Stochastic system identification without an a priori chosen kinetic model—exploring feasible cell regulation with piecewise linear functions

Model properties and data fit. Production (P) and degradation (D) rates and the simulated (F3) and experimental (F3 Exp) frequency distributions after 3 days of cell culture for minimum error parameters and a maximum number of molecules N？=？30. a Piecewise linear model. b Basic birth and death process model (constant P, linear D). D is identified to be zero, which for bacteria has also been assumed in the literature.38,46 This contrasts the co-upregulation of P and D identified in a. Thus, very small differences in data fit and varying model assumptions can result in largely different final parameters and lead to opposing conclusions. This is clearly indicative of serious identifiability problems. In a, the three individual x- and y-set points for P and D are indicated by vertical lines and red and blue points, respectively. Rates are set constant right of the 3rd set-point. For degradation rates the lower boundary (D(0)？=？0) is omitted from the line graph. Frequencies were scaled to match the upper rate limit (12/h). The number of molecules per cell n is displayed up to the 99% percentile of the experimental frequency distribution (n？≤？20). Reduced growth rate: 0.65·0.5·ln(2)/h. Original data by courtesy of Kashiwagi and Yom