Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective.

Calcium is tightly regulated in mammals because of the critical role of calcium ion concentrations in many physiological functions. In this work, we develop a model for calcium homeostasis and identify integral feedback control as a functional module that maintains this homeostasis. We argue that maintaining calcium concentrations in a narrow range and perfect adaptation seen when the calcium homeostatic mechanism is subjected to extreme disturbances are the result of a feedback control system implementing integral control through specific interactions of the regulating hormones. Based on the constraints imposed by the suggested integral control, we arrive at a simple dynamical model for calcium homeostasis. We show that the model is biologically plausible and is consistent with known physiology. Furthermore, the utility of the integral-feedback model is revealed by examining an extreme calcium perturbation, parturient paresis in dairy cows.     

Harmonic Oscillations in Homeostatic Controllers: Dynamics of the p53 Regulatory System

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.     

Robust Concentration and Frequency Control in Oscillatory Homeostats

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.     

Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network

It has long been known to control theorists and engineers that integral feedback control leads to, and is necessary for, “perfect” adaptation to step input perturbations in most systems. Consequently, implementation of this robust control strategy in a synthetic gene network is an attractive prospect. However, the nature of genetic regulatory networks (density-dependent kinetics and molecular signals that easily reach saturation) implies that the design and construction of such a device is not straightforward. In this study, we propose a generic two-promoter genetic regulatory network for the purpose of exhibiting perfect adaptation; our treatment highlights the challenges inherent in the implementation of a genetic integral controller. We also present a numerical case study for a specific realization of this two-promoter network, “constructed” using commonly available parts from the bacterium Escherichia coli. We illustrate the possibility of optimizing this network's transient response via analogy to a linear, free-damped harmonic oscillator. Finally, we discuss extensions of this two-promoter network to a proportional-integral controller and to a three-promoter network capable of perfect adaptation under conditions where first-order protein removal effects would otherwise disrupt the adaptation.     

Analysis of Homeostatic Mechanisms in Biochemical Networks

Cell metabolism is an extremely complicated dynamical system that maintains important cellular functions despite large changes in inputs. This “homeostasis” does not mean that the dynamical system is rigid and fixed. Typically, large changes in external variables cause large changes in some internal variables so that, through various regulatory mechanisms, certain other internal variables (concentrations or velocities) remain approximately constant over a finite range of inputs. Outside that range, the mechanisms cease to function and concentrations change rapidly with changes in inputs. In this paper we analyze four different common biochemical homeostatic mechanisms: feedforward excitation, feedback inhibition, kinetic homeostasis, and parallel inhibition. We show that all four mechanisms can occur in a single biological network, using folate and methionine metabolism as an example. Golubitsky and Stewart have proposed a method to find homeostatic nodes in networks. We show that their method works for two of these mechanisms but not the other two. We discuss the many interesting mathematical and biological questions that emerge from this analysis, and we explain why understanding homeostatic control is crucial for precision medicine.     

Integrating fluctuating nitrate uptake and assimilation to robust homeostasis

Nitrate is an important nitrogen source used by plants. Despite of the considerable variation in the amount of soil nitrate, plants keep cytosolic nitrate at a homeostatic controlled level. Here we describe a set of homeostatic controller motifs and their interaction that can maintain robust cytosolic nitrate homeostasis at fluctuating external nitrate concentrations and nitrate assimilation levels. The controller motifs are divided into two functional classes termed as inflow and outflow controllers. In the presence of high amounts of environmental nitrate, the function of outflow controllers is associated to efflux mechanisms removing excess of nitrate from the cytosol that is taken up by low-affinity transporter systems (LATS). Inflow controllers on the other hand maintain homeostasis in the presence of a high demand of nitrate by the cell relative to the amount of available environmental nitrate. This is achieved by either remobilizing nitrate from a vacuolar store, or by taking up nitrate by means of high-affinity transporter systems (HATS). By combining inflow and outflow controllers we demonstrate how nitrate uptake, assimilation, storage and efflux are integrated to a regulatory network that maintains cytosolic nitrate homeostasis at changing environmental conditions.     

A Basic Set of Homeostatic Controller Motifs

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.     

Neuronal control of energy homeostasis

Neuronal control of body energy homeostasis is the key mechanism by which animals and humans regulate their long-term energy balance. Various hypothalamic neuronal circuits (which include the hypothalamic melanocortin, midbrain dopamine reward and caudal brainstem autonomic feeding systems) control energy intake and expenditure to maintain body weight within a narrow range for long periods of a life span. Numerous peripheral metabolic hormones and nutrients target these structures providing feedback signals that modify the default "settings" of neuronal activity to accomplish this balance. A number of molecular genetic tools for manipulating individual components of brain energy homeostatic machineries, in combination with anatomical, electrophysiological, pharmacological and behavioral techniques, have been developed, which provide a means for elucidating the complex molecular and cellular mechanisms of feeding behavior and metabolism. This review will highlight some of these advancements and focus on the neuronal circuitries of energy homeostasis.     

