Identification Of Growth Phase Research Articles

Identification of growth phases and influencing factors in cultivations with AGE1.HN cells using set-based methods.

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.

Quantifying the Relationship between Phases of Stem Elongation and Flower Initiation in Poinsettia

Stem elongation of poinsettia (Euphorbia pulcherrima Klotz.) was quantified using an approach that explicitly modelled the three phases of a sigmoidal growth curve: 1) an initial lag phase characterized by an exponentially increasing stem length, 2) a phase in which elongation is nearly linear, and 3) a plateau phase in which elongation rate declines as stem length reaches an asymptotic maximum. For each growth phase, suitable mathematical functions were selected for smooth height and slope transitions between phases. The three growth phases were linked to developmental events, particularly flower initiation and the first observation of a visible flower bud. The model was fit to a data set of single-stemmed poinsettia grown with vegetative periods of 13, 26, or 54 days, resulting in excellent conformance (R2 = 0.99). The model was validated against two independent data sets, and the elongation pattern was similar to that predicted by the model, particularly during the linear and plateau phases. The model was formulated to allow dynamic simulation or adaptation in a graphical control chart. Model parameters in the three-phase function have clear biological meaning. The function is particularly suited to situations in which identification of growth phases in relation to developmental and horticultural variables is an important objective. Further validation under a range of conditions is required before the model can be applied to horticultural situations.