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

Abstract

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.

Entropy as a Robustness Marker in Genetic Regulatory Networks

“…A previous work [ 40 ] gives an algebraic formula allowing for the calculation of the number of attractors of a Boolean network; in their Jacobian interaction graph were two tangential circuits ( Table 1 ): one positive of length right, (involved in the richness in attractors, as predicted by [ 32 , 33 , 34 ], and one negative of length four (responsible of the trajectory stability, as predicted by [ 36 , 89 ]). This predicted number (11) is the same as that calculated from the simulation of all trajectories from all possible initial conditions summarized in Figure 8 , and more results both theoretical and applied to real Boolean networks can be found in more recent literature [ 46 , 47 , 48 , 49 , 90 ] showing a large spectrum of possible applications in genetic, metabolic or social Boolean networks.…”

“…In the present paper, we will focus on the study of robustness of genetic regulatory networks driven by Hopfield’ stochastic rule [ 35 ], by using the Kolmogorov-Sinaï entropy of the Markov process underlying the state transition dynamics [ 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ]. In Section 2 , we define the concepts underlying the relationships between complexity, stability and robustness in the Markov framework of genetic threshold Boolean random regulatory networks.…”

Temperature Decreases Spread Parameters of the New Covid-19 Case Dynamics

“…These seasonal changes could occur in exactly the same way as for other pathogens, like the common cold or influenza [9][10][11][12]. This phenomenon can be modelled and the deterministic as well as stochastic models [2,[13][14][15][16][17][18][19][20][21][22][23][24][25] include potentially temperature-dependent parameters, like the contagion coefficient increasing with cold, dry weather because of faster evaporation of aerosol droplets. The present paper aims to identify such parameters from the covid-19 spread dynamics.…”

Determining Levels of Biological Geometric Information at Polygonal Shape Patterns

“…In some sense, it is not a novel question. There is an important amount of works related with that issue of quantifying information at different complexity levels in biological networks [16][17][18][19], ecosystems [20][21][22][23][24], molecular entropy [25] and cellular entropy [26], just to mention some. Also, forms of spatial entropy looking for the characterization of ecological landscape heterogeneity, such as urban, sociological and economical properties at multiple scales associated with them have been broadly approached [27][28][29], using some geometrical tools.…”