Entropy

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23 pages, 7450 KiB

Open AccessArticle

Multispectral Remote Sensing Data Application in Modelling Non-Extensive Tsallis Thermodynamics for Mountain Forests in Northern Mongolia

by Robert Sandlersky, Nataliya Petrzhik, Tushigma Jargalsaikhan and Ivan Shironiya

Entropy 2023, 25(12), 1653; https://doi.org/10.3390/e25121653 - 13 Dec 2023

Viewed by 1381

Abstract

The imminent threat of Mongolian montane forests facing extinction due to climate change emphasizes the pressing need to study these ecosystems for sustainable development. Leveraging multispectral remote sensing data from Landsat 8 OLI TIRS (2013–2021), we apply Tsallis non-extensive thermodynamics to assess spatiotemporal [...] Read more.

The imminent threat of Mongolian montane forests facing extinction due to climate change emphasizes the pressing need to study these ecosystems for sustainable development. Leveraging multispectral remote sensing data from Landsat 8 OLI TIRS (2013–2021), we apply Tsallis non-extensive thermodynamics to assess spatiotemporal fluctuations in the absorbed solar energy budget (exergy, bound energy, internal energy increment) and organizational parameters (entropy, information increment, q-index) within the mountain taiga–meadow landscape. Using the principal component method, we discern three functional subsystems: evapotranspiration, heat dissipation, and a structural-informational component linked to bioproductivity. The interplay among these subsystems delineates distinct landscape cover states. By categorizing ecosystems (pixels) based on these processes, discrete states and transitional areas (boundaries and potential disturbances) emerge. Examining the temporal dynamics of ecosystems (pixels) within this three-dimensional coordinate space facilitates predictions of future landscape states. Our findings indicate that northern Mongolian montane forests utilize a smaller proportion of received energy for productivity compared to alpine meadows, which results in their heightened vulnerability to climate change. This approach deepens our understanding of ecosystem functioning and landscape dynamics, serving as a basis for evaluating their resilience amid ongoing climate challenges. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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22 pages, 1120 KiB

Open AccessArticle

Fractal-Cluster Theory and Its Applications for the Description of Biological Organisms

by Vyacheslav Theodorovich Volov

Entropy 2023, 25(10), 1433; https://doi.org/10.3390/e25101433 - 10 Oct 2023

Viewed by 690

Abstract

This article presents an overview of an alternative approach to the systematization and evolution of biological organisms on the basis of the fractal-cluster theory. It presents the foundations of the fractal-cluster theory for the self-organizing systems of the organism class. Static and dynamic [...] Read more.

This article presents an overview of an alternative approach to the systematization and evolution of biological organisms on the basis of the fractal-cluster theory. It presents the foundations of the fractal-cluster theory for the self-organizing systems of the organism class. Static and dynamic efficiency criteria based on the fractal-cluster relations and the analytical apparatus of nonequilibrium thermodynamics are presented. We introduce a highly sensitive static criterion, D, which determines the deviation in the value of the clusters and subclusters of the fractal-cluster system structures from their reference values. Other static criteria are the fractal-cluster entropy H and the free energy F of an organism. The dynamic criterion is based on Prigogine’s theorem and is determined by the second differential of the temporal trend of the fractal-cluster entropy H. By using simulations of the cluster variations for biological organisms in the (H, D, F)-space, the criteria for the fractal-cluster stochastics as well as for energy and evolution laws are obtained. The relationship between the traditional and fractal-cluster approaches for identifying an organism is discussed. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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51 pages, 2705 KiB

Open AccessArticle

Entropy of Charge Inversion in DNA including One-Loop Fluctuations

by Matthew D. Sievert, Marilyn F. Bishop and Tom McMullen

Entropy 2023, 25(10), 1373; https://doi.org/10.3390/e25101373 - 24 Sep 2023

Viewed by 832

Abstract

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in [...] Read more.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice gas model, each adsorption site is assumed to have either a vacancy or a positively charged dimer attached with the dimer oriented either parallel or perpendicular to the double-helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak-binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean-field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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13 pages, 4024 KiB

