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

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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.

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References

  • 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 

  • M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, 4th edn. (Springer, New York, 1993)

    Book  Google Scholar 

  • G.E. Briggs, J.B.S. Haldane, A note on the kinetics of enzyme action. Biochem. J. 19, 338–339 (1928)

    Article  Google Scholar 

  • J.C. Butcher, Numerical Methods for Ordinary Differential Equations, 3rd edn. (Wiley, New York, 2016)

    Book  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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 

  • 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 

  • D.F. Griffiths, D.J. Higham, Numerical Methods for Ordinary Differential Equations: Initial Value Problems. Springer Undergraduate Mathematics Series (Springer, New York, 2010). ISBN 9780857291486

    Google Scholar 

  • J.K. Hale, H. Kocak, Dynamics and Bifurcations (Springer, New York, 1996)

    MATH  Google Scholar 

  • V. Henri, Lois générales de l’action des diastases (Librairie Scientifique A. Hermann, Paris, 1903)

    Google Scholar 

  • N.E. Henriksen, F.Y. Hansen, Theories of Molecular Reaction Dynamics: The Microscopic Foundation of Chemical Kinetics (Oxford University Press, Oxford, 2008)

    Book  Google Scholar 

  • M.H. Holmes, Introduction to Scientific Computing and Data Analysis. Texts in Computational Science and Engineering, vol. 13 (Springer, New York, 2016)

    Google Scholar 

  • F. Horn, R. Jackson, General mass action kinetics. Arch. Ration. Mech. Anal. 47 (2), 81–116 (1972). https://doi.org/10.1007/BF00251225. ISSN 1432-0673

    Article  MathSciNet  Google Scholar 

  • P.L. Houston, Chemical Kinetics and Reaction Dynamics (Dover, New York, 2006)

    Google Scholar 

  • 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)

    Article  Google Scholar 

  • L. Michaelis, M. Menten, Die kinetik der invertinwirkung. Biochem Z 49, 333–369 (1913)

    Google Scholar 

  • 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

  • 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

  • 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

  • W. Rudin, Principles of Mathematical Analysis, 3rd edn. (McGraw-Hill, New York, 1976)

    MATH  Google Scholar 

  • D. Schomburg, D. Stephan, Enzyme Handbook (Springer, New York, 1997)

    Book  Google Scholar 

  • 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

    Article  Google Scholar 

  • L.A. Segel, M. Slemrod, The quasi-steady-state assumption: A case study in perturbation. SIAM Rev. 31, 446–477 (1989)

    Article  MathSciNet  Google Scholar 

  • S.H. Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, 2nd edn. (Westview Press, Cambridge, 2014)

    MATH  Google Scholar 

  • Thoisoi2, Chemical Clock, Briggs-Rauscher oscillating Reaction! Website (2014), https://www.youtube.com/watch?v=WpBwlSn1XPQ

  • 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)

    Article  Google Scholar 

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Holmes, M.H. (2019). Kinetics. In: Introduction to the Foundations of Applied Mathematics. Texts in Applied Mathematics, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-030-24261-9_3

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