Development of A Recursive Time Series Model for Growth of Mammalian Cells Used in Monoclonal Antibody Production
Jingwei Gan, Satish J. Parulekar, and Ali Cinar
Department of Chemical and Biological Engineering
Illinois Institute of Technology, Chicago, IL 60616
Monoclonal antibodies (MAbs) are high value proteins with wide variety of applications including diagnostic testing and therapeutic treatment. MABs derived from hybridoma cell cultures are used extensively in diagnostic assays and have found increasing use in therapeutic applications, affinity production systems, and in vivo imaging. The cell lines, hybridoma, are produced by fusing B cells (lymphocytes) from immunized animals with myeloma cells. The simplest approach for producing a MAb in vitro is to grow the hybridoma cells in batch and fed-batch cultures and recover and purify the MAb from the culture medium. The large scale production of MAbs occurs via in vitro cultivation of hybridoma cell lines in bioreactors using techniques similar to those used for microbial cultivation. A cost-effective production of MAbs requires an understanding of the effects of bioreactor process variables on the physiology of hybridoma cells. Within mammalian expression platforms, Chinese hamster ovary cell-based system remain the most commonly used expression system. The development of methods for optimization of cell growth and cell productivity has become a crucial issue to enhance MAb yield in in vitro production.
Traditional operations of these culture systems at production scales are mainly based on empirical knowledge. There has been limited effort on development of first principle-based mathematical models for these cultures at laboratory scale operations. Due to complexity of the models and uncertainties associated with estimation of model parameters, the first principle models are not suitable for online prediction and control of mammalian cell cultures. In order to achieve accurate online prediction and control, simple data driven models may be more suitable for this. In this work, time series models for viable cell, glucose and glutamine concentrations in fed-batch mammalian cell cultures are developed. Results from non-recursive and recursive models are compared. The framework for developing these models is described. The key culture variables considered are concentrations of viable cells, glucose, and glutamine.
In order to generate ‘experiment data’, we use a first principles model proposed by Kontoravdi et al. (2005). This model structure is suggested by many researcherswhile the values suggested for each parameter may vary. In order to generate random ‘experiments’ when using this model, random variation for each parameter is used with their mean values suggested by Kontoravdi et al. (2005) and standard deviations computed by using the reported values by all authors who used the same cell line.
Viable cell concentration in cell culture is expressed by a recursive ARMAX model with stability constrain proposed by Turksoy et al. (2014). The time series model expresses current and future viable cell concentrations as a function of past values of viable cell concentrations and multiple inputs. Model parameters are recursively estimated by using a least square estimation algorithm. Model stability is guaranteed by converting the time series model into state space representation and ensuring that all eigenvalues lie within unit circle. Glucose and glutamine concentrations are modeled by using a dual rate model proposed by Ding and Chen (2004). After modifying the time series model by using a polynomial transformation technique, the resulting dual rate model can be used to represent dual sampling rate systems where inputs and outputs have different sampling rates. Using a dual rate model combined with recursive estimation with stability constraint, we propose recursive dual rate model with stable recursive parameter estimation to estimate the glucose and glutamine concentrations in fed-batch culture.
 Ding, Feng, and Tongwen Chen. "Combined parameter and output estimation of dual-rate systems using an auxiliary model." Automatica 40.10 (2004): 1739-1748.
 Turksoy, Kamuran, et al. "Multivariable adaptive identification and control for artificial pancreas systems." Biomedical Engineering, IEEE Transactions on61.3 (2014): 883-891.
 Kontoravdi, Cleo, et al. "Application of Global Sensitivity Analysis to Determine Goals for Design of Experiments: An Example Study on Antibody‐Producing Cell Cultures." Biotechnology progress 21.4 (2005): 1128-1135.