Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction -the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model. NomenclatureC ij -component i concentration in jth model compartment; R ijk -transport rate of component i into or out of compartment j from the kth source or sink compartment; N in -number of source compartments; N outnumber of sink compartments; r ijl -reaction rate of component i in compartment j in the lth i-generating or i-consuming reaction; N gen -number of reactions generating component i; N con -number of reactions consuming component i; -specific growth rate; app max -apparent maximum specific growth rate; K dspecific death rate; N v -viable cell number; N t -total cell number; D -dilution rate; -parameter; 0 -parameter; -parameter; m -cell mass; m 0 -mass of a dividing cell; t -time; N -cell number; r -single cell growth rate; S -nutrient concentration; s -nutrient concentration vector; À -cell transition rate; ppartition probability density function; Y -yield coefficient; f (m) -the division probability density function; B -coefficient for the beta distribution incorporating the gamma function; x max -vector of maximum XPS 120742 (CYTO) -ms-code CYTO853 -product element 5254543 -23 September 2004 -Newgen

A practical strategy is presented addressing the related issues of model parameter identifiability and estimability that was applied to a large-scale, dynamic, and highly nonlinear biological process model describing the metabolic behavior of mammalian cell cultures in a continuous bioreactor. The model used consists of 27 inputs, 32 outputs, and more than 350 parameters; is compartmental in nature; and represents the state of the art in terms of model complexity and fidelity. The strategy adopted falls under the scope of estimability and comprises of two parts:  (a) a parameter perturbation study that singly perturbs parameters under a number of deterministically sampled model input vectors and consequently partitions them into those that yield significant changes in the outputs (the estimable parameter set) and those that do not and (b) subsequent evaluation of Monte Carlo estimates of global sensitivity indices of these two sets, which quantitatively assess the amount of parameter sensitivity contained both within and between the sets. Of the 357 parameters, 37 were found to be estimable to within at least ±25% of their nominal parameter value and, under nominal experiment conditions, accounted for 48% of the model's sensitivity. The remaining 320 parameters accounted for just 4% of the model's sensitivity. As expected, significant interactions were found to exist between these two sets. Interactions of the estimable parameter set with the inestimable set accounted for 48% of the model's sensitivity.

Mainstream modeling of cell culture systems to date has followed two distinct approaches:  cell population-balance modeling and single-cell modeling. The former aims to capture increasing heterogeneity between cells, while the latter attempts to faithfully capture intracellular processes. However, the oversimplistic expressions used in the single-cell kernels, the functions that characterize single-cell behavior, are the main predictive bottleneck of population-balance models (PBMs). Single-cell models (SCMs) do not describe differences between cells, such as the mass variation. We present a new model that captures certain strengths of both approaches. It uses a highly structured SCM to characterize the single-cell growth and death rates that are applied to terms in each stage of a multistaged PBM. The high degree of intracellular detail, however, also leads to more than 700 parameters. The parameter set is significantly reduced by employing an estimability method on the model. The model is subsequently compared using literature data for batch and fed-batch conditions.

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