A two-dimensional population balance model for cell growth including multiple uptake systems

Population Mass Balance Model for Precipitation with Turbidity Measurements

The discretized population balance theory has been proven to be a useful method to simulate systems in which solid particles are present. In this work, we introduce a new approach to model precipitation reactions based on the temporal evolution of product concentration, from which particle size distribution, its dynamics, and the specific interfacial energies can be obtained. For a reference study, the previously investigated calcium oxalate precipitation was selected, where the reaction was followed via turbidity measurement. From the obtained particle size distribution, we can show that at low supersaturation, growth is the dominant process, while at higher supersaturation, nucleation is the dominant process. Moreover, the temporal change of the distribution curve has allowed us to split the precipitation into a nucleation, a growth-driven intermediate, and a saturation regime. Furthermore, the comparison between the experimental and calculated results has proved that the method is suitable for predicting particle size distributions and specific interfacial energies.

Modeling large-scale bioreactors with diffusion equations. Part II: Characterizing substrate, oxygen, temperature, carbon dioxide, and pH profiles

Large-scale fermentation processes involve complex dynamic interactions between mixing, reaction, mass transfer, and the suspended biomass. Empirical correlations or case-specific computational simulations are usually used to predict and estimate the performance of large-scale bioreactors based on data acquired at bench scale. In this two-part-study, one-dimensional axial diffusion equations were studied as a general and predictive model of large-scale bioreactors. This second part focused on typical fed-batch operations where substrate gradients are known to occur, and characterized the profiles of substrate, pH, oxygen, carbon dioxide, and temperature. The physically grounded steady-state axial diffusion equations with first- and zeroth-order kinetics yielded analytical solutions to the relevant variables. The results were compared with large-scale Escherichia coli and Saccharomyces cerevisiae experiments and simulations from the literature, and good agreement was found in substrate profiles. The analytical profiles obtained for dissolved oxygen, temperature, pH, andCO 2 ${\text{CO}}_{2}$ were also consistent with the available data. Distribution functions for the substrate were defined, and efficiency factors for biomass growth and oxygen uptake rate were derived. In conclusion, this study demonstrated that axial diffusion equations can be used to model the effects of mixing and reaction on the relevant variables of typical large-scale fed-batch fermentations.

Mechanistic modeling of viral particle production

Viral systems such as wild-type viruses, viral vectors, and virus-like particles are essential components of modern biotechnology and medicine. Despite their importance, the commercial-scale production of viral systems remains highly inefficient for multiple reasons. Computational strategies are a promising avenue for improving process development, optimization, and control, but require a mathematical description of the system. This article reviews mechanistic modeling strategies for the production of viral particles, both at the cellular and bioreactor scales. In many cases, techniques and models from adjacent fields such as epidemiology and wild-type viral infection kinetics can be adapted to construct a suitable process model. These process models can then be employed for various purposes such as in-silico testing of novel process operating strategies and/or advanced process control.

Digital models in biotechnology: Towards multi-scale integration and implementation

Industrial biotechnology encompasses a large area of multi-scale and multi-disciplinary research activities. With the recent megatrend of digitalization sweeping across all industries, there is an increased focus in the biotechnology industry on developing, integrating and applying digital models to improve all aspects of industrial biotechnology. Given the rapid development of this field, we systematically classify the state-of-art modelling concepts applied at different scales in industrial biotechnology and critically discuss their current usage, advantages and limitations. Further, we critically analyzed current strategies to couple cell models with computational fluid dynamics to study the performance of industrial microorganisms in large-scale bioprocesses, which is of crucial importance for the bio-based production industries. One of the most challenging aspects in this context is gathering intracellular data under industrially relevant conditions. Towards comprehensive models, we discuss how different scale-down concepts combined with appropriate analytical tools can capture intracellular states of single cells. We finally illustrated how the efforts could be used to develop digitals models suitable for both cell factory design and process optimization at industrial scales in the future.

Population balance modelling captures host cell protein dynamics in CHO cell cultures

Monoclonal antibodies (mAbs) have been extensively studied for their wide therapeutic and research applications. Increases in mAb titre has been achieved mainly by cell culture media/feed improvement and cell line engineering to increase cell density and specific mAb productivity. However, this improvement has shifted the bottleneck to downstream purification steps. The higher accumulation of the main cell-derived impurities, host cell proteins (HCPs), in the supernatant can negatively affect product integrity and immunogenicity in addition to increasing the cost of capture and polishing steps. Mathematical modelling of bioprocess dynamics is a valuable tool to improve industrial production at fast rate and low cost. Herein, a single stage volume-based population balance model (PBM) has been built to capture Chinese hamster ovary (CHO) cell behaviour in fed-batch bioreactors. Using cell volume as the internal variable, the model captures the dynamics of mAb and HCP accumulation extracellularly under physiological and mild hypothermic culture conditions. Model-based analysis and orthogonal measurements of lactate dehydrogenase activity and double-stranded DNA concentration in the supernatant show that a significant proportion of HCPs found in the extracellular matrix is secreted by viable cells. The PBM then served as a platform for generating operating strategies that optimise antibody titre and increase cost-efficiency while minimising impurity levels.

The closure issue related to liquid-cell mass transfer and substrate uptake dynamics in biological systems

An original dynamic model for substrate uptake under transient conditions is established and used to simulate a variety of biological responses to external perturbations. The actual uptake and growth rates, treated as cell properties, are part of the model variables as well as the substrate concentration at the cell-liquid interface. Several regulatory loops inspired by the structure of the glycolytic chain are considered to establish a set of ordinary differential equations. The uptake rate evolves so as to reach an equilibrium between the cell demand and the environmental supply. This model does not contain any of the usual algebraic closure laws relating to the instantaneous uptake, growth rates, and the substrate concentration, nor does it enforce the continuity of mass fluxes at the liquid-cell interface. However, these relationships are found in the steady-state solution. Previously unexplained experimental observations are well reproduced by this model. Also, the model structure is suitable for further coupling with flux-based metabolic models and fluid-flow equations.

A critical analysis of Powell's results on the interdivision time distribution

The cell-age and interdivision-time probability density functions (PDFs) have been extensively investigated since the 1940s due to their fundamental role in cell growth. The pioneering work of Powell established the first relationship between the interdivision-time and cell-age PDFs. In the literature, two definitions for the interdivision-time PDF have been proposed. One stands for the age-at-rupture PDF and is experimentally observable, whereas the other is the probability density that a cell divides at a certain age and is unobservable. From Powell’s results pertaining to the unobservable interdivision-time PDF, Painter and Marr derived an inequality that is true but is incorrectly used by experimentalists to analyse single-cell data. Unfortunately, the confusion between these two PDFs persists. To dissipate this confusion, exact relationships between the cell-age and the interdivision-time PDFs are derived in this work from an age-structured model, which can be used by experimentalists to analyse cell growth in batch and continuous culture modes.