Molecular and cellular control of T1/T2 immunity at the interface between antimicrobial defense and immune pathology

The immune system evolved to rapidly recognize infectious threats and promptly mobilize cellular effectors to the infection site. Establishment of a robust T1-type immunity is a prerequisite for effective defense against most viruses and intracellular bacteria. However, accumulating evidence shows that T1 and T2 responses during such infections are not mutually exclusive. A possibility may be that the dual T1-T2 nature of antiviral immune responses is merely a byproduct of less than perfect crossregulatory mechanisms. Herein, we discuss molecular and cellular mechanisms of T-cell differentiation along with recent evidence supporting the hypothesis that rather than representing an epiphenomenon, coinduction of virus-specific T2 cells plays a significant homeostatic role. Thus, molecular pathways that regulate IL-4 production during influenza virus infection monitor T1-mediated immune responses in vital organs such as lungs and prevent immune pathology that may otherwise interfere with recovery from disease. Such evidence suggests that coinduction of T2 immunity maintains immune homeostasis during T1-mediated defense reactions. Finally, we outline implications on the earlier concept of T1/T2 dichotomy, supporting a model in which these two subsets, rather than being mutually antagonistic, together facilitate the recovery from infection.     

Maintenance of Mitochondrial Oxygen Homeostasis by Cosubstrate Compensation

Mitochondria maintain a constant rate of aerobic respiration over a wide range of oxygen levels. However, the control strategies underlying oxygen homeostasis are still unclear. Using mathematical modeling, we found that the mitochondrial electron transport chain (ETC) responds to oxygen level changes by undergoing compensatory changes in reduced electron carrier levels. This emergent behavior, which we named cosubstrate compensation (CSC), enables the ETC to maintain homeostasis over a wide of oxygen levels. When performing CSC, our ETC models recapitulated a classic scaling relationship discovered by Chance [Chance B (1965) J. Gen. Physiol. 49:163-165] relating the extent of oxygen homeostasis to the kinetics of mitochondrial electron transport. Analysis of an in silico mitochondrial respiratory system further showed evidence that CSC constitutes the dominant control strategy for mitochondrial oxygen homeostasis during active respiration. Our findings indicate that CSC constitutes a robust control strategy for homeostasis and adaptation in cellular biochemical networks.     

Physiological basis of differences in the body tolerance to submaximal physical load to capacity in healthy young individuals

A complex approach to studying the physiological basis of the individual and typological features of functional states and tolerance of physical load in healthy young individuals using superslow physiological processes (SSPP) was elaborated. Statistically significant differences were found in the values of central hemodynamics, physicochemical homeostasis, the level of oxygen consumption by the tissues and general nonspecific adaptation reactions of the body. These reactions correlated with differences in the integral values of the wakefulness level, as judged by the SSPP data, in healthy individuals tolerant of physical fatigue and quickly fatigued individuals at rest and after a two-step individually submaximal physical stress to capacity. The possibilities of the use of this approach to substantiate the physiological significance of SSPP in the differential diagnosis of the optimal level of wakefulness, the state of physical tension, the state of fatigue, and asthenic states of a different degree of severity in healthy individuals with regulatory and homeostatic control inherent in these states were revealed.     

Rab3-GAP controls the progression of synaptic homeostasis at a late stage of vesicle release

Homeostatic signaling systems stabilize neural function through the modulation of neurotransmitter receptor abundance, ion channel density, and presynaptic neurotransmitter release. Molecular mechanisms that drive these changes are being unveiled. In theory, molecular mechanisms may also exist to oppose the induction or expression of homeostatic plasticity, but these mechanisms have yet to be explored. In an ongoing electrophysiology-based genetic screen, we have tested 162 new mutations for genes involved in homeostatic signaling at the Drosophila NMJ. This screen identified a mutation in the rab3-GAP gene. We show that Rab3-GAP is necessary for the induction and expression of synaptic homeostasis. We then provide evidence that Rab3-GAP relieves an opposing influence on homeostasis that is catalyzed by Rab3 and which is independent of any change in NMJ anatomy. These data define roles for Rab3-GAP and Rab3 in synaptic homeostasis and uncover a mechanism, acting at a late stage of vesicle release, that opposes the progression of homeostatic plasticity.     

Osteoporosis: A neuroskeletal disease?

Osteoporosis is caused by a failure of bone homeostasis, but the precise molecular mechanisms controlling bone homeostasis are largely unknown. Increasing evidence that neurons and neurotransmitters are intimately involved in bone remodelling has shed light on a novel regulatory mechanism for bone homeostasis. Namely, like all other homeostatic functions, bone remodelling is under the control of the hypothalamus, and osteoporosis is considered to be a neuroskeletal disease.     

