Adaptation and homeostasis are essential properties of all living systems. However, our knowledge about the reaction kinetic mechanisms leading to robust homeostatic behavior in the presence of environmental perturbations is still poor. Here, we describe, and provide physiological examples of, a set of two-component controller motifs that show robust homeostasis. This basic set of controller motifs, which can be considered as complete, divides into two operational work modes, termed as inflow and outflow control. We show how controller combinations within a cell can integrate uptake and metabolization of a homeostatic controlled species and how pathways can be activated and lead to the formation of alternative products, as observed, for example, in the change of fermentation products by microorganisms when the supply of the carbon source is altered. The antagonistic character of hormonal control systems can be understood by a combination of inflow and outflow controllers.

Circadian rhythms are considered to play an essential part in the adaptation of organisms to their environments. The occurrence of circadian oscillations appears to be based on the presence of transcriptional-translational negative feedback loops. In Neurospora crassa, the protein FREQUENCY (FRQ) is part of such a negative feedback loop apparently by a direct interaction with its transcription factor WHITE COLLAR-1 (WC-1). Based on the observation that nuclear FRQ levels are significantly lower than nuclear WC-1 levels, it was suggested that FRQ would act more like a catalyst in inhibiting WC-1 rather than binding to WC-1 and making an inactive FRQ:WC-1 complex. Intrigued by this hypothesis, we constructed a model for the Neurospora circadian clock, which includes expression of the frq and the wc-1 genes and their possible interactions. The model suggests that even small amounts of nuclear FRQ-protein are capable of inhibiting frq transcription in a rhythmic manner by binding to WC-1 and promoting its degradation. Our model predicts the importance of a FRQ dependent degradation of WC-1 in closing the negative feedback loop. The model shows good agreement with experimental levels in nuclear and cytosolic FRQ and WC-1, their phase relationships, and several clock mutant phenotypes.

Robust homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Integral feedback is a control-engineering concept that leads to robust, i.e., perturbation-independent, adaptation and homeostatic behavior in the controlled variable. Addressing two-component negative feedback loops of a controlled variable A and a controller molecule E, we have shown that integral control is closely related to the presence of zero-order fluxes in the removal of the manipulated variable E. Here we show that autocatalysis is an alternative mechanism to obtain integral control. Although the conservative and marginal stability of the Lotka-Volterra oscillator (LVO) with autocatalysis in both A and E is often considered as a major inadequacy, homeostasis in the average concentrations of both A and E ( and ) is observed. Thus, autocatalysis does not only represent a mere driving force, but may also have regulatory roles.

Homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Previously, we have described molecular mechanisms that lead to robust homeostasis/adaptation under inflow or outflow perturbations. Here we report that harmonic oscillations occur in models of such homeostatic controllers and that a close relationship exists between the control of the p53/Mdm2 system and that of a homeostatic inflow controller. This homeostatic control model of the p53 system provides an explanation why large fluctuations in the amplitude of p53/Mdm2 oscillations may arise as part of the homeostatic regulation of p53 by Mdm2 under DNA-damaging conditions. In the presence of DNA damage p53 is upregulated, but is subject to a tight control by Mdm2 and other factors to avoid a premature apoptotic response of the cell at low DNA damage levels. One of the regulatory steps is the Mdm2-mediated degradation of p53 by the proteasome. Oscillations in the p53/Mdm2 system are considered to be part of a mechanism by which a cell decides between cell cycle arrest/DNA repair and apoptosis. In the homeostatic inflow control model, harmonic oscillations in p53/Mdm2 levels arise when the binding strength of p53 to degradation complexes increases. Due to the harmonic character of the oscillations rapid fluctuating noise can lead, as experimentally observed, to large variations in the amplitude of the oscillation but not in their period, a behavior which has been difficult to simulate by deterministic limit-cycle models. In conclusion, the oscillatory response of homeostatic controllers may provide new insights into the origin and role of oscillations observed in homeostatically controlled molecular networks.

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.