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Biological Statistical Mechanics
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Biological Statistical Mechanics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (15 March 2020) | Viewed by 32476

Special Issue Editors

Prof. Dr. Alessandro Giuliani

E-Mail Website
Guest Editor
Environment and Health Department, Istituto Superiore di Sanità, 00161 Rome, Italy
Interests: data analysis; complex systems; systems biology; statistical mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Mariano Bizzarri

E-Mail Website
Guest Editor
Department of Experimental Medicine, Systems Biology Group Lab, Sapienza University of Rome, Via A. Scarpa 16, 00163 Rome, Italy
Interests: inositol in endocrine control and carcinogenesis; tumor reversion through epigenetic and microenvironment modification; biophysical control of morphogenesis and differentiation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Any natural entity can be imagined as a system made up of interacting elements. This allows for the development of phenomenological "laws" shared by network-like systems only dependent on their wiring architecture. We can compare this situation with the success of classical thermodynamics, even if the founding fathers of this science were erroneously convinced that heat was a fluid. The difference with classical thermodynamics is that in the case of biological systems we cannot rely on macro-parameters like volume or pressure, but we must seriously consider the particular correlation structure of the system at hand. This is why focusing on state transitions (e.g., differentiation, development, onset of diseases, ecosystem de-stabilization) in which we expect abrupt changes of the system correlation structure is probably the most fruitful direction to establish a "biological statistical mechanics". This Special Issue is devoted to the collection of statistical mechanics-inspired approaches to biological systems at any scale of definition from cell biology to ecology and epidemiology. The issue is of crucial importance given the evident failure of strictly deterministic molecular biology approaches to predicting system-level properties of biological entities.

Prof. Alessandro Giuliani
Prof. Mariano Bizzarri
Guest Editors

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Keywords

  • network dynamics
  • cell differentiation
  • biocomplexity
  • order and organization
  • ecology
  • epidemics
  • correlation dynamics
  • complex networks, systems

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Published Papers (6 papers)

