On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Conradi, Carsten; Feliu, Elisenda; Mincheva, Maya

doi:10.3934/mbe.2020027

Cited by 13 publications

(32 citation statements)

References 35 publications

(58 reference statements)

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“…Random mechanisms with different combinations of different/common kinase and different/common phosphatase can all exhibit both multistability and oscillations 21 . The ordered (distributive) model exhibits bistability, but has not been shown to intrinsically exhibit oscillations (there are theoretical studies which rule out oscillations in certain regimes 23 ). The basic cyclic model exhibits oscillations but not bistability or biphasic behaviour.…”

Section: Resultsmentioning

confidence: 99%

“…Oscillatory behaviour has been revealed in different cases: in random mechanisms with a single kinase/phosphatase pair, and also resulting from the interplay of distributive and processive mechanisms in ordered modification systems, or even arising from an enzyme activation step 19 – 21 . Other studies have focussed on the presence or absence of oscillations in these systems 22 , 23 . Processive systems by contrast behave in a simpler way and exhibit a unique asymptotically stable steady state 24 – 26 .…”

Section: Introductionmentioning

confidence: 99%

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Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Suwanmajo

Ramesh

Krishnan

2020

Sci Rep

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Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Suwanmajo

Ramesh

Krishnan

2020

Sci Rep

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“…For Proposition 5.2(i), we consider minimal generators of the cone

\ker false(N false) \cap ℝ_{> 0}^{r}

(cf. Conradi et al 21 ). See Example 5.6 for an example.…”

Section: Local Acr and Zero Sensitivitymentioning

confidence: 99%

Local and global robustness at steady state

Pascual-Escudero

Feliu

2021

Math Methods in App Sciences

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We study the robustness of the steady states of a class of systems of autonomous ordinary differential equations (ODEs), having as a central example those arising from (bio)chemical reaction networks. More precisely, we study under what conditions the steady states of the system are contained in a parallel translate of a coordinate hyperplane. To this end, we focus mainly on ODEs consisting of generalized polynomials and make use of algebraic and geometric tools to relate the local and global structure of the set of steady states. Specifically, we consider the local property termed zero sensitivity at a coordinate xi, which means that the tangent space is contained in a hyperplane of the form xi = c, and provide a criterion to identify it. We consider the global property termed absolute concentration robustness (ACR), meaning that all steady states are contained in a hyperplane of the form xi = c. We clarify and formalize the relation between the two approaches. In particular, we show that ACR implies zero sensitivity and identify when the two properties do not agree, via an intermediate property we term local ACR. For families of systems arising from modeling biochemical reaction networks, we obtain the first practical and automated criterion to decide upon (local) ACR.

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“…It has also been shown that there are choices of parameters for which there are two asymptotically stable steady states and one unstable steady state [21], see also [37]. It is currently unknown whether it admits Hopf bifurcations or periodic solutions [3].…”

Section: Introductionmentioning

confidence: 99%

The kinetic space of multistationarity in dual phosphorylation

Feliu¹,

Kaihnsa²,

Wolff³

et al. 2020

Preprint

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Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the set of kinetic parameters that enable multistationarity in a ubiquitous motif involved in cell signaling, namely a dual phosphorylation cycle. We model the dynamics of the concentrations of the proteins over time by means of a parametrized polynomial ordinary differential equation (ODE) system arising from the mass-action assumption. Since this system has three linear first integrals defined by the total amounts of the substrate and the two enzymes, we study for what parameter values the ODE system has at least two positive steady states after suitably choosing the total amounts. We employ a suite of techniques from (real) algebraic geometry, which in particular concern the study of the signs of a multivariate polynomial over the positive orthant and sums of nonnegative circuit polynomials.

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On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Cited by 13 publications

References 35 publications

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Local and global robustness at steady state

The kinetic space of multistationarity in dual phosphorylation

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