Skip to main content
Log in

Ribozymes: Analytical Solution of the One-substrate, Two-intermediate Reversible Scheme for Enzyme Reactions

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

The paper presents a kinetic analysis of a reversible enzymatic reaction S⇄P involving two intermediate compounds under the condition [E]0 ≫ [S]0 + [P]0. For the case of mono-exponential behavior, we derive an equation for k obs as a function of [E]0, which emphasizes the pitfalls of oversimplifying kinetic schemes (such as the Michaelis-Menten model) for ribozyme studies. This novel apparent rate constant, which has been arrived at through mechanistic considerations, is analyzed, and the characteristic parameters obtained. The equation, which seems to fit experimental data better than conventional approximations, is used to analyze a single turnover study on an ADC1 ribozyme drawn from hepatitis delta virus RNA. The microscopic kinetic constants for such enzyme are evaluated and its mono-exponential behavior verified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Segel, L.H.: Enzyme Kinetics, pp. 54–64. Wiley, New York (1975)

    Google Scholar 

  2. Waley, S.G.: Kinetics of suicide substrates. Biochem. J. 185, 771–773 (1980)

    Google Scholar 

  3. Waley, S.G.: Kinetics of suicide substrates. Practical procedures for determining parameters. Biochem. J. 227, 843–849 (1985)

    Google Scholar 

  4. Tudela, J., García-Cánovas, F., Varón, R., García-Carmona, F., Gálvez, J., Lozano, J.A.: Transient-phase kinetics of enzyme inactivation induced by suicide substrates. Biochim. Biophys. Acta 912, 408–416 (1987)

    Google Scholar 

  5. Swoboda, P.A.T.: The kinetics of enzyme action. Biochim. Biophys. Acta 23, 70–81 (1957)

    Article  Google Scholar 

  6. Ignetik, R., Deakin, M.A.B.: Asymptotic analysis of the Michaelis-Menten reaction equations. Bull. Math. Biol. 43, 375–388 (1981)

    MATH  MathSciNet  Google Scholar 

  7. Tzafriri, A.R.: Michaelis-Menten kinetics at high enzyme concentrations. Bull. Math. Biol. 65, 1111–1129 (2003)

    Article  Google Scholar 

  8. Tzafriri, A.R., Edelman, E.R.J.: The total quasi-steady-state approximation is valid for reversible enzyme kinetics. J. Theor. Biol. 226, 303–313 (2004)

    Article  MathSciNet  Google Scholar 

  9. Varon, R., Garrido-del Solo, C., Garcia-Moreno, M., Garcia Canovas, F., Moya-Garcia, G., Vidal de Labra, J., Havsteen, B.H.: Kinetics of enzyme systems with unstable suicide substrates. Biosystems 47, 177–192 (1998)

    Article  Google Scholar 

  10. Shih, I., Been, M.D.: Kinetic scheme for intermolecular RNA cleavage by a ribozyme derived from hepatitis delta virus RNA. Biochemistry 39, 9055–9066 (2000)

    Article  Google Scholar 

  11. Victoria, J., DeRose, V.J.: Two decades of RNA catalysis. Chem. Biol. 9, 961–969 (2002)

    Article  Google Scholar 

  12. Bergman, N.H, Johnston, W.K., Bartel, D.P.: Kinetic framework for ligation by an efficient RNA ligase ribozyme. Biochemistry 39, 3115–3123 (2000)

    Article  Google Scholar 

  13. Kurz, J.K., Niranjanakumari, S., Fierke, C.A.: Protein component of bacillus subtilis RNase P specifically enhances the affinity for precursor-tRNA. Biochemistry 37, 2393–2400 (1998)

    Article  Google Scholar 

  14. Oh, B.K., Frank, D.N., Pace, N.R.: Participation of the 3′-CCA of tRNA in the binding of catalytic Mg2+ ions by ribonuclease P. Biochemistry 37, 7277–7283 (1998)

    Article  Google Scholar 

  15. Siew, D., Zahler, N.H., Cassano, A.G., Strobel, S.A., Harris, M.E.: Identification of adenosine functional groups involved in substrate binding by the ribonuclease P ribozyme. Biochemistry 38, 1873–1883 (1999)

    Article  Google Scholar 

  16. Jeong, S., Sefcikova, J., Tinsley, R.A., Rueda, D., Nils, G., Walter, N.G.: Trans-acting hepatitis delta virus ribozyme: Catalytic core and global structure are dependent on the 5′ substrate sequence. Biochemistry 42, 7727–7740 (2003)

    Article  Google Scholar 

  17. Kaye, N.M., Christian, E.L., Harris, M.E.: NAIM and site-specific functional group modification analysis of RNase P RNA: Magnesium dependent structure within the conserved P1–P4 multihelix junction contributes to catalysis. Biochemistry 41, 4533–4545 (2002)

    Article  Google Scholar 

  18. Schenter, G.K., Lu, H.P., Xie, X.S.: Statistical analysis and theoretical models of single-molecule enzymatic dynamics. J. Phys. Chem. 103, 10477–10488 (1999)

    Google Scholar 

  19. Laidler, K.J.: Theory of the transient phase in kinetics, with special reference to enzyme systems. Can. J. Chem. 33, 1614–1624 (1955)

    Article  Google Scholar 

  20. Galvez, J.R., Varon, R., Carmona, F.G.: III kinetics of enzyme reactions with inactivation steps. J. Theor. Biol. 89, 37–44 (1981)

    Article  MathSciNet  Google Scholar 

  21. Harris, D.A., Rueda, D., Walter, N.G.: Local conformational changes in the catalytic core of the trans-acting hepatitis delta virus ribozyme accompany catalysis. Biochemistry 41, 12051–12061 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Carlo Bauer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Toti, P., Sbordone, L., Sbordone, C. et al. Ribozymes: Analytical Solution of the One-substrate, Two-intermediate Reversible Scheme for Enzyme Reactions. J Biol Phys 32, 473–488 (2006). https://doi.org/10.1007/s10867-006-9030-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-006-9030-z

Key words

Navigation