Making sense of parameter estimation and model simulation in bioprocesses

Pushing the boundaries of phosphorylase cascade reaction for cellobiose production I: Kinetic model development

One-pot cascade reactions of coupled disaccharide phosphorylases enable an efficient transglycosylation via intermediary α-d-glucose 1-phosphate (G1P). Such transformations have promising applications in the production of carbohydrate commodities, including the disaccharide cellobiose for food and feed use. Several studies have shown sucrose and cellobiose phosphorylase for cellobiose synthesis from sucrose, but the boundaries on transformation efficiency that result from kinetic and thermodynamic characteristics of the individual enzyme reactions are not known. Here, we assessed in a step-by-step systematic fashion the practical requirements of a kinetic model to describe cellobiose production at industrially relevant substrate concentrations of up to 600 mM sucrose and glucose each. Mechanistic initial-rate models of the two-substrate reactions of sucrose phosphorylase (sucrose + phosphate → G1P + fructose) and cellobiose phosphorylase (G1P + glucose → cellobiose + phosphate) were needed and additionally required expansion by terms of glucose inhibition, in particular a distinctive two-site glucose substrate inhibition of the cellobiose phosphorylase (from Cellulumonas uda). Combined with mass action terms accounting for the approach to equilibrium, the kinetic model gave an excellent fit and a robust prediction of the full reaction time courses for a wide range of enzyme activities as well as substrate concentrations, including the variable substoichiometric concentration of phosphate. The model thus provides the essential engineering tool to disentangle the highly interrelated factors of conversion efficiency in the coupled enzyme reaction; and it establishes the necessary basis of window of operation calculations for targeted optimizations toward different process tasks.

A reinforcement learning-based hybrid modeling framework for bioprocess kinetics identification

Constructing predictive models to simulate complex bioprocess dynamics, particularly time-varying (i.e., parameters varying over time) and history-dependent (i.e., current kinetics dependent on historical culture conditions) behavior, has been a longstanding research challenge. Current advances in hybrid modeling offer a solution to this by integrating kinetic models with data-driven techniques. This article proposes a novel two-step framework: first (i) speculate and combine several possible kinetic model structures sourced from process and phenomenological knowledge, then (ii) identify the most likely kinetic model structure and its parameter values using model-free Reinforcement Learning (RL). Specifically, Step 1 collates feasible history-dependent model structures, then Step 2 uses RL to simultaneously identify the correct model structure and the time-varying parameter trajectories. To demonstrate the performance of this framework, a range of in-silico case studies were carried out. The results show that the proposed framework can efficiently construct high-fidelity models to quantify both time-varying and history-dependent kinetic behaviors while minimizing the risks of over-parametrization and over-fitting. Finally, the primary advantages of the proposed framework and its limitation were thoroughly discussed in comparison to other existing hybrid modeling and model structure identification techniques, highlighting the potential of this framework for general bioprocess modeling.

Investigating a Stirred Bioreactor: Impact of Evolving Fermentation Broth Pseudoplastic Rheology on Mixing Mechanisms

The culture medium in many fermentations is a non-Newtonian fluid. In bacterial alginate batch production, the broth becomes more pseudoplastic as the alginate concentration increases, which impairs the mixing process. This work characterizes the effect of the interaction between changing broth rheology and impeller mixing on a bioreactor fluid dynamics. Experimentally, a fermentation with evolving broth pseudoplastic rheology is reproduced. Three fermentation stages are mimicked using appropriate solutions of water and xanthan gum. Impeller torque measurements are reported. The weakening of the impellers’ interaction over the fermentation process is identified. To overcome the experimental limitations, CFD is applied to study the evolution of the fermentation fluid flow patterns, velocity field, dead zones, and vortical structures. Precessional vortex macro-instabilities are identified as being responsible for the unstable flow patterns identified at the earlier stages of the fermentation. A stable parallel flow pattern accounts for the weakest impellers’ interaction at the final stage. Overall, this work contributes with a complete workflow to adapt CFD models for characterization and aided design of stirred tanks with changing broth pseudoplastic rheology as well as an evolving flow regime.

A transfer learning approach for predictive modeling of bioprocesses using small data

Predictive modeling of new biochemical systems with small data is a great challenge. To fill this gap, transfer learning, a subdomain of machine learning that serves to transfer knowledge from a generalized model to a more domain-specific model, provides a promising solution. While transfer learning has been used in natural language processing, image analysis, and chemical engineering fault detection, its application within biochemical engineering has not been systematically explored. In this study, we demonstrated the benefits of transfer learning when applied to predict dynamic behaviors of new biochemical processes. Two different case studies were presented to investigate the accuracy, reliability, and advantage of this innovative modeling approach. We thoroughly discussed the different transfer learning strategies and the effects of topology on transfer learning, comparing the performance of the transfer learning models against benchmark kinetic and data-driven models. Furthermore, strong connections between the underlying process mechanism and the transfer learning model's optimal structure were highlighted, suggesting the interpretability of transfer learning to enable more accurate prediction than a naive data-driven modeling approach. Therefore, this study shows a novel approach to effectively combining data from different resources for bioprocess simulation.

Kinetic and hybrid modeling for yeast astaxanthin production under uncertainty

Astaxanthin is a high-value compound commercially synthesized through Xanthophyllomyces dendrorhous fermentation. Using mixed sugars decomposed from biowastes for yeast fermentation provides a promising option to improve process sustainability. However, little effort has been made to investigate the effects of multiple sugars on X. dendrorhous biomass growth and astaxanthin production. Furthermore, the construction of a high-fidelity model is challenging due to the system's variability, also known as batch-to-batch variation. Two innovations are proposed in this study to address these challenges. First, a kinetic model was developed to compare process kinetics between the single sugar (glucose) based and the mixed sugar (glucose and sucrose) based fermentation methods. Then, the kinetic model parameters were modeled themselves as Gaussian processes, a probabilistic machine learning technique, to improve the accuracy and robustness of model predictions. We conclude that although the presence of sucrose does not affect the biomass growth kinetics, it introduces a competitive inhibitory mechanism that enhances astaxanthin accumulation by inducing adverse environmental conditions such as osmotic gradients. Moreover, the hybrid model was able to greatly reduce model simulation error and was particularly robust to uncertainty propagation. This study suggests the advantage of mixed sugar-based fermentation and provides a novel approach for bioprocess dynamic modeling.

Modeling the Influence of Temperature, Light Intensity and Oxygen Concentration on Microalgal Growth Rate

Dissolved oxygen plays a key role in microalgal growth at high density. This effect was so far rarely quantified. Here we propose a new model to represent the combined effect of light, oxygen concentration and temperature (LOT-model) on microalgae growth. The LOT-model introduces oxygen concentration in order to represent the oxidative stress affecting the cultures, adding a toxicity term in the expression of the net growth rate. The model was validated with experimental data for several species such as Chlorella minutissima, Chlorella vulgaris, Dunaliella salina, Isochrysis galbana. It successfully predicted experimental records with an average error lower than 5.5%. The model was also validated using dynamical data where oxygen concentration varies. It highlights a strong impact of oxygen concentration on productivity, depending on temperature. The model quantifies the sensitivity to oxidative stress of different species and shows, for example, that Dunaliella salina is much less affected than Chlorella vulgaris by oxidative stress. The modeling approach can support an optimization strategy to improve productivity, especially for managing high oxygen levels.