Hybrid elementary flux analysis/nonparametric modeling: application for bioprocess control

Abstract

Background: The progress in the "-omic" sciences has allowed a deeper knowledge on many biological systems with industrial interest. This knowledge is still rarely used for advanced bioprocess monitoring and control at the bioreactor level. In this work, a bioprocess control method is presented, which is designed on the basis of the metabolic network of the organism under consideration. The bioprocess dynamics are formulated using hybrid rigorous/data driven systems and its inherent structure is defined by the metabolism elementary modes.

Results: The metabolic network of the system under study is decomposed into elementary modes (EMs), which are the simplest paths able to operate coherently in steady-state. A reduced reaction mechanism in the form of simplified reactions connecting substrates with end-products is obtained. A dynamical hybrid system integrating material balance equations, EMs reactions stoichiometry and kinetics was formulated. EMs kinetics were defined as the product of two terms: a mechanistic/empirical known term and an unknown term that must be identified from data, in a process optimisation perspective. This approach allows the quantification of fluxes carried by individual elementary modes which is of great help to identify dominant pathways as a function of environmental conditions. The methodology was employed to analyse experimental data of recombinant Baby Hamster Kidney (BHK-21A) cultures producing a recombinant fusion glycoprotein. The identified EMs kinetics demonstrated typical glucose and glutamine metabolic responses during cell growth and IgG1-IL2 synthesis. Finally, an online optimisation study was conducted in which the optimal feeding strategies of glucose and glutamine were calculated after re-estimation of model parameters at each sampling time. An improvement in the final product concentration was obtained as a result of this online optimisation.

Conclusion: The main contribution of this work is a novel bioreactor optimal control method that uses detailed information concerning the metabolism of the underlying biological system. Moreover, the method allows the identification of structural modifications in metabolism over batch time.

Figure 1

General hybrid structure for bioprocesses. This hybrid model structure integrates knowledge concerning the metabolism, transport phenomena and empirical process data. The bioreactor dynamics are then described by the material balance equations of each component occurring in the EMs. The EMs kinetics are identified with data from exploratory experiments, using chemometric techniques.

Figure 2

Proposed model-based optimisation scheme. On-line optimisation supported by the hybrid model. The process performance function includes a penalty term that accounts for the risk of model unreliability, i.e., extrapolation outside the model trust region. The parameter estimation as well as the optimisation of the future process course occurs every time a new measurement becomes available.

Figure 3

BHK cells metabolic network. The figure shows important pathways in the central metabolism of BHK cells. The dashed arrows indicate lumped pathways towards biomass and desired product synthesis.

Figure 4

Elementary modes of the metabolic network considered.

Figure 5

Hybrid modeling results. Modeling results of all seven state variables for both training (I-V) and validation data sets (VI-VII). Experiments I-III are Batch cultures and IV-VII are Fed-batch cultures.

Figure 6

Kinetic rates identified by the hybrid model. The kinetic rates over the time course of bioreaction can provide valuable information concerning the evolution of BHK metabolism, (a) Batch culture; (b) Fed-batch culture.

Figure 7

Optimal trajectories during a fed-batch on-line optimization. Optimised trajectories of process variables for five periods of cultivation: 0,46, 75, 92 and 195 h (lines are model predictions and symbols are experimental data).

Figure 8

Optimisation results with optimised medium. (a) Predicted optimal trajectories of viable cells, glucose, glutamine and product concentrations starting with low levels of glucose and glutamine. (b) Distribution of intracellular elementary modes over the time course of the process for the optimal strategy.