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Kinetics

Chapter
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Part of the Texts in Applied Mathematics book series (TAM, volume 56)

Abstract

We now investigate how to model, and analyze, the interactions of multiple species and how these interactions produce changes in their populations. Examples of such problems are below.

References

  1. D. Agnani, P. Acharya, E. Martinez, T.T. Tran, F. Abraham, F. Tobin, J. Bentz, Fitting the elementary rate constants of the P-gp transporter network in the hMDR1-MDCK confluent cell monolayer using a particle swarm algorithm. PLoS ONE 6 (10), e25086-1–e25086-11 (2011)Google Scholar
  2. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, 4th edn. (Springer, New York, 1993)CrossRefGoogle Scholar
  3. G.E. Briggs, J.B.S. Haldane, A note on the kinetics of enzyme action. Biochem. J. 19, 338–339 (1928)CrossRefGoogle Scholar
  4. J.C. Butcher, Numerical Methods for Ordinary Differential Equations, 3rd edn. (Wiley, New York, 2016)CrossRefGoogle Scholar
  5. R. Engbert, F. Drepper, Chance and chaos in population biology, models of recurrent epidemics and food chain dynamics. Chaos Solutions Fractals 4, 1147–1169 (1994)CrossRefGoogle Scholar
  6. I. Famili, B.O. Palsson, The convex basis of the left null space of the stoichiometric matrix leads to the definition of metabolically meaningful pools. Biophys. J. 85 (1), 16–26 (2003)CrossRefGoogle Scholar
  7. R.J. Field, R.M. Noyes, Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J. Am. Chem. Soc. 60, 1877–1884 (1974)Google Scholar
  8. R.J. Field, E. Koros, R.M. Noyes, Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system. J. Am. Chem. Soc. 94, 8649–8664 (1972)Google Scholar
  9. D.F. Griffiths, D.J. Higham, Numerical Methods for Ordinary Differential Equations: Initial Value Problems. Springer Undergraduate Mathematics Series (Springer, New York, 2010). ISBN 9780857291486Google Scholar
  10. J.K. Hale, H. Kocak, Dynamics and Bifurcations (Springer, New York, 1996)zbMATHGoogle Scholar
  11. V. Henri, Lois générales de l’action des diastases (Librairie Scientifique A. Hermann, Paris, 1903)Google Scholar
  12. N.E. Henriksen, F.Y. Hansen, Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics (Oxford University Press, Oxford, 2008)CrossRefGoogle Scholar
  13. M.H. Holmes, Introduction to Scientific Computing and Data Analysis. Texts in Computational Science and Engineering, vol. 13 (Springer, New York, 2016)Google Scholar
  14. F. Horn, R. Jackson, General mass action kinetics. Arch. Ration. Mech. Anal. 47 (2), 81–116 (1972). https://doi.org/10.1007/BF00251225. ISSN 1432-0673MathSciNetCrossRefGoogle Scholar
  15. P.L. Houston, Chemical Kinetics and Reaction Dynamics (Dover, New York, 2006)Google Scholar
  16. S.V. Kryatov, E.V. Rybak-Akimova, A.Y. Nazarenko, P.D. Robinson, A dinuclear iron(III) complex with a bridging urea anion: implications for the urease mechanism. Chem. Commun. 11, 921–922 (2000)CrossRefGoogle Scholar
  17. L. Michaelis, M. Menten, Die kinetik der invertinwirkung. Biochem Z 49, 333–369 (1913)Google Scholar
  18. M. Polettini, M. Esposito, Irreversible thermodynamics of open chemical networks. i. emergent cycles and broken conservation laws. J. Chem. Phys. 141 (2), 024117 (2014). https://doi.org/10.1063/1.4886396
  19. M. Ramírez-Escudero, M. Gimeno-Pérez, B. González, D. Linde, Z. Merdzo, M. Fernández-Lobato, J. Sanz-Aparicio, Structural analysis of β-fructofuranosidase from Xanthophyllomyces dendrorhous reveals unique features and the crucial role of N-glycosylation in oligomerization and activity. J. Biol. Chem. 291 (13), 6843–6857 (2016).  https://doi.org/10.1074/jbc.M115.708495. http://www.jbc.org/content/291/13/6843.abstract
  20. C. Reder, Metabolic control theory: a structural approach. J. Theor. Biol. 135 (2), 175–201 (1988) https://doi.org/10.1016/S0022-5193(88)80073-0. http://www.sciencedirect.com/science/article/pii/S0022519388800730. ISSN 0022-5193
  21. W. Rudin, Principles of Mathematical Analysis, 3rd edn. (McGraw-Hill, New York, 1976)zbMATHGoogle Scholar
  22. D. Schomburg, D. Stephan, Enzyme Handbook (Springer, New York, 1997)CrossRefGoogle Scholar
  23. S. Schuster, T. Hofer, Determining all extreme semi-positive conservation relations in chemical reaction systems: a test criterion for conservativity. J. Chem. Soc. Faraday Trans. 87, 2561–2566 (1991) https://doi.org/10.1039/FT9918702561 CrossRefGoogle Scholar
  24. L.A. Segel, M. Slemrod, The quasi-steady-state assumption: A case study in perturbation. SIAM Rev. 31, 446–477 (1989)MathSciNetCrossRefGoogle Scholar
  25. S.H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, 2nd edn. (Westview Press, Cambridge, 2014)zbMATHGoogle Scholar
  26. Thoisoi2, Chemical Clock, Briggs-Rauscher oscillating Reaction! Website (2014), https://www.youtube.com/watch?v=WpBwlSn1XPQ
  27. T.T. Tran, A. Mittal, T. Aldinger, J.W. Polli, A. Ayrton, H. Ellens, J. Bentz, The elementary mass action rate constants of P-gp transport for a confluent monolayer of MDCKII-hMDR1 cells. Biophys. J. 88, 715–738 (2005)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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