Open AccessArticle

Packaging of DNA Integrated with Metal Nanoparticles in Solution

by Nina Kasyanenko, Andrei Baryshev, Daria Artamonova and Petr Sokolov

Entropy 2023, 25(7), 1052; https://doi.org/10.3390/e25071052 - 12 Jul 2023

Viewed by 908

Abstract

The transformation of high-molecular DNA from a random swollen coil in a solution to a discrete nanosized particle with the ordered packaging of a rigid and highly charged double-stranded molecule is one of the amazing phenomena of polymer physics. DNA condensation is a [...] Read more.

The transformation of high-molecular DNA from a random swollen coil in a solution to a discrete nanosized particle with the ordered packaging of a rigid and highly charged double-stranded molecule is one of the amazing phenomena of polymer physics. DNA condensation is a well-known phenomenon in biological systems, yet its molecular mechanism is not clear. Understanding the processes occurring in vivo is necessary for the usage of DNA in the fabrication of new biologically significant nanostructures. Entropy plays a very important role in DNA condensation. DNA conjugates with metal nanoparticles are useful in various fields of nanotechnology. In particular, they can serve as a basis for creating multicomponent nanoplatforms for theranostics. DNA must be in a compact state in such constructions. In this paper, we tested the methods of DNA integration with silver, gold and palladium nanoparticles and analyzed the properties of DNA conjugates with metal nanoparticles using the methods of atomic force microscopy, spectroscopy, viscometry and dynamic light scattering. DNA size, stability and rigidity (persistence length), as well as plasmon resonance peaks in the absorption spectra of systems were studied. The methods for DNA condensation with metal nanoparticles were analyzed. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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12 pages, 2079 KiB

Open AccessArticle

Quantifying Information of Dynamical Biochemical Reaction Networks

by Zhiyuan Jiang, You-Hui Su and Hongwei Yin

Entropy 2023, 25(6), 887; https://doi.org/10.3390/e25060887 - 1 Jun 2023

Viewed by 1112

Abstract

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this [...] Read more.

A large number of complex biochemical reaction networks are included in the gene expression, cell development, and cell differentiation of in vivo cells, among other processes. Biochemical reaction-underlying processes are the ones transmitting information from cellular internal or external signaling. However, how this information is measured remains an open question. In this paper, we apply the method of information length, based on the combination of Fisher information and information geometry, to study linear and nonlinear biochemical reaction chains, respectively. Through a lot of random simulations, we find that the amount of information does not always increase with the length of the linear reaction chain; instead, the amount of information varies significantly when this length is not very large. When the length of the linear reaction chain reaches a certain value, the amount of information hardly changes. For nonlinear reaction chains, the amount of information changes not only with the length of this chain, but also with reaction coefficients and rates, and this amount also increases with the length of the nonlinear reaction chain. Our results will help to understand the role of the biochemical reaction networks in cells. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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14 pages, 4750 KiB

Open AccessArticle

A New Model of Hemoglobin Oxygenation

by Igor A. Lavrinenko, Gennady A. Vashanov, José L. Hernández Cáceres, Anatoly S. Buchelnikov and Yury D. Nechipurenko

Entropy 2022, 24(9), 1214; https://doi.org/10.3390/e24091214 - 30 Aug 2022

Cited by 4 | Viewed by 2807

Abstract

The study of hemoglobin oxygenation, starting from the classical works of Hill, has laid the foundation for molecular biophysics. The cooperative nature of oxygen binding to hemoglobin has been variously described in different models. In the Adair model, which better fits the experimental [...] Read more.

