Dynamic properties of a delayed protein cross talk model

Николов, Светослав; Vera, Julio; Kotev, Vladimir; Petrov, Valko

doi:10.1016/j.biosystems.2007.07.004

Cited by 25 publications

(10 citation statements)

References 40 publications

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“…In Nova´k and Tyson (2008) it is shown how even simple signalling pathways that include positive and negative feedback loops can generate complex dynamical behaviour, including toggle, amplifier, switches and oscillators. When the mathematical models include numerous equations with non-linear equations kinetics and control structures such as feedback loops, the complex dynamics of the system can only be elucidated with the support of more sophisticated tools, such as sensitivity analysis (SA) (Yue et al 2006;Joo, Plimpton, Martin, Swiler and Faulon 2007;Balsa-Canto, Alonso and Banga 2008), model reduction (Danø, Madsen, Schmidt and Cedersund 2006), and bifurcation analysis (Tyson, Csikasz-Nagy and Novak 2002;Tyson, Chen and Novak 2003;Nikolov, Vera, Rath, Kolch and Wolkenhauer 2008;Nikolov, Vera, Kotev, Wolkenhauer and Petrov 2008).…”

Section: Introductionmentioning

confidence: 99%

Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

Николов

Lai

Liebal

et al. 2010

International Journal of Systems Science

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In this article we present and test a strategy to integrate, in a sequential manner, sensitivity analysis, bifurcation analysis and predictive simulations. Our strategy uses some of these methods in a coordinated way such that information, generated in one step, feeds into the definition of further analyses and helps refining the structure of the mathematical model. The aim of the method is to help in the designing of more informative predictive simulations, which focus on critical model parameters and the biological effects of their modulation. We tested our methodology with a multilevel model, accounting for the effect of erythropoietin (Epo)-mediated JAK2-STAT5 signalling in erythropoiesis. Our analysis revealed that time-delays associated with the proliferation-differentiation process are critical to induce pathological sustained oscillations, whereas the modulation of time-delays related to intracellular signalling and hypoxia-controlled physiological dynamics is not enough to induce self-oscillations in the system. Furthermore, our results suggest that the system is able to compensate (through the physiological-level feedback loop on hypoxia) the partial impairment of intracellular signalling processes (downregulation or overexpression of Epo receptor complex and STAT5), but cannot control impairment in some critical physiological-level processes, which provoke the emergence of pathological oscillations.

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Section: Introductionmentioning

confidence: 99%

Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

Николов

Lai

Liebal

et al. 2010

International Journal of Systems Science

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“…Time delay combined with positive/ negative feedback loops (regulatory structures in which the activation of a signalling event positive/negative regulates a signalling process upstream the signalling pathway) can sometimes destabilize the stable unique equilibrium of a biochemical network and vice versa. If the time delay is large/small enough, we find that periodic solutions (sustained oscillations in the levels of the proteins and RNAs integrating the network) can arise from equilibrium by the so-called Andronov-Hopf bifurcation (Goldbeter et al 2001;Nikolov et al 2008;Nikolov 2008). In line with this notion, oscillations have been experimentally detected in several signalling networks showing time delays in protein expression ).…”

Section: Appendixmentioning

confidence: 97%

“…Bifurcation theory studies persistence and exchange of qualitative properties of dynamical systems under continuous perturbations. From the point of view of dynamic systems theory, the Hopf bifurcation theorem (Marsden and McCracken 1976;Goldbeter 2002;Nikolov et al 2008;Nikolov et al 2010) together with other elements of the bifurcation theory is basic analytical tools to investigate pathological conditions in biological systems (Glass and Mackey 1988;Fall et al 2002).…”

Section: Appendixmentioning

confidence: 99%

A model-based strategy to investigate the role of microRNA regulation in cancer signalling networks

et al. 2010

Self Cite

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In this paper we present and discuss a model-based approach to link miRNA translational control with cell signalling networks. MicroRNAs are small regulatory RNAs that are able to regulate the activity and the stability of specific messenger RNA and have been implicated in tumour progression due to their ability to translationally regulate critical oncogenes and tumour suppressors. In our approach, data on protein-protein interactions and miRNA regulation, obtained from bioinformatics databases, are integrated with quantitative experimental data using mathematical modelling. Predictive computational simulations and qualitative (bifurcation) analyses of those mathematical models are employed to further support the investigation of such multifactorial networks in the context of cancer progression. We illustrate our approach with the C-Myc/E2F signalling network, involved in the progression of several tumour subtypes, including colorectal cancer.

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“…At a process level, metabolic time delays can be observed macroscopically by recognizing a certain time delay between substrate uptake and the corresponding biomass growth or product formation as in cultivations of Saccharomyces cerevisiae [1] or Pichia pastoris [2]. The nature of time delays in regulatory networks is twofold [3]. They are either related to a process that takes an intrinsic time to be accomplished, i.e.…”

Section: Introductionmentioning

confidence: 99%

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

et al. 2010

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BackgroundThis paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.ResultsThe proposed hybrid modelling methodology was evaluated using two case studies. The first of these deals with dynamic modelling of transcriptional factor A in mammalian cells. The protein transport from the cytosol to the nucleus introduced a delay that was accounted for by discrete time series formulation. The second case study focused on a simple network with distributed time delays that demonstrated that the discrete time delay formalism has broad applicability to both discrete and distributed delay problems.ConclusionsSignificantly better prediction qualities of the novel hybrid model were obtained when compared to dynamical structures without time delays, being the more distinctive the more significant the underlying system delay is. The identification of the system delays by studies of different discrete modelling delays was enabled by the proposed structure. Further, it was shown that the hybrid discrete delay methodology is not limited to discrete delay systems. The proposed method is a powerful tool to identify time delays in ill-defined biochemical networks.

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Dynamic properties of a delayed protein cross talk model

Cited by 25 publications

References 40 publications

Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics

A model-based strategy to investigate the role of microRNA regulation in cancer signalling networks

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

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