Article

# Defining Network Topologies that Can Achieve Biochemical Adaptation

Center for Theoretical Biology, Peking University, Beijing 100871, China..
(Impact Factor: 32.24). 09/2009; 138(4):760-73. DOI: 10.1016/j.cell.2009.06.013
Source: PubMed

ABSTRACT Many signaling systems show adaptation-the ability to reset themselves after responding to a stimulus. We computationally searched all possible three-node enzyme network topologies to identify those that could perform adaptation. Only two major core topologies emerge as robust solutions: a negative feedback loop with a buffering node and an incoherent feedforward loop with a proportioner node. Minimal circuits containing these topologies are, within proper regions of parameter space, sufficient to achieve adaptation. More complex circuits that robustly perform adaptation all contain at least one of these topologies at their core. This analysis yields a design table highlighting a finite set of adaptive circuits. Despite the diversity of possible biochemical networks, it may be common to find that only a finite set of core topologies can execute a particular function. These design rules provide a framework for functionally classifying complex natural networks and a manual for engineering networks. For a video summary of this article, see the PaperFlick file with the Supplemental Data available online.

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Available from: Chao Tang, Sep 26, 2015
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• "Following an osmotic shock, nuclear enrichment of the MAP kinase Hog1 adapts perfectly to changes in external osmolarity, a result of an integral feedback action that requires Hog1 kinase activity. Adaptation, however, may not be necessarily related to integral control as some theoretical studies have suggested [12] [20]. "
##### Research: A new motif for robust perfect adaptation in noisy biomolecular networks
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DESCRIPTION: Homeostasis is a running theme in biology. Often achieved through feedback regulation strategies, homeostasis allows living cells to control their internal environment as a means for surviving changing and unfavourable environments. While many endogenous homeostatic motifs have been studied in living cells, synthetic homeostatic circuits have received far less attention. The tight regulation of the abundance of cellular products and intermediates in the noisy environment of the cell is now recognised as a critical requirement for several biotechnology and therapeutic applications. Here we lay the foundation for a regulation theory at the molecular level that explicitly takes into account the noisy nature of biochemical reactions and provides novel tools for the analysis and design of robust synthetic homeostatic circuits. Using these ideas, we propose a new regulation motif that implements an integral feedback strategy which can generically and effectively regulate a wide class of reaction networks. By combining tools from probability and control theory, we show that the proposed control motif preserves the stability of the overall network, steers the population of any regulated species to a desired set point, and achieves robust perfect adaptation -- all without any prior knowledge of reaction rates. Moreover, our proposed control motif can be implemented using a very small number of molecules and hence has a negligible metabolic load. Strikingly, the regulatory motif exploits stochastic noise, leading to enhanced regulation in scenarios where noise-free implementations result in dysregulation. Several examples demonstrate the potential of the approach.
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• "Following an osmotic shock, nuclear enrichment of the MAP kinase Hog1 adapts perfectly to changes in external osmolarity, a result of an integral feedback action that requires Hog1 kinase activity. Adaptation, however, may not be necessarily related to integral control as some theoretical studies have suggested [5], [6]. "
##### Article: Generic low-copy integral feedback for robust in-vivo adaptation
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ABSTRACT: Homeostasis is a running theme in biology. Often achieved through feedback regulation strategies, homeostasis allows living cells to control their internal environment as a means for surviving changing and unfavourable environments. While many endogenous homeostatic motifs have been studied in living cells, synthetic homeostatic circuits have received far less attention. The tight regulation of the abundance of cellular products and intermediates in the noisy environment of the cell is now recognised as a critical requirement for several biotechnology and therapeutic applications. Here we lay the foundation for a regulation theory at the molecular level that explicitly takes into account the noisy nature of biochemical reactions and provides novel tools for the analysis and design of robust synthetic homeostatic circuits. Using these ideas, we propose a new regulation motif that implements an integral feedback strategy which can generically and effectively regulate a wide class of reaction networks. By combining tools from probability and control theory, we show that the proposed control motif preserves the stability of the overall network, steers the population of any regulated species to a desired set point, and achieves robust perfect adaptation -- all without any prior knowledge of reaction rates. Moreover, our proposed control motif can be implemented using a very small number of molecules and hence has a negligible metabolic load. Strikingly, the regulatory motif exploits stochastic noise, leading to enhanced regulation in scenarios where noise-free implementations result in dysregulation. Several examples demonstrate the potential of the approach.
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• "Recently, significant progresses have been made in the study of the physical essence of adaptation [23] [24] [25] [26]. These results have become one of the most important developments in biophysics in recent years. "
##### Article: An allosteric model of the inositol trisphosphate receptor with nonequilibrium binding
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ABSTRACT: The inositol trisphosphate receptor (IPR) is a crucial Ca$^{2+}$ channel that regulates the Ca$^{2+}$ influx from the endoplasmic reticulum (ER) to the cytoplasm. A thorough study of this receptor contributes to a better understanding of calcium oscillations and waves. Based on the patch-clamp experimental data obtained from the outer membranes of isolated nuclei of the \emph{Xenopus} oocyte, we construct an allosteric competition model of single IPR channels on their native ER membrane environment. In our model, each IPR channel consists of four subunits, each of which can exist in two configurations. Each subunit in both configurations has one IP$_3$ binding site, together with one activating and one inhibitory Ca$^{2+}$ binding site. Based on the idea of the well-known Monod-Wyman-Changeux allosteric model, we construct our model from the subunit level to the channel level. It turns out that our model successfully reproduces the patch-clamp experimental data of the steady-state open probability, the mean close duration, and the bi-exponential distribution of the open duration. Particularly, our model successfully describes the bimodal [Ca$^{2+}$] dependence of the mean open duration at high [IP$_3$], a steady-state behavior which fails to be correctly described in previous IPR models, and the adaptation of the IPR channel, an important dynamic behavior which is seldom discussed in previous IPR models. In addition, we find that the gating of the IPR channel is most likely to be a biochemical process that consumes energy.
Physical Biology 10/2014; 11(5):056001. DOI:10.1088/1478-3975/11/5/056001 · 2.54 Impact Factor