Laboratory for Process Modeling and Distributed Computing, Department of Chemical Engineering and Biotechnology, Faculty of Physical and Mathematical Sciences, University of Chile, Santiago, Chile

Millennium Institute for Cell Dynamics and Biotechnology, Department of Chemical Engineering and Biotechnology, Faculty of Physical and Mathematical Sciences University of Chile, Santiago, Chile

Department of Chemical Engineering and Biotechnology, Faculty of Physical and Mathematical Sciences, University of Chile, Santiago, Chile

Centre for Biochemical Engineering and Biotechnology, Department of Chemical Engineering and Biotechnology, Faculty of Physical and Mathematical Sciences University of Chile, Santiago, Chile

Background

Experimental evidence shows the existence of multiple steady states in mammalian cell culture with distinct cellular metabolism

Gene level fold changes corresponding to low over high ΔL/ΔG states

**Enzyme**

**Real Time PCR**

**Microarray cDNA**

Lactate Dehydrogenase

↓ 2.4

↓ 1.9

Pyruvate Kinase

↓ 2.9

↓ 2.0

Phosphofructokinase

↓ 2.0

↓ 1.3

Changes on the cell culture’s metabolic state have been found to be related to the amount of residual glucose in a reactor

The problem of providing an optimized strategy for glucose feeding in order to achieve a specific metabolic state is yet to be studied. We propose a model based strategy for designing a control system for metabolic state regulation that considers the biological complexity of the regulation of the cellular system.

Materials and methods

A detailed metabolic model for mammalian cell metabolism was formulated (complete model); a system of ordinary differential equations for the main metabolic variables of the following form:

wherein is the metabolite concentration vector, **S** is the stoichiometric matrix, is the reaction rate vector, and

where

The model’s parameters were obtained from literature and through a fitting process to experimental data; said fitting process was by the least squares method using the Nelder-Mead simplex method

Once the experimental curves were obtained with the detailed model a simplified model was traced that includes the main metabolic reactions in CHO cells, and the same fitting process was carried out. Stability analysis was carried out on both the detailed and the simplified model in order to establish the number of feasible steady states for both models.

Enzyme kinetic for lactate dehydrogenase was weighted with an enzyme factor

The objective of the same was to associate low

Results

The results of the curve fitting of the detailed and simplified models are depicted in Figure

Simulation results for detailed and simplified model

Simulation results for detailed and simplified model

Stability analysis confirmed that both the simplified and detailed metabolic models exhibit only one steady state. The existence of only one stable attractor supports the idea that metabolic regulation alone cannot explain the metabolic shift. Therefore, gene regulation is an element that should be considered in a model that correctly describes this phenomenon.

(a) Simulation results for complete model without metabolic shift, (b) Simulation results for unregulated simplified model without metabolic shift, (c) Simulation results for unregulated simplified model with metabolic shift, (d) Simulation results for regulated simplified model with metabolic shift. **-** : Simulated Glucose,

The implemented regulation model consists of a Hill activation function that depends on the residual glucose concentration, which modifies the enzyme kinetic for lactate dehydrogenase in the following manner:

wherein _{glc}^{e}_{glc} is the glucose concentration within the bioreactor. The result of the implementation of the above function is presented in Figure

Conclusions

Metabolic shift is caused by regulation at gene expression and metabolic levels. A reduction of the

The final objective of said model is to design a model based controller capable of maintaining a low metabolic state (ΔL/ΔG ratio under 0.5) under continuous operation. The tentative input variables are the glucose and lactate concentrations as well as the ΔL/ΔG ratio. The controller will modify the response of the system by manipulating the dilution rate and the glucose feed concentration of the culture.

Acknowledgments

Conicyt, This work has been supported by FONDECYT Initiation Grants 11080016 and 11090268