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23 pages, 2929 KiB  
Article
A Study on Non-Linear DPL Model for Describing Heat Transfer in Skin Tissue during Hyperthermia Treatment
by Sunil Kumar Sharma and Dinesh Kumar
Entropy 2020, 22(4), 481; https://doi.org/10.3390/e22040481 - 22 Apr 2020
Cited by 18 | Viewed by 4044
Abstract
The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues during hyperthermia treatment of infected cells. The perfusion term, metabolic heat source, [...] Read more.
The article studies the simulation-based mathematical modeling of bioheat transfer under the Dirichlet boundary condition. We used complex non-linear dual-phase-lag bioheat transfer (DPLBHT) for analyzing the temperature distribution in skin tissues during hyperthermia treatment of infected cells. The perfusion term, metabolic heat source, and external heat source were the three parts of the volumetric heat source that were used in the model. The non-linear DPLBHT model predicted a more accurate temperature within skin tissues. The finite element Runge–Kutta (4,5) (FERK (4,5)) method, which was based on two techniques, finite difference and Runge–Kutta (4,5), was applied for calculating the result in the case of our typical non-linear problem. The paper studies and presents the non-dimensional unit. Thermal damage of normal tissue was observed near zero during hyperthermia treatment. The effects of the non-dimensional time, non-dimensional space coordinate, location parameter, regional parameter, relaxation and thermalization time, metabolic heat source, associated metabolic heat source parameter, perfusion rate, associated perfusion heat source parameter, and external heat source coefficient on the dimensionless temperature profile were studied in detail during the hyperthermia treatment process. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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18 pages, 1123 KiB  
Article
On the Statistical Mechanics of Life: Schrödinger Revisited
by Kate Jeffery, Robert Pollack and Carlo Rovelli
Entropy 2019, 21(12), 1211; https://doi.org/10.3390/e21121211 - 10 Dec 2019
Cited by 31 | Viewed by 8682
Abstract
We study the statistical underpinnings of life, in particular its increase in order and complexity over evolutionary time. We question some common assumptions about the thermodynamics of life. We recall that contrary to widespread belief, even in a closed system entropy growth can [...] Read more.
We study the statistical underpinnings of life, in particular its increase in order and complexity over evolutionary time. We question some common assumptions about the thermodynamics of life. We recall that contrary to widespread belief, even in a closed system entropy growth can accompany an increase in macroscopic order. We view metabolism in living things as microscopic variables directly driven by the second law of thermodynamics, while viewing the macroscopic variables of structure, complexity and homeostasis as mechanisms that are entropically favored because they open channels for entropy to grow via metabolism. This perspective reverses the conventional relation between structure and metabolism, by emphasizing the role of structure for metabolism rather than the converse. Structure extends in time, preserving information along generations, particularly in the genetic code, but also in human culture. We argue that increasing complexity is an inevitable tendency for systems with these dynamics and explain this with the notion of metastable states, which are enclosed regions of the phase-space that we call “bubbles,” and channels between these, which are discovered by random motion of the system. We consider that more complex systems inhabit larger bubbles (have more available states), and also that larger bubbles are more easily entered and less easily exited than small bubbles. The result is that the system entropically wanders into ever-larger bubbles in the foamy phase space, becoming more complex over time. This formulation makes intuitive why the increase in order/complexity over time is often stepwise and sometimes collapses catastrophically, as in biological extinction. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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13 pages, 934 KiB  
Article
Extinction Analysis of Stochastic Predator–Prey System with Stage Structure and Crowley–Martin Functional Response
by Conghui Xu, Guojian Ren and Yongguang Yu
Entropy 2019, 21(3), 252; https://doi.org/10.3390/e21030252 - 6 Mar 2019
Cited by 17 | Viewed by 3435
Abstract
In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we [...] Read more.
In this paper, we researched some dynamical behaviors of a stochastic predator–prey system, which is considered under the combination of Crowley–Martin functional response and stage structure. First, we obtained the existence and uniqueness of the global positive solution of the system. Then, we studied the stochastically ultimate boundedness of the solution. Furthermore, we established two sufficient conditions, which are separately given to ensure the stochastic extinction of the prey and predator populations. In the end, we carried out the numerical simulations to explain some cases. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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18 pages, 6616 KiB  
Article
Flexibility of Boolean Network Reservoir Computers in Approximating Arbitrary Recursive and Non-Recursive Binary Filters
by Moriah Echlin, Boris Aguilar, Max Notarangelo, David L. Gibbs and Ilya Shmulevich
Entropy 2018, 20(12), 954; https://doi.org/10.3390/e20120954 - 11 Dec 2018
Cited by 9 | Viewed by 4865
Abstract
Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and [...] Read more.
Reservoir computers (RCs) are biology-inspired computational frameworks for signal processing that are typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying the factors that determine the effective approximation of Boolean functions applied in a sliding-window fashion over a binary signal, both non-recursively and recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate three-bit, five-bit, and three-bit recursive binary functions, respectively. We analyze how BN RC parameters and function average sensitivity, which is a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible, and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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15 pages, 3943 KiB  
Article
Spatial Organization of Five-Fold Morphology as a Source of Geometrical Constraint in Biology
by Juan López-Sauceda, Jorge López-Ortega, Gerardo Abel Laguna Sánchez, Jacobo Sandoval Gutiérrez, Ana Paola Rojas Meza and José Luis Aragón
Entropy 2018, 20(9), 705; https://doi.org/10.3390/e20090705 - 14 Sep 2018
Cited by 1 | Viewed by 4499
Abstract
A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some [...] Read more.
A basic pattern in the body plan architecture of many animals, plants and some molecular and cellular systems is five-part units. This pattern has been understood as a result of genetic blueprints in development and as a widely conserved evolutionary character. Despite some efforts, a definitive explanation of the abundance of pentagonal symmetry at so many levels of complexity is still missing. Based on both, a computational platform and a statistical spatial organization argument, we show that five-fold morphology is substantially different from other abundant symmetries like three-fold, four-fold and six-fold symmetries in terms of spatial interacting elements. We develop a measuring system to determine levels of spatial organization in 2D polygons (homogeneous or heterogeneous partition of defined areas) based on principles of regularity in a morphospace. We found that spatial organization of five-fold symmetry is statistically higher than all other symmetries studied here (3 to 10-fold symmetries) in terms of spatial homogeneity. The significance of our findings is based on the statistical constancy of geometrical constraints derived from spatial organization of shapes, beyond the material or complexity level of the many different systems where pentagonal symmetry occurs. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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15 pages, 828 KiB  
Essay
Complexity in Biological Organization: Deconstruction (and Subsequent Restating) of Key Concepts
by Mariano Bizzarri, Oleg Naimark, José Nieto-Villar, Valeria Fedeli and Alessandro Giuliani
Entropy 2020, 22(8), 885; https://doi.org/10.3390/e22080885 - 12 Aug 2020
Cited by 22 | Viewed by 5243
Abstract
The “magic” word complexity evokes a multitude of meanings that obscure its real sense. Here we try and generate a bottom-up reconstruction of the deep sense of complexity by looking at the convergence of different features shared by complex systems. We specifically focus [...] Read more.
The “magic” word complexity evokes a multitude of meanings that obscure its real sense. Here we try and generate a bottom-up reconstruction of the deep sense of complexity by looking at the convergence of different features shared by complex systems. We specifically focus on complexity in biology but stressing the similarities with analogous features encountered in inanimate and artefactual systems in order to track an integrative path toward a new “mainstream” of science overcoming the actual fragmentation of scientific culture. Full article
(This article belongs to the Special Issue Biological Statistical Mechanics)
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