(184aa) Advancing Kinetic Parameter Estimation: A Metabolism-Informed Variational Bayesian Inference Approach

The biopharmaceutical industry must ensure safe and consistent biological products. To meet these demands, mathematical models are increasingly used to design, predict, optimize, and control processes, from development to manufacturing. In the field of mammalian cell cultures, which accounts for 80% of the commercially available therapeutic proteins [1], the exploitation of mathematical models, such as kinetic models, has also become a useful tool to maximize information gained from experimentation and to reduce expense. However, developing reliable kinetic models for cell cultures is challenging as they are typically parameterized for a specific range of conditions and often face challenges related to generalizability. This leads to limited extrapolation power of the model and a lack of trust in the estimated parameters, which restricts the model exploitation.

One of the common ways of addressing the extrapolation power of models is through the integration of different models and their philosophies. While, ideally, mechanistic models such as the flux balance analysis (FBA) approach alone should be able to produce reliable results, these are often limited either by a poor understanding of mechanisms, or the simplistic assumptions that are made to facilitate their solution through partial representation of biological pathways. Hence, hybrid modeling approaches that combine different modeling paradigms resulting in the best of both worlds are often preferred. An example of this is provided by dynamic FBA, which integrates common semi-empirical kinetic model structures and FBA [2].

In this work, we propose a hybrid model construction framework that leverages variational Bayesian inference (VBI) for the parameterisation of a kinetic cell culture model informed by a stoichiometric metabolic model. VBI allows one to conveniently combine different modelling paradigms along with the experimental data to obtain probabilistic hybrid models. Unlike traditional methods such as maximum likelihood estimation, it allows the embedding of mechanistic knowledge via the prior distribution. Our model uses metabolic knowledge from flux sampling (FS) and FBA as priors for the estimation of the model’s parameters. By using distributions from FS and FBA as prior knowledge, our framework can utilize mechanistic knowledge from a metabolic network model, thus improving the reliability of the kinetic parameters and generalizability of the model. Moreover, being a probabilistic model, it allows for the quantification of model uncertainty through the distribution of the parameters while also handling measurement uncertainties.

We demonstrate the applicability of our framework in the estimation of kinetic parameters of a Chinese Hamster Ovary cell culture model, using published data from a fed-batch experiment [3]. Available daily measurements include viable cell density, viability and extracellular glucose, lactate, ammonia, and amino acid concentrations. The priors for the yields are obtained via FS a metabolic model constrained by experimental data and those for maximum growth rate are obtained by solving a metabolic model with FBA under a biomass maximization objective. The priors for the remaining parameters are given through the analysis of metabolite concentrations. Finally, the posterior distributions of the model parameters are estimated using the coordinate ascent mean-field variational inference approach [4]. Our methodology successfully estimates kinetic parameters, and additionally predicts asparagine concentration, a typically unmeasured growth-limiting metabolite.

The incorporation of mechanistic knowledge in the proposed framework improves the generalizability of the obtained models rendering them suitable for optimization and control of cell cultures over a wide range of operating conditions. Additionally, the framework also allows the models to be conveniently adapted to new experimental data, showcasing the versatility of the proposed framework.

References:

[1] Al-Majmaie, R., Kuystermans, D., & Al-Rubeai, M. (2022). Biopharmaceuticals produced from cultivated mammalian cells. In Cell Culture Engineering and Technology: In appreciation to Professor Mohamed Al-Rubeai (pp. 3-52). Cham: Springer International Publishing.

[2] Mahadevan, R., Edwards, J. S., & Doyle, F. J. (2002). Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophysical journal, 83(3), 1331-1340.

[3] Kyriakopoulos, S., & Kontoravdi, C. (2014). A framework for the systematic design of fed‐batch strategies in mammalian cell culture. Biotechnology and Bioengineering, 111(12), 2466-2476.

[4] Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American statistical Association, 112(518), 859-877.