Integration of Reaction Kinetics Theory and Gene Expression Programming to Infer Reaction Mechanism

  • Jason R. White
  • Ranjan Srivastava
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10199)


Mechanistic mathematical models of biomolecular systems have been used to describe biological phenomena in the hope that one day these models may be used to enhance our fundamental understanding of these phenomena, as well as to optimize and engineer biological systems. An evolutionary algorithm capable of formulating mass action kinetic models of biological systems from time series data sets was developed for a system of n-species. The strategy involved using a gene expression programming (GEP) based approach and heuristics based on chemical kinetic theory. The resulting algorithm was successfully validated by recapitulating a nonlinear model of viral dynamics using only a “noisy” set of time series data. While the system analyzed for this proof-of-principle study was relatively small, the approach presented here is easily parallelizable making it amenable for use with larger systems. Additionally, greater efficiencies may potentially be realized by further taking advantage of the problem domain along with future breakthroughs in computing power and algorithmic advances.


Evolutionary algorithm Biochemical kinetics Mechanistic modeling Genetic programming Gene expression programming 



This material is based upon work supported by the National Science Foundation under Grant No. 1137249 and 1517133.

Supporting Information.

Mathematica source code and instructions are available from under a BSD open source license.


  1. 1.
    Aviran, S., Shah, P.S., Schaffer, D.V., Arkin, A.P.: Computational models of HIV-1 resistance to gene therapy elucidate therapy design principles. PLoS Comput. Biol. 6(8), e1000883 (2010)CrossRefGoogle Scholar
  2. 2.
    Bonhoeffer, S., Coffin, J.M., Nowak, M.A.: Human immunodeficiency virus drug therapy and virus load. J. Virol. 71, 3275–3278 (1997)Google Scholar
  3. 3.
    Bonhoeffer, S., May, R.M., Shaw, G.M., Nowak, M.A.: Virus dynamics and drug therapy. PNAS 94, 6971–6976 (1997)CrossRefGoogle Scholar
  4. 4.
    Burg, D., Rong, L., Neumann, A.U., Dahari, H.: Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection. J. Theor. Biol. 259, 751–759 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Perelson, A.S.: Modelling viral and immune system dynamics. Nat. Rev. Immunol. 2, 28–36 (2002)CrossRefGoogle Scholar
  6. 6.
    Prosperi, M.C.F., D’Autilia, R., Incardona, F., De Luca, A., Zazzi, M., et al.: Stochastic modelling of genotypic drug-resistance for human immunodeficiency virus towards long-term combination therapy optimization. Bioinformatics 25, 1040–1047 (2009)CrossRefGoogle Scholar
  7. 7.
    Ribeiro, R.M., Bonhoeffer, S.: Production of resistant HIV mutants during antiretroviral therapy. PNAS 97, 7681–7686 (2000)CrossRefzbMATHGoogle Scholar
  8. 8.
    von Kleist, M., Menz, S., Huisinga, W.: Drug-class specific impact of antivirals on the reproductive capacity of HIV. PLoS Comput. Biol. 6, e1000720 (2010)CrossRefGoogle Scholar
  9. 9.
    Sugimoto, M., Kikuchi, S., Tomita, M.: Reverse engineering of biochemical equations from time-course data by means of genetic programming. BioSystems 80, 155–164 (2005)CrossRefGoogle Scholar
  10. 10.
    Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324, 81–85 (2009)CrossRefGoogle Scholar
  11. 11.
    Chattopadhyay, I., Kuchina, A., Süel, G.M., Lipson, H.: Inverse gillespie for inferring stochastic reaction mechanisms from intermittent samples. PNAS 110(32), 12990–12995 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Bazil, J.N., Qi, F., Beard, D.A.: A parallel algorithm for reverse engineering of biological networks. Integr. Biol. 3(12), 1215–1223 (2011)CrossRefGoogle Scholar
  13. 13.
    Koza, J.: Genetic Programming, p. 819. MIT Press, Cambridge (1992)Google Scholar
  14. 14.
    Iba, H.: Inference of differential equation models by genetic programming. Inf. Sci. 178, 4453–4468 (2008)CrossRefGoogle Scholar
  15. 15.
    Rodriguez-Fernandez, M., Rehberg, M., Banga, J.R.: Simultaneous model discrimination and parameter estimation in dynamic models of cellular systems. BMC Syst. Biol. 7, 76–89 (2013)CrossRefGoogle Scholar
  16. 16.
    Lillacci, G., Khammash, M.: Parameter estimation and model selection in computational biology. PLoS Comput. Biol. 6, e1000696 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Ferreira, C.: Gene Expression Programming, vol. 21. Springer, Heidelberg (2006). 478 p.zbMATHGoogle Scholar
  18. 18.
    Du, X., et al.: Convergence analysis of gener expression programming based on maintaining elitist. In: Proceedings og the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation (GEC 2009), pp. 823–826. ACM, New York (2009)Google Scholar
  19. 19.
    Srivastava, R., You, L., Summers, J., Yin, J.: Stochastic vs. deterministic modeling of intracellular viral kinetics. J. Theor. Biol. 218, 309–321 (2002)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Levenspiel, O.: Chemical Reaction Engineering, 2nd edn. Wiley, New York (1972)Google Scholar
  21. 21.
    Motulsky, H., Christopoulos, A.: Fitting Models to Biological Data Using Linear and Nonlinear Regression. Oxford University Press, Oxford (2004). 351 p.zbMATHGoogle Scholar
  22. 22.
    Bautista, E.J., et al.: Semi-automated curation of metabolic models via flux balance analysis: a case study with Mycoplasma gallisepticum. PLoS Comput. Biol. 9(9), 1003208 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Chemical and Biomolecular EngineeringUniversity of ConnecticutStorrsUSA
  2. 2.Department of Chemical EngineeringUniversity of CaliforniaDavisUSA

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