Interplay of positive and negative feedback loops governs robustness in multistable biological networks

Biological networks are widely reported to be robust to both external and internal perturbations. However, the exact mechanisms and design principles that enable robustness are not yet fully understood. Here we investigated dynamic and structural robustness in biological networks with regards to phenotypic distribution and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yield similar phenotypic distributions. Using perturbations to network topology and by varying network parameters, we show that multistable biological networks are structurally and dynamically more robust as compared to their randomized counterparts. These features of robustness are governed by an interplay of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths and sign, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology based approach to quantify robustness in multistable biological networks.

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The principle of homeostasis in the hypothalamus-pituitary-adrenal system: new insight from positive feedback

AJP Regulatory Integrative and Comparative Physiology ◽

10.1152/ajpregu.00907.2006 ◽

2007 ◽

Vol 293 (1) ◽

pp. R83-R98 ◽

Cited By ~ 29

Author(s):

A. Peters ◽

M. Conrad ◽

C. Hubold ◽

U. Schweiger ◽

B. Fischer ◽

...

Keyword(s):

Negative Feedback ◽

Positive Feedback ◽

Glucocorticoid Receptors ◽

Current Knowledge ◽

Biological Systems ◽

Feedback Loops ◽

Endocrine Disorders ◽

Negative Feedback Loops ◽

Adrenal System ◽

Positive And Negative Feedback

Feedback control, both negative and positive, is a fundamental feature of biological systems. Some of these systems strive to achieve a state of equilibrium or “homeostasis”. The major endocrine systems are regulated by negative feedback, a process believed to maintain hormonal levels within a relatively narrow range. Positive feedback is often thought to have a destabilizing effect. Here, we present a “principle of homeostasis,” which makes use of both positive and negative feedback loops. To test the hypothesis that this homeostatic concept is valid for the regulation of cortisol, we assessed experimental data in humans with different conditions (gender, obesity, endocrine disorders, medication) and analyzed these data by a novel computational approach. We showed that all obtained data sets were in agreement with the presented concept of homeostasis in the hypothalamus-pituitary-adrenal axis. According to this concept, a homeostatic system can stabilize itself with the help of a positive feedback loop. The brain mineralocorticoid and glucocorticoid receptors—with their known characteristics—fulfill the key functions in the homeostatic concept: binding cortisol with high and low affinities, acting in opposing manners, and mediating feedback effects on cortisol. This study supports the interaction between positive and negative feedback loops in the hypothalamus-pituitary-adrenal system and in this way sheds new light on the function of dual receptor regulation. Current knowledge suggests that this principle of homeostasis could also apply to other biological systems.

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Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system

PLoS Computational Biology ◽

10.1371/journal.pcbi.1008130 ◽

2021 ◽

Vol 17 (1) ◽

pp. e1008130

Author(s):

Satyajit D Rao ◽

Oleg A Igoshin

Keyword(s):

Steady State ◽

Negative Feedback ◽

Positive Feedback ◽

Feedback Loops ◽

General Mechanism ◽

Response Dynamics ◽

Negative Feedback Loops ◽

Two Component ◽

Positive And Negative Feedback ◽

Dynamical Properties

Bacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression in response to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their expression when activated. Escherichia coli Mg2+ -sensing TCS, PhoPQ, in addition to the positive feedback, includes a negative feedback loop via the upregulation of the MgrB protein that inhibits PhoQ. How the interplay of these feedback loops shapes steady-state and dynamical responses of PhoPQ TCS to change in Mg2+ remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady-state response to decreasing Mg2+ is biphasic, i.e. plateaus over a range of Mg2+ concentrations, and then increases again at growth-limiting Mg2+. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose a novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg2+ and MgrB. Finally, we show how the interplay of positive and negative feedback loops affects the network’s steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results improve the understanding of TCS signaling and other networks with overlaid positive and negative feedback.

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Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system

10.1101/2020.07.09.194944 ◽

2020 ◽

Author(s):

Satyajit D Rao ◽

Oleg A Igoshin

Keyword(s):

Steady State ◽

Negative Feedback ◽

Positive Feedback ◽

Feedback Loops ◽

Dynamic Responses ◽

Negative Feedback Loops ◽

Two Component ◽

Positive And Negative Feedback ◽

Gene Regulatory ◽

Dynamical Properties

AbstractBacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression to adapt to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their own expression when activated. In E. coli, Mg2+-sensing TCS, PhoPQ, in addition to the positive feedback includes a negative feedback via upregulation of MgrB protein that inhibits PhoQ. How interplay of these feedback loops shapes steady state and dynamical responses of PhoPQ TCS to change in Mg2+remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady state response to decreasing Mg2+is biphasic, i.e. plateaus over a range of Mg2+concentrations and then increases again at growth-limiting Mg2+. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg2+and MgrB. Finally, we show how interplay of positive and negative feedback loops affect networks steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results help better understanding of TCS signaling and other networks with overlaid positive and negative feedback.Author summaryFeedback loops are commonly observed in bacterial gene-regulatory networks to enable proper dynamical responses to stimuli. Positive feedback loops often amplify the response to stimulus, whereas negative feedback loops are known to speed-up the response and increase robustness. Here we demonstrate how combination of positive and negative feedback in network sensing extracellular ion concentrations affects its steady state and dynamic responses. We utilize published experimental data to calibrate mathematical models of the gene regulatory network. The resulting model quantitatively matches experimentally observed behavior and can make predictions on the mechanism of negative feedback control. Our results show the advantages of such a combination feedback loops and predict the effect of their perturbation on the steady state and dynamic responses. This study improves our understanding of how feedback loops shape dynamical properties of signaling networks.

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