Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks

Beck, Gary L.; Matache, Mihaela Teodora

doi:10.1016/j.physa.2008.04.032

Cited by 10 publications

(2 citation statements)

References 31 publications

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“…To this aim, we defined a random procedure for changing the state of each node at every time step. A noise intensity parameter N I is introduced so that the state of each node is randomly re-assigned at every time step as follows [ 39 , 40 ]: where O i is the state of the i th node of total M nodes: {O i } i = 1,…, M . The i th node is connected to P(i) nodes of the network (0<P(i)≤M), which define the states of the regulators of the i th node: {O ij } j = 1,…, P(i) .…”

Section: Methodsmentioning

confidence: 99%

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

2015

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From the perspective of systems science, tumorigenesis can be hypothesized as a critical transition (an abrupt shift from one state to another) between proliferative and apoptotic attractors on the state space of a molecular interaction network, for which an attractor is defined as a stable state to which all initial states ultimately converge, and the region of convergence is called the basin of attraction. Before the critical transition, a cellular state might transit between the basin of attraction for an apoptotic attractor and that for a proliferative attractor due to the noise induced by the inherent stochasticity in molecular interactions. Such a flickering state transition (state transition between the basins of attraction for alternative attractors from the impact of noise) would become more frequent as the cellular state approaches near the boundary of the basin of attraction, which can increase the variation in the estimate of the respective basin size. To investigate this for colorectal tumorigenesis, we have constructed a stochastic Boolean network model of the molecular interaction network that contains an important set of proteins known to be involved in cancer. In particular, we considered 100 representative sequences of 20 gene mutations that drive colorectal tumorigenesis. We investigated the appearance of cancerous cells by examining the basin size of apoptotic, quiescent, and proliferative attractors along with the sequential accumulation of gene mutations during colorectal tumorigenesis. We introduced a measure to detect the flickering state transition as the variation in the estimate of the basin sizes for three-phenotype attractors from the impact of noise. Interestingly, we found that this measure abruptly increases before a cell becomes cancerous during colorectal tumorigenesis in most of the gene mutation sequences under a certain level of stochastic noise. This suggests that a frequent flickering state transition can be a precritical phenomenon of colorectal tumorigenesis.

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Section: Methodsmentioning

confidence: 99%

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

2015

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“…This is the generalized ECA rule 22 studied in Ref. 12 in the context of synchronous Boolean networks evolving under this rule, whose dynamics is studied also under a stochastic noise procedure. As specified in that paper, this generalization allows insight into Boolean systems governed by rules meaningful for neural networks or biology.…”

Section: Fixed Parameters In the Context Of Boolean Network The Rulmentioning

confidence: 99%

On the sensitivity to noise of a Boolean function

Matache¹,

Matache²

2009

Journal of Mathematical Physics

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In this paper we generate upper and lower bounds for the sensitivity to noise of a Boolean function using relaxed assumptions on input choices and noise. The robustness of a Boolean network to noisy inputs is related to the average sensitivity of that function. The average sensitivity measures how sensitive to changes in the inputs the output of the function is. The average sensitivity of Boolean functions can indicate whether a specific random Boolean network constructed from those functions is ordered, chaotic, or in critical phase. We give an exact formula relating the sensitivity to noise and the average sensitivity of a Boolean function. The analytic approach is supplemented by numerical results that illustrate the overall behavior of the sensitivities as various Boolean functions are considered. It is observed that, for certain parameter combinations, the upper estimates in this paper are sharper than other estimates in the literature and that the lower estimates are very close to the actual values of the sensitivity to noise of the selected Boolean functions.

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A Study of Stochastic Noise and Asynchronism in Elementary Cellular Automata

Silva

Correia

2012

Lecture Notes in Computer Science

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Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks

Cited by 10 publications

References 31 publications

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

Precritical State Transition Dynamics in the Attractor Landscape of a Molecular Interaction Network Underlying Colorectal Tumorigenesis

On the sensitivity to noise of a Boolean function

A Study of Stochastic Noise and Asynchronism in Elementary Cellular Automata

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