The study of hemoglobin oxygenation, starting from the classical works of Hill, has laid the foundation for molecular biophysics. The cooperative nature of oxygen binding to hemoglobin has been variously described in different models. In the Adair model, which better fits the experimental data, the constants of oxygen binding at various stages differ. However, the physical meaning of the parameters in this model remains unclear. In this work, we applied Hill’s approach, extending its interpretation; we obtained a good agreement between the theory and the experiment. The equation in which the Hill coefficient is modulated by the Lorentz distribution for oxygen partial pressure approximates the experimental data better than not only the classical Hill equation, but also the Adair equation. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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Review

Jump to: Research

15 pages, 2398 KiB

Open AccessFeature PaperReview

It’s Time for Entropic Clocks: The Roles of Random Chain Protein Sequences in Timing Ion Channel Processes Underlying Action Potential Properties

by Esraa Nsasra, Irit Dahan, Jerry Eichler and Ofer Yifrach

Entropy 2023, 25(9), 1351; https://doi.org/10.3390/e25091351 - 17 Sep 2023

Cited by 1 | Viewed by 994

Abstract

In recent years, it has become clear that intrinsically disordered protein segments play diverse functional roles in many cellular processes, thus leading to a reassessment of the classical structure–function paradigm. One class of intrinsically disordered protein segments is entropic clocks, corresponding to unstructured [...] Read more.

In recent years, it has become clear that intrinsically disordered protein segments play diverse functional roles in many cellular processes, thus leading to a reassessment of the classical structure–function paradigm. One class of intrinsically disordered protein segments is entropic clocks, corresponding to unstructured random protein chains involved in timing cellular processes. Such clocks were shown to modulate ion channel processes underlying action potential generation, propagation, and transmission. In this review, we survey the role of entropic clocks in timing intra- and inter-molecular binding events of voltage-activated potassium channels involved in gating and clustering processes, respectively, and where both are known to occur according to a similar ‘ball and chain’ mechanism. We begin by delineating the thermodynamic and timing signatures of a ‘ball and chain’-based binding mechanism involving entropic clocks, followed by a detailed analysis of the use of such a mechanism in the prototypical Shaker voltage-activated K⁺ channel model protein, with particular emphasis on ion channel clustering. We demonstrate how ‘chain’-level alternative splicing of the Kv channel gene modulates entropic clock-based ‘ball and chain’ inactivation and clustering channel functions. As such, the Kv channel model system exemplifies how linkage between alternative splicing and intrinsic disorder enables the functional diversity underlying changes in electrical signaling. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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37 pages, 1441 KiB

Open AccessReview

The Entropy of Entropy: Are We Talking about the Same Thing?

by Søren Nors Nielsen and Felix Müller

Entropy 2023, 25(9), 1288; https://doi.org/10.3390/e25091288 - 1 Sep 2023

Cited by 3 | Viewed by 1644

Abstract

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on “thermodynamics in ecology” revealed huge variation in [...] Read more.

In the last few decades, the number of published papers that include search terms such as thermodynamics, entropy, ecology, and ecosystems has grown rapidly. Recently, background research carried out during the development of a paper on “thermodynamics in ecology” revealed huge variation in the understanding of the meaning and the use of some of the central terms in this field—in particular, entropy. This variation seems to be based primarily on the differing educational and scientific backgrounds of the researchers responsible for contributions to this field. Secondly, some ecological subdisciplines also seem to be better suited and applicable to certain interpretations of the concept than others. The most well-known seems to be the use of the Boltzmann–Gibbs equation in the guise of the Shannon–Weaver/Wiener index when applied to the estimation of biodiversity in ecology. Thirdly, this tendency also revealed that the use of entropy-like functions could be diverted into an area of statistical and distributional analyses as opposed to real thermodynamic approaches, which explicitly aim to describe and account for the energy fluxes and dissipations in the systems. Fourthly, these different ways of usage contribute to an increased confusion in discussions about efficiency and possible telos in nature, whether at the developmental level of the organism, a population, or an entire ecosystem. All the papers, in general, suffer from a lack of clear definitions of the thermodynamic functions used, and we, therefore, recommend that future publications in this area endeavor to achieve a more precise use of language. Only by increasing such efforts it is possible to understand and resolve some of the significant and possibly misleading discussions in this area. Full article

(This article belongs to the Special Issue Entropy in Biological Systems)

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