Implementation of integral feedback control in biological systems

Design principles as minimal models

In this essay I suggest that we view design principles in systems biology as minimal models, for a design principle usually exhibits universal behaviors that are common to a whole range of heterogeneous (living and nonliving) systems with different underlying mechanisms. A well-known design principle in systems biology, integral feedback control, is discussed, showing that it satisfies all the conditions for a model to be a minimal model. This approach has significant philosophical implications: it not only accounts for how design principles explain, but also helps clarify one dispute over design principles, e.g., whether design principles provide mechanistic explanations or a distinct kind of explanations called design explanations.

Self-complexification through integral feedback in eusocial paper wasps of various levels of sociality

We investigate how simple physical interactions can generate remarkable diversity in the life history of social agents using data of social wasps, yielding complex scalable task partitioning. We built and analyzed a computational model to investigate how diverse task allocation patterns found in nature can emerge from the same behavioral blueprint. Self-organizing mechanisms of interwoven behavioral feedback loops, task-dependent time delays and simple material flows between interacting individuals yield an emergent homeostatic self-regulation while keeping the global colony performance scalable. Task allocation mechanisms based on implicitly honest signaling via material flows are not only very robust but are also highly evolvable due to their simplicity and reliability. We find that task partitioning has evolved to be scalable and adaptable to life history traits, such as expected colony size or temporal bottlenecks in the available workforce or materials. By tuning solely the total number of agents and a social connectivity-related parameter in the model, our simulations yield the whole range of emergent patterns in task allocation and task fidelity akin to observed field data. Our model suggests that the material exchange ("common stomach mechanism") found in many paper wasps provides a common functional "core" across these genera, which not only provides self-regulation of the colony, but also provides a scalable mechanism allowing natural selection to yield complex social integration in larger colonies over the course of their evolutionary trajectory.

Robust adaptation of PKCζ-IRS1 insulin signaling pathways through integral feedback control

Insulin signaling pathways in muscle tissue play a major role in maintaining glucose homeostasis. Dysregulation in these pathways results in the onset of serious metabolic disorders like type 2 diabetes. Robustness is an essential characteristic of insulin signaling pathways that ensures reliable signal transduction in the presence of perturbations as a result of several feedback mechanisms. Integral control, according to control engineering, provides reliable setpoint tracking and disturbance rejection. The presence of negative feedback and integrating process is crucial for biological processes to achieve integral control. The existence of an integral controller leads to the rejection of perturbations which resulted in the robust regulation of biochemical entities within acceptable levels. In the presentin silicoresearch work, the presence of integral control in the protein kinase Cζ- insulin receptor substrate-1 (PKCζ-IRS1) pathway is identified, verified mathematically and model is simulated in Cell Designer. The data is exported to Minitab software and robustness analysis is carried out statistically using the Mann-Whitney test. The p-value of the results obtained with given parameters perturbed by ±1% is greater than the significance level of 0.05 (0.2132 for 1% error in k7(rate constant of IRS1 phosphorylation), 0.2096 for -1% error in k7, 0.9037 for both ±1% error in insulin and 0.9037 for ±1% error in k1(association rate constant of the first molecule of insulin to bind the insulin receptor), indicated that our hypothesis is proved The results satisfactorily indicate that even when perturbations are present, glucose homeostasis in muscle tissue is robust due to the presence of integral regulation in the PKCζ-IRS1 insulin signaling pathways. In this paper, we have analysed the findings from the framework of robust control theory, which has allowed us to examine that how PKCζ-IRS1 insulin signaling pathways produces desired output in presence of perturbations.

An Autonomous Oscillation Times and Executes Centriole Biogenesis

The accurate timing and execution of organelle biogenesis is crucial for cell physiology. Centriole biogenesis is regulated by Polo-like kinase 4 (Plk4) and initiates in S-phase when a daughter centriole grows from the side of a pre-existing mother. Here, we show that a Plk4 oscillation at the base of the growing centriole initiates and times centriole biogenesis to ensure that centrioles grow at the right time and to the right size. The Plk4 oscillation is normally entrained to the cell-cycle oscillator but can run autonomously of it-potentially explaining why centrioles can duplicate independently of cell-cycle progression. Mathematical modeling indicates that the Plk4 oscillation can be generated by a time-delayed negative feedback loop in which Plk4 inactivates the interaction with its centriolar receptor through multiple rounds of phosphorylation. We hypothesize that similar organelle-specific oscillations could regulate the timing and execution of organelle biogenesis more generally.

