Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

Tyson, John J.; Chen, Katherine; Novák, Béla

doi:10.1016/s0955-0674(03)00017-6

Cited by 1,452 publications

(1,306 citation statements)

References 60 publications

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“…The steady-states are defined by: (4) equal to: (5) And the dependence on k 0 for the given rate constants, and starting concentrations will be: To analyze the stability of the steady-states we wrote a Jacobian matrix (J) as follows: (7) We used a Mathematica script (supplementary file, x ≡ k 0 ; h 0 ≡ I 0 ) to compute the stability of the steady states. …”

Section: Linear Stability Analysis Of the Three Variable Model Of Thementioning

confidence: 99%

“…To explain the trends in period and amplitude of the oscillations, and the nature of the bifurcations at low and high limiting values of SV, we constructed a simple kinetic model [1][2][3][4] to rate constants, and k 0 to space velocity. Linear stability analysis 13 carried out with this model shows that increasing k 0 from low to high values causes two transitions: first, the system transitions from one having a stable focus (damped oscillations) to one having a stable orbit (sustained oscillations); this transition marks an Andronov-Hopf bifurcation.…”

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confidence: 99%

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Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

Semenov

Kraft

Ainla

et al. 2016

Nature

308

274

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(ii) a trigger that controls autocatalytic growth; and (iii) inhibitory processes that remove activating thiol species produced during the autocatalytic cycle. In contrast to previous studies demonstrating oscillations and bistability using highly evolved biomolecules (i.e., enzymes 15 and DNA 16,17 ) or inorganic molecules of questionable biochemical relevance (e.g. those used in Belousov-Zhabotinsky-type reactions), 18,19 the organic molecules used in our network are relevant to current metabolism and similar to those that might have existed on early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable, and oscillatory behavior, we identified principles that clarify how dynamic networks relevant to life might possibly have developed. In the future, modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks, and of synthetic self-regulating and evolving chemical systems.3 Figure 1 summarizes the network of organic reactions that we used to assemble our model system. All of these reactions are nearly quantitative, and the structure of their reactants can be varied by synthesis to control rates of reactions. Thiols and thioesters, which are central to these reactions, are important in many biological processes (e.g., the formation of disulfide bonds in proteins, transformations involving coenzyme-A, the reduction of oxidized molecules by glutathione, 20 the synthesis of polyketides, 21 and the nonribosomal synthesis of peptides 21 ), and thus, might represent reactions that enabled life to emerge on early Earth. 22 To control the dynamics of these processes, we constructed a modular chemical reaction network (CRN) shown schematically in control-theoretic terms 23 in Fig. 1a. A "trigger" produces an initial chemical signal, and an "auto-amplifier" amplifies this signal, which may or may not be suppressed by inhibition. To keep the reactions out of equilibrium-and thus, to enable the self-organization of reactions by communication through concentrations of reactants and products -we used a continuous-stirred tank reactor (CSTR) to mix reactants and products, while allowing a flux of species into and out of the network over time. A biological cell has some conceptual analogies to a micron-scale, diffusively mixed, tank reactor. The dynamic behavior of this system -especially bistability and oscillationsreflects the balances of triggering, auto-amplification, and inhibition.We first constructed a chemical network capable of auto-amplification using thiols and thioesters (Fig. 1b). The starting components of the network are cystamine (CSSC, 3) and L-alanine ethyl thioester (AlaSEt, 2). Trace amounts of cysteamine (CSH, 1) are generated as follows: AlaSEt slowly hydrolyzes, generating alanine (8) and ethanethiol (ESH, 4); EtSH then reacts with CSSC via thiolate-disulfide interchange, 24 yielding disulfide 6 and CSH. With CSH present, self-amplification oc...

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Section: Linear Stability Analysis Of the Three Variable Model Of Thementioning

confidence: 99%

mentioning

confidence: 99%

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

Semenov

Kraft

Ainla

et al. 2016

Nature

308

274

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“…More explanation of switches of this form and their relation to Michaelis-Menten kinetics can be found in Tyson et al (2003).…”

Section: The Modelmentioning

confidence: 99%

A simple molecular mathematical model of mammalian hibernation

Hampton

Andrews

2007

Journal of Theoretical Biology

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A simple model of the dynamics of the body temperature of a hibernating mammal is presented. Our model provides a good match to experimental data, showing the interruption of lowtemperature torpor bouts with periodic interbout arousals (IBAs). In this paper we present a mathematical model of the molecules that participate in the initiation, regulation and maintenance of the hibernating state. This model can be used to describe the role of regulatory molecules, signal transducers, downstream target enzymes, structural proteins or metabolites. Because many of the biochemical mechanisms are unknown, this is a preliminary and largely phenomenological model that we hope will inspire further investigation.

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“…Or are these circuits instead capable of multistable (N > 2) behaviour? (Kaufman and Thomas (1987); Ma and Wu (2007) ;Demongeot et al (2000); Ozbudak et al (2004); Tyson et al (2003)). We can pose these problems in terms of general questions such as: Is the logic of cellular decisions Boolean?…”

Section: Introductionmentioning

confidence: 99%

Why are cellular switches Boolean? General conditions for multistable genetic circuits

Macía

Widder

Solé

2009

Journal of Theoretical Biology

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The logic of cellular decision making is largely controlled by regulatory circuits defining molecular switches. Such switching elements allow to turn a graded input signal into an all-or-nothing output. Traditional studies have focused on this bistable picture of regulation, but higher-order scenarios involving tristable and tetrastable states are possible too. Are these multiswitches allowed in simple gene regulatory networks? Are they likely to be observed? If not, why not? In this paper we present the examination of this question by means of a simple but powerful geometric approach. We examine the relation between multistability, the degree of multimerization of the regulators and the role of autoloops within a deterministic setting, finding that N-stable circuits are possible, although their likelihood to occur rapidly decays with the order of the switch. Our work indicates that, despite twocomponent circuits are able to implement multistability, they are optimal for Boolean switches. The evolutionary implications are outlined.

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Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

Cited by 1,452 publications

References 60 publications

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions

A simple molecular mathematical model of mammalian hibernation

Why are cellular switches Boolean? General conditions for multistable genetic circuits

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