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Petelczyc M, Czechowski Z. Effect of nonlinearity and persistence on multiscale irreversibility, non-stationarity, and complexity of time series-Case of data generated by the modified Langevin model. CHAOS (WOODBURY, N.Y.) 2023; 33:2888088. [PMID: 37141570 DOI: 10.1063/5.0141160] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 04/15/2023] [Indexed: 05/06/2023]
Abstract
Stochastic models of a time series can take the form of a nonlinear equation and have a built-in memory mechanism. Generated time series can be characterized by measures of certain features, e.g., non-stationarity, irreversibility, irregularity, multifractality, and short/long-tail distribution. Knowledge of the relationship between the form of the model and features of data seems to be the key to model time series. The paper presents a systematic analysis of the multiscale behavior of selected measures of irreversibility, irregularity, and non-stationarity vs degree of nonlinearity and persistence. As a time series generator, the modified nonlinear Langevin equation with built-in persistence is adopted. The modes of nonlinearity are determined by one parameter and do not change the half-Gaussian form of the marginal distribution function. The expected direct dependencies (sometimes non-trivial) were found and explained using the simplicity of the model. It has been shown that the change in nonlinearity, although subjected to a strong constraint (the same marginal distribution), causes significant changes in the tested markers of irregularity and non-stationarity. However, a synergy of non-linearity and persistence is needed to induce greater changes in irreversibility.
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Affiliation(s)
- Monika Petelczyc
- Faculty of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
| | - Zbigniew Czechowski
- Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warsaw, Poland
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Entransy-Based Depletion Index and Its Application for Assessing Efficiency and Sustainability. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022. [DOI: 10.1007/s13369-022-07111-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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Abstract
Microbial growth is a clear example of organization and structure arising in nonequilibrium conditions. Due to the complexity of the microbial metabolic network, elucidating the fundamental principles governing microbial growth remains a challenge. Here, we present a systematic analysis of microbial growth thermodynamics, leveraging an extensive dataset on energy-limited monoculture growth. A consistent thermodynamic framework based on reaction stoichiometry allows us to quantify how much of the available energy microbes can efficiently convert into new biomass while dissipating the remaining energy into the environment and producing entropy. We show that dissipation mechanisms can be linked to the electron donor uptake rate, a fact leading to the central result that the thermodynamic efficiency is related to the electron donor uptake rate by the scaling law [Formula: see text] and to the growth yield by [Formula: see text] These findings allow us to rederive the Pirt equation from a thermodynamic perspective, providing a means to compute its coefficients, as well as a deeper understanding of the relationship between growth rate and yield. Our results provide rather general insights into the relation between mass and energy conversion in microbial growth with potentially wide application, especially in ecology and biotechnology.
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Zanin M, Papo D. Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1474. [PMID: 34828172 PMCID: PMC8622570 DOI: 10.3390/e23111474] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Revised: 11/04/2021] [Accepted: 11/06/2021] [Indexed: 11/25/2022]
Abstract
The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that "one size does not fit all", as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.
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Affiliation(s)
- Massimiliano Zanin
- Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - David Papo
- Department of Neuroscience and Rehabilitation, Section of Physiology, University of Ferrara, 44121 Ferrara, Italy;
- Fondazione Istituto Italiano di Tecnologia, 44121 Ferrara, Italy
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Palazzo P. Chemical and Mechanical Aspect of Entropy-Exergy Relationship. ENTROPY (BASEL, SWITZERLAND) 2021; 23:972. [PMID: 34441112 PMCID: PMC8394777 DOI: 10.3390/e23080972] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/23/2021] [Revised: 07/13/2021] [Accepted: 07/19/2021] [Indexed: 11/20/2022]
Abstract
The present research focuses the chemical aspect of entropy and exergy properties. This research represents the complement of a previous treatise already published and constitutes a set of concepts and definitions relating to the entropy-exergy relationship overarching thermal, chemical and mechanical aspects. The extended perspective here proposed aims at embracing physical and chemical disciplines, describing macroscopic or microscopic systems characterized in the domain of industrial engineering and biotechnologies. The definition of chemical exergy, based on the Carnot chemical cycle, is complementary to the definition of thermal exergy expressed by means of the Carnot thermal cycle. These properties further prove that the mechanical exergy is an additional contribution to the generalized exergy to be accounted for in any equilibrium or non-equilibrium phenomena. The objective is to evaluate all interactions between the internal system and external environment, as well as performances in energy transduction processes.
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Entropy Density Acceleration and Minimum Dissipation Principle: Correlation with Heat and Matter Transfer in Glucose Catabolism. ENTROPY 2018; 20:e20120929. [PMID: 33266653 PMCID: PMC7512517 DOI: 10.3390/e20120929] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Revised: 12/02/2018] [Accepted: 12/03/2018] [Indexed: 11/17/2022]
Abstract
The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine's minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration for a single cell is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells.
