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

Fjeld, Gunhild; Thorsen, Kristian; Drengstig, Tormod; Ruoff, Peter

doi:10.1021/acs.jpcb.7b01989

Cited by 17 publications

(31 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth mentioning that the exponential integral controller is not new and has been studied in the past, for instance, in [14,22,26,34,53]. In particular, [53] studied its role in fold-change detection whereas [26] focused on the controller ability to reject non-constant disturbances. In the present paper, we observe for the first time that this controller can be obtained using positively regularizing functions and we mainly focus on its stability properties and on the characterization of the different classes of systems that can be controlled using such a controller motif.…”

Section: Introductionmentioning

confidence: 99%

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

Briat¹

2020

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

The integral control of positive systems using nonnegative control input is an important problem arising, among others, in biochemistry, epidemiology and ecology. An immediate solution is to use an ON-OFF nonlinearity between the controller and the system. However, this solution is only available when controllers are implemented in computer systems. When this is not the case, like in biology, alternative approaches need to be explored. Based on recent research in the control of biological systems [7,14], we propose to develop a theory for the integral control of positive systems using nonnegative controls based on the so-called antithetic integral controller and two positively regularized integral controllers, the so-called exponential integral controller and logistic integral controller. For all these controllers, we establish several qualitative results, which we connect to standard results on integral control. We also obtain additional results which are specific to the type of controllers. For instance, we show an interesting result stipulating that if the gain of the antithetic integral controller is suitably chosen, then the local stability of the equilibrium point of the closed-loop system does not depend on the choice for the coupling parameter, an additional parameter specific to this controller. Conversely, we also show that if the coupling parameter is suitably chosen, then the equilibrium point of the closed-loop system is locally stable regardless the value of the gain. For the exponential integral controller, we can show that the local stability of the equilibrium point of the closed-loop system is independent of the gain of the controller and the gain of the system. The stability only depends on the exponential rate of the controller, again a parameter that is specific to this type of controllers. Several examples are given for illustration.

show abstract

Section: Introductionmentioning

confidence: 99%

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

Briat¹

2020

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

show abstract

“…It became clear that certain reaction kinetic conditions are necessary for the occurrence of integral control leading to the robustness of the feedback controller. These conditions include zero-order kinetics [9,10,14–19], autocatalysis [20–22], and second-order (bimolecular/antithetic) reaction [23,24], which were implemented into various controller motifs, synthetic gene networks, and other negative feedback structures [18,25–27].…”

