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Statistical mechanics in biology: how ubiquitous are long-range correlations?

Author

Listed:
  • Stanley, H.E.
  • Buldyrev, S.V.
  • Goldberger, A.L.
  • Goldberger, Z.D.
  • Havlin, S.
  • Mantegna, R.N.
  • Ossadnik, S.M.
  • Peng, C.-K.
  • Simons, M.

Abstract

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent α characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 104 heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range “anti-correlations” (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain “constancy,” should be extended to account for this type of dynamical, far from equilibrium, behavior.

Suggested Citation

  • Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Goldberger, Z.D. & Havlin, S. & Mantegna, R.N. & Ossadnik, S.M. & Peng, C.-K. & Simons, M., 1994. "Statistical mechanics in biology: how ubiquitous are long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 214-253.
    • Handle: RePEc:eee:phsmap:v:205:y:1994:i:1:p:214-253
    DOI: 10.1016/0378-4371(94)90502-9
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    Cited by:

    1. Chiarucci, Riccardo & Ruzzenenti, Franco & Loffredo, Maria I., 2014. "Detecting spatial homogeneity in the World Trade Web with Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 1-7.
    2. Staudacher, M. & Telser, S. & Amann, A. & Hinterhuber, H. & Ritsch-Marte, M., 2005. "A new method for change-point detection developed for on-line analysis of the heart beat variability during sleep," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 582-596.
    3. Peng, C.-K. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Mantegna, R.N. & Simons, M. & Stanley, H.E., 1995. "Statistical properties of DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 180-192.
    4. Frank Emmert-Streib, 2013. "Structural Properties and Complexity of a New Network Class: Collatz Step Graphs," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-14, February.
    5. Cizeau, Pierre & Liu, Yanhui & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Volatility distribution in the S&P500 stock index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 441-445.
    6. Podobnik, Boris & Ivanov, Plamen Ch. & Grosse, Ivo & Matia, Kaushik & Eugene Stanley, H., 2004. "ARCH–GARCH approaches to modeling high-frequency financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 216-220.
    7. Liu, Yanhui & Cizeau, Pierre & Meyer, Martin & Peng, C.-K. & Eugene Stanley, H., 1997. "Correlations in economic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 437-440.
    8. Riccardo Chiarucci & Franco Ruzzenenti & Maria I. Loffredo, 2013. "Detecting spatial homogeneity in the world trade web with Detrended Fluctuation Analysis," Papers 1308.0526, arXiv.org, revised Nov 2013.
    9. Alvarez-Ramirez, Jose & Espinosa-Paredes, Gilberto & Vazquez, Alejandro, 2005. "Detrended fluctuation analysis of the neutronic power from a nuclear reactor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 227-240.
    10. Buldyrev, S.V. & Dokholyan, N.V. & Goldberger, A.L. & Havlin, S. & Peng, C.-K. & Stanley, H.E. & Viswanathan, G.M., 1998. "Analysis of DNA sequences using methods of statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 249(1), pages 430-438.
    11. Cannon, Michael J. & Percival, Donald B. & Caccia, David C. & Raymond, Gary M. & Bassingthwaighte, James B., 1997. "Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 241(3), pages 606-626.
    12. Vitanov, Nikolay K. & Yankulova, Elka D., 2006. "Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 768-775.
    13. Silva, R. & Silva, J.R.P. & Anselmo, D.H.A.L. & Alcaniz, J.S. & da Silva, W.J.C. & Costa, M.O., 2020. "An alternative description of power law correlations in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. Koscielny-Bunde, Eva & Bunde, Armin & Havlin, Shlomo & Goldreich, Yair, 1996. "Analysis of daily temperature fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 393-396.
    15. Ortiz-Tánchez, Eduardo & Ebeling, Werner & Lanius, Karl, 2002. "MEI, SOI and mid-range correlations in the onset of El Niño–Southern Oscillation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 509-520.
    16. Urbanowicz, Krzysztof & Kantz, Holger & Holyst, Janusz A., 2005. "Anti-deterministic behaviour of discrete systems that are less predictable than noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 189-198.
    17. Vandewalle, N. & Ausloos, M., 1997. "Coherent and random sequences in financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 454-459.
    18. Oikonomou, Thomas & Kaloudis, Konstantinos & Bagci, G. Baris, 2021. "The q-exponentials do not maximize the Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    19. Karakatsanis, L.P. & Pavlos, G.P. & Iliopoulos, A.C. & Pavlos, E.G. & Clark, P.M. & Duke, J.L. & Monos, D.S., 2018. "Assessing information content and interactive relationships of subgenomic DNA sequences of the MHC using complexity theory approaches based on the non-extensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 77-93.
    20. Zebende, G.F. & Pereira, M.G. & Nogueira Jr., E. & Moret, M.A., 2005. "Universal persistence in astrophysical sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 452-458.
    21. Bertrand M. Roehner, 2010. "Fifteen years of econophysics: worries, hopes and prospects," Papers 1004.3229, arXiv.org.
    22. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.

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