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Ashrafizadeh S. Thermodynamic paths for calculating energy balance in systems containing nanoparticles. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.05.013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Lucia U, Deisboeck TS. The importance of ion fluxes for cancer proliferation and metastasis: A thermodynamic analysis. J Theor Biol 2018; 445:1-8. [PMID: 29474857 DOI: 10.1016/j.jtbi.2018.02.019] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Accepted: 02/19/2018] [Indexed: 01/28/2023]
Abstract
Following a thermodynamic approach, we develop a new theoretical analysis of ion transfer across cell membranes. Supported also by experimental data from the literature, we highlight that ion channels determine the typical features of cancer cells, i.e. independence from growth-regulatory signals, avoidance of apoptosis, indefinite proliferative potential, and the capability of inducing angiogenesis. Specifically, we analyse how ion transport, with particular regards to Ca2+ fluxes, modulates cancer cell proliferation, and regulates cell cycle checkpoints. Finally, our analysis also suggests that in malignant tumours aerobic glycolysis is the more efficient metabolic process when taking the required solvent capacity into account.
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Affiliation(s)
- Umberto Lucia
- Dipartimento Energia "Galileo Ferraris", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | - Thomas S Deisboeck
- Department of Radiology, Harvard-MIT Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA.
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Rate of entropy model for irreversible processes in living systems. Sci Rep 2017; 7:9134. [PMID: 28831153 PMCID: PMC5567375 DOI: 10.1038/s41598-017-09530-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2017] [Accepted: 07/17/2017] [Indexed: 12/28/2022] Open
Abstract
In living systems, it is crucial to study the exchange of entropy that plays a fundamental role in the understanding of irreversible chemical reactions. However, there are not yet works able to describe in a systematic way the rate of entropy production associated to irreversible processes. Hence, here we develop a theoretical model to compute the rate of entropy in the minimum living system. In particular, we apply the model to the most interesting and relevant case of metabolic network, the glucose catabolism in normal and cancer cells. We show, (i) the rate of internal entropy is mainly due to irreversible chemical reactions, and (ii) the rate of external entropy is mostly correlated to the heat flow towards the intercellular environment. The future applications of our model could be of fundamental importance for a more complete understanding of self-renewal and physiopatologic processes and could potentially be a support for cancer detection.
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Lucia U, Ponzetto A. Thermodynamic considerations on Ca2+-induced biochemical reactions in living cells. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2015.12.034] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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Lucia U, Ponzetto A, Deisboeck TS. Constructal approach to cell membranes transport: Amending the 'Norton-Simon' hypothesis for cancer treatment. Sci Rep 2016; 6:19451. [PMID: 26822208 PMCID: PMC4731791 DOI: 10.1038/srep19451] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2015] [Accepted: 12/14/2015] [Indexed: 12/27/2022] Open
Abstract
To investigate biosystems, we propose a new thermodynamic concept that analyses ion, mass and energy flows across the cell membrane. This paradigm-shifting approach has a wide applicability to medically relevant topics including advancing cancer treatment. To support this claim, we revisit ‘Norton-Simon’ and evolving it from an already important anti-cancer hypothesis to a thermodynamic theorem in medicine. We confirm that an increase in proliferation and a reduction in apoptosis trigger a maximum of ATP consumption by the tumor cell. Moreover, we find that positive, membrane-crossing ions lead to a decrease in the energy used by the tumor, supporting the notion of their growth inhibitory effect while negative ions apparently increase the cancer’s consumption of energy hence reflecting a growth promoting impact. Our results not only represent a thermodynamic proof of the original Norton-Simon hypothesis but, more concretely, they also advance the clinically intriguing and experimentally testable, diagnostic hypothesis that observing an increase in negative ions inside a cell in vitro, and inside a diseased tissue in vivo, may indicate growth or recurrence of a tumor. We conclude with providing theoretical evidence that applying electromagnetic field therapy early on in the treatment cycle may maximize its anti-cancer efficacy.
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Affiliation(s)
- Umberto Lucia
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Antonio Ponzetto
- Department of Medical Sciences, University of Torino, Corso A.M. Dogliotti 14, 10126 Torino, Italy
| | - Thomas S Deisboeck
- Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Charlestown, MA 02129, USA.,ThinkMotu LLC, Wellesley, MA 02481, USA
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Abstract
BACKGROUND Cells are open complex thermodynamic systems. They can be also regarded as complex engines that execute a series of chemical reactions. Energy transformations, thermo-electro-chemical processes and transports phenomena can occur across the cells membranes. Moreover, cells can also actively modify their behaviours in relation to changes in their environment. METHODS Different thermo-electro-biochemical behaviours occur between health and disease states. But, all the living systems waste heat, which is no more than the result of their internal irreversibility. This heat is dissipated into the environment. But, this wasted heat represent also a sort of information, which outflows from the cell toward its environment, completely accessible to any observer. RESULTS The analysis of irreversibility related to this wasted heat can represent a new approach to study the behaviour of the cells themselves and to control their behaviours. So, this approach allows us to consider the living systems as black boxes and analyze only the inflows and outflows and their changes in relation to the modification of the environment. Therefore, information on the systems can be obtained by analyzing the changes in the cell heat wasted in relation to external perturbations. CONCLUSIONS The bioengineering thermodynamics bases are summarized and used to analyse possible controls of the calls behaviours based on the control of the ions fluxes across the cells membranes.
