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      Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

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          Summary

          Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

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          Highlights

          • The AC-DC circuit shows robust coexistence between oscillatory and steady expression

          • The circuit allows control over the coherence of oscillations in a cell population

          • The circuit shows excitable properties, allowing the spatial propagation of signals

          • These suggest its prominence in development and its potential in synthetic biology

          Abstract

          The AC-DC circuit, formed by the combination of a repressilator and a toggle switch, is explored in detail using dynamical systems theory and stochastic simulations. These analyses reveal that the coexistence of oscillatory and stable gene expression gives rise to novel dynamical behaviors such as control of oscillation coherence and spatial signal propagation.

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          Most cited references61

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          The chemical Langevin equation

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            A synthetic multicellular system for programmed pattern formation.

            Pattern formation is a hallmark of coordinated cell behaviour in both single and multicellular organisms. It typically involves cell-cell communication and intracellular signal processing. Here we show a synthetic multicellular system in which genetically engineered 'receiver' cells are programmed to form ring-like patterns of differentiation based on chemical gradients of an acyl-homoserine lactone (AHL) signal that is synthesized by 'sender' cells. In receiver cells, 'band-detect' gene networks respond to user-defined ranges of AHL concentrations. By fusing different fluorescent proteins as outputs of network variants, an initially undifferentiated 'lawn' of receivers is engineered to form a bullseye pattern around a sender colony. Other patterns, such as ellipses and clovers, are achieved by placing senders in different configurations. Experimental and theoretical analyses reveal which kinetic parameters most significantly affect ring development over time. Construction and study of such synthetic multicellular systems can improve our quantitative understanding of naturally occurring developmental processes and may foster applications in tissue engineering, biomaterial fabrication and biosensing.
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              NEURAL EXCITABILITY, SPIKING AND BURSTING

              Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing. We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.
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                Author and article information

                Contributors
                Journal
                Cell Syst
                Cell Syst
                Cell Systems
                Cell Press
                2405-4712
                2405-4720
                25 April 2018
                25 April 2018
                : 6
                : 4
                : 521-530.e3
                Affiliations
                [1 ]Department of Mathematics, University College London, Gower Street, WC1E 6BT London, UK
                [2 ]Department of Cell and Developmental Biology, University College London, Gower Street, WC1E 6BT London, UK
                [3 ]Department of Genetics, Evolution and Environment, University College London, Gower Street, WC1E 6BT London, UK
                [4 ]Department of Fundamental Microbiology, University of Lausanne, Biophore Building, 1015 Lausanne, Switzerland
                [5 ]Department of Life Sciences, Imperial College London, SW7 2AZ London, UK
                [6 ]The Francis Crick Institute, 1 Midland Road, NW1 1AT London, UK
                Author notes
                []Corresponding author r.carrasco@ 123456ucl.ac.uk
                [7]

                Lead Contact

                Article
                S2405-4712(18)30061-9
                10.1016/j.cels.2018.02.008
                5929911
                29574056
                f0e60b13-15ed-4908-9a6b-459a648306fd
                © 2018 The Author(s)

                This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

                History
                : 26 September 2017
                : 14 December 2017
                : 13 February 2018
                Categories
                Article

                gene regulatory networks,dynamical systems,multistability,oscillations,coherence,multifunctional circuits,excitable systems,synthetic biology,coherence resonance

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