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Gao B, Li L, Peng H, Kurths J, Zhang W, Yang Y. Principle for performing attractor transits with single control in Boolean networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062706. [PMID: 24483485 DOI: 10.1103/physreve.88.062706] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2013] [Revised: 09/12/2013] [Indexed: 06/03/2023]
Abstract
We present an algebraic approach to reveal attractor transitions in Boolean networks under single control based on the recently developed matrix semitensor product theory. In this setting, the reachability of attractors is estimated by the state transition matrices. We then propose procedures that compute the shortest control sequence and the result of each step of input (control) exactly. The general derivation is exemplified by numerical simulations for two kinds of gene regulation networks, the protein-nucleic acid interactions network and the cAMP receptor of Dictyostelium discoideum network.
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Affiliation(s)
- Bo Gao
- School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China and Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China and School of Computer Information management, Inner Mongolia University of Finance and Economics, Hohhot 010051, China
| | - Lixiang Li
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Haipeng Peng
- Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam D-14473, Germany
| | - Wenguang Zhang
- College of Animal Science, Inner Mongolia Agricultural University, Hohhot 010018, China
| | - Yixian Yang
- School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China and Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
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Aoki H, Kaneko K. Slow stochastic switching by collective chaos of fast elements. PHYSICAL REVIEW LETTERS 2013; 111:144102. [PMID: 24138241 DOI: 10.1103/physrevlett.111.144102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2013] [Indexed: 06/02/2023]
Abstract
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic limit. The dynamics without the limit are found to be represented by stochastic switching over these branches mediated by the collective chaos of the fast elements, while the switching frequency shows a complicated dependence on the ratio of the two time scales with some resonance structure. The ubiquity of the phenomena in the slow-fast dynamics is also discussed.
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Affiliation(s)
- Hidetoshi Aoki
- Research Center for Complex Systems Biology, Graduate School of Arts and Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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Villarreal C, Padilla-Longoria P, Alvarez-Buylla ER. General theory of genotype to phenotype mapping: derivation of epigenetic landscapes from N-node complex gene regulatory networks. PHYSICAL REVIEW LETTERS 2012; 109:118102. [PMID: 23005679 DOI: 10.1103/physrevlett.109.118102] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2011] [Indexed: 05/23/2023]
Abstract
We propose a systematic methodology to construct a probabilistic epigenetic landscape of cell-fate attainment associated with N-node Boolean genetic regulatory networks. The general derivation proposed here is exemplified with an Arabidopsis thaliana network underlying floral organ determination grounded on qualitative experimental data.
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Affiliation(s)
- Carlos Villarreal
- Instituto de Física, Universidad Nacional Autónoma de México, D.F. México, Mexico
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CHEN AIMIN, ZHANG JIAJUN, YUAN ZHANJIANG, ZHOU TIANSHOU. NOISE-INDUCED ALTERNATIVE RESPONSE IN MAP KINASE PATHWAYS WITH MUTUAL INHIBITION. J BIOL SYST 2011. [DOI: 10.1142/s021833900900282x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
All organisms have the ability to detect and respond to changes in the environment for survival, and as a result, specific cellular signaling pathways have evolved by which organisms sense their environment and respond to signals that they detect. However, an important unsolved problem in cell biology is to understand how specificity from signal to cellular response is maintained between different signal transduction pathways that share similar or identical components. Here, we show, using mathematical and computational modeling, that two typical signaling pathways in a single cell, hyperosmolar and pheromone motigen-avtivated protein kinase in the yeast Saccharomyces cerevisiae with mutual inhibition, can respond alternatively to two costimulated signals in a stochastically fluctuated environment. Within a bistable region over two input signals, noise plays an essential role in achieving specificity of response, while outside it, these pathways achieve specificity by filtering out spurious crosstalk through mutual inhibition.
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Affiliation(s)
- AIMIN CHEN
- School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
| | - JIAJUN ZHANG
- School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
| | - ZHANJIANG YUAN
- School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
| | - TIANSHOU ZHOU
- School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
- State Key Laboratory of Biocontrol and Guangzhou Center for Bioinformatics, School of Life Science, Sun Yat-Sen University, Guangzhou, 510275, China
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Wolf DM, Fontaine-Bodin L, Bischofs I, Price G, Keasling J, Arkin AP. Memory in microbes: quantifying history-dependent behavior in a bacterium. PLoS One 2008; 3:e1700. [PMID: 18324309 PMCID: PMC2264733 DOI: 10.1371/journal.pone.0001700] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2007] [Accepted: 01/28/2008] [Indexed: 11/19/2022] Open
Abstract
Memory is usually associated with higher organisms rather than bacteria. However, evidence is mounting that many regulatory networks within bacteria are capable of complex dynamics and multi-stable behaviors that have been linked to memory in other systems. Moreover, it is recognized that bacteria that have experienced different environmental histories may respond differently to current conditions. These “memory” effects may be more than incidental to the regulatory mechanisms controlling acclimation or to the status of the metabolic stores. Rather, they may be regulated by the cell and confer fitness to the organism in the evolutionary game it participates in. Here, we propose that history-dependent behavior is a potentially important manifestation of memory, worth classifying and quantifying. To this end, we develop an information-theory based conceptual framework for measuring both the persistence of memory in microbes and the amount of information about the past encoded in history-dependent dynamics. This method produces a phenomenological measure of cellular memory without regard to the specific cellular mechanisms encoding it. We then apply this framework to a strain of Bacillus subtilis engineered to report on commitment to sporulation and degradative enzyme (AprE) synthesis and estimate the capacity of these systems and growth dynamics to ‘remember’ 10 distinct cell histories prior to application of a common stressor. The analysis suggests that B. subtilis remembers, both in short and long term, aspects of its cell history, and that this memory is distributed differently among the observables. While this study does not examine the mechanistic bases for memory, it presents a framework for quantifying memory in cellular behaviors and is thus a starting point for studying new questions about cellular regulation and evolutionary strategy.
