On the robustness of update schedules in Boolean networks

Aracena, Julio; Goles, Éric; Moreira, Andrés; Salinas, Lilian

doi:10.1016/j.biosystems.2009.03.006

Cited by 114 publications

(72 citation statements)

References 29 publications

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“…The general principles that are responsible for these characteristics have not yet been fully identified [6], although dynamical robustness has been studied for a variety of biological systems [7][8][9][10][11]. Most studies focused on two types of perturbations: noise which directly affects the states of individual nodes in the system [12][13][14][15][16][17], or fluctuations in the update sequence of the nodes [4,6,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Reliable dynamics in Boolean and continuous networks

2012

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We investigate the dynamical behavior of a model of robust gene regulatory networks which possess 'entirely reliable' trajectories. In a Boolean representation, these trajectories are characterized by being insensitive to the order in which the nodes are updated, i.e. they always go through the same sequence of states. The Boolean model for gene activity is compared with a continuous description in terms of differential equations for the concentrations of mRNA and proteins. We found that entirely reliable Boolean trajectories can be reproduced perfectly in the continuous model when realistic Hill coefficients are used. We investigate to what extent this high correspondence between Boolean and continuous trajectories depends on the extent of reliability of the Boolean trajectories, and we identify simple criteria that enable the faithful reproduction of the Boolean dynamics in the continuous description.

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Section: Introductionmentioning

confidence: 99%

Reliable dynamics in Boolean and continuous networks

2012

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“…Several definitions of the transition relation → can be used depending on the update schedule of the components [2], ranging from so-called parallel (or synchronous) updates where each transition updates the value of all the components, to the asynchronous update where each transition updates the value of only one component chosen nondeterministically. As the over-approximation results presented in this article are independent from the update schedule, we use the general definition, where any number of components can be updated during a transition: for any x, x ∈ B n ,…”

Section: Admissible Boolean Network and Multiplex Time Series Datamentioning

confidence: 99%

Boolean Network Identification from Multiplex Time Series Data

Ostrowski

Paulevé

Schaub

et al. 2015

Computational Methods in Systems Biology

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Abstract. Boolean networks (and more general logic models) are useful frameworks to study signal transduction across multiple pathways. Logical models can be learned from a prior knowledge network structure and multiplex phosphoproteomics data. However, most efficient and scalable training methods focus on the comparison of two time-points and assume that the system has reached an early steady state. In this paper, we generalize such a learning procedure to take into account the time series traces of phosphoproteomics data in order to discriminate Boolean networks according to their transient dynamics. To that goal, we exhibit a necessary condition that must be satisfied by a Boolean network dynamics to be consistent with a discretized time series trace. Based on this condition, we use a declarative programming approach (Answer Set Programming) to compute an over-approximation of the set of Boolean networks which fit best with experimental data. Combined with modelchecking approaches, we end up with a global learning algorithm and compare it to learning approaches based on static data.

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“…In stochastic schemes, the node(s) that is (are) updated in the next time step t + 1 is (are) chosen randomly [85], whereas in deterministic asynchronous schemes, the nodes are updated according to a predetermined order [86]. The choice of the updating scheme highly determines the system's dynamics [87], and the differences between synchronous and asynchronous as well as between different asynchronous approaches have been extensively studied [36,87-91]. The possible sequences of states that can take place in a network according to the logical functions and the chosen switching schemes can be represented in a state transition graph (also called graph of sequence of states; see [36]).…”

Section: Reviewmentioning

confidence: 99%

Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks

2013

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A central goal of systems biology is the construction of predictive models of bio-molecular networks. Cellular networks of moderate size have been modeled successfully in a quantitative way based on differential equations. However, in large-scale networks, knowledge of mechanistic details and kinetic parameters is often too limited to allow for the set-up of predictive quantitative models.Here, we review methodologies for qualitative and semi-quantitative modeling of cellular signal transduction networks. In particular, we focus on three different but related formalisms facilitating modeling of signaling processes with different levels of detail: interaction graphs, logical/Boolean networks, and logic-based ordinary differential equations (ODEs). Albeit the simplest models possible, interaction graphs allow the identification of important network properties such as signaling paths, feedback loops, or global interdependencies. Logical or Boolean models can be derived from interaction graphs by constraining the logical combination of edges. Logical models can be used to study the basic input–output behavior of the system under investigation and to analyze its qualitative dynamic properties by discrete simulations. They also provide a suitable framework to identify proper intervention strategies enforcing or repressing certain behaviors. Finally, as a third formalism, Boolean networks can be transformed into logic-based ODEs enabling studies on essential quantitative and dynamic features of a signaling network, where time and states are continuous.We describe and illustrate key methods and applications of the different modeling formalisms and discuss their relationships. In particular, as one important aspect for model reuse, we will show how these three modeling approaches can be combined to a modeling pipeline (or model hierarchy) allowing one to start with the simplest representation of a signaling network (interaction graph), which can later be refined to logical and eventually to logic-based ODE models. Importantly, systems and network properties determined in the rougher representation are conserved during these transformations.

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On the robustness of update schedules in Boolean networks

Cited by 114 publications

References 29 publications

Reliable dynamics in Boolean and continuous networks

Reliable dynamics in Boolean and continuous networks

Boolean Network Identification from Multiplex Time Series Data

Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks

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