Bulletin of Mathematical Biology

, Volume 73, Issue 9, pp 2132–2151 | Cite as

Dynamic Stabilization in the PU1-GATA1 Circuit Using a Model with Time-Dependent Kinetic Change

  • Jay L. MichaelsEmail author
  • Vincent Naudot
  • Larry S. Liebovitch
Open Access
Original Article


The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these two genes reveals that constant levels of self-excitation and cross-inhibition allow the most self-exciting or cross-inhibiting gene to dominate the system. However, since biological systems rarely exist in an unchanging equilibrium, we modeled this gene circuit using discrete time-dependent changes in the parameters in lieu of steady state parameters. These time-dependent parameters lead to new phenomena, including the development of new limit cycles and basins of attraction. These phenomena are not present in models using constant parameter values. Our findings suggest that even small perturbations in the PU.1 and GATA1 feedback loops may substantially alter the gene expression and therefore the cell phenotype. These time-dependent parameter models may also have implications for other gene systems and provide new ways to understand the mechanisms of cellular differentiation.


Computational biology of gene regulatory networks Blood stem cell fate commitment 


  1. Bokes, P., King, J. R., & Loose, M. (2009). A bistable genetic switch which does not require high co-operativity at the promoter: a two-time-scale model for the PU.1-GATA1 interaction. Math. Med. Biol. doi: 10.1093/imammb/dqn026. zbMATHGoogle Scholar
  2. Chang, H.H., Hemberg, M., Barahona, M., Ingber, D. E., & Huang, S. (2008). Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature, 453, 544–547. CrossRefGoogle Scholar
  3. Chickarmane, V., Enver, T., & Peterson, C. (2009). Computational modeling of the hematopoietic erythroid-myleoid switch reveals insights into cooperativity, priming, and irreversibility. PLoS Comput. Biol., 5, e1000268. CrossRefGoogle Scholar
  4. Day, C. (2009). Analysis reveals when evolution favors one mode of gene regulation over another. Phys. Today, July, 20–23. Google Scholar
  5. Dormand, J. R., & Prince, P. J. (1980). A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math., 6, 19–26. MathSciNetzbMATHCrossRefGoogle Scholar
  6. Gardner, T. S., Cantor, C. R., & Collins, J. J. (2000). Construction of a genetic toggle switch in Escherichia coli. Nature, 403, 339–342. CrossRefGoogle Scholar
  7. Gerland, U., & Hwa, T. (2009). Evolutionary selection between alternative modes of gene regulation. Proc. Natl. Acad. Sci. USA, 106, 8841–8846. CrossRefGoogle Scholar
  8. Goldbeter, A. (1996). Biochemical oscillations and cellular rhythms: the molecular bases of periodic and chaotic behavior. New York: Cambridge University Press. zbMATHCrossRefGoogle Scholar
  9. Graf, T. (2002). Differentiation plasticity of hematopoietic cells. Blood, 99, 3089–3101. CrossRefGoogle Scholar
  10. Graf, T., & Stadtfeld, M. (2008). Heterogeneity of embryonic and adult stem cells. Cell, 3, 480–483. Google Scholar
  11. Henzler-Wildman, K., & Kern, D. (2007). Dynamic personalities of proteins. Nature, 450, 964–972. CrossRefGoogle Scholar
  12. Huang, S., Guo, Y. P., May, F., & Enver, R. (2007). Bifurcation dynamics in lineage-commitment in bipotent progenitor cells. Dev. Biol., 305, 695–713. CrossRefGoogle Scholar
  13. Kaern, M., Elston, T. C., Blake, W. J., & Collins, J. J. (2005). Stochasticity in gene expression: From theories to phenotypes. Nat. Rev. Genet., 6, 451–464. CrossRefGoogle Scholar
  14. Koga, S., Yamaguchi, N., Abe, T., Minegishi, M., Tsuchiya, S., Yamamoto, M., & Minegishi, N. (2007). Cell-cycle-dependent oscillation of GATA2 expression in hematopoietic cells. Blood, 109, 4200–4208. CrossRefGoogle Scholar
  15. Lei, J. (2008). Stochasticity in single gene expression with both intrinsic noise and fluctuation in kinetic parameters. J. Theor. Biol., 256, 485–492. CrossRefGoogle Scholar
  16. Levens, D., & Gupta, A. (2010). Reliable noise. Science, 327, 1088–1089. CrossRefGoogle Scholar
  17. Losick, R., & Desplan, C. (2008). Stochasticity and cell fate. Science, 320, 65–68. CrossRefGoogle Scholar
  18. Mendez-Ferrer, S., Lucas, D., Battista, M., & Frenette, P. S. (2008). Haematopoietic stem cell release is regulated by circadian oscillations. Nature, 452, 442–447. CrossRefGoogle Scholar
  19. Okuno, Y., Huang, G., Rosenbauer, F., Evans, E. K., Raomska, H. S. et al. (2002). Potential autoregulation of transcript factor PU.1 by an upstream regulatory element. Mol. Biol. Cell, 25, 2832–2845. Google Scholar
  20. Ptashne, M., & Gann, A. (2002). Genes and signals. New York: Cold Spring Harbor Library Press. Google Scholar
  21. Ravid, K., & Licht, J. D. (2001). Transcription factors: normal and malignant development of blood cells. New York: Wiley-Liss. Google Scholar
  22. Roeder, I., & Glauche, I. (2006). Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors PU.1 and GATA1. J. Theor. Biol., 241, 852–865. MathSciNetGoogle Scholar
  23. Roeder, I., & Loeffler, M. (2002). A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp. Hematol., 30, 853–861. CrossRefGoogle Scholar
  24. To, T., & Maheshri, N. (2010). Noise can induce bimodality in positive transcriptional feedback loops without bistability. Science, 327, 1142–1145. CrossRefGoogle Scholar
  25. Yu, C., Cantor, A. B., Yang, H., Brown, C., Wells, R. A. et al. (2002). Targeted deletion of high-affinity GATA-bining site in the GATA1 promoter leads to selective loss of the eosinophil lineage in vivo. J. Exp. Med., 195, 1387–1395. CrossRefGoogle Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Jay L. Michaels
    • 1
    Email author
  • Vincent Naudot
    • 2
  • Larry S. Liebovitch
    • 3
  1. 1.Department of PsychologyFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Department of Mathematical ScienceFlorida Atlantic UniversityBoca RatonUSA
  3. 3.Division of Mathematics and Natural Sciences, Queens CollegeCity University of New YorkFlushingUSA

Personalised recommendations