Unveiling Steady-State Multiplicity
in Hybridoma Cultures:
The Cybernetic Approach
Abhijit Anand Namjoshi,
1
Wei-Shou Hu,
2
Doraiswami Ramkrishna
1
1
1283 Chemical Engineering Building, Purdue University, West Lafayette,
Indiana 47907; telephone: 765-494-4052; fax: 765-494-4052;
e-mail: ramkrish@ecn.purdue.edu
2
Chemical Engineering and Materials Science Department, University of
Minnesota, Minneapolis, Minnesota
Received 5 April 2002; accepted 5 June 2002
DOI: 10.1002/bit.10447
Abstract: Mammalian cells grown in suspension produce
waste metabolites such as lactate, alanine, and ammo-
nia, which reduce the yield of cell mass and the desired
product on the nutrients supplied. Previous studies (Cruz
et al., 1999; Europa et al., 2000; Follstad et al., 1999) have
shown that the cells can be made to alter their metabo-
lism by starving them on their nutrients in continuous
cultures at low dilution rates or starting the culture as a
fed-batch. This leads to multiple steady states in continu-
ous reactors, with some states being more favorable
than others. Mathematical models that take into account
the metabolic regulation that leads to these multiple
steady states are invaluable tools for bioreactor control.
In this article we present a cybernetic modeling strategy
in which Metabolic Flux Analysis (MFA) is used to guide
the cybernetic formulation. The hybridoma model pre-
sented as a result of this strategy considers the partially
substitutable, partially complementary nature of glucose
and glutamine. The choice of competitions within the
network is guided by MFA and the model is successful in
explaining the three multiple steady states observed. The
cybernetic model though identified for the hybridoma
experiments of Hu and others (Europa et al., 2000) seem
generally applicable to mammalian systems as it cap-
tures the pathways that are common to mammalian cells
grown in suspension. The model presented here could
be used for start-up strategies for continuous reactors
and model-based feedback control for maintaining high
productivity of the reactor. © 2002 Wiley Periodicals, Inc.
Biotechnol Bioeng 81: 80–91, 2003.
Keywords: Mammalian cells; metabolic flux analysis, cy-
bernetic modeling strategy; hybridoma cultures; multi-
plicity
INTRODUCTION
Hybridoma cells when cultured on a well-defined medium
comprising glucose, glutamine and other amino acids pro-
duce cell mass, monoclonal antibodies and waste metabo-
lites such as lactate, alanine and ammonia (Hu and Oberg,
1990). Hybridoma cells [in particular, and mammalian cells
in general (Cruz et al., 1999)] display multiple steady states
with widely varying concentrations of cell mass, desired
product as well as waste metabolites (Follstad et al., 1999;
Zhou et al., 1997). This means that for identical input con-
ditions to a continuous reactor, the outlet conditions change
depending on how the culture is made continuous. These
multiple states are manifestations of the complex interaction
between cells and their environment. Cells channel sub-
strates through myriads of intracellular reactions to generate
new cell mass and energy and in the process generate and
excrete different byproducts. These cellular reactions,
termed metabolic pathways are the key to understanding
cellular behavior. What makes this process difficult is the
additional level of complexity present in biological systems
in contrast with purely chemical systems because of the
genetic information present in living cells. The genetic code
not only alters the extents of different reactions but also the
reactions themselves, by inducing (and activating) new en-
zymes while repressing (and deactivating) existing ones, in
response to changes in the abiotic environment. This under-
lying phenomenon of cellular regulation dictates the non-
linear behavior in biological systems and is the chief reason
of multiplicity in continuous bioreactors. Here we address
the peculiar features of hybridoma cell growth in batch,
fed-batch, and continuous operating conditions and con-
struct a mathematical model capable of explaining the ob-
served phenomenon. The mathematical models available in
literature (Brian et al., 1989; Bree et al., 1988; Glacken et
al., 1988; Guardia et al., 2000; Miller et al., 1988), with one
exception, do not address this phenomena of multiple steady
states. The cybernetic modeling approach (Kompala et al.,
1986; Ramkrishna, 1982; Ramkrishna et al., 1987) is com-
missioned toward this task because cybernetic models have,
over the years, been extremely successful in modeling cel-
lular regulation (Baloo and Ramkrishna, 1991a; 1991b;
Jones and Kompala, 1999). We also illustrate how model
Correspondence to: Doraiswami Ramkrishna
Contract grant sponsor: NSF
Contract grant number: 9818054-CTS
© 2002 Wiley Periodicals, Inc.