The interplay of spatial organization and biochemistry in building blocks of cellular signalling pathways

Biochemical pathways and networks are central to cellular information processing. While a broad range of studies have dissected multiple aspects of information processing in biochemical pathways, the effect of spatial organization remains much less understood. It is clear that space is central to intracellular organization, plays important roles in cellular information processing and has been exploited in evolution; additionally, it is being increasingly exploited in synthetic biology through the development of artificial compartments, in a variety of ways. In this paper, we dissect different aspects of the interplay between spatial organization and biochemical pathways, by focusing on basic building blocks of these pathways: covalent modification cycles and two-component systems, with enzymes which may be monofunctional or bifunctional. Our analysis of spatial organization is performed by examining a range of 'spatial designs': patterns of localization or non-localization of enzymes/substrates, theoretically and computationally. Using these well-characterized in silico systems, we analyse the following. (i) The effect of different types of spatial organization on the overall kinetics of modification, and the role of distinct modification mechanisms therein. (ii) How different information processing characteristics seen experimentally and studied from the viewpoint of kinetics are perturbed, or generated. (iii) How the activity of enzymes (bifunctional enzymes in particular) may be spatially manipulated, and the relationship between localization and activity. (iv) How transitions in spatial organization (encountered either through evolution or through the lifetime of cells, as seen in multiple model organisms) impacts the kinetic module (and pathway) behaviour, and how transitions in chemistry may be impacted by prior spatial organization. The basic insights which emerge are central to understanding the role of spatial organization in biochemical pathways in both bacteria and eukaryotes, and are of direct relevance to engineering spatial organization of pathways in bottom-up synthetic biology in cellular and cell-free systems.

Combined mechanisms of neural firing rate homeostasis

Spikes in the membrane potential of neurons comprise the currency of information processing in the brain. The ability of neurons to convert any information present across their multiple inputs into a significant modification to the pattern of their emitted spikes depends on the rate at which they emit spikes. If the mean rate is near the neuron's maximum, or if the rate is near zero, then changes in the inputs have minimal impact on the neuron's firing rate. Therefore, a neuron needs to control its mean rate. Protocols that either dramatically increase or decrease a neuron's firing rate lead to multiple compensatory changes that return the neuron's mean rate toward its prior value. In this primer, first as a summary of our previous work (Cannon and Miller in J Neurophysiol 116(5):2004-2022, 2016; Cannon and Miller in J Math Neurosci 7(1):1, 2017), we describe the advantages and disadvantages of having more than one such control mechanism responding to the neuron's firing rate. We suggest how problems of two, coexisting, potentially competing mechanisms can be overcome. Key requirements are: (1) the control be of a distribution of values, which the controlled variable achieves over a fast timescale compared to the timescale of the control system; (2) at least one of the control mechanisms be nonlinear; and (3) the two control systems are satisfied by a stable distribution or range of values that can be achieved by the variable. We show examples of functional control systems, including the previously studied integral feedback controller and new simulations of a "bang-bang" controller, that allow for compensation when inputs to the system change. Finally, we present new results describing how the underlying signal processing pathways would produce mechanisms of dual control, as opposed to a single mechanism with two outputs, and compare the responses of these systems to changes of input statistics.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Integral feedback control is at the core of task allocation and resilience of insect societies

Homeostatic self-regulation is a fundamental aspect of open dissipative systems. Integral feedback has been found to be important for homeostatic control on both the cellular and molecular levels of biological organization and in engineered systems. Analyzing the task allocation mechanisms of three insect societies, we identified a model of integral control residing at colony level. We characterized a general functional core mechanism, called the "common stomach," where a crucial shared substance for colony function self-regulates its own quantity via reallocating the colony's workforce, which collects and uses this substance. The central component in a redundant feedback network is the saturation level of this substance in the colony. An interaction network of positive and negative feedback loops ensures the homeostatic state of this substance and the workforce involved in processing this substance. Extensive sensitivity and stability analyses of the core model revealed that the system is very resilient against perturbations and compensates for specific types of stress that real colonies face in their ecosystems. The core regulation system is highly scalable, and due to its buffer function, it can filter noise and find a new equilibrium quickly after environmental (supply) or colony-state (demand) changes. The common stomach regulation system is an example of convergent evolution among the three different societies, and we predict that similar integral control regulation mechanisms have evolved frequently within natural complex systems.

