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.