Variable setpoint as a relaxing component in physiological control

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so-called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

Systemic inflammation as a biomarker of seizure propensity and a target for treatment to reduce seizure propensity

People with diabetes can wear a device that measures blood glucose and delivers just the amount of insulin needed to return the glucose level to within bounds. Currently, people with epilepsy do not have access to an equivalent wearable device that measures a systemic indicator of an impending seizure and delivers a rapidly acting medication or other intervention (e.g., an electrical stimulus) to terminate or prevent a seizure. Given that seizure susceptibility is reliably increased in systemic inflammatory states, we propose a novel closed-loop device where release of a fast-acting therapy is governed by sensors that quantify the magnitude of systemic inflammation. Here, we review the evidence that patients with epilepsy have raised levels of systemic indicators of inflammation than controls, and that some anti-inflammatory drugs have reduced seizure occurrence in animals and humans. We then consider the options of what might be incorporated into a responsive anti-seizure system.

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

CoRa-A general approach for quantifying biological feedback control

Feedback control is a fundamental underpinning of life, underlying homeostasis of biological processes at every scale of organization, from cells to ecosystems. The ability to evaluate the contribution and limitations of feedback control mechanisms operating in cells is a critical step for understanding and ultimately designing feedback control systems with biological molecules. Here, we introduce CoRa—or Control Ratio—a general framework that quantifies the contribution of a biological feedback control mechanism to adaptation using a mathematically controlled comparison to an identical system that does not contain the feedback. CoRa provides a simple and intuitive metric with broad applicability to biological feedback systems.

Sodium, volume and pressure control in haemodialysis patients for improved cardiovascular outcomes

Chronic volume overload is pervasive in patients on chronic haemodialysis and substantially increases the risk of cardiovascular death. The rediscovery of the three-compartment model in sodium metabolism revolutionizes our understanding of sodium (patho-)physiology and is an effect modifier that still needs to be understood in the context of hypertension and end-stage kidney disease. Assessment of fluid overload in haemodialysis patients is central yet difficult to achieve, because traditional clinical signs of volume overload lack sensitivity and specificity. The highest all-cause mortality risk may be found in haemodialysis patients presenting with high fluid overload but low blood pressure before haemodialysis treatment. The second highest risk may be found in patients with both high blood pressure and fluid overload, while high blood pressure but normal fluid overload may only relate to moderate risk. Optimization of fluid overload in haemodialysis patients should be guided by combining the traditional clinical evaluation with objective measurements such as bioimpedance spectroscopy in assessing the risk of fluid overload. To overcome the tide of extracellular fluid, the concept of time-averaged fluid overload during the interdialytic period has been established and requires possible readjustment of a negative target post-dialysis weight. ²³Na-magnetic resonance imaging studies will help to quantitate sodium accumulation and keep prescribed haemodialytic sodium mass balance on the radar. Cluster-randomization trials (e.g. on sodium removal) are underway to improve our therapeutic approach to cardioprotective haemodialysis management.

Homeostatic controllers compensating for growth and perturbations

Cells and organisms have developed homeostatic mechanisms which protect them against a changing environment. How growth and homeostasis interact is still not well understood, but of increasing interest to the molecular and synthetic biology community to recognize and design control circuits which can oppose the diluting effects of cell growth. In this paper we describe the performance of selected negative feedback controllers in response to different applied growth laws and time dependent outflow perturbations of a controlled variable. The approach taken here is based on deterministic mass action kinetics assuming that cell content is instantaneously mixed. All controllers behave ideal in the sense that they for step-wise perturbations in volume and a controlled compound A are able to drive A precisely back to the controllers' theoretical set-points. The applied growth kinetics reflect experimentally observed growth laws, which range from surface to volume ratio growth to linear and exponential growth. Our results show that the kinetic implementation of integral control and the structure of the negative feedback loop are two properties which affect controller performance. Best performance is observed for controllers based on derepression kinetics and controllers with an autocatalytic implementation of integral control. Both are able to defend exponential growth and perturbations, although the autocatalytic controller shows an offset from its theoretical set-point. Controllers with activating signaling using zero-order or bimolecular (antithetic) kinetics for integral control behave very similar but less well. Their performance can be improved by implementing negative feedback structures having repression/derepression steps or by increasing controller aggressiveness. Our results provide a guide what type of feedback structures and integral control kinetics are suitable to oppose the dilution effects by different growth laws and time dependent perturbations on a deterministic level.

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 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.