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access icon openaccess Describing function-based approximations of biomolecular systems

This is an open access article published by the IET under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/3.0/)
Received 12/05/2017, Accepted 12/11/2017, Revised 02/11/2017, Published 21/11/2017

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.

Inspec keywords: molecular biophysics; physiological models; approximation theory

Other keywords: describing-function-based approximations; analytical upper bounds; computational error estimates; mathematical methods; biomolecular signalling systems; saturating dynamics; hysteretic dynamics; computational approaches; oscillation amplitude

Subjects: Biomolecular dynamics, molecular probes, molecular pattern recognition; Numerical approximation and analysis; Macromolecular conformation (statistics and dynamics)

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