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Balcerzak T. Application of the integral operator method for multispin correlation function calculations in the one-dimensional Ising model. Phys Rev E 2024; 109:024133. [PMID: 38491711 DOI: 10.1103/physreve.109.024133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 02/05/2024] [Indexed: 03/18/2024]
Abstract
The one-dimensional (1D) Ising model is revisited. The integral operator method is used for the model to derive the general statistical identity for multispin correlation functions. As an application of this identity to generate various correlations, recursive formulas are derived for the correlations of pairs, threes, fours, and fives of spins. Both compact clusters and disjoint sets of spins are considered. It is shown that multispin correlations for the 1D Ising model can be exactly expressed in terms of pairwise correlations using recursive procedures. For clusters with different structures, numerical calculations of multispin correlations as a function of temperature and external magnetic field are performed. The results of these calculations are presented in the figures and discussed.
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Affiliation(s)
- T Balcerzak
- Department of Solid State Physics, Faculty of Physics and Applied Informatics, University of Łódź, ulica Pomorska 149/153, 90-236 Łódź, Poland
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2
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Costa MO, Silva R, Anselmo DHAL. Superstatistical and DNA sequence coding of the human genome. Phys Rev E 2022; 106:064407. [PMID: 36671113 DOI: 10.1103/physreve.106.064407] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 11/16/2022] [Indexed: 12/14/2022]
Abstract
In this work, by considering superstatistics we investigate the short-range correlations (SRCs) and the fluctuations in the distribution of lengths of strings of nucleotides. To this end, a stochastic model provides the distributions of the size of the exons based on the q-Gamma and inverse q-Gamma distributions. Specifically, we define a time series for exon sizes to investigate the SRC and the fluctuations through the superstatistics distributions. To test the model's viability, we use the Project Ensembl database of genes to extract the time evolution of exon sizes, calculated in terms of the number of base pairs (bp) in these biological databases. Our findings show that, depending on the chromosome, both distributions are suitable for describing the length distribution of human DNA for lengths greater than 10 bp. In addition, we used Bayesian statistics to perform a selection model approach, which revealed weak evidence for the inverse q-Gamma distribution for a considerable number of chromosomes.
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Affiliation(s)
- M O Costa
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil
| | - R Silva
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil and Programa de Pós-Graduação em Física, Universidade do Estado do Rio Grande do Norte, Mossoró - Rio Grande do Norte, 59610-210, Brasil
| | - D H A L Anselmo
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil and Programa de Pós-Graduação em Física, Universidade do Estado do Rio Grande do Norte, Mossoró - Rio Grande do Norte, 59610-210, Brasil
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3
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de Lima MMF, Anselmo DHAL, Silva R, Nunes GHS, Fulco UL, Vasconcelos MS, Mello VD. A Bayesian Analysis of Plant DNA Length Distribution via κ-Statistics. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1225. [PMID: 36141111 PMCID: PMC9497530 DOI: 10.3390/e24091225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 08/29/2022] [Accepted: 08/31/2022] [Indexed: 06/16/2023]
Abstract
We report an analysis of the distribution of lengths of plant DNA (exons). Three species of Cucurbitaceae were investigated. In our study, we used two distinct κ distribution functions, namely, κ-Maxwellian and double-κ, to fit the length distributions. To determine which distribution has the best fitting, we made a Bayesian analysis of the models. Furthermore, we filtered the data, removing outliers, through a box plot analysis. Our findings show that the sum of κ-exponentials is the most appropriate to adjust the distribution curves and that the values of the κ parameter do not undergo considerable changes after filtering. Furthermore, for the analyzed species, there is a tendency for the κ parameter to lay within the interval (0.27;0.43).
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Affiliation(s)
- Maxsuel M. F. de Lima
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Natal 59072-970, RN, Brazil
| | - Dory H. A. L. Anselmo
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Natal 59072-970, RN, Brazil
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59072-970, RN, Brazil
| | - Raimundo Silva
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Natal 59072-970, RN, Brazil
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59072-970, RN, Brazil
| | - Glauber H. S. Nunes
- Departamento de Ciências Vegetais, Universidade Federal Rural do Semi-Árido, Mossoró 59625-900, RN, Brazil
| | - Umberto L. Fulco
- Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, Natal 59072-970, RN, Brazil
| | - Manoel S. Vasconcelos
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59072-970, RN, Brazil
| | - Vamberto D. Mello
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Natal 59072-970, RN, Brazil
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Ancona M, Michieletto D, Marenduzzo D. Competition between local erasure and long-range spreading of a single biochemical mark leads to epigenetic bistability. Phys Rev E 2021; 101:042408. [PMID: 32422714 DOI: 10.1103/physreve.101.042408] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Accepted: 02/19/2020] [Indexed: 11/07/2022]
Abstract
The mechanism through which cells determine their fate is intimately related to the spreading of certain biochemical (so-called epigenetic) marks along their genome. The mechanisms behind mark spreading and maintenance are not yet fully understood, and current models often assume a long-range infectionlike process for the dynamics of marks, due to the polymeric nature of the chromatin fiber which allows looping between distant sites. While these existing models typically consider antagonizing marks, here we propose a qualitatively different scenario which analyses the spreading of a single mark. We define a one-dimensional stochastic model in which mark spreading/infection occurs as a long-range process whereas mark erasure/recovery is a local process, with an enhanced rate at boundaries of infected domains. In the limiting case where our model exhibits absorbing states, we find a first-order-like transition separating the marked/infected phase from the unmarked/recovered phase. This suggests that our model, in this limit, belongs to the long-range compact directed percolation universality class. The abrupt nature of the transition is retained in a more biophysically realistic situation when a basal infection/recovery rate is introduced (thereby removing absorbing states). Close to the transition there is a range of bistability where both the marked/infected and unmarked/recovered states are metastable and long lived, which provides a possible avenue for controlling fate decisions in cells. Increasing the basal infection/recovery rate, we find a second transition between a coherent (marked or unmarked) phase, and a mixed, or random, one.
