Journal of Mathematical Biology

, Volume 64, Issue 1–2, pp 131–147 | Cite as

On the impact of the distance between two genes on their interaction curve

  • Siamak Taati
  • Enrico Formenti
  • Jean-Paul Comet
  • Gilles Bernot


We analyze a basic building block of gene regulatory networks using a stochastic/geometric model in search of a mathematical backing for the discrete modeling frameworks. We consider a network consisting only of two interacting genes: a source gene and a target gene. The target gene is activated by the proteins encoded by the source gene. The interaction is therefore mediated by activator proteins that travel, like a signal, from the source to the target. We calculate the production curve of the target proteins in response to a constant-rate production of activator proteins. The latter has a sigmoidal shape (like a simple delay line) that is sharper and taller when the two genes are closer to each other. This provides further support for the use of discrete models in the analysis gene regulatory networks. Moreover, it suggests an evolutionary pressure towards making the interacting genes closer to each other to make their interactions more efficient and more reliable.


Gene regulatory networks Stochastic model Poisson process Brownian motion 

Mathematics Subject Classification (2000)

92B05 92C42 60G55 60J70 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bernot G, Comet J-P, Richard A, Guespin J (2004) Application of formal methods to biological regulatory networks: Extending Thomas’ asynchronous logical approach with temporal logic. J Theor Biol 229(3): 339–347CrossRefMathSciNetGoogle Scholar
  2. Folland GB (1999) Real analysis: modern techniques and their applications 2nd edn. Wiley-Interscience, LondonzbMATHGoogle Scholar
  3. Glass L, Kauffman SA (1973) The logical analysis of continuous, nonlinear biochemical control networks. J Theor Biol 39: 103–129CrossRefGoogle Scholar
  4. Halford SE (2009) An end to 40 year of mistakes in DNA-protein association kinetics. Biochem Soc Trans 37: 343–348CrossRefGoogle Scholar
  5. Halford SE, Marko JF (2004) How do site-specific DNA-binding proteins find their targets. Nucleic Acids Res 32(10): 3040–3052CrossRefGoogle Scholar
  6. Jensen RB, Shapiro L (2000) Proteins on the move: dynamic protein localization in prokaryotes. Trends Cell Biol 10(11): 483–488CrossRefGoogle Scholar
  7. Junier I, Martin O, Képès F (2010) Spatial and topological organization of DNA chains induced by gene co-localization. PLoS Comput Biol 6(2): e1000678CrossRefGoogle Scholar
  8. Kingman JFC (1993) Poisson processes. Oxford University Press, USAzbMATHGoogle Scholar
  9. Krylov NV (1994) Introduction to the theory of diffusion processes. Translation of mathematical monographs, vol 142. Am Math Soc. (English Translation)Google Scholar
  10. Leloup J-C, Goldbeter A (2004) Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms. J Theor Biol 230(4): 541–562CrossRefMathSciNetGoogle Scholar
  11. Norris V, den Blaauwen T, Cabin-Flaman A, Doi RH, Harshey R, Janniere L, Jimenez-Sanchez A, Jin DJ, Levin PA, Mileykovskaya E, Minsky A, Saier M Jr, Skarstad K (2007) A functional taxonomy of bacterial hyperstructures. Microbiol Mol Biol Rev 71(1): 230–253CrossRefGoogle Scholar
  12. Redner S (2001) A guide to first-passage processes. Cambridge University Press, LondonzbMATHGoogle Scholar
  13. Thellier M, Legent G, Amar P, Norris V, Ripoll C (2006) Steady-state kinetic behaviour of functioning-dependent structures. FEBS J 273(18): 4287–4299CrossRefGoogle Scholar
  14. Thomas R, Kaufman M (2001a) Multistationarity, the basis of cell differentiation and memory. I. structural conditions of multistationarity and other nontrivial behavior. Chaos 11: 170–179CrossRefzbMATHMathSciNetGoogle Scholar
  15. Thomas R, Kaufman M (2001b) Multistationarity, the basis of cell differentiation and memory. II. logical analysis of regulatory networks in terms of feedback circuits. Chaos 11: 180–195CrossRefzbMATHMathSciNetGoogle Scholar
  16. Tyson J, Reka A, Goldbeter A, Ruoff P, Sible J (2008) Biological switches and clocks. J R Soc Interface 5(Suppl 1): S1–S8CrossRefGoogle Scholar
  17. Wunderlich Z, Mirny LA (2008) Spatial effects on the speed and reliability of protein-DNA search. Nucleic Acids Res 36(11): 3570–3578CrossRefGoogle Scholar
  18. Yin C, Wu R (1996) Some problems on balls and spheres for Brownian motion. Sci China Ser A Math 39(6): 572–582zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Siamak Taati
    • 1
  • Enrico Formenti
    • 1
  • Jean-Paul Comet
    • 1
  • Gilles Bernot
    • 1
  1. 1.Université Nice-Sophia AntipolisSophia AntipolisFrance

Personalised recommendations