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Accueil > EN > Research Areas > Complex Systems Dynamics > BIological Systems > Small Networks

Dynamics of small genetic networks

par Benjamin PFEUTY, Marc LEFRANC, Webmestre - publié le , mis à jour le

The dynamic regulation of gene expression and their transcriptions is a fundamental problem in biology. This regulation determines the behavior of genetic networks underlying the major cellular functions. In this topic, we have developed several lines of research

Dynamics of self-repressed gene :

The regulation of a gene by its protein product (self-regulation) is a frequently encountered pattern, and which also enables the analytical developments pushed. We studied how complex mechanisms of degradation of RNA and protein can interact with the inherent delays in the transcription or transportation for the emergence of oscillations [1]. Because of the complexity of the transcriptional machinery, the rate of synthesis of RNA adapts delay with protein concentration, contrary to what is generally assumed in theoretical studies, and should be considered a dynamic variable.

Reaction diagram of the self-regulated gene circuit.
Reaction diagram of the self-regulated gene circuit.

We showed a deterministic model that the oscillations are easier to obtain for a characteristic value of the delay time [1]. This result is confirmed by the stochastic stimulation. The analytical expression of that time used to identify the region of the parameter space where the dynamics of transcription can not be overlooked. In a more detailed study, we investigated analytically the influence of another source of delay (transportation cytoplasm - nucleus) and highlighted the fact that the combination of a cascade of two times and saturated degradation dramatically amplifies the oscillations [2].

Finally, we have studied the influence of molecular fluctuations on the dynamics of self-regulated gene and showed a resonance between the gene response time and lifetimes of the protein and RNA leads to a sub-Poisson statistics of the distribution of protein peaks over time, similar to the photon anti - bunching and that can be interpreted as an analogue of a deterministic oscillation. [3]

Molecular fluctuations in the self repressed gene.
Molecular fluctuations in the self repressed gene.
(A) Biochemical reactions composing the network. P, M, G, and G:P denote protein, mRNA, free gene and bound gene chemical species, respectively. The kinetic constants of the reactions are indicated, with \Omega denoting cell volume. In the limit where \Omega is large, the mRNA and protein copy numbers become macroscopic variables, with decreasing fluctuations, while the gene state remains microscopic and displays full-scale variations. (B) Block diagram representation of the network, consisting of a random telegraph signal generator representing the gene state-flip dynamics, and of a low-pass filter of cut-off frequency \omega_c representing proteins and mRNA dynamics. The telegraph signal regulates its frequency and duty cycle through feedback from the low pass filter.

Transcriptional kinetics

The study of transcriptional kinetics resulting from the stochastic dynamics of RNA polymerase, the enzyme that binds to DNA and travels the to synthesize RNA molecule (Thesis J. Wang and collaboration with Romano ). This is a non equilibrium statistical physics problem that can be described by TASEP models [4].

TASEP model with pausing.
TASEP model with pausing.
(A) Particles can transition from an active state (in white) to a paused state (in grey) and back, with respective rates f and 1/\tau. (B) Active particles can hop to the next site if it is empty (exclusion process), with unit-time probability \epsilon. Paused particles do not move.

Regulation patterns

Study of genetic oscillators operating principles and circadian clocks by methods of evolution in silico and analysis revealed patterns (Thesis B. Lannoo and collaboration with E. Carlon). We are particularly interested in the titration of a self-regulatory protein with another protein.


- [1] P.-E. Morant, Q. Thommen, F. Lemaire, C. Vandermoere, B. Parent and M. Lefranc, "Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics", Phys. Rev. Lett. 102, 068104 (2009)
- [2] J. Wang, et al., "Interacting time delays in a self-repressing gene", in preparation
- [3] J. Wang, M. Lefranc, Q. Thommen, "Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene", Biophysical Journal (2014) in press.
- [4] J. Wang, B. Pfeuty, Q. Thommen, M. C. Romano and M. Lefranc "Minimal model of transcriptional elongation processes with pauses", Phys Rev E (2014) in press


- Mamen Romano (Institute for Complex Systems and Mathematical Biology, and Institute of Medical Sciences, University of Aberdeen)
- Enrico Carlon (Institute for theoretical physics, Katholiek Universiteit Leuven)


- Marc Lefranc (
- Quentin Thommen (