The Distribution of Mutational Effects on Fitness in a Simple Circadian Clock

  • Laurence Loewe
  • Jane Hillston
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5307)


The distribution of mutational effects on fitness (DME F ) is of fundamental importance for many questions in biology. Previously, wet-lab experiments and population genetic methods have been used to infer the sizes of effects of mutations. Both approaches have important limitations. Here we propose a new framework for estimating the DME F by constructing fitness correlates in molecular systems biology models. This new framework can complement the other approaches in estimating small effects on fitness. We present a notation for the various DMEs that can be present in a molecular systems biology model. Then we apply this new framework to a simple circadian clock model and estimate various DMEs in that system. Circadian clocks are responsible for the daily rhythms of activity in a wide range of organisms. Mutations in the corresponding genes can have large effects on fitness by changing survival or fecundity. We define potential fitness correlates, describe methods for automatically measuring them from simulations and implement a simple clock using the Gillespie stochastic simulation algorithm within StochKit. We determine what fraction of examined mutations with small effects on the rates of the reactions involved in this system are advantageous or deleterious for emerging features of the system like a fitness correlate, cycle length and cycle amplitude. We find that the DME can depend on the wild type reference used in its construction. Analyzing many models with our new approach will open up a third source of information about the distribution of mutational effects, one of the fundamental quantities that shape life.


Cycle Length Circadian Clock Parameter Combination Stochastic Simulation Fitness Correlate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Eyre-Walker, A., Keightley, P.D.: The distribution of fitness effects of new mutations. Nat. Rev. Genet. 8, 610–618 (2007)CrossRefPubMedGoogle Scholar
  2. 2.
    Loewe, L., Charlesworth, B.: Inferring the distribution of mutational effects on fitness in Drosophila. Biology Letters 2, 426–430 (2006)CrossRefPubMedPubMedCentralGoogle Scholar
  3. 3.
    Keightley, P.D., Eyre-Walker, A.: Joint inference of the distribution of fitness effects of deleterious mutations and population demography based on nucleotide polymorphism frequencies. Genetics 177, 2251–2261 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Martin, G., Lenormand, T.: A general multivariate extension of Fisher’s geometrical model and the distribution of mutation fitness effects across species. Evolution 60, 893–907 (2006)CrossRefPubMedGoogle Scholar
  5. 5.
    Kitano, H.: Towards a theory of biological robustness. Mol. Syst. Biol. 3, 137 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Kitano, H.: A robustness-based approach to systems-oriented drug design. Nat. Rev. Drug Disc. 6, 202–210 (2007)CrossRefGoogle Scholar
  7. 7.
    Brommer, J.E.: The evolution of fitness in life-history theory. Biol. Rev. Camb. Philos. Soc. 75, 377–404 (2000)CrossRefPubMedGoogle Scholar
  8. 8.
    Stearns, S.C.: The evolution of life histories. Oxford University Press, Oxford (1992)Google Scholar
  9. 9.
    Rust, M.J., Markson, J.S., Lane, W.S., Fisher, D.S., O’Shea, E.K.: Ordered phosphorylation governs oscillation of a three-protein circadian clock. Science 318, 809–812 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Panda, S., Hogenesch, J.B., Kay, S.A.: Circadian rhythms from flies to human. Nature 417, 329–335 (2002)CrossRefPubMedGoogle Scholar
  11. 11.
    Brunner, M., Káldi, K.: Interlocked feedback loops of the circadian clock of Neurospora crassa. Mol. Microbiol. 68(2), 255–262 (2008)CrossRefPubMedGoogle Scholar
  12. 12.
    Gjuvsland, A.B., Plahte, E., Omholt, S.W.: Threshold-dominated regulation hides genetic variation in gene expression networks. BMC Syst. Biol. 1, 57 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Efron, B., Tibshirani, R.D.: An introduction to the bootstrap. Chapman & Hall, New York (1993)CrossRefGoogle Scholar
  14. 14.
    Leloup, J.C., Gonze, D., Goldbeter, A.: Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J. Biol. Rhythms 14(6), 433–448 (1999)CrossRefPubMedGoogle Scholar
  15. 15.
    Goodwin, B.C.: Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regul. 3, 425–438 (1965)CrossRefPubMedGoogle Scholar
  16. 16.
    Gonze, D., Halloy, J., Goldbeter, A.: Deterministic versus stochastic models for circadian rhythms. J. Biol. Phys. 28, 637–653 (2002)CrossRefPubMedPubMedCentralGoogle Scholar
  17. 17.
    Bundschuh, R., Hayot, F., Jayaprakash, C.: Fluctuations and Slow Variables in Genetic Networks. Biophys. J. 84, 1606–1615 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Arkin, A.P., Rao, C.V.: Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 11, 4999–5010 (2003)Google Scholar
  19. 19.
    Cao, Y., Gillespie, D.T., Petzold, L.: Accelerated Stochastic Simulation of the Stiff Enzyme-Substrate Reaction. J. Chem. Phys. 123(14), 144917–144929 (2005)CrossRefPubMedGoogle Scholar
  20. 20.
    Cao, Y., Gillespie, D.T., Petzold, L.: Adaptive explicit-implicit tau-leaping method with automatic tau selection. J. Chem. Phys. 126, 224101 (2007)CrossRefPubMedGoogle Scholar
  21. 21.
    Gillespie, D.T.: Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35–55 (2007)CrossRefPubMedGoogle Scholar
  22. 22.
    Bradley, J.T., Thorne, T.: Stochastic Process Algebra models of a Circadian Clock. In: Nicol, D.M., Priami, C., Nielson, H.R., Uhrmacher, A.M. (eds.) Simulation and Verification of Dynamic Systems, Dagstuhl Seminar Proceedings, Dagstuhl, Germany (2006),
  23. 23.
    Stenico, M.: Modelling molecular systems with discrete concentration levels in the context of process algebra PEPA: Stochastic and deterministic interpretations. MSc.Thesis, University of Trento (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Laurence Loewe
    • 1
  • Jane Hillston
    • 1
    • 2
  1. 1.Centre for System Biology at EdinburghThe University of EdinburghEdinburghScotland
  2. 2.Laboratory for Foundations of Computer ScienceThe University of EdinburghEdinburghScotland

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