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Affiliation(s)
- Umberto Lucia
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
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On the Calculation of System Entropy in Nonlinear Stochastic Biological Networks. ENTROPY 2015. [DOI: 10.3390/e17106801] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Lucia U, Grazzini G, Montrucchio B, Grisolia G, Borchiellini R, Gervino G, Castagnoli C, Ponzetto A, Silvagno F. Constructal thermodynamics combined with infrared experiments to evaluate temperature differences in cells. Sci Rep 2015; 5:11587. [PMID: 26100383 PMCID: PMC4650705 DOI: 10.1038/srep11587] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2015] [Accepted: 05/27/2015] [Indexed: 11/26/2022] Open
Abstract
The aim of this work was to evaluate differences in energy flows between normal and immortalized cells when these distinct biological systems are exposed to environmental stimulation. These differences were considered using a constructal thermodynamic approach, and were subsequently verified experimentally. The application of constructal law to cell analysis led to the conclusion that temperature differences between cells with distinct behaviour can be amplified by interaction between cells and external fields. Experimental validation of the principle was carried out on two cellular models exposed to electromagnetic fields. By infrared thermography we were able to assess small changes in heat dissipation measured as a variation in cell internal energy. The experimental data thus obtained are in agreement with the theoretical calculation, because they show a different thermal dispersion pattern when normal and immortalized cells are exposed to electromagnetic fields. By using two methods that support and validate each other, we have demonstrated that the cell/environment interaction can be exploited to enhance cell behavior differences, in particular heat dissipation. We propose infrared thermography as a technique effective in discriminating distinct patterns of thermal dispersion and therefore able to distinguish a normal phenotype from a transformed one.
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Affiliation(s)
- Umberto Lucia
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Giuseppe Grazzini
- Dipartimento di Ingegneria Industriale, Università di Firenze, Via Santa Marta 3, 50139 Firenze, Italy
| | - Bartolomeo Montrucchio
- Dipartimento di Automatica e Informatica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Giulia Grisolia
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Romano Borchiellini
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Gianpiero Gervino
- Dipartimento di Fisica, Università di Torino, via P. Giuria 1, 10125 Torino, Italy
| | - Carlotta Castagnoli
- Dipartimento di Chirurgia Generale e Specialistiche, Banca della Cute, AOU Città della Salute e della Scienza Torino, Via Zuretti 29, 10126 Torino
| | - Antonio Ponzetto
- Dipartimento di Scienze Mediche, Università di Torino, corso A.M. Dogliotti 14, 10126 Torino
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A Link between Nano- and Classical Thermodynamics: Dissipation Analysis (The Entropy Generation Approach in Nano-Thermodynamics). ENTROPY 2015. [DOI: 10.3390/e17031309] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Lucia U, Ponzetto A, Deisboeck TS. A thermo-physical analysis of the proton pump vacuolar-ATPase: the constructal approach. Sci Rep 2014; 4:6763. [PMID: 25342534 PMCID: PMC4208057 DOI: 10.1038/srep06763] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2014] [Accepted: 10/07/2014] [Indexed: 01/23/2023] Open
Abstract
Pumping protons across a membrane was a critical step at the origin of life on earth, and it is still performed in all living organisms, including in human cells. Proton pumping is paramount to keep normal cells alive, e.g. for lysosomal digestion and for preparing peptides for immune recognition, but it goes awry in cancer cells. They acidify their microenvironment hence membrane voltage is lowered, which in turn induces cell proliferation, a hallmark of cancer. Proton pumping is achieved by means of rotary motors, namely vacuolar ATPases (V-ATPase), which are present at many of the multiple cellular interfaces. Therefore, we undertook an examination of the thermodynamic properties of V-ATPases. The principal result is that the V-ATPase-mediated control of the cell membrane potential and the related and consequent environmental pH can potentially represent a valuable support strategy for anticancer therapies. A constructal theory approach is used as a new viewpoint to study how V-ATPase can be modulated for therapeutic purposes. In particular, V-ATPase can be regulated by using external fields, such as electromagnetic fields, and a theoretical approach has been introduced to quantify the appropriate field strength and frequency for this new adjuvant therapeutic strategy.
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Affiliation(s)
- Umberto Lucia
- Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Antonio Ponzetto
- Department of Medical Sciences, University of Torino, Corso A.M. Dogliotti 14, 10126 Torino, Italy
| | - Thomas S. Deisboeck
- Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Charlestown, MA 02129, USA
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