Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated (original) (raw)

Abstract

Living cells differ from most other chemical systems in that they involve regulation pathways that depend very nonlinearly on chemical species that are present in low copy numbers per cell. This leads to a variety of intracellular kinetic phenomena that elude macroscopic modeling, which implicitly assumes that cells are infinitely large and fluctuations negligible. It is of particular importance to assess how fluctuations affect regulation in cases where precision and reliability are required. Here, taking finite cell size and stochastic aspects into account, we reinvestigate theoretically the mechanism of zero-order ultrasensitivity for covalent modification of target enzymes ( Proc. Natl. Acad. Sci. USA. 78:6840-6844). Macroscopically, this mechanism can produce a very sharp transition in target concentrations for very small changes in the activity of the converter enzymes. This study shows that the transition is much more gradual in a finite cell or a population of finite cells. It also demonstrates that the switch is exactly analogous to a thermodynamic phase transition and that ultrasensitivity is inevitably coupled to random ultravariation. As a consequence, the average response in a large population of cells will often be much more gradual than predicted from macroscopic descriptions.

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Selected References

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  1. Arkin A., Ross J., McAdams H. H. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics. 1998 Aug;149(4):1633–1648. doi: 10.1093/genetics/149.4.1633. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. BENZER S. Induced synthesis of enzymes in bacteria analyzed at the cellular level. Biochim Biophys Acta. 1953 Jul;11(3):383–395. doi: 10.1016/0006-3002(53)90057-2. [DOI] [PubMed] [Google Scholar]
  3. Berg O. G. A model for the statistical fluctuations of protein numbers in a microbial population. J Theor Biol. 1978 Apr 20;71(4):587–603. doi: 10.1016/0022-5193(78)90326-0. [DOI] [PubMed] [Google Scholar]
  4. Ferrell J. E., Jr, Machleder E. M. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science. 1998 May 8;280(5365):895–898. doi: 10.1126/science.280.5365.895. [DOI] [PubMed] [Google Scholar]
  5. Goldbeter A., Koshland D. E., Jr An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci U S A. 1981 Nov;78(11):6840–6844. doi: 10.1073/pnas.78.11.6840. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Goldbeter A., Koshland D. E., Jr Sensitivity amplification in biochemical systems. Q Rev Biophys. 1982 Aug;15(3):555–591. doi: 10.1017/s0033583500003449. [DOI] [PubMed] [Google Scholar]
  7. LaPorte D. C., Koshland D. E., Jr Phosphorylation of isocitrate dehydrogenase as a demonstration of enhanced sensitivity in covalent regulation. Nature. 1983 Sep 22;305(5932):286–290. doi: 10.1038/305286a0. [DOI] [PubMed] [Google Scholar]
  8. McAdams H. H., Arkin A. It's a noisy business! Genetic regulation at the nanomolar scale. Trends Genet. 1999 Feb;15(2):65–69. doi: 10.1016/s0168-9525(98)01659-x. [DOI] [PubMed] [Google Scholar]
  9. McAdams H. H., Arkin A. Stochastic mechanisms in gene expression. Proc Natl Acad Sci U S A. 1997 Feb 4;94(3):814–819. doi: 10.1073/pnas.94.3.814. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Paulsson J., Berg O. G., Ehrenberg M. Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci U S A. 2000 Jun 20;97(13):7148–7153. doi: 10.1073/pnas.110057697. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Paulsson J., Ehrenberg M. Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks. Phys Rev Lett. 2000 Jun 5;84(23):5447–5450. doi: 10.1103/PhysRevLett.84.5447. [DOI] [PubMed] [Google Scholar]
  12. Paulsson J., Ehrenberg M. Trade-off between segregational stability and metabolic burden: a mathematical model of plasmid ColE1 replication control. J Mol Biol. 1998 May 29;279(1):73–88. doi: 10.1006/jmbi.1998.1751. [DOI] [PubMed] [Google Scholar]
  13. Savageau M. A. Parameter sensitivity as a criterion for evaluating and comparing the performance of biochemical systems. Nature. 1971 Feb 19;229(5286):542–544. doi: 10.1038/229542a0. [DOI] [PubMed] [Google Scholar]
  14. Spudich J. L., Koshland D. E., Jr Non-genetic individuality: chance in the single cell. Nature. 1976 Aug 5;262(5568):467–471. doi: 10.1038/262467a0. [DOI] [PubMed] [Google Scholar]