Analytical study of robustness of a negative feedback oscillator by multiparameter sensitivity

Abstract

BackgroundOne of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators.ResultsWe present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop).ConclusionsSince a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period.

The interaction of psychological and physiological homeostatic drives and role of general control principles in the regulation of physiological systems, exercise and the fatigue process – The Integrative Governor theory

“…That these traces are always usually non‐monotonic indicates that changes are continuously being made to the system being studied in a deterministic manner (Terblanche et al., 1999; Tucker et al., 2006), and they are created by tactical ‘decisions’ associated with maintaining the strategic plan for the entire athletic event the individual is participating in, related we suggest to the weighting of the competing requirements of psychological and physiological homeostasis (St Clair Gibson et al., 2013). Whether this is the case or not, whatever underpins them, oscillations occur in a dynamic manner in all physiological systems, and are a ‘signature’ of the negative feedback control mechanism which underpin them (Maeda & Kurata, 2014; Novak & Tyson, 2008; St Clair Gibson et al., 2006).…”

Not Just a Sum? Identifying Different Types of Interplay between Constituents in Combined Interventions

“…Another form of interplay is of an emergent (sometimes also called coalistic) type [ 6 ]: No effect is seen for each of the constituents, unlike for the combined manipulation. This form of interplay could, for example, occur when the expression of a target gene requires that two transcription factors each need to bind, with each constituent intervention activating one transcription factor only [ 10 ].…”