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 controller's 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.

In this paper we investigate how the disturbance rejection properties of physiological regulatory systems depend on the signalling kinetics between the biochemical species being considered as controlled and manipulated variables. Based on the mathematical model of a physiological regulatory system, we analyse the impact of three different signalling models, i.e. linear signalling, first order and second order Hill kinetics. We separate the analysis in two parts. First we identify to what extend the signalling from the manipulated variable to the controlled variable affect the range and ratio of manageable disturbances. In the second part we investigate whether and how the signalling from the controlled variable to the manipulated variable will affect the parameters of the controller part of the regulatory system. In this context, saturable Hill kinetics display advantages compared to linear signalling.

Genetic manipulation is increasingly used to fine tune organisms like bacteria and yeast for production of chemical compounds such as biofuels and pharmaceuticals. The process of creating the optimal organism is difficult as manipulation may destroy adaptation and compensation mechanisms that have been tuned by evolution to keep the organisms fit. The continued progress in synthetic biology depends on our ability to understand, manipulate, and tune these mechanisms. Concepts from control theory and control engineering are very applicable to these challenges. From a control theoretic viewpoint, disturbances rejection and set point tracking describe how adaptation mechanisms relate to perturbations and to signaling events. In this paper we investigate a set regulatory mechanisms in the form of biochemical reaction schemes, socalled controller motifs. We show how parameters related to the molecular and kinetic mechanisms influence on the dynamical behavior of disturbance rejection and set point tracking of each controller motif. This gives insight into how a molecular controller motif can be tuned to a specified regulatory response.