Deterministic and stochastic simulations of simple genetic circuits

Volume 80 / 2008

Ofer Biham, Nathalie Q. Balaban, Adiel Loinger, Azi Lipshtat, Hagai B. Perets Banach Center Publications 80 (2008), 71-82 MSC: Primary 92D10. DOI: 10.4064/bc80-0-4

Abstract

We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated using rate equations, that account for the concentrations of the mRNAs and proteins produced by these genes. Rate equations are suitable when the concentrations of the relevant molecules in a cell are large and fluctuations are negligible. However, when some of the proteins in the circuit appear in low copy numbers, fluctuations become important and the rate equations fail. In this case stochastic methods, such as direct numerical integration of the master equation or Monte Carlo simulations are required. Here we present deterministic and stochastic simulations of the autorepressor, the switch and the repressilator. We show that fluctuations give rise to quantitative and qualitative changes in the dynamics of these systems. In particular, we demonstrate a fluctuations-induced bistability in a variant of the genetic switch and and noisy oscillations obtained in the repressilator circuit.

Authors

  • Ofer BihamRacah Institute of Physics
    The Hebrew University
    Jerusalem 91904, Israel
    e-mail
  • Nathalie Q. BalabanRacah Institute of Physics
    The Hebrew University
    Jerusalem 91904, Israel
    e-mail
  • Adiel LoingerRacah Institute of Physics
    The Hebrew University
    Jerusalem 91904, Israel
    e-mail
  • Azi LipshtatDepartment of Pharmacology and Biological Chemistry
    Mount Sinai
    School of Medicine
    New York, NY 10029, U.S.A.
    e-mail
  • Hagai B. PeretsFaculty of Physics
    Weizmann Institute of Science
    Rehovot 76100, Israel
    e-mail

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