protein be modified by labeling or immobilization on a surface. Not only can such modifications be difficult to do but also they can drastically affect the kinetic parameters of the interaction. To solve this problem, we present kinetic size-exclusion chromatography with mass spectrometry detection (KSEC-MS), a solution-based label-free approach. KSEC-MS utilizes the ability of size-exclusion chromatography (SEC) to separate any small molecule from any protein-small molecule complex without immobilization and the ability of mass spectrometry (MS) to detect a small molecule without a label. The rate constants of complex formation and dissociation are deconvoluted from the temporal pattern of small molecule elution measured with MS at the exit from the SEC column. This work describes the concept of KSEC-MS and proves it in principle by measuring the rate constants of interaction between carbonic anhydrase and acetazolamide.

Modelling approaches for bio-manufacturing operations

Fast and cost-effective methods are needed to reduce the time and money needed for drug commercialisation and to determine the risks involved in adopting specific manufacturing strategies. Simulations offer one such approach for exploring design spaces before significant process development is carried out and can be used from the very earliest development stages through to scale-up and optimisation of operating conditions and resource deployment patterns both before and after plant start-up. The advantages this brings in terms of financial savings can be considerable, but to achieve these requires a full appreciation of the complexities of processes and how best to represent them mathematically within the context of in silico software. This chapter provides a summary of some of the work that has been carried out in the areas of mathematical modelling and discrete event simulations for production, recovery and purification operations when designing bio-pharmaceutical processes, looking at both financial and technical modelling.

Purification of cell culture-derived human influenza A virus by size-exclusion and anion-exchange chromatography

A process comprising of size-exclusion chromatography (SEC) and anion-exchange chromatography (AEC) was investigated for downstream processing of cell culture-derived influenza A virus. Human influenza virus A/PR/8/34 (H1N1) was propagated in serum-free medium using MDCK cells as a host. Concentrates of the virus were prepared from clarified and inactivated cell culture supernatants by cross-flow ultrafiltration as described before. SEC on Sepharose 4 FF resulted in average product yields of 85% based on hemagglutination (HA) activity. Productivity was maximized to 0.15 column volumes (cv) of concentrate per hour yielding a reduction in total protein and host cell DNA (hcDNA) to 35 and 34%, respectively. AEC on Sepharose Q XL was used to separate hcDNA from virus at a salt concentration of 0.65 M sodium chloride. Product yields >80% were achieved for loads >160 kHAU/mL of resin. The reduction in hcDNA was 67-fold. Split peak elution and bimodal particle volume distributions suggested aggregation of virions. Co-elution with hcDNA and constant amounts of hcDNA per dose indiciated association of virions to hcDNA. An overall product yield of 52% was achieved. Total protein was reduced more than 19-fold; hcDNA more than 500-fold by the process. Estimation of the dose volume from HA activity predicted a protein content at the limit for human vaccines. Reduction of hcDNA was found insufficient (about 500 ng per dose) requiring further optimization of AEC or additional purification steps. All operations were selected to be scalable and independent of the virus strain rendering the process suitable for vaccine production.