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10.3390/e22030260 http://scihub22266oqcxt.onion/10.3390/e22030260 33286034!7516706!33286034     free     free     free Deprecated: Implicit conversion from float 215.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Entropy+(Basel) 2020 ; 22 (3): ä Nephropedia Template TP {{tp|p=33286034|t=2020. Entropy as a Robustness Marker in Genetic Regulatory Networks |pdf=|usr=}}{{33286034}} gab.com Text Entropy as a Robustness Marker in Genetic Regulatory Networks JO: Entropy (Basel) http://www.kidney.de/pget.php?&tw=1&pmid=33286034 #FOAvip Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinai entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors. Twit Text FOAVip Entropy as a Robustness Marker in Genetic Regulatory Networks ????Entropy (Basel) http://www.kidney.de/pget.php?&tw=1&pmid=33286034 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=33286034 #FOAvip English Wikipedia <ref>{{Cite pmid|33286034}}</ref> Entropy as a Robustness Marker in Genetic Regulatory Networks #MMPMID33286034 Rachdi M; Waku J; Hazgui H; Demongeot J Entropy (Basel) 2020[Feb]; 22 (3): ä PMID33286034show ga Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinai entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors. äEntropy as a Robustness Marker in Genetic Regulatory Networks (epmc).pdf DeepDyve Pubget Overpricing