# Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

## TL;DR

This paper introduces a model linking intracellular metabolism to extracellular bioreactor variables in continuous cell cultures, revealing key control parameters and complex steady-state behaviors that inform experimental and industrial practices.

## Contribution

It presents a tractable method for analyzing steady states in complex metabolic networks and uncovers invariant laws and multiple metabolic switches in continuous cell culture systems.

## Key findings

- Cell density to dilution rate ratio controls steady states.
- Multi-stability arises from toxic byproduct feedback.
- Chemostats effectively model large-scale perfusion cultures.

## Abstract

We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. More importantly, we derive a number of consequences from the model that are independent of parameter values. First, that the ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties invariant across perfusion systems. This conclusion is robust even in the presence of multi-stability, which is explained in our model by the negative feedback loop on cell growth due to toxic byproduct accumulation. Moreover, a complex landscape of steady states in continuous cell culture emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced. Thus, in order to actually reflect the expected behavior in perfusion, performance benchmarks of cell-lines and culture media should be carried out in a chemostat.