Deep hybrid modeling of a HEK293 process: Combining long short-term memory networks with first principles equations.

The combination of physical equations with deep learning is becoming a promising methodology for bioprocess digitalization. In this paper, we investigate for the first time the combination of long short-term memory (LSTM) networks with first principles equations in a hybrid workflow to describe human embryonic kidney 293 (HEK293) culture dynamics. Experimental data of 27 extracellular state variables in 20 fed-batch HEK293 cultures were collected in a parallel high throughput 250 mL cultivation system in an industrial process development setting. The adaptive moment estimation method with stochastic regularization and cross-validation were employed for deep learning. A total of 784 hybrid models with varying deep neural network architectures, depths, layers sizes and node activation functions were compared. In most scenarios, hybrid LSTM models outperformed classical hybrid Feedforward Neural Network (FFNN) models in terms of training and testing error. Hybrid LSTM models revealed to be less sensitive to data resampling than FFNN hybrid models. As disadvantages, Hybrid LSTM models are in general more complex (higher number of parameters) and have a higher computation cost than FFNN hybrid models. The hybrid model with the highest prediction accuracy consisted in a LSTM network with seven internal states connected in series with dynamic material balance equations. This hybrid model correctly predicted the dynamics of the 27 state variables (R2 = 0.93 in the test data set), including biomass, key substrates, amino acids and metabolic by-products for around 10 cultivation days.

Hybrid deep modeling of a CHO-K1 fed-batch process: combining first-principles with deep neural networks.

Introduction: Hybrid modeling combining First-Principles with machine learning is becoming a pivotal methodology for Biopharma 4.0 enactment. Chinese Hamster Ovary (CHO) cells, being the workhorse for industrial glycoproteins production, have been the object of several hybrid modeling studies. Most previous studies pursued a shallow hybrid modeling approach based on three-layered Feedforward Neural Networks (FFNNs) combined with macroscopic material balance equations. Only recently, the hybrid modeling field is incorporating deep learning into its framework with significant gains in descriptive and predictive power. Methods: This study compares, for the first time, deep and shallow hybrid modeling in a CHO process development context. Data of 24 fed-batch cultivations of a CHO-K1 cell line expressing a target glycoprotein, comprising 30 measured state variables over time, were used to compare both methodologies. Hybrid models with varying FFNN depths (3-5 layers) were systematically compared using two training methodologies. The classical training is based on the Levenberg-Marquardt algorithm, indirect sensitivity equations and cross-validation. The deep learning is based on the Adaptive Moment Estimation Method (ADAM), stochastic regularization and semidirect sensitivity equations. Results and conclusion: The results point to a systematic generalization improvement of deep hybrid models over shallow hybrid models. Overall, the training and testing errors decreased by 14.0% and 23.6% respectively when applying the deep methodology. The Central Processing Unit (CPU) time for training the deep hybrid model increased by 31.6% mainly due to the higher FFNN complexity. The final deep hybrid model is shown to predict the dynamics of the 30 state variables within the error bounds in every test experiment. Notably, the deep hybrid model could predict the metabolic shifts in key metabolites (e.g., lactate, ammonium, glutamine and glutamate) in the test experiments. We expect deep hybrid modeling to accelerate the deployment of high-fidelity digital twins in the biopharma sector in the near future.

Genome-scale modeling of Chinese hamster ovary cells by hybrid semi-parametric flux balance analysis.

Flux balance analysis (FBA) is currently the standard method to compute metabolic fluxes in genome-scale networks. Several FBA extensions employing diverse objective functions and/or constraints have been published. Here we propose a hybrid semi-parametric FBA extension that combines mechanistic-level constraints (parametric) with empirical constraints (non-parametric) in the same linear program. A CHO dataset with 27 measured exchange fluxes obtained from 21 reactor experiments served to evaluate the method. The mechanistic constraints were deduced from a reduced CHO-K1 genome-scale network with 686 metabolites, 788 reactions and 210 degrees of freedom. The non-parametric constraints were obtained by principal component analysis of the flux dataset. The two types of constraints were integrated in the same linear program showing comparable computational cost to standard FBA. The hybrid FBA is shown to significantly improve the specific growth rate prediction under different constraints scenarios. A metabolically efficient cell growth feed targeting minimal byproducts accumulation was designed by hybrid FBA. It is concluded that integrating parametric and nonparametric constraints in the same linear program may be an efficient approach to reduce the solution space and to improve the predictive power of FBA methods when critical mechanistic information is missing.

A dynamic model linking cell growth to intracellular metabolism and extracellular by-product accumulation.

Mathematical modeling of animal cell growth and metabolism is essential for the understanding and improvement of the production of biopharmaceuticals. Models can explain the dynamic behavior of cell growth and product formation, support the identification of the most relevant parameters for process design, and significantly reduce the number of experiments to be performed for process optimization. Few dynamic models have been established that describe both extracellular and intracellular dynamics of growth and metabolism of animal cells. In this study, a model was developed, which comprises a set of 33 ordinary differential equations to describe batch cultivations of suspension AGE1.HN.AAT cells considered for the production of α1-antitrypsin. This model combines a segregated cell growth model with a structured model of intracellular metabolism. Overall, it considers the viable cell concentration, mean cell diameter, viable cell volume, concentration of extracellular substrates, and intracellular concentrations of key metabolites from the central carbon metabolism. Furthermore, the release of metabolic by-products such as lactate and ammonium was estimated directly from the intracellular reactions. Based on the same set of parameters, this model simulates well the dynamics of four independent batch cultivations. Analysis of the simulated intracellular rates revealed at least two distinct cellular physiological states. The first physiological state was characterized by a high glycolytic rate and high lactate production. Whereas the second state was characterized by efficient adenosine triphosphate production, a low glycolytic rate, and reactions of the TCA cycle running in the reverse direction from α-ketoglutarate to citrate. Finally, we show possible applications of the model for cell line engineering and media optimization with two case studies.