Section: Introductionmentioning

confidence: 99%

Frequency switching between oscillatory homeostats and the regulation of p53

Ruoff

Nishiyama

2020

Preprint

Self Cite

View full text Add to dashboard Cite

1Homeostasis is an essential concept to understand the stability of organisms and their 2 adaptive behaviors when coping with external and internal assaults. Many hormones 3 that take part in homeostatic control come in antagonistic pairs, such as glucagon and 4 insulin reflecting the inflow and outflow compensatory mechanisms to control a certain 5 internal variable, such as blood sugar levels. By including negative feedback loops 6 homeostatic controllers can exhibit oscillations with characteristic frequencies. In this 7 paper we demonstrate the associated frequency changes in homeostatic systems when 8 individual controllers in a set of interlocked feedback loops gain control in response to 9 environmental changes. Taking p53 as an example, we show how the Per2, ATM and 10 Mdm2 feedback loops -interlocked with p53-gain individual control in dependence to 11 DNA damage and how each of these controllers provide certain functionalities in their 12 regulation of p53. In unstressed cells, the circadian regulator Per2 ensures a basic p53 13 level to allow its rapid up-regulation in case of DNA damage. When DNA damage 14 occurs the ATM controller increases the level of p53 and defends it towards uncontrolled 15 degradation, which despite DNA damage, would drive p53 to lower values and p53 16dysfunction. Mdm2 on its side keeps p53 at a maximum level to avoid premature 17 apoptosis. However, with on-going DNA damage the Mdm2 set-point is increased by 18 HSP90 and other p53 stabilizers leading finally to apoptosis. An essential aspect in p53 19 regulation at occurring cell stress is the coordinated inhibition of ubiquitin-independent 20 and ubiquitin-dependent degradation reactions and the increasing stabilizing 21 mechanisms of p53. Whether oscillations serve a function or are merely a by-product of 22 the controllers are discussed in view of the finding that homeostatic control of p53, as 23 indicated above, does in principle not require oscillatory homeostats. 24 30 control [8], alongside with integral feedback [9][10][11], and systems biology methods [12, 13]. 31 It became clear that certain reaction kinetic conditions are necessary for the occurrence 32December 24, 2019 1/17 of integral control leading to the robustness of the feedback controller. These conditions 33 include zero-order kinetics [9, 10,[14][15][16][17][18][19], autocatalysis [20][21][22], and second-order 34 (bimolecular/antithetic) reaction [23, 24], which were implemented into various controller 35 motifs, synthetic gene networks, and other negative feedback structures [18,[25][26][27]. 36A particular interesting aspect is that, under certain conditions, the homeostatic 37 controllers may become oscillatory and preserve, if integral control is present, their 38 homeostatic property by keeping the average value of the controlled variable at its 39 set-point [28]. While the occurrence of oscillations is generally avoided in control 40 engineering, natural systems show generally oscillatory behaviors, as found in circadian 41 or ultradian rhythms ...

show abstract

“…It became evident that certain kinetic conditions within a negative feedback loop, such as zero-order kinetics [18][19][20][22][23][24], autocatalysis [25][26][27], or second-order (bimolecular/antithetic) kinetics [28,29] can lead to robust adaptation [30,31] by integral control where an intrinsic integration of the error between set-point and the actual value of the controlled variable is automatically performed. When these feedback motifs were investigated towards time-dependent perturbations, it turned out that controller performances can differ significantly, either due to the structure of the feedback loop or due to the kinetics of how the integral controller is implemented [32,33].…”

Section: Introductionmentioning

confidence: 99%

“…Feedback structures which have been found to perform well when exposed to different time-dependent perturbations are based on derepression kinetics [32].…”

Section: Introductionmentioning

confidence: 99%

An amplified derepression controller with multisite inhibition and positive feedback

Drobac

Waheed

Heidari

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

How organisms are able to maintain robust homeostasis has in recent years received increased attention by the use of combined control engineering and kinetic concepts, which led to the discovery of robust controller motifs. While these motifs employ kinetic conditions showing integral feedback and homeostasis for step-wise perturbations, the motifs' performance differ significantly when exposing them to time dependent perturbations. One type of controller motifs which are able to handle exponentially and even hyperbolically growing perturbations are based on derepression. In these controllers the compensatory reaction, which neutralizes the perturbation, is derepressed, i.e. its reaction rate is increased by the decrease of an inhibitor acting on the compensatory flux. While controllers in this category can deal well with different time-dependent perturbations they have the disadvantage that they break down once the concentration of the regulatory inhibitor becomes too low and the compensatory flux has gained its maximum value. We wondered whether it would be possible to bypass this restriction, while still keeping the advantages of derepression kinetics. In this paper we show how the inclusion of multisite inhibition and the presence of positive feedback loops lead to an amplified controller which is still based on derepression kinetics but without showing the breakdown due to low inhibitor concentrations. By searching for the amplified feedback motif in natural systems, we found it as a part of the plant circadian clock where it is highly interlocked with other feedback loops.

show abstract

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

Cited by 17 publications

References 38 publications

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

A Biology-Inspired Approach to the Positive Integral Control of Positive Systems: The Antithetic, Exponential, and Logistic Integral Controllers

Frequency switching between oscillatory homeostats and the regulation of p53

An amplified derepression controller with multisite inhibition and positive feedback

Contact Info

Product

Resources

About