Spontaneous and homeostatic proliferation of CD4 T cells are regulated by different mechanisms

Transfer of naive CD4 T cells into lymphopenic mice initiates a proliferative response of the transferred cells, often referred to as homeostatic proliferation. Careful analysis reveals that some of the transferred cells proliferate rapidly and undergo robust differentiation to memory cells, a process we have designated spontaneous proliferation, and other cells proliferate relatively slowly and show more limited evidence of differentiation. In this study we report that spontaneous proliferation is IL-7 independent, whereas the slow proliferation (referred to as homeostatic proliferation) is IL-7 dependent. Administration of IL-7 induces homeostatic proliferation of naive CD4 T cells even within wild-type recipients. Moreover, the activation/differentiation pattern of the two responses are clearly distinguishable, indicating that different activation mechanisms may be involved. Our results reveal the complexity and heterogeneity of lymphopenia-driven T cell proliferation and suggest that they may have fundamentally distinct roles in the maintenance of CD4 T cell homeostasis.     

Negative regulation of T cell homeostasis by lymphocyte activation gene-3 (CD223)

Lymphocyte homeostasis is a central biological process that is tightly regulated. However, its molecular and cellular control is poorly understood. We show that aged mice deficient in lymphocyte activation gene 3 (LAG-3), an MHC class II binding CD4 homologue, have twice as many T cells as wild-type controls. CD4(+) and CD8(+) LAG-3-deficient T cells showed enhanced homeostatic expansion in lymphopenic hosts, which was abrogated by ectopic expression of wild-type LAG-3, but not by a signaling-defective mutant. In addition, in vivo treatment with anti-LAG-3 mAb resulted in enhanced T cell expansion to a level comparable to that in LAG-3-deficient cells. This deregulation of T cell homeostasis also resulted in the expansion of multiple cell types, including B cells, macrophages, granulocytes, and dendritic cells. Lastly, regulatory T cells were dependent on LAG-3 for their optimal control of T cell homeostasis. Our data suggest that LAG-3 negatively regulates T cell homeostasis by regulatory T cell-dependent and independent mechanisms.     

Long-lasting alterations in neuronal calcium homeostasis in an in vitro model of stroke-induced epilepsy

Altered calcium homeostatic mechanisms have been implicated in the development of acquired epilepsy in numerous models. Stroke is one of the leading brain injuries that cause acquired epilepsy, yet little is known concerning the molecular mechanisms underlying stroke-induced epileptogenesis. Recently an in vitro model of stroke-induced epilepsy was developed and characterized as a powerful tool to study the pathophysiology of injury and stroke-induced epileptogenesis. Using this glutamate injury-induced epileptogenesis model, we have investigated the role of altered calcium homeostatic mechanisms in the development and maintenance of stroke-induced epilepsy. Epileptic neurons manifested elevated intracellular calcium levels compared to control neurons independent of neuronal activity and seizure discharge for the remainder of the life of the neurons in culture. In addition, epileptic neurons were found to have alterations in the ability to reduce intracellular calcium levels following a calcium load. These long-term epileptic changes in calcium homeostasis were dependent on calcium during the initial glutamate injury. The data demonstrate that significant alterations in calcium homeostatic mechanisms occur in association with stroke-induced epilepsy and suggest that these changes may play a role in both the induction and maintenance of the epileptic phenotype in this model.     

A Diffusive Homeostatic Signal Maintains Neural Heterogeneity and Responsiveness in Cortical Networks

Gaseous neurotransmitters such as nitric oxide (NO) provide a unique and often overlooked mechanism for neurons to communicate through diffusion within a network, independent of synaptic connectivity. NO provides homeostatic control of intrinsic excitability. Here we conduct a theoretical investigation of the distinguishing roles of NO-mediated diffusive homeostasis in comparison with canonical non-diffusive homeostasis in cortical networks. We find that both forms of homeostasis provide a robust mechanism for maintaining stable activity following perturbations. However, the resulting networks differ, with diffusive homeostasis maintaining substantial heterogeneity in activity levels of individual neurons, a feature disrupted in networks with non-diffusive homeostasis. This results in networks capable of representing input heterogeneity, and linearly responding over a broader range of inputs than those undergoing non-diffusive homeostasis. We further show that these properties are preserved when homeostatic and Hebbian plasticity are combined. These results suggest a mechanism for dynamically maintaining neural heterogeneity, and expose computational advantages of non-local homeostatic processes.     

Mechanisms underlying the rapid induction and sustained expression of synaptic homeostasis

Homeostatic signaling systems are thought to interface with the mechanisms of neural plasticity to achieve stable yet flexible neural circuitry. However, the time course, molecular design, and implementation of homeostatic signaling remain poorly defined. Here we demonstrate that a homeostatic increase in presynaptic neurotransmitter release can be induced within minutes following postsynaptic glutamate receptor blockade. The rapid induction of synaptic homeostasis is independent of new protein synthesis and does not require evoked neurotransmission, indicating that a change in the efficacy of spontaneous quantal release events is sufficient to trigger the induction of synaptic homeostasis. Finally, both the rapid induction and the sustained expression of synaptic homeostasis are blocked by mutations that disrupt the pore-forming subunit of the presynaptic Ca(V)2.1 calcium channel encoded by cacophony. These data confirm the presynaptic expression of synaptic homeostasis and implicate presynaptic Ca(V)2.1 in a homeostatic retrograde signaling system.