The Control of the Controller: Molecular Mechanisms for Robust Perfect Adaptation and Temperature Compensation

Abstract

Organisms have the property to adapt to a changing environment and keep certain components within a cell regulated at the same level (homeostasis). "Perfect adaptation" describes an organism's response to an external stepwise perturbation by regulating some of its variables/components precisely to their original preperturbation values. Numerous examples of perfect adaptation/homeostasis have been found, as for example, in bacterial chemotaxis, photoreceptor responses, MAP kinase activities, or in metal-ion homeostasis. Two concepts have evolved to explain how perfect adaptation may be understood: In one approach (robust perfect adaptation), the adaptation is a network property, which is mostly, but not entirely, independent of rate constant values; in the other approach (nonrobust perfect adaptation), a fine-tuning of rate constant values is needed. Here we identify two classes of robust molecular homeostatic mechanisms, which compensate for environmental variations in a controlled variable's inflow or outflow fluxes, and allow for the presence of robust temperature compensation. These two classes of homeostatic mechanisms arise due to the fact that concentrations must have positive values. We show that the concept of integral control (or integral feedback), which leads to robust homeostasis, is associated with a control species that has to work under zero-order flux conditions and does not necessarily require the presence of a physico-chemical feedback structure. There are interesting links between the two identified classes of homeostatic mechanisms and molecular mechanisms found in mammalian iron and calcium homeostasis, indicating that homeostatic mechanisms may underlie similar molecular control structures.

Protein sequestration versus Hill‐type repression in circadian clock models

“…5), the major difference between HT and PS models has not been reported or investigated, to our knowledge. Future work can also investigate whether PS models follow the entrainment properties [37,45,47,142,[156][157][158] or temperature compensation mechanisms [38,40,42,[159][160][161][162][163][164][165][166] identified with HT models. Furthermore, stochastic simulations of HT models commonly indicate that circadian clocks can maintain rhythms even with low numbers of molecules [167][168][169][170].…”

Transepithelial glucose transport and Na+/K+ homeostasis in enterocytes: an integrative model

“…With K 0.5 E set NaK Ͻ Ͻ n NaK (saturation) the degradation term is approximately constant at V max E set NaK , and thus ṅ NaK is zero when [Na c ] is at the setpoint V max E set NaK /k NaK . We have previously shown that zero-order kinetics is a sufficient condition for integral control (58). The outflow of Na ϩ is still given by the J NaK expression (Eq.…”

Modelling and Analysis of Feedback Control Mechanisms Underlying Osmoregulation in Yeast

“…Mettetal et al [24] developed a concise model by using linear systems theory, and then revised this model arguing for the necessity of at least one branch of the system to implement integral control to achieve the experimentally observed adaptive responses in the system, Muzzey et al [26]. The role of integral feedback in perfectly adaptive systems is by now well-studied in the Systems Biology literature (see [26,27]), and it is highly likely that the osmoregulation system in yeast does indeed include a biochemical implementation of integral feedback, as seen in other systems (see [6,27,39]). It is still unclear, however, exactly how biological control systems such as osmoregulation might have evolved to use integral feedback control, and whether other alternative mechanisms might produce similar (or better) performance properties.…”

“…In particular, the experimental input, using a first harmonic approximation (see [5] pp. [26][27][28][29][30], can be written as…”