Robustness in biological regulatory networks I: Mathematical approach

Demongeot, Jacques; Waku, Jules

doi:10.1016/j.crma.2012.01.003

Cited by 11 publications

(21 citation statements)

References 13 publications

(13 reference statements)

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“…We define first the functions energy U , frustration F and dynamic entropy E of a genetic network N with n genes in interaction [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 ].

where x is a configuration of gene expression (

, if the gene i is expressed and

, if not),

denotes the set of all configurations of gene expression (i.e., the hypercube

) and

is the sign of the interaction weight quantifying the influence the gene j exerts on the gene i :

(resp.…”

Section: Resultsmentioning

confidence: 99%

“…An example of calculation of Relative Attraction Basin Sizes is given in the Table 1 . We will estimate E between

and

from the attractor entropy

[ 51 ] by using the following approximate equality:

…”

Section: Resultsmentioning

confidence: 99%

“…E serves as robustness parameter, being related to the capacity the genetic network has to return to the equilibrium after endogenous or exogenous perturbations [ 53 , 59 ]. We can more generally prove that the robustness of the network, supposed to be sequentially updated, decreases when the variance of the frustration F of the network increases, because of the formula:

, where

is the absolute value supposed to be the same for all the non zero interaction weights between the genes of the network [ 51 ].…”

Section: Resultsmentioning

confidence: 99%

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Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks

Demongeot

Jelassi

Hazgui

et al. 2018

Entropy

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Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction graph G(J) associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J), kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.

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where x is a configuration of gene expression (

, if the gene i is expressed and

, if not),

denotes the set of all configurations of gene expression (i.e., the hypercube

) and

is the sign of the interaction weight quantifying the influence the gene j exerts on the gene i :

(resp.…”

Section: Resultsmentioning

confidence: 99%

“…An example of calculation of Relative Attraction Basin Sizes is given in the Table 1 . We will estimate E between

and

from the attractor entropy

[ 51 ] by using the following approximate equality:

…”

Section: Resultsmentioning

confidence: 99%

, where

is the absolute value supposed to be the same for all the non zero interaction weights between the genes of the network [ 51 ].…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks

Demongeot

Jelassi

Hazgui

et al. 2018

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…More systematic studies have to be performed in order to confirm the dominant influence of boundary negative interactions, thanks to which the Hopfield-like regulatory interaction networks seem to become more robust [21][22], and also to make more precise their influence on the number of attractors, which is conjectured to diminish, when microRNAs are multiple on the boundary of the interaction graph of the network. …”

Section: Discussionmentioning

confidence: 95%

“…We will use in the following the notion of genetic threshold Boolean random regulatory network (getBren), which is a set N of n random automata defined as follows [13][14][15][16][17][18][19][20][21][22]: 1) any random automaton i of the getBren N owns at time t a state x i (t) valued in {0,1}, 0 (resp. 1) meaning that gene i is inactivated (resp.…”

Section: Micrornas Chromatine Clock and Geneticmentioning

confidence: 99%

MitomiRs and Energetic Regulation

Demongeot

Cohen

Doncescu

et al. 2013

2013 27th International Conference on Advanced Information Networking and Applications Workshops

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MicroRNAs are parts of nuclear and mitochondrial genomes which pertain to the not coding genome. They have a partly unspecific role of inhibition, preventing the weakest part of the genetic regulatory networks to be expressed and preventing the appearance of a too large number of attractors in these networks, i.e., forcing the network to have only one or two possible dynamic behaviours for fulfilling a precise function. They have also a great influence on the chromatin clock, which ensures the real mode of updating of genetic regulatory networks. We analyze this influence as well as their impact on important functions like p53 network control.

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MitomiRs, ChloromiRs and Modelling of the microRNA Inhibition

et al. 2013

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MicroRNAs are non-coding parts of nuclear and mitochondrial genomes, preventing the weakest part of the genetic regulatory networks from being expressed and preventing the appearance of a too many attractors in these networks. They have also a great influence on the chromatin clock, which ensures the updating of the genetic regulatory networks. The post-transcriptional inhibitory activity by the microRNAs, which is partly unspecific, is due firstly to their possibly direct negative action during translation by hybridizing tRNAs, especially those inside the mitochondrion, hence slowing mitochondrial respiration, and secondly to their action on a large number of putative m-RNA targets like those involved in immunetworks; We show that the circuits in the core of the interaction graphs are responsible for the small number of dedicated attractors that correspond to genetically controlled functions, partly due to a general filtering by the microRNAs. We analyze this influence as well as their impact on important functions like the control by the p53 network over the apoptosis/proliferation system and the homeostasis of the energy metabolism. In this last case, we show the role of two kinds of microRNAs, both involved in the control of the mitochondrial genome: (1) nuclear microRNAs, called mitoMirs, inhibiting mitochondrial genes and (2) putative mitochondrial microRNAs inhibiting the tRNAs functioning.

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Robustness in biological regulatory networks I: Mathematical approach

Cited by 11 publications

References 13 publications

Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks

Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks

MitomiRs and Energetic Regulation

MitomiRs, ChloromiRs and Modelling of the microRNA Inhibition

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