Kristian Thorsen

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.

Robust Adaptation and Homeostasis by Autocatalysis

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.

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

The uptake of glucose and the nutrient coupled transcellular sodium traffic across epithelial cells in the small intestine has been an ongoing topic in physiological research for over half a century. Driving the uptake of nutrients like glucose, enterocytes must have regulatory mechanisms that respond to the considerable changes in the inflow of sodium during absorption. The Na-K-ATPase membrane protein plays a major role in this regulation. We propose the hypothesis that the amount of active Na-K-ATPase in enterocytes is directly regulated by the concentration of intracellular Na(+) and that this regulation together with a regulation of basolateral K permeability by intracellular ATP gives the enterocyte the ability to maintain ionic Na(+)/K(+) homeostasis. To explore these regulatory mechanisms, we present a mathematical model of the sodium coupled uptake of glucose in epithelial enterocytes. Our model integrates knowledge about individual transporter proteins including apical SGLT1, basolateral Na-K-ATPase, and GLUT2, together with diffusion and membrane potentials. The intracellular concentrations of glucose, sodium, potassium, and chloride are modeled by nonlinear differential equations, and molecular flows are calculated based on experimental kinetic data from the literature, including substrate saturation, product inhibition, and modulation by membrane potential. Simulation results of the model without the addition of regulatory mechanisms fit well with published short-term observations, including cell depolarization and increased concentration of intracellular glucose and sodium during increased concentration of luminal glucose/sodium. Adding regulatory mechanisms for regulation of Na-K-ATPase and K permeability to the model show that our hypothesis predicts observed long-term ionic homeostasis.

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.

Control theoretic properties of physiological controller motifs

Identifying biophysical mechanisms that provide regulation and control is essential for our understanding of living systems. However, the distance between life sciences and control theory can be a challenge. Here, we describe, and show the control theoretic properties of a set of biochemical reaction schemes, so-called controller motifs. These controller motifs have similarities with industrial control systems, and have properties such as setpoints, integral gain, and setpoint weight. Once identified, a system understanding of such mechanisms can help synthetic biologists in selecting suitable targets to alter in construction of new biological systems. From a control theoretic viewpoint we identify which biochemical rate constant or property affect the setpoint and the dynamic response of a biophysical controller motif. We also show how a biological system consisting of two antagonistic regulatory mechanisms can be compared to a control engineering problem of controlling the water level in a tank. The similarity between biological systems and control engineering provides theoretical insight, and clears the way to an engineers approach to synthetic biology.

The Organization of Controller Motifs Leading to Robust Plant Iron Homeostasis.

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.

Antagonistic regulation with a unique setpoint, integral and double integral action

Several biochemical species are in organisms controlled in a pairwise manner i.e., two different species (e.g., hormone, enzyme, transporter protein) work to control the concentration of a third chemical species. Such pairs are often antagonistic, meaning that one of the controller species acts to increase whereas the other controller species acts to decrease the amount of the controlled species. How antagonistic systems interact to achieve regulation and to avoid competing against each other is not fully understood. An issue is how two antagonistic hormones can agree upon one common setpoint. We present here a new type of antagonistic regulatory system that has a single unique setpoint inherently defined by the system. The regulatory system controls the concentration of a chemical species with both integral and double integral action, achieving tight control. We show by the use of an analytical stability analysis, using the principle of vanishing perturbations, that the setpoint is asymptotically stable. Finally the prospect of treating the presented system as a part of a larger family of antagonistic regulatory systems with unique setpoints, integral and double integral action is discussed.

Variable setpoint as a relaxing component in physiological control

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controllers ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

Performance of Homeostatic Controller Motifs Dealing with Perturbations of Rapid Growth and Depletion

An essential property of life is that cells and organisms have the ability to protect themselves against external disturbances/attacks by using homeostatic mechanisms. These defending mechanisms are based on negative feedback regulation and often contain additional features, such as integral control, where the integrated error between a controlled variable and its set-point is used to achieve homeostasis. Although the concept of integral control has its origin in industrial processes, recent findings suggest that biological systems are also capable of showing integral control. We recently described a basic set of negative feedback structures (controller motifs) where robust homeostasis is achieved against different but constant perturbations. As many perturbations in biology, such as infections, increase rapidly over time, we investigated how the different controller motifs equipped with different implementations of integral control perform in relation to rapidly changing perturbations, including exponential and hyperbolic changes. The findings show that the construction of an optimum biochemical controller design for time-dependent perturbations requires a certain match between the structure of the negative feedback loop, its signaling kinetics, and the kinetics of how integral control is implemented within the negative feedback loop.