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**Regulatory network of drug-induced enzyme production: parameter estimation based on the periodic dosing response measurement.**
*(English)*
Zbl 1488.92031

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 20. Proceedings of the 20th seminar (PANM), Hejnice, Czech Republic, June 21–26, 2020. Prague: Czech Academy of Sciences, Institute of Mathematics. 89-97 (2021).

This work is a sort of continuation of [J. Duintjer Tebbens et al., Appl. Math., Praha 64, No. 2, 253–277 (2019; Zbl 07088739)] and [N. S. Luke et al., Bull. Math. Biol. 72, No. 7, 1799–1819 (2010; Zbl 1202.92029)]. A network of drug-induced enzyme production is modeled by a system of five first order ordinary differential equations (ODEs) where the unknown functions represent the concentration of the constituents involved in the process. In the ODEs, one can distinguish a linear, quadratic, and constant part as well as an input function, the dosing rate of the drug added to the system. The model and its initial conditions depend on nine constant parameters in total. Although the values of the parameters can be found in the literature (and the authors list them), they can hardly be considered accurate or guaranteed. This is why the authors focus on the estimation of them. For brevity, they limit themselves to only one of them, namely to the drug degradation parameter. Since the input dosing is periodic, the model response converges to a periodic function. Using the periodicity and the fast Fourier transform, the authors propose an algorithm addressing the estimation problem. The proposed method is demonstrated through a numerical example.

For the entire collection see [Zbl 1466.65003].

For the entire collection see [Zbl 1466.65003].

Reviewer: Jan Chleboun (Praha)

### MSC:

92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |

92C42 | Systems biology, networks |

34A34 | Nonlinear ordinary differential equations and systems |