The paper introduces a relay feedback oscillator for modeling circadian rhythms in cyanobacteria. The relay feedback oscillator is equipped with low pass filter F(jω), hysteresis-type relay and negative feedback. This negative feedback represents an autoregulatory mechanism of the circadian clock and the notion of this autoregulatory mechanism is based on the well-known Goodwin biochemical oscillator . The relay is responsible for the mediation of both the activation and degradation of oscillator state variables (protein concentrations) and in this way the pacemaker is constituted. Later on, low pass filter poles are identified for the purpose of modeling auto-oscillations with the free running period of 24h and the method of the pole identification consists in an ultimate frequency test providing stability margin of a single-loop composed of the filter and the relay in the feedback. Next, a relay output / input ratio of amplitudes and hysteresis are found out by the graphical test of the single-loop on the stability margin which is carried out in Bode graph. Finally, the output correspondence of relay feedback oscillator model with Miyoshi oscillator  is provided because the Miyoshi oscillator is well recognized among biochemical oscillators for species of cyanobacteria.
Relay Feedback Oscillator Design for Modeling Circadian Rhythms in Cyanobacteria
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Fiser, J, Zitek, P, & Cerveny, J. "Relay Feedback Oscillator Design for Modeling Circadian Rhythms in Cyanobacteria." Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 2: Biomedical and Biotechnology Engineering; Nanoengineering for Medicine and Biology. Denver, Colorado, USA. November 11–17, 2011. pp. 549-556. ASME. https://doi.org/10.1115/IMECE2011-64996
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