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Affiliation(s)
- Denise M. Wolf
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- * To whom correspondence should be addressed. E-mail: (DW); (AA)
| | - Lisa Fontaine-Bodin
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Bioengineering, University of California, Berkeley, California, United States of America
| | - Ilka Bischofs
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Bioengineering, University of California, Berkeley, California, United States of America
| | - Gavin Price
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Bioengineering, University of California, Berkeley, California, United States of America
| | - Jay Keasling
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Bioengineering, University of California, Berkeley, California, United States of America
- Department of Chemical Engineering, University of California, Berkeley, California, United States of America
| | - Adam P. Arkin
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Bioengineering, University of California, Berkeley, California, United States of America
- * To whom correspondence should be addressed. E-mail: (DW); (AA)
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Wackerbauer R, Kobayashi S. Noise can delay and advance the collapse of spatiotemporal chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:066209. [PMID: 17677342 DOI: 10.1103/physreve.75.066209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2006] [Revised: 02/12/2007] [Indexed: 05/16/2023]
Abstract
Spatiotemporal chaos on a regular ring network of excitable Gray-Scott dynamical elements collapses to a stable asymptotic state. We find that the addition of dynamical noise clearly influences the spatiotemporal pattern and the transient lifetime of spatiotemporal chaos. Spatially uniform noise significantly decreases the average lifetime of spatiotemporal chaos due to an enlargement of regions of local collapse. For spatially inhomogeneous noise the collapse is maximally delayed at an intermediate noise level, but drastically advanced for larger noise levels.
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Affiliation(s)
- Renate Wackerbauer
- Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920, USA.
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Kashiwagi A, Urabe I, Kaneko K, Yomo T. Adaptive response of a gene network to environmental changes by fitness-induced attractor selection. PLoS One 2006; 1:e49. [PMID: 17183678 PMCID: PMC1762378 DOI: 10.1371/journal.pone.0000049] [Citation(s) in RCA: 113] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2006] [Accepted: 10/11/2006] [Indexed: 11/19/2022] Open
Abstract
Cells switch between various stable genetic programs (attractors) to accommodate environmental conditions. Signal transduction machineries efficiently convey environmental changes to the gene regulation apparatus in order to express the appropriate genetic program. However, since the number of environmental conditions is much larger than that of available genetic programs so that the cell may utilize the same genetic program for a large set of conditions, it may not have evolved a signaling pathway for every environmental condition, notably those that are rarely encountered. Here we show that in the absence of signal transduction, switching to the appropriate attractor state expressing the genes that afford adaptation to the external condition can occur. In a synthetic bistable gene switch in Escherichia coli in which mutually inhibitory operons govern the expression of two genes required in two alternative nutritional environments, cells reliably selected the “adaptive attractor” driven by gene expression noise. A mathematical model suggests that the “non-adaptive attractor” is avoided because in unfavorable conditions, cellular activity is lower, which suppresses mRNA metabolism, leading to larger fluctuations in gene expression. This, in turn, renders the non-adaptive state less stable. Although attractor selection is not as efficient as signal transduction via a dedicated cascade, it is simple and robust, and may represent a primordial mechanism for adaptive responses that preceded the evolution of signaling cascades for the frequently encountered environmental changes.
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Affiliation(s)
- Akiko Kashiwagi
- Department of Bioinformatics Engineering, Graduate School of Information Science and Technology, Osaka UniversitySuita, Osaka, Japan
| | - Itaru Urabe
- Department of Biotechnology, Graduate School of Engineering, Osaka UniversitySuita, Osaka, Japan
| | - Kunihiko Kaneko
- Graduate School of Frontier Biosciences, Osaka UniversitySuita, Osaka, Japan
- Department of Pure and Applied Sciences, The University of TokyoTokyo, Japan
- Complex Systems Biology Project, Exploratory Research for Advanced Technology, Japan Science and Technology Agency, The University of TokyoTokyo, Japan
| | - Tetsuya Yomo
- Department of Bioinformatics Engineering, Graduate School of Information Science and Technology, Osaka UniversitySuita, Osaka, Japan
- Graduate School of Frontier Biosciences, Osaka UniversitySuita, Osaka, Japan
- Complex Systems Biology Project, Exploratory Research for Advanced Technology, Japan Science and Technology Agency, Osaka UniversitySuita, Osaka, Japan
- * To whom correspondence should be addressed. E-mail:
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