Skip to main content
Top

2015 | OriginalPaper | Chapter

Optimal Observation Time Points in Stochastic Chemical Kinetics

Authors : Charalampos Kyriakopoulos, Verena Wolf

Published in: Hybrid Systems Biology

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Wet-lab experiments, in which the dynamics within living cells are observed, are usually costly and time consuming. This is particularly true if single-cell measurements are obtained using experimental techniques such as flow-cytometry or fluorescence microscopy. It is therefore important to optimize experiments with respect to the information they provide about the system. In this paper we make a priori predictions of the amount of information that can be obtained from measurements. We focus on the case where the measurements are made to estimate parameters of a stochastic model of the underlying biochemical reactions. We propose a numerical scheme to approximate the Fisher information of future experiments at different observation time points and determine optimal observation time points. To illustrate the usefulness of our approach, we apply our method to two interesting case studies.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Parameter identification for markov models of biochemical reactions. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 83–98. Springer, Heidelberg (2011) CrossRef Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Parameter identification for markov models of biochemical reactions. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 83–98. Springer, Heidelberg (2011) CrossRef
2.
go back to reference Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Approximate maximum likelihood estimation for stochastic chemical kinetics. EURASIP J. Bioinf. Syst. Biol. 9 (2012) Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Approximate maximum likelihood estimation for stochastic chemical kinetics. EURASIP J. Bioinf. Syst. Biol. 9 (2012)
4.
go back to reference Burrage, K., Hegland, M., Macnamara, F., Sidje, B.: A krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems. In: Proceedings of the Markov 150th Anniversary Conference, pp. 21–38. Boson Books (2006) Burrage, K., Hegland, M., Macnamara, F., Sidje, B.: A krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems. In: Proceedings of the Markov 150th Anniversary Conference, pp. 21–38. Boson Books (2006)
5.
go back to reference Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRef Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRef
6.
go back to reference Henzinger, T.A., Mateescu, M., Wolf, V.: Sliding window abstraction for infinite markov chains. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 337–352. Springer, Heidelberg (2009) CrossRef Henzinger, T.A., Mateescu, M., Wolf, V.: Sliding window abstraction for infinite markov chains. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 337–352. Springer, Heidelberg (2009) CrossRef
7.
go back to reference Komorowski, M., Costa, M.J., Rand, D.A., Stumpf, M.P.H.: Sensitivity, robustness, and identifiability in stochastic chemical kinetics models. Proc. Nat. Acad. Sci. 108(21), 8645–8650 (2011)CrossRef Komorowski, M., Costa, M.J., Rand, D.A., Stumpf, M.P.H.: Sensitivity, robustness, and identifiability in stochastic chemical kinetics models. Proc. Nat. Acad. Sci. 108(21), 8645–8650 (2011)CrossRef
8.
go back to reference Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall PTR, Upper Saddle River (1998) MATH Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall PTR, Upper Saddle River (1998) MATH
9.
go back to reference Loinger, A., Lipshtat, A., Balaban, N.Q., Biham, O.: Stochastic simulations of genetic switch systems. Phys. Rev. E 75, 021904 (2007)CrossRef Loinger, A., Lipshtat, A., Balaban, N.Q., Biham, O.: Stochastic simulations of genetic switch systems. Phys. Rev. E 75, 021904 (2007)CrossRef
10.
go back to reference Mateescu, M., Wolf, V., Didier, F., Henzinger, T.A.: Fast adaptive uniformisation of the chemical master equation. IET Syst. Biol. 4(6), 441–452 (2010)CrossRef Mateescu, M., Wolf, V., Didier, F., Henzinger, T.A.: Fast adaptive uniformisation of the chemical master equation. IET Syst. Biol. 4(6), 441–452 (2010)CrossRef
11.
go back to reference Merlé, Y., Mentré, F.: Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model. J. Pharmacokinet. Biopharm. 23(1), 101–125 (1995)CrossRef Merlé, Y., Mentré, F.: Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model. J. Pharmacokinet. Biopharm. 23(1), 101–125 (1995)CrossRef
12.
go back to reference Munsky, B., Khammash, M.: The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys. 124, 044144 (2006)CrossRefMATH Munsky, B., Khammash, M.: The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys. 124, 044144 (2006)CrossRefMATH
14.
go back to reference Reinker, S., Altman, R.M., Timmer, J.: Parameter estimation in stochastic biochemical reactions. IEEE Proc. Syst. Biol 153, 168–178 (2006)CrossRef Reinker, S., Altman, R.M., Timmer, J.: Parameter estimation in stochastic biochemical reactions. IEEE Proc. Syst. Biol 153, 168–178 (2006)CrossRef
15.
go back to reference Ruess, J., Milias-Argeitis, A., Lygeros, J.: Designing experiments to understand the variability in biochemical reaction networks. J. R. Soc. Interface 10(88), 20130588–20130588 (2013). arXiv:1304.1455 [q-bio]CrossRef Ruess, J., Milias-Argeitis, A., Lygeros, J.: Designing experiments to understand the variability in biochemical reaction networks. J. R. Soc. Interface 10(88), 20130588–20130588 (2013). arXiv:​1304.​1455 [q-bio]CrossRef
16.
go back to reference Sidje, R., Burrage, K., MacNamara, S.: Inexact uniformization method for computing transient distributions of Markov chains. SIAM J. Sci. Comput. 29(6), 2562–2580 (2007)MathSciNetCrossRefMATH Sidje, R., Burrage, K., MacNamara, S.: Inexact uniformization method for computing transient distributions of Markov chains. SIAM J. Sci. Comput. 29(6), 2562–2580 (2007)MathSciNetCrossRefMATH
17.
go back to reference van den Bos, A.: Parameter Estimation for Scientists and Engineers. Wiley-Interscience, Hoboken (2007) MATH van den Bos, A.: Parameter Estimation for Scientists and Engineers. Wiley-Interscience, Hoboken (2007) MATH
Metadata
Title
Optimal Observation Time Points in Stochastic Chemical Kinetics
Authors
Charalampos Kyriakopoulos
Verena Wolf
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-27656-4_5

Premium Partner