On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks

Chen, Bor‐Sen; Wong, Shang-Wen; Li, Chengwei

doi:10.3390/e17106801

Cited by 13 publications

(21 citation statements)

References 65 publications

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“…PPIs have revealed global topological and dynamic features related to well-understood biological properties [ 20 ]. This indicates that studying PPIs will allow further understanding of disease mechanisms at a systematic level [ 21 - 23 ]. Wang et al identified C. albicans -zebrafish interspecies PPIs and used this information to highlight the association between C. albicans pathogenesis and the zebrafish redox process, indicating that redox status is critical in the battle between the host and pathogen [ 24 ].…”

Section: Introductionmentioning

confidence: 99%

Investigating the specific core genetic-and-epigenetic networks of cellular mechanisms involved in human aging in peripheral blood mononuclear cells

Wang

Chen

2016

Oncotarget

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Aging is an inevitable part of life for humans, and slowing down the aging process has become a main focus of human endeavor. Here, we applied a systems biology approach to construct protein-protein interaction networks, gene regulatory networks, and epigenetic networks, i.e. genetic and epigenetic networks (GENs), of elderly individuals and young controls. We then compared these GENs to extract aging mechanisms using microarray data in peripheral blood mononuclear cells, microRNA (miRNA) data, and database mining.The core GENs of elderly individuals and young controls were obtained by applying principal network projection to GENs based on Principal Component Analysis. By comparing the core networks, we identified that to overcome the accumulated mutation of genes in the aging process the transcription factor JUN can be activated by stress signals, including the MAPK signaling, T-cell receptor signaling, and neurotrophin signaling pathways through DNA methylation of BTG3, G0S2, and AP2B1 and the regulations of mir-223 let-7d, and mir-130a. We also address the aging mechanisms in old men and women. Furthermore, we proposed that drugs designed to target these DNA methylated genes or miRNAs may delay aging. A multiple drug combination comprising phenylalanine, cholesterol, and palbociclib was finally designed for delaying the aging process.

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Section: Introductionmentioning

confidence: 99%

Investigating the specific core genetic-and-epigenetic networks of cellular mechanisms involved in human aging in peripheral blood mononuclear cells

Wang

Chen

2016

Oncotarget

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“…Based on the configuration of its attractor (in deterministic case) or confiner (in random case) landscape in the network state space, it is related to the richness of the network attractor or confiner landscape [ 11 ]. The literature on network entropies is abundant [ 19 , 20 , 21 , 22 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 ] and concerns both discrete or continuous dynamical systems, which share common mathematical concepts, such as attractor, attraction basin, Jacobian interaction graph, stability and robustness. We take as the definition of an attractor, that given in [ 63 , 64 ], available for both continuous and discrete cases.…”

Section: Methodsmentioning

confidence: 99%

Entropy as a Robustness Marker in Genetic Regulatory Networks

Rachdi

Waku

Hazgui

et al. 2020

Entropy

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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-Sinaï 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.

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“…The indirect entropy measurement method we proposed can deal with the nonlinear stochastic continuous systems. Though the study in [24] is about the continuous nonlinear stochastic system, many physical systems are always modeled using stochastic partial differential dynamic equation in the spatio-temporal domain. The indirect entropy measurement method we proposed can be employed to solve the system entropy measurement in nonlinear stochastic partial differential system problem.…”

Section: Bypx Tqmentioning

confidence: 99%

“…Therefore, if system randomness can be measured, the system entropy can be easily obtained from its logarithm. The system entropy of biological systems modeled using ordinary differential equations was discussed in [24]. However, since many real physical and biological systems are modeled using partial differential dynamic equations, in this study, we will discuss the system entropy of SPDSs.…”

Section: Introductionmentioning

confidence: 99%

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

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System entropy describes the dispersal of a system's energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs) in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton-Jacobi integral inequality (HJII)-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs). To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3). Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

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On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks

Cited by 13 publications

References 65 publications

Investigating the specific core genetic-and-epigenetic networks of cellular mechanisms involved in human aging in peripheral blood mononuclear cells

Investigating the specific core genetic-and-epigenetic networks of cellular mechanisms involved in human aging in peripheral blood mononuclear cells

Entropy as a Robustness Marker in Genetic Regulatory Networks

System Entropy Measurement of Stochastic Partial Differential Systems

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