Thresholds in transient dynamics of signal transduction pathways

Rateitschak, Katja

doi:10.1016/j.jtbi.2010.02.001

Cited by 13 publications

(22 citation statements)

References 32 publications

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“…is the so-called relative instability exponent, which is introduced by Rateitschak and Wolkenhauer [19] to measure the largest relative change in the system response when the initial conditions are perturbed.…”

Section: Proof: Define a Family Of Linear Operatorsmentioning

confidence: 99%

“…Another common feature of stimulus-response curves is their sigmoidal form [3], characterized by a bell-shaped first derivative, as will be made precise later. Rateitschak and Wolkenhauer [19] took advantage of this geometrical attribute and defined a threshold value as the inflection point of a sigmoidal stimulus-response curve. These thresholds play an important role in biological applications, as they can be associated to an initial condition (e.g.…”

Section: Sigmoidal Stimulus-response Curvesmentioning

confidence: 99%

“…Mechanisms leading to sigmoidal (also referred to as ultrasensitive) stimulus-response curves include cooperativity, feed-forward loops and enzymes operating under saturation [3]. Rateitschak and Wolkenhauer [19] pointed out the importance of having quantitative measures that allow the detection of thresholds in a reliable manner. Their empirical study suggested that FTLE may be a suitable choice for such a measure, and in this section we will present a rigorous discussion regarding this conjecture.…”

Section: Sigmoidal Stimulus-response Curvesmentioning

confidence: 99%

“…Examples of quantitative measures to characterize the transient dynamics of signal transduction pathways include metabolic control coefficients (MCC) [14] and finite-time Lyapunov exponents (FTLE) [1,19]. In fact, MCC were originally introduced to study the dynamics near steady states (see [10,15]), but then proved to be still effective for the analysis of transient behaviour.…”

Section: Introductionmentioning

confidence: 99%

“…Rateitschak and Wolkenhauer [19] suggested that FTLE can be used to reliably identify thresholds as inflection points of stimulus-response curves in transient dynamics, while MCC are more suitable for comparing the amplitude of different thresholds. Nevertheless, their conclusions are based on numerical simulations of three examples and mathematical proofs of their claims are missing.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

Duc

Chávez

Doàn

et al. 2016

Journal of Biological Dynamics

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In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape. ARTICLE HISTORY

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Section: Proof: Define a Family Of Linear Operatorsmentioning

confidence: 99%

Section: Sigmoidal Stimulus-response Curvesmentioning

confidence: 99%

Section: Sigmoidal Stimulus-response Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

Duc

Chávez

Doàn

et al. 2016

Journal of Biological Dynamics

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Finite-Time Attractivity for Semilinear Fractional Differential Equations

Ke¹,

Tuấn²

2018

Results Math

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Linearization of hyperbolic finite-time processes

Karrasch

2013

Journal of Differential Equations

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We adapt the notion of processes to introduce an abstract framework for dynamics in finite time, i.e. on compact time-sets. For linear finite-time processes a notion of hyperbolicity namely exponential monotonicity dichotomy (EMD) is introduced, thereby generalizing and unifying several existing approaches. We present a spectral theory for linear processes in a coherent way, based only on a logarithmic difference quotient. In this abstract setting we introduce a new topology, prove robustness of EMD and provide exact perturbation bounds. We suggest a new, intrinsic approach for the investigation of linearizations of finite-time processes, including finite-time analogues of the local (un-)stable manifold theorem and theorem of linearized asymptotic stability. As an application, we discuss our results for ordinary differential equations on a compact time-interval.

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Thresholds in transient dynamics of signal transduction pathways

Cited by 13 publications

References 32 publications

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

Finite-Time Attractivity for Semilinear Fractional Differential Equations

Linearization of hyperbolic finite-time processes

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