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Affiliation(s)
- Marco Ancona
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom.,MRC Human Genetics Unit, Institute of Genetics and Molecular Medicine, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom.,Centre for Mathematical Biology, and Department of Mathematical Sciences, University of Bath, North Road, Bath BA2 7AY, United Kingdom
| | - Davide Marenduzzo
- SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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Krishnan J, Torabi R, Schuppert A, Napoli ED. A modified Ising model of Barabási-Albert network with gene-type spins. J Math Biol 2020; 81:769-798. [PMID: 32897406 PMCID: PMC7519008 DOI: 10.1007/s00285-020-01518-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 05/02/2020] [Indexed: 12/30/2022]
Abstract
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.
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Affiliation(s)
- Jeyashree Krishnan
- Aachen Institute for Advanced Study in Computational Engineering Science (AICES) Graduate School, RWTH Aachen University, Aachen, Germany. .,Joint Research Center for Computational Biomedicine (JRC-Combine), RWTH Aachen University, Aachen, Germany.
| | - Reza Torabi
- Department of Physics and Astronomy, University of Calgary, Calgary, AB, Canada
| | - Andreas Schuppert
- Aachen Institute for Advanced Study in Computational Engineering Science (AICES) Graduate School, RWTH Aachen University, Aachen, Germany.,Joint Research Center for Computational Biomedicine (JRC-Combine), RWTH Aachen University, Aachen, Germany
| | - Edoardo Di Napoli
- Aachen Institute for Advanced Study in Computational Engineering Science (AICES) Graduate School, RWTH Aachen University, Aachen, Germany.,Jülich Supercomputing Center, Forschungszentrum Jülich, Jülich, Germany
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Anvari Z, Masoodi HR, Bagheri S. DFT simulation of Watson–Crick-like guanine–thymine mismatch in quaternary systems involving DNA bases. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1686149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Zahra Anvari
- Faculty of Science, Department of Chemistry, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
| | - Hamid Reza Masoodi
- Faculty of Science, Department of Chemistry, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
| | - Sotoodeh Bagheri
- Faculty of Science, Department of Chemistry, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
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7
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Costa MO, Silva R, Anselmo DHAL, Silva JRP. Analysis of human DNA through power-law statistics. Phys Rev E 2019; 99:022112. [PMID: 30934358 DOI: 10.1103/physreve.99.022112] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2018] [Indexed: 11/07/2022]
Abstract
We report an analysis of Homo sapiens DNA through the formalism of κ statistics, which encompasses power-law correlations and provides an optimization principle that permits us to model distinct physical systems; i.e., the power-law distribution of the length of DNA bases is calculated from a general model which follows arguments similar to those proposed in Maxwell's deduction of statistical distributions. The viability of the model is tested using a data set from a catalog of proteins collected from the Ensembl Project. The results indicate that the short-range correlations, always present in coding DNA sequences, are appropriately captured through the Kaniadakis power-law distribution, adequately describing the cumulative length distribution of DNA bases, in contrast with the case of the traditional exponential statistical model.
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Affiliation(s)
- M O Costa
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Mossoró, 59610-210, Brazil
| | - R Silva
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Mossoró, 59610-210, Brazil.,Universidade Federal do Rio Grande do Norte, Departamento de Física, Natal-RN, 59072-970, Brazil
| | - D H A L Anselmo
- Universidade Federal do Rio Grande do Norte, Departamento de Física, Natal-RN, 59072-970, Brazil
| | - J R P Silva
- Departamento de Física, Universidade do Estado do Rio Grande do Norte, Mossoró, 59610-210, Brazil
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Metze K, Adam R, Florindo JB. The fractal dimension of chromatin - a potential molecular marker for carcinogenesis, tumor progression and prognosis. Expert Rev Mol Diagn 2019; 19:299-312. [DOI: 10.1080/14737159.2019.1597707] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Konradin Metze
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - Randall Adam
- Department of Pathology, Faculty of Medical Sciences, State University of Campinas (UNICAMP), Campinas, Brazil
| | - João Batista Florindo
- Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, Brazil
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Papale A, Rosa A. The Ising model in swollen vs. compact polymers: Mean-field approach and computer simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:144. [PMID: 30552518 DOI: 10.1140/epje/i2018-11752-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 11/09/2018] [Indexed: 06/09/2023]
Abstract
We study the properties of the classical Ising model with nearest-neighbor interaction for spins located at the monomers of long polymer chains in 2 and 3 dimensions. We compare results for two ensembles of polymers with very different single chain properties: 1) swollen, self-avoiding linear polymer chains in good solvent conditions and 2) compact, space-filling randomly branching polymers in melt. By employing a mean-field approach and Monte Carlo computer simulations, we show that swollen polymers cannot sustain an ordered phase. On the contrary, compact polymers may indeed produce an observable phase transition. Finally, we briefly consider the statistical properties of the ordered phase by comparing polymer chains within the same universality class but characterized by very different shapes.
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Affiliation(s)
- Andrea Papale
- Sissa (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italy
| | - Angelo Rosa
- Sissa (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136, Trieste, Italy.
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