Copyright © IFAC Computer Applications in Biotechnology,
Osaka, Japan, 1998
MODELING OF MULTIPLE STEADY STATES IN MAMMALIAN CELLS.
A CYBERNETIC APPROACH
M. J. Guardia', A. Europa', A. Gamhhir', R. Ramakrishna 2, D. Ramkrishna
2
and W-S. Hu.'
I Department of Chemical Engineering and Materials Science,
University of Minnesota, Minneapolis, MN 55455-0132.
2School of Chemical Engineering, Purdue University, West Lafayette, IN 47907
Abstract: Mammalian cells utilize glucose and glutamine as the two key substrates. These two
nutrients are complementary and substitutable in nature and, in cellular metabolism, can be
oxidized completely, or be converted to excreted metabolites. The ability of cells to grow at the
same rate at different physiological states gives rise to multiple steady states in continuous culture.
Experimental results indicate that the steady state reached is strongly dependent on the initial
condition of cultivation, or the reaction path. However, it has been elusive to develop a correlation
between initial conditions and the resulting steady states. We have used a cybernetic model as the
conceptual framework to explore the effect of initial conditions on the behavior of continuous
cultures. The results of simulation demonstrate that a cybernetic model is capable of illustrating
the effect of the history of a culture on the resulting steady state. Copyright © 1998 IFAC
Keywords: Multiple steady states, Cybernetic model, Mammalian cells, Initial conditions
1. INTRODUCTION
A typical mammalian cell culture medium consists
of glucose and glutamine as the main sources for
carbon and energy. The metabolism of glucose and
glutamine in mammalian cells are related as
illustrated in the simplified metabolic chart shown in
Figure 1. Both provide the carbon skeleton for
cellular molecules and are catabolized for energy
generation. They are often referred to as partially
substitutable and partially complementary substrates.
Mammalian cells are capable of utilizing varying
proportions of glucose and glutamine, and
metabolize them differently under different chemical
environments. Glutamine becomes a predominant
source of energy at low glucose concentrations. The
metabolism of glucose is also greatly affected by
glucose concentration (Zielke et at. 1978). At high
glucose levels, glucose is consumed at a faster rate;
however, the majority of that consumed is converted
to lactate. At low glucose concentrations, the
consumption rate is lower and a larger proportion is
completely oxidized to CO
2
. Glutamine is taken up
by cells at a rate far exceeding what is needed for
incorporation into biomass (as cellular protein or
nucleotides) and protein products. Under normal
455
growth conditions, excess nitrogen is excreted as
some amino acids, including NH3 and alanine.
However, under the condition of low glucose
concentration, glutamine also serves as an energy
source and the source of carbon skeleton for other
cellular constituents.
It has been shown previously that the metabolism of
the cells can be altered in fed-batch cultures under
low-glucose conditions, while maintaining a
constant growth rate. In this experiment, on-line
measurements were employed to estimate the
metabolic demand of nutrients and the feeding rate
of concentrated medium (without bulk salts) in fed-
batch culture to maintain glucose concentration at a
low level throughout the exponential growth period
(Zhou et aI., 1995). Lactate production was reduced
to near zero towards the end of the cultivation. At
the beginning of the cultivation, 85% of the glucose
carbon was excreted as lactate; each mole of glucose
consumed was accompanied by one mole of oxygen
consumption. Towards the end of cultivation almost
no glucose carbon was excreted as lactate and the
stoichiometric ratio between oxygen to glucose
increased to six. With the lower degree of
accumulation of lactate, a high cell concentration of