Journal of Systems Science and Complexity

, Volume 32, Issue 2, pp 510–525 | Cite as

Energy Cost and Mean Dwell Times for the Activity of Promoter with Complex Structure

  • Qingqing Li
  • Anwarud Din
  • Tianshou ZhouEmail author


Regulatory molecules present on the core promoter of a gene interact often in a dynamic, highly combinatorial and possibly energy-dependent manner, leading to complex promoter structure and even complex global dynamics. The authors analyze dynamics of an arbitrarily complex promoter from the view of thermodynamics combined with statistic physics. First, the authors formulize transcription factors-mediated promoter kinetics in terms of energy. Then, the authors analyze energetic cost in several representative cases of promoter structure, deriving useful analytical results. Third, the authors derive analytical expressions for mean dwell times of the promoter activity states, experimentally measurable quantities related to the energy cost of promoter dynamics. The overall framework lays a theoretical foundation for analysis of complex promoter kinetics and gene expression dynamics.


Energetic cost master equation mean dwell time promoter kinetics regulation 


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  1. [1]
    Vilar J M G and Saiz L, CplexA: A mathematica package to study macromolecular-assembly control of gene expression, Bioinformatics, 2010, 26: 2060–2061.CrossRefGoogle Scholar
  2. [2]
    Hornung G, Bar-Ziv R, Rosin D, et al., Noise-mean relationship in mutated promoters, Genome Research, 2012, 22: 2409–2417.CrossRefGoogle Scholar
  3. [3]
    Halme A, Bumgarner S, Styles C, et al., Genetic and epigenetic regulation of the FLO gene family generates cell-surface variation in yeast, Cell, 2004, 116: 405–415.CrossRefGoogle Scholar
  4. [4]
    Octavio L M, Gedeon K, and Maheshri N, Epigenetic and conventional regulation is distributed among activators of FLO11 allowing tuning of population-level heterogeneity in its expression, PLoS Genetics, 2009, 5: e1000673.Google Scholar
  5. [5]
    Weinberger L, Voichek Y, Tirosh I, et al., Expression noise and acetylation profiles distinguish HDAC functions, Molecular Cell, 2012, 47: 193–202.CrossRefGoogle Scholar
  6. [6]
    Eldar A and Elowitz M B, Functional roles for noise in genetic circuits, Nature, 2010, 467: 167–173.CrossRefGoogle Scholar
  7. [7]
    McNally J, Müller W, Walker D, et al., The glucocorticoid receptor: rapid exchange with regulatory sites in living cells, Science, 2000, 287: 1262–1265.CrossRefGoogle Scholar
  8. [8]
    Becker M, Baumann C, John S, et al., Dynamic behavior of transcription factors on a natural promoter in living cells, EMBO Reports, 2002, 3: 1188–1194.CrossRefGoogle Scholar
  9. [9]
    Phair R, Scaffdi P, Elbi C, et al., Global nature of dynamic protein-chromatin interactions in vivo: Three-dimensional genome scanning and dynamic interaction networks of chromatin proteins, Molecule Cell Biology, 2004, 24: 6393–6402.CrossRefGoogle Scholar
  10. [10]
    Karpova T S, Kim M J, Spriet C, et al., Concurrent fast and slow cycling of a transcriptional activator at an endogenous promoter, Science, 2008, 319: 466–469.CrossRefGoogle Scholar
  11. [11]
    Shang Y, Hu X, DiRenzo J, et al., Cofactor dynamics and sufficiency in estrogen receptorregulated transcription, Cell, 2000, 103: 843–852.CrossRefGoogle Scholar
  12. [12]
    Mtivier R, Penot G, Hubner M, et al., Estrogen receptor-alpha directs ordered, cyclical, and combinatorial recruitment of cofactors on a natural target promoter, Cell, 2003, 115: 751–763.CrossRefGoogle Scholar
  13. [13]
    Nagaich A, Walker D, Wolford R, et al., Rapid periodic binding and displacement of the glucocorticoid receptor during chromatin remodeling, Molecular Cell, 2004, 14: 163–174.CrossRefGoogle Scholar
  14. [14]
    Degenhardt T, Rybakova K N, Tomaszewska A, et al., Population-level transcription cycles derive from stochastic timing of single-cell transcription, Cell, 2009, 138: 489–501.CrossRefGoogle Scholar
  15. [15]
    Mtivier R, Reid G, and Gannon F, Transcription in four dimensions: Nuclear receptor-directed initiation of gene expression, EMBO Reports, 2006, 7: 161–167.CrossRefGoogle Scholar
  16. [16]
    Hager G, Elbi C, Johnson T, et al., Chromatin dynamics and the evolution of alternate promoter states, Chromosome Research, 2006, 14: 107–116.CrossRefGoogle Scholar
  17. [17]