Stem cell homeostasis by integral feedback through the niche

Hematopoiesis is a paradigm for tissue development and renewal from stem cells. Experiments show that the maintenance of hematopoietic stem cells (HSCs) relies on signals from niche cells. However, it is not known how the size of the HSC compartment is set. Competition by HSCs for niche access has been suggested, yet niche cells in the bone marrow outnumber HSCs. Here we propose a cooperative model of HSC homeostasis in which stem and niche cells mutually interact such that niche cells function as negative feedback regulators of HSC proliferation. This model explains puzzling experimental findings, including homeostatic recovery of the HSC compartment after irradiation versus apparent lack of recovery after HSC ablation. We show that bidirectional niche-stem cell regulation has properties of a proportional-integral feedback controller. Moreover, we predict that the outflux of differentiated cells from HSCs can be regulated by the affinity of HSCs for niche cells. Much effort has been devoted to elucidating niche cell signaling to stem cells; our theoretical insights indicate that studying the effect of stem cells on the niche may be equally important for understanding stem cell homeostasis.

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.

Complexity-aware simple modeling

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches.

A biomolecular proportional integral controller based on feedback regulations of protein level and activity

Homeostasis is the capacity of living organisms to keep internal conditions regulated at a constant level, despite environmental fluctuations. Integral feedback control is known to play a key role in this behaviour. Here, I show that a feedback system involving transcriptional and post-translational regulations of the same executor protein acts as a proportional integral (PI) controller, leading to enhanced transient performances in comparison with a classical integral loop. Such a biomolecular controller-which I call a level and activity-PI controller (LA-PI)-is involved in the regulation of ammonium uptake by Escherichia coli through the transporter AmtB. The P _II molecules, which reflect the nitrogen status of the cell, inhibit both the production of AmtB and its activity (via the NtrB-NtrC system and the formation of a complex with GlnK, respectively). Other examples of LA-PI controller include copper and zinc transporters, and the redox regulation in photosynthesis. This scheme has thus emerged through evolution in many biological systems, surely because of the benefits it offers in terms of performances (rapid and perfect adaptation) and economy (protein production according to needs).

Receptor uptake arrays for vitamin B12, siderophores, and glycans shape bacterial communities

Molecular variants of vitamin B₁₂, siderophores, and glycans occur. To take up variant forms, bacteria may express an array of receptors. The gut microbe Bacteroides thetaiotaomicron has three different receptors to take up variants of vitamin B₁₂ and 88 receptors to take up various glycans. The design of receptor arrays reflects key processes that shape cellular evolution. Competition may focus each species on a subset of the available nutrient diversity. Some gut bacteria can take up only a narrow range of carbohydrates, whereas species such as B. thetaiotaomicron can digest many different complex glycans. Comparison of different nutrients, habitats, and genomes provides opportunity to test hypotheses about the breadth of receptor arrays. Another important process concerns fluctuations in nutrient availability. Such fluctuations enhance the value of cellular sensors, which gain information about environmental availability and adjust receptor deployment. Bacteria often adjust receptor expression in response to fluctuations of particular carbohydrate food sources. Some species may adjust expression of uptake receptors for specific siderophores. How do cells use sensor information to control the response to fluctuations? This question about regulatory wiring relates to problems that arise in control theory and artificial intelligence. Control theory clarifies how to analyze environmental fluctuations in relation to the design of sensors and response systems. Recent advances in deep learning studies of artificial intelligence focus on the architecture of regulatory wiring and the ways in which complex control networks represent and classify environmental states. I emphasize the similar design problems that arise in cellular evolution, control theory, and artificial intelligence. I connect those broad conceptual aspects to many testable hypotheses for bacterial uptake of vitamin B₁₂, siderophores, and glycans.

Design of a Synthetic Integral Feedback Circuit: Dynamic Analysis and DNA Implementation

The design and implementation of regulation motifs ensuring robust perfect adaptation are challenging problems in synthetic biology. Indeed, the design of high-yield robust metabolic pathways producing, for instance, drug precursors and biofuels, could be easily imagined to rely on such a control strategy in order to optimize production levels and reduce production costs, despite the presence of environmental disturbance and model uncertainty. We propose here a motif that ensures tracking and robust perfect adaptation for the controlled reaction network through integral feedback. Its metabolic load on the host is fully tunable and can be made arbitrarily close to the constitutive limit, the universal minimal metabolic load of all possible controllers. A DNA implementation of the controller network is finally provided. Computer simulations using realistic parameters demonstrate the good agreement between the DNA implementation and the ideal controller dynamics.