Describing function‐based approximations of biomolecular systems. Issue 3 (18th December 2017)

• Record Type: Journal Article
• Authors: Dey, Abhishek; Sen, Shaunak
• Is Part Of: IET systems biology. Volume 12:Issue 3(2018)
• Page Start: 93
• Page End: 100
• Publication Date: 2017-12-18
• Subjects: molecular biophysics -- physiological models -- approximation theory; describing‐function‐based approximations -- mathematical methods -- computational approaches -- biomolecular signalling systems -- hysteretic dynamics -- saturating dynamics -- analytical upper bounds -- computational error estimates -- oscillation amplitude; Systems biology -- Periodicals; Cell physiology -- Periodicals; Biological systems -- Mathematical models -- Periodicals; Genetics -- Mathematical models -- Periodicals; Computational biology -- Periodicals; 573
• DOI: 10.1049/iet-syb.2017.0026
• Languages: English
• ISSNs: 1751-8849

Abstract

Abstract : Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of analytical and computational approaches, the authors adapt and develop the method of describing functions to represent the input–output responses of biomolecular signalling systems. They approximate representative systems exhibiting various saturating and hysteretic dynamics in a way that is better than the standard linearisation. Furthermore, they develop analytical upper bounds for the computational error estimates. Finally, they use these error estimates to augment the limit cycle analysis with a simple and quick way to bound the predicted oscillation amplitude. These results provide system approximations that can add more insight into the local behaviour of these systems than standard linearisation, compute responses to other periodic inputs and to analyse limit cycles.