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.

Iron is an essential element needed by all organisms for growth and development. Because iron becomes toxic at higher concentrations iron is under homeostatic control. Plants face also the problem that iron in the soil is tightly bound to oxygen and difficult to access. Plants have therefore developed special mechanisms for iron uptake and regulation. During the last years key components of plant iron regulation have been identified. How these components integrate and maintain robust iron homeostasis is presently not well understood. Here we use a computational approach to identify mechanisms for robust iron homeostasis in non-graminaceous plants. In comparison with experimental results certain control arrangements can be eliminated, among them that iron homeostasis is solely based on an iron-dependent degradation of the transporter IRT1. Recent IRT1 overexpression experiments suggested that IRT1-degradation is iron-independent. This suggestion appears to be misleading. We show that iron signaling pathways under IRT1 overexpression conditions become saturated, leading to a breakdown in iron regulation and to the observed iron-independent degradation of IRT1. A model, which complies with experimental data places the regulation of cytosolic iron at the transcript level of the transcription factor FIT. Including the experimental observation that FIT induces inhibition of IRT1 turnover we found a significant improvement in the system’s response time, suggesting a functional role for the FIT-mediated inhibition of IRT1 degradation. By combining iron uptake with storage and remobilization mechanisms a model is obtained which in a concerted manner integrates iron uptake, storage and remobilization. In agreement with experiments the model does not store iron during its high-affinity uptake. As an iron biofortification approach we discuss the possibility how iron can be accumulated even during high-affinity uptake.

The level of cytosolic calcium (Ca2+) in cells is tightly regulated to about 100 nM (pCa ≈ 7). Due to external stimuli, the basal cytosolic Ca2+ level can temporarily be raised to much higher values. The resulting Ca2+ transients take part in cell-intrinsic signals, which result in cellular responses. Because of its signaling importance and that high levels of Ca2+ can lead to apoptosis, regulation and homeostatic control of cytosolic Ca2+ is essential. Based on experimentally known molecular interactions and kinetic data together with control theoretic concepts (integral feedback) we developed a basic computational model describing robust cytosolic Ca2+ homeostasis. The aim of the model is to describe the integrative mechanisms involved in cytosolic Ca2+ homeostasis in non-excitable cells. From a model perspective, the cytosolic steady state value (set point) of 100 nM is determined by negative feedback loops (outflow controllers), one of these represented by the plasma membrane Ca2+ ATPase (PMCA) - calmodulin (CaM) pump and its activation by cytosolic Ca2+. Hysteretic behaviors of the Ca pumps and transporters have been added leading to improved kinetic behaviors indicatingthat hysteretic properties of the Ca2+ pumps appear important how cytosolic Ca2+ transients are formed. Supported by experimental data the model contains new findings that the activation of the inositol 1,4,5,-tris-phosphate receptor by cytosolic Ca2+ has a cooperativity of 1, while increased Ca2+ leads to a pronounced inhibition with a cooperativity of 2. The model further suggests that the capacitative inflow of Ca2+ into the cytosol at low Ca2+ storage levels in the ER undergoes a successive change in the cooperativity of the Store Operated calcium Channel (SOCC) as Ca2+ levels in the ER change. Integrating these aspects the model can show sustained oscillations with period lengths between 2 seconds and 30 hours.