Population balance modeling of a microalgal culture in photobioreactors: Comparison between experiments and simulations

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

A multiscale modelling approach for Haematococcus pluvialis cultivation under different environmental conditions

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We develop a novel multiscale model for microalgal photoautotrophic growth.

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The model is segregated-structured type based on Population Balance Equations.

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We combine the model with cultivation experiments of Haematococcus pluvialis.

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We successfully predict cell number, average volume and density distribution dynamics.

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Model can accurately describe the nutrient depletion phase including cell lysis.

Haematococcus pluvialis can produce significant amounts of industrially important compounds belonging to lipids and starch classes, including various specific pigments such as β-carotene, lutein and astaxanthin, as well as lipids, carbohydrates and proteins. Their production can vary depending on environmental stress conditions like nutrient starvation. However, stress conditions lead also to undesired phenomena such as cell lysis, which is likely to be related to products loss. The microorganism develops towards smaller single cell volumes during the growth process, and eventually, more likely towards lysis when fission (i.e. cell division) slows down. The lysis process takes place simultaneously with nutrient depletion, so both growth and lysis are linked to the change of environmental conditions. In this work, we develop a novel multiscale segregated-structured model based on Population Balance Equations (PBEs) to describe the photoautotrophic growth of H.pluvialis, in particular cell growth, and lysis, making possible the description of the relationship between cell volume/transition, cell loss, and metabolic product availability. Cell volume is the internal coordinate of the population balance model, and its link with intrinsic concentrations is also presented. The model parameters are fitted against experimental data, extensive sensitivity analysis is performed and the model predictive capabilities are tested in terms of cell density distributions, as well as 0th and 1st order moments.

Modelling of Harvesting Techniques for the Evaluation of the Density of Microalgae

A better estimation of the density of cells has great relevance in the design of harvesting units. In the case of microalgae, the density is a function of the internal composition, which in turn is affected by external environmental conditions. The density of microalgae is often regarded as a constant or a generic value is retrieved from literature. This study proposes a procedure to evaluate the density of Chlorococcum sp. with simple sedimentation and centrifugation experiments coupled with the population balance equation (PBE), which is solved numerically. The density of cells is not constant; instead, it is a function of the size of particles, which in turn changes with the cells' phase of their life cycle. The calculated cellular density ranged between 1000 and 1100 kg m^-3 in function of the cell size in both the sedimentation and centrifugation tests. The method can be extended to other microalgae species as well as to other types of cells.

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.

A practical approach for modelling the growth of microalgae with population balance equation

Microalgae are versatile microorganisms with applications in food, energy and fine chemicals, among others. Modelling the dynamics of microalgae inside a photobioreactor is a convenient and inexpensive way to determine the concentration of cells over time. Numerous models have been developed in the literature, but only a few are able to give relevant biological information. Such information can then be used to further improve the production process. The objective of this work was to develop a model for the determination of microalgal dynamics inside a photobioreactor as a function of the environmental conditions, to retrieve the size-specific growth and division rates as well as the number of daughter cells. The results demonstrate how to evaluate the time needed for microalgae to complete a full life-cycle. Inexpensive laboratory-based procedures and mathematical modelling are combined for the determination of relevant biological parameters.