    Misteli T, Beyond the sequence: Cellular organization of genome function, Cell, 2007, 128: 787–800.CrossRefGoogle Scholar
  18. [18]
    Browning D and Busby S, The regulation of bacterial transcription initiation, Nature Review Microbiology, 2004, 2: 57–65.CrossRefGoogle Scholar
  19. [19]
    Dodd I, Shearwin K, Perkins A, et al., Cooperativity in long-range gene regulation by the lambda CI repressor, Genes Development, 2004, 18: 344–354.CrossRefGoogle Scholar
  20. [20]
    Adams C and Workman J, Binding of disparate transcriptional activators to nucleosomal DNA is inherently cooperative, Molecule Cell Biology, 1995, 15: 1405–1421.CrossRefGoogle Scholar
  21. [21]
    Agresti A, Scaffidi P, Riva A, et al., GR and HMGB1 interact only within chromatin and influence each other’s residence time, Molecular Cell, 2005, 18: 109–121.CrossRefGoogle Scholar
  22. [22]
    Mellor J, Dynamic nucleosomes and gene transcription, Trends Genet, 2006, 22: 320–329.CrossRefGoogle Scholar
  23. [23]
    Li B, Carey M, and Workman J, The role of chromatin during transcription, Cell, 2007, 128: 707–719.CrossRefGoogle Scholar
  24. [24]
    Ackers G, Johnson A, and Shea M, Quantitative model for gene regulation by lambda phage repressor, Proceedings of National Academy of Sciences of the United States of America, 1982, 79: 1129–1133.CrossRefGoogle Scholar
  25. [25]
    Bintu L, Buchler N, Garcia H, et al., Transcriptional regulation by the numbers: Models, Current Opinion in Genetic Development, 2005, 15: 116–124.CrossRefGoogle Scholar
  26. [26]
    Coulon A, Gandrillon O, and Beslon G, On the spontaneous stochastic dynamics of a single gene: Complexity of the molecular interplay at the promoter, BMC Systems Biology, 2010, 4: 2.CrossRefGoogle Scholar
  27. [27]
    Vilar J and Saiz L, DNA looping in gene regulation: From the assembly of macromolecular complexes to the control of transcriptional noise, Current Opinion in Genetic Development, 2005, 15: 136–144.CrossRefGoogle Scholar
  28. [28]
    Saiz L and Vilar J, Stochastic dynamics of macromolecular-assembly networks, Molecular Systems Biology, 2006, 2(1): 20060024.Google Scholar
  29. [29]
    Raser J and O’Shea E, Control of stochasticity in eukaryotic gene expression, Science, 2004, 304: 1811–1814.CrossRefGoogle Scholar
  30. [30]
    Ge H and Qian H, The physical origins of entropy production, free energy dissipation and their mathematical representations, Physical Review E, 2009, 81: 561–578.Google Scholar
  31. [31]
    Zhang J J, Chen J J, and Zhou T S, Analytical distribution and tunability of noise in a model of promoter progress, Biophysical Journal, 2012, 102: 1247–1257.CrossRefGoogle Scholar
  32. [32]
    Pedraza J and Paulsson J, Effects of molecular memory and bursting on fluctuations in gene expression, Science, 2008, 319: 339–343.CrossRefGoogle Scholar
  33. [33]
    Gillespie D T, Exact stochastic simulation of coupled chemical-reactions, Journal of Physical Chemistry, 1977, 81: 2340–2361.CrossRefGoogle Scholar
  34. [34]
    Zhang J J and Zhou T S, Promoter-mediated transcriptional dynamics, Biophysical Journal, 2014, 106: 479–488.CrossRefGoogle Scholar
  35. [35]
    Zhou T S and Zhang J S, Analytical results for a multistate gene model, SIAM Journal of Applied Mathematics, 2010, 72: 789–818.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    Tu Y, The nonequilibrium mechanism for ultrasensitivity in a biological switch: Sensing by Maxwell’s demons, Proceedings of National Academy of Sciences of the United States of America, 2008, 105: 11737–11741.CrossRefGoogle Scholar
  37. [37]
    Li G and Qian H, Kinetic timing: A novel mechanism that improves the accuracy of GTPase timers in endosome fusion and other biological processes, Traffic, 2002, 3: 249–255.CrossRefGoogle Scholar
  38. [38]
    Mehta P and Schwab D J, Energetic costs of cellular computation, Proceedings of National Academy of Sciences of the United States of America, 2012, 109: 17978–17982.CrossRefGoogle Scholar
  39. [39]
    Qian H, Phosphorylation energy hypothesis: Open chemical systems and their biological functions, Annual Review of Physical Chemistry, 2007, 58: 113–142.CrossRefGoogle Scholar

Copyright information

© The Editorial Office of JSSC & Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  1. 1.Guangdong Province Key Laboratory of Computational Science, School of MathematicsSun Yat-Sen UniversityGuangzhouChina

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