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. 1999 Mar;76(3):1320–1329. doi: 10.1016/S0006-3495(99)77294-2

General method of analysis of kinetic equations for multistep reversible mechanisms in the single-exponential regime: application to kinetics of open complex formation between Esigma70 RNA polymerase and lambdaP(R) promoter DNA.

O V Tsodikov 1, M T Record Jr 1
PMCID: PMC1300111  PMID: 10049315

Abstract

A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] >> [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation.

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Selected References

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  1. Buc H., McClure W. R. Kinetics of open complex formation between Escherichia coli RNA polymerase and the lac UV5 promoter. Evidence for a sequential mechanism involving three steps. Biochemistry. 1985 May 21;24(11):2712–2723. doi: 10.1021/bi00332a018. [DOI] [PubMed] [Google Scholar]
  2. Craig M. L., Suh W. C., Record M. T., Jr HO. and DNase I probing of E sigma 70 RNA polymerase--lambda PR promoter open complexes: Mg2+ binding and its structural consequences at the transcription start site. Biochemistry. 1995 Dec 5;34(48):15624–15632. doi: 10.1021/bi00048a004. [DOI] [PubMed] [Google Scholar]
  3. Craig M. L., Tsodikov O. V., McQuade K. L., Schlax P. E., Jr, Capp M. W., Saecker R. M., Record M. T., Jr DNA footprints of the two kinetically significant intermediates in formation of an RNA polymerase-promoter open complex: evidence that interactions with start site and downstream DNA induce sequential conformational changes in polymerase and DNA. J Mol Biol. 1998 Nov 6;283(4):741–756. doi: 10.1006/jmbi.1998.2129. [DOI] [PubMed] [Google Scholar]
  4. Hammes G. G., Haslam J. L. A kinetic investigation of the interaction of erythro-beta-hydroxyaspartic acid with aspartate aminotransferase. Biochemistry. 1969 Apr;8(4):1591–1598. doi: 10.1021/bi00832a040. [DOI] [PubMed] [Google Scholar]
  5. Hammes G. G., Schimmel P. R. Relaxation spectra of enzymatic reactions. J Phys Chem. 1967 Mar;71(4):917–923. doi: 10.1021/j100863a023. [DOI] [PubMed] [Google Scholar]
  6. Haslam J. L. Calculation of rate constants from relaxation spectra of enzyme reactions. J Phys Chem. 1972 Feb 3;76(3):366–369. doi: 10.1021/j100647a015. [DOI] [PubMed] [Google Scholar]
  7. McClure W. R. Rate-limiting steps in RNA chain initiation. Proc Natl Acad Sci U S A. 1980 Oct;77(10):5634–5638. doi: 10.1073/pnas.77.10.5634. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Roe J. H., Burgess R. R., Record M. T., Jr Kinetics and mechanism of the interaction of Escherichia coli RNA polymerase with the lambda PR promoter. J Mol Biol. 1984 Jul 15;176(4):495–522. doi: 10.1016/0022-2836(84)90174-8. [DOI] [PubMed] [Google Scholar]
  9. Roe J. H., Burgess R. R., Record M. T., Jr Temperature dependence of the rate constants of the Escherichia coli RNA polymerase-lambda PR promoter interaction. Assignment of the kinetic steps corresponding to protein conformational change and DNA opening. J Mol Biol. 1985 Aug 5;184(3):441–453. doi: 10.1016/0022-2836(85)90293-1. [DOI] [PubMed] [Google Scholar]
  10. Roe J. H., Record M. T., Jr Regulation of the kinetics of the interaction of Escherichia coli RNA polymerase with the lambda PR promoter by salt concentration. Biochemistry. 1985 Aug 27;24(18):4721–4726. doi: 10.1021/bi00339a002. [DOI] [PubMed] [Google Scholar]
  11. Schlax P. J., Capp M. W., Record M. T., Jr Inhibition of transcription initiation by lac repressor. J Mol Biol. 1995 Jan 27;245(4):331–350. doi: 10.1006/jmbi.1994.0028. [DOI] [PubMed] [Google Scholar]
  12. Suh W. C., Leirmo S., Record M. T., Jr Roles of Mg2+ in the mechanism of formation and dissociation of open complexes between Escherichia coli RNA polymerase and the lambda PR promoter: kinetic evidence for a second open complex requiring Mg2+. Biochemistry. 1992 Sep 1;31(34):7815–7825. doi: 10.1021/bi00149a011. [DOI] [PubMed] [Google Scholar]
  13. Suh W. C., Ross W., Record M. T., Jr Two open complexes and a requirement for Mg2+ to open the lambda PR transcription start site. Science. 1993 Jan 15;259(5093):358–361. doi: 10.1126/science.8420002. [DOI] [PubMed] [Google Scholar]
  14. Tsodikov O. V., Craig M. L., Saecker R. M., Record M. T., Jr Quantitative analysis of multiple-hit footprinting studies to characterize DNA conformational changes in protein-DNA complexes: application to DNA opening by Esigma70 RNA polymerase. J Mol Biol. 1998 Nov 6;283(4):757–769. doi: 10.1006/jmbi.1998.2130. [DOI] [PubMed] [Google Scholar]
  15. Zaychikov E., Denissova L., Meier T., Götte M., Heumann H. Influence of Mg2+ and temperature on formation of the transcription bubble. J Biol Chem. 1997 Jan 24;272(4):2259–2267. doi: 10.1074/jbc.272.4.2259. [DOI] [PubMed] [Google Scholar]

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