Non-Linear Parameter Estimation for a Dynamic Model of Mammalian Cell Culture
Adam C. Baughman, Chemical & Biological Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Ricketts Building, Troy, NY 12180, Susan Sharfstein, Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Biotech 2nd Floor, Troy, NY 12180, and Lealon L. Martin, Chemical and Biological Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180.
To appropriately capture the behavior of intricate biological processes, dynamic models of mammalian cell culture systems may be formulated using non-linear kinetic expressions or other complex mathematical constructions. Such models can potentially incorporate a large number of parameters, only a few of which may be experimentally measurable. As a result, it is diffcult to obtain or estimate parameter values that are both mathematically suitable and physically relevant. In the present work, we describe a systematic, optimization-based, technique for the estimation of unknown parameter values in dynamic models. The approach is general, and applicable to any model intended to describe a fundamentally smooth process (i.e. a process described by continuous functions). Explicit Euler discretization is used to convert the given (continuous) differential model into an equivalent series of differential-algebraic equations. The discretized expressions are then used to pose a constrained non-linear optimization problem whose solution is the set of ideal parameter estimates. We demonstrate efficacy of this approach using the example of a dynamic model of mammalian cell culture proposed by Gao, et al.  Our parameter estimation technique is shown to provide parameters that are both consistent with established biological behavior in the cell culture and that also provide noticeably improved agreement between the experimental data and model proposed by the original authors.