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
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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. However, as some theoretical studies have suggested [14] [23], adaptation may not be solely related to integral control . "
##### Research: Antithetic Integral Feedback: 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, some other motifs may remain under-explored or even undiscovered. At the same time, known regulatory motifs have been mostly analyzed at the deterministic level, and the effect of noise on their regulatory function has received low attention. 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 homeostatic circuits. Using these ideas, we propose a new regulation motif, which we refer to as {\em antithetic integral feedback}, and demonstrate its effectiveness as a strategy for generically regulating a wide class of reaction networks. By combining tools from probability and control theory, we show that the proposed 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 with low prior knowledge of reaction rates. Moreover, our proposed regulatory 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. Finally, we discuss the possible manifestation of the proposed antithetic integral feedback motif in endogenous biological circuits and its realization in synthetic circuits.
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• "So C is independent from the concentration of ligand L: technically C is a biochemically adaptive variable at τ = τ c [10] [11]. "
##### Article: Phenotypic spandrel: absolute discrimination and ligand antagonism
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ABSTRACT: Recent works in quantitative evolution have shown that biological structures are constrained by selected phenotypes in unexpected ways . This is also observed in simulations of gene network evolution, where complex realistic traits naturally appear even if they have not been explicitly selected . An important biological example is the absolute discrimination between different ligand "qualities", such as immune decisions based on binding times to T cell receptors (TCRs) or Fc$\epsilon$RIs. In evolutionary simulations, the phenomenon of absolute discrimination is not achieved without detrimental ligand antagonism: a "dog in the manger" effect in which ligands unable to trigger response prevent agonists to do so. A priori it seems paradoxical to improve ligand discrimination in a context of increased ligand antagonism, and how such contradictory phenotypes can be disentangled is unclear. Here we establish for the first time a direct mathematical causal link between absolute discrimination and ligand antagonism. Inspired by the famous discussion by Gould and Lewontin, we thus qualify antagonism as a "phenotypic spandrel": a phenotype existing as a necessary by-product of another phenotype. We exhibit a general model for absolute discrimination, and further show how addition of proofreading steps inverts the expected hierarchy of antagonism without fully cancelling it. Phenotypic spandrels reveal the internal feedbacks and constraints structuring response in signalling pathways, in very similar way to symmetries structuring physical laws.
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• "For example, boolean network models were used to study the gene evolution [44], attractor number variation with asynchronous stochastic updating [45], gene expression in the state space [39], and organism system growth rate improvement [46]. Another approach is to abstract key regulation genetic networks [47] [48] (or motifs) from all associated interactions, and to employ synthetic biology to modify, control and finally understand the biological mechanisms within these complicated systems [38] [42]. An earlier application of this approach led to a good understanding of the ubiquitous phenomenon of bistability in biological systems [49], where there are typically limit cycle attractors and, during cell cycle control, noise can trigger a differentiation process by driving the system from a limit circle to another steady state attractor [38]. "
##### Article: Control and controllability of nonlinear dynamical networks: a geometrical approach
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ABSTRACT: In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.