Robust Concentration and Frequency Control in Oscillatory Homeostats

Abstract

Homeostatic and adaptive control mechanisms are essential for keeping organisms structurally and functionally stable. Integral feedback is a control theoretic concept which has long been known to keep a controlled variable robustly (i.e. perturbation-independent) at a given set-point by feeding the integrated error back into the process that generates . The classical concept of homeostasis as robust regulation within narrow limits is often considered as unsatisfactory and even incompatible with many biological systems which show sustained oscillations, such as circadian rhythms and oscillatory calcium signaling. Nevertheless, there are many similarities between the biological processes which participate in oscillatory mechanisms and classical homeostatic (non-oscillatory) mechanisms. We have investigated whether biological oscillators can show robust homeostatic and adaptive behaviors, and this paper is an attempt to extend the homeostatic concept to include oscillatory conditions. Based on our previously published kinetic conditions on how to generate biochemical models with robust homeostasis we found two properties, which appear to be of general interest concerning oscillatory and homeostatic controlled biological systems. The first one is the ability of these oscillators (“oscillatory homeostats”) to keep the average level of a controlled variable at a defined set-point by involving compensatory changes in frequency and/or amplitude. The second property is the ability to keep the period/frequency of the oscillator tuned within a certain well-defined range. In this paper we highlight mechanisms that lead to these two properties. The biological applications of these findings are discussed using three examples, the homeostatic aspects during oscillatory calcium and p53 signaling, and the involvement of circadian rhythms in homeostatic regulation.

An analog to digital converter creates nuclear localization pulses in yeast calcium signaling

“…We noticed that these “calcium pulses” (defined by a threshold ratio above background, see Methods) are followed by an overshoot of calcium concentration below the resting level (average of 50 largest calcium local maxima in a representative time lapse movie is shown in Figure 1B left panel), whose depth is positively correlated to the height of the pulse (Figure 1B, right panel, R 2 = 0.37). This overshoot cannot fit an exponential curve and suggests negative feedback on [Ca 2 +] cyt , which is consistent with the predictions of calcium models constructed in previous studies of homeostasis(24,25).…”

Frequency switching between oscillatory homeostats and the regulation of p53

“…For the m3 feedback we can apply an “harmonic oscillator approximation” [28], which leads to where < A > is the average value of A defined as …”

“…A particular interesting aspect is that, under certain conditions, the homeostatic controllers may become oscillatory and preserve, if integral control is present, their homeostatic property by keeping the average value of the controlled variable at its set-point [28]. While the occurrence of oscillations is generally avoided in control engineering, natural systems show generally oscillatory behaviors, as found in circadian or ultradian rhythms [29–31].…”

Rhythms in Plants

“…Many of the fundamental advances in understanding have come from studies of these organisms and have resulted in an enormous literature (Lloyd 1998;Lakin-Thomas 2000;Lakin-Thomas and Brody 2004;Gillette and Sejnowski 2005). The mechanism of 370 D. Lloyd et al temperature compensation, a key characteristic of circadian periodicity, has been intensively studied in Lingulodinium (Hastings and Sweeney 1957) and modelled specifically in Neurospora (Tseng et al 2012), as well as in more general terms (Ruoff et al 2007; Thorsen et al 2014). Transcriptomics and functional proteomics enable a rich diversity of components involved in the expression of circadian systems and reveal evolutionary exploitation of very many distinct scenarios .…”