Identification and automatic segmentation of multiphasic cell growth using a linear hybrid model

This article considers a new mathematical model for the description of multiphasic cell growth. A linear hybrid model is proposed and it is shown that the two-parameter logistic model with switching parameters can be represented by a Switched affine AutoRegressive model with eXogenous inputs (SARX). The growth phases are modeled as continuous processes, while the switches between the phases are considered to be discrete events triggering a change in growth parameters. This framework provides an easily interpretable model, because the intrinsic behavior is the same along all the phases but with a different parameterization. Another advantage of the hybrid model is that it offers a simpler alternative to recent more complex nonlinear models. The growth phases and parameters from datasets of different microorganisms exhibiting multiphasic growth behavior such as Lactococcus lactis, Streptococcus pneumoniae, and Saccharomyces cerevisiae, were inferred. The segments and parameters obtained from the growth data are close to the ones determined by the experts. The fact that the model could explain the data from three different microorganisms and experiments demonstrates the strength of this modeling approach for multiphasic growth, and presumably other processes consisting of multiple phases.