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Classical Analytical Solutions

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Numerical Methods for the Life Scientist
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Abstract

Reversible binding to one site can be calculated with analytical solutions. On the basis of these formulas, data can be transformed to appear linear. Straight lines of equilibrium-binding studies in double reciprocal plots or of enzyme kinetics in Lineweaver-Burk plots or of dissociation kinetics in half logarithmic plots indicate simple mechanisms. Deviations from these are discussed in detail as cooperative or independent sites. Logistic functions commonly used to calculate dose–response curves, only correspond to a binding mechanism when the Hill coefficient is one. At the end of this chapter, the reader should be able to identify simple biochemical reactions.

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References

  1. Langley JN (1905) On the reaction of cells and of nerve-endings to certain poisons, chiefly as regards the reaction of striated muscle to nicotine and to curare. J Physiol 33:374–413

    PubMed  Google Scholar 

  2. http://de.wikipedia.org/wiki/Scatchard-Diagramm

    Google Scholar 

  3. http://en.dogeno.us/2004/03/scatchard-plot/

    Google Scholar 

  4. Voet DJ, Voet JG (1995) Biochemistry. John Wiley & Sons, New York

    Google Scholar 

  5. Gutfreund H (1995) Kinetics for the life sciences. Receptors, transmitters and catalysts. Cambridge University press, Cambridge

    Book  Google Scholar 

  6. Segel LA, Slemrod M (1989) The quasi-steady-state assumption: a case study in perturbation. SIAM Rev 31:446–477. doi:10.1137/1031091

    Article  Google Scholar 

  7. Michaelis L, Menten ML (1913) Die Kinetik der Invertin-Wirkung. Biochem Z 49:333–369

    CAS  Google Scholar 

  8. Segel IH (1993) Enzyme kinetics: behavior and analysis of rapid equilibrium and steady-state enzyme systems. Wiley Classical Library, New York

    Google Scholar 

  9. Copeland RA (2005) Evaluation of enzyme inhibitors in drug discovery: a guide for medicinal chemists and pharmacologists. Wiley-VCH, Weinheim

    Google Scholar 

  10. Copeland RA (2000) Enzymes: a practical introduction to structure, mechanism, and data analysis. Wiley, New York

    Google Scholar 

  11. Purich DL (2010) Enzyme kinetics: catalysis & control: a reference of theory and best-practice methods. Elsevier, London

    Google Scholar 

  12. Cook PF, Cleland WW (2007) Enzyme kinetics and mechanism. Garland Science, New York

    Google Scholar 

  13. Leskovac V (2003) Comprehensive enzyme kinetics, Kindle Edition. Amazon

    Google Scholar 

  14. Lineweaver H, Burk D (1934) The determination of enzyme dissociation constants. J Am Chem Soc 56:658–666

    Article  CAS  Google Scholar 

  15. Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol (Lond) 40:iv–vii

    Google Scholar 

  16. Verhulst PF (1845) Recherches mathématiques sur la loi d'accroissement de la population. Nouv mém de l'Academie Royale des Sci et Belles-Lettres de Bruxelles 18:1–41

    Google Scholar 

  17. Weiss JN (1997) The Hill equation revisited: uses and misuses. FASEB J 11:835–841

    PubMed  CAS  Google Scholar 

  18. Prinz H (2010) Hill coefficients, dose-response curves and allosteric mechanisms. J Chem Biol 3:37–44

    Article  PubMed  Google Scholar 

  19. Prinz H, Schönichen A (2008) Transient binding patches: a plausible concept for drug binding. J Chem Biol 1:95–104

    Article  PubMed  Google Scholar 

Download references

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Correspondence to Heino Prinz .

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Prinz, H. (2011). Classical Analytical Solutions. In: Numerical Methods for the Life Scientist. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20820-1_3

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