Skip to main content
SpringerLink
Log in

Modeling of a control induced system for product formation in enzyme kinetics

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Double substrate enzyme kinetics has a leading role for product quantification and optimization in different chemical and biochemical sectors. Mathematical approach for controlling these reactions in different stages by suitable parameters adds a new dimension in this interdisciplinary field of research. Applying control theoretic approach in the reversible backward stages of double substrate enzymatic model, time economization with regard to product formation is significant. In this article, we formulate a double substrate mathematical model of enzymatic dynamical reaction system with control measures with a view to observe the effect of changes of these measures with respect to the concentration of substrates, enzyme, complexes and finally product. Here, Pontryagin Minimum Principle is used for observing the effect of control measures in the system dynamics with the help of Hamiltonian. We compare the relevant numerical solutions for the substrates, enzyme, complexes and product concentration profile for a specified time interval with respect to control factors.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. S.I. Rubinow, Introduction to Mathematical Biology (Wiley, New York, 1975)

    Google Scholar 

  2. J.D. Murray, Mathematical Biology, 2nd edn, vol. 19 (Springer-Verlag, Berlin, 1989), pp. 109–113

  3. L.A. Segel, Mathematical Models in Molecular and Cellular Biology (Cambridge University Press, Cambridge, 1980)

  4. D.V. Roberts, Enzyme Kinetics (Cambridge University Press, Cambridge, 1977)

  5. M.C. Hogan, J.M. Woodley, Modeling of two enzyme reactions in a linked cofactor recycle system for chiral lactones synthesis. Chem. Eng. Sci. 55, 2001–2008 (2000)

    Article  CAS  Google Scholar 

  6. A.J.J. Straathof, Development of a computer program for analysis of enzyme kinetics by progress curve ftting. J. Mol. Catal. B Enzym. 11, 991–998 (2001)

    Article  CAS  Google Scholar 

  7. A.J. Brown, J. Chem. Soc. Trans. 81, 373 (1902)

    Article  CAS  Google Scholar 

  8. F.R. Sharpe, A.J. Lotka, Am. J. Hyg. 3(Suppl. 1), 96–112 (1923)

    Google Scholar 

  9. V. Volterra, Mem. Res. Com. Tolassog 1, 131 (1927)

    Google Scholar 

  10. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, Selected Works, Classics of Soviet Mathematics, in Mathematical Theory of Optimal Processes, vol. 4 (Gordon and Breach Science Publishers, New York, 1986)

  11. R.M. Alicea, A Mathematical Model for Enzyme Kinetics: Multiple Timescales Analysis, in Dynamics at the Horsetooth: Asymptotics and Perturbations, vol. 2A (2010)

  12. G. Varadharajan, L. Rajendran, Analytical solution of coupled non-linear second order reaction differential equations in enzyme kinetics. Nat. Sci. 3, 459–465 (2011)

    CAS  Google Scholar 

Download references

Acknowledgments

The research is supported by UGC-DRS Program, Department of Mathematics, Jadavpur University, Kolkata 700032, India.

Author information

Authors and Affiliations

  1. Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, 700032, India

    Priti Kumar Roy & Mithun Kumar Ghosh

  2. Department of Chemistry, Narula Institute of Technology, Kolkata, 700109, India

    Sumit Nandi

Authors
  1. Priti Kumar Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sumit Nandi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mithun Kumar Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Priti Kumar Roy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roy, P.K., Nandi, S. & Ghosh, M.K. Modeling of a control induced system for product formation in enzyme kinetics. J Math Chem 51, 2704–2717 (2013). https://doi.org/10.1007/s10910-013-0232-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-013-0232-x

Keywords

Search

Navigation