Variable setpoint as a relaxing component in physiological control

Abstract

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.

Exploring Mechanisms of Glucose Uptake Regulation and Dilution Resistance in Growing Cancer Cells

“…Thus, it is likely that sufficient regulation can be achieved even if the growth associated offsets are fairly large. This variability in steady state can then be viewed as a relaxing condition on the control mechanisms employed (83).…”

CoRa –A general approach for quantifying biological feedback control

“…Importantly, the nature of biological organization with extensive coupling of parameters and processes makes the extraction of engineering-centric quantities needed for traditional analyses of feedback quantities, such as setpoints and regulation errors, challenging. Debate about whether these quantities are defined for biological systems has a long history and no concrete resolution [12]. One advantage of CoRa is that it does not make any assumptions about the existence of such quantities, replacing this debate with a comparison to a system that would have evolved identically but without the feedback structure.…”

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

“…Note that the goal here is to present this new motif and show how it works; the relative simple kinetic expressions for activation and removal can of course be replaced with more complex expressions that include features such as saturation, e.g., Hill functions. Refer to [20] and [21] for a treatment of such features affects the performance of the original two species controller motifs.…”