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A Simple Negative Interaction in the Positive Transcriptional Feedback of a Single Gene Is Sufficient to Produce Reliable Oscillations
Figure 3
Stochastic and deterministic simulations of the model.
A, C, E, G, I, K. Stochastic time evolution of the protein (
), repressor (
), protein-repressor complex (
), mRNA (
), gene (
) and activated gene (
), respectively. B, D, F, H, J, L. Deterministic time evolution of 
, 
, 
, 
, 
, and 
, respectively. In both simulations, the time evolution of 
(A and B), 
(C and D) and 
(E and F) are very similar except for the presence of fluctuations in the stochastic case. This phenomenon is more pronounced in the time evolution of 
(G and H). The oscillations in 
show sawtooth waveforms. There is a single gene in the model; hence 
molecule. In the time evolution of 
(I and J) and 
(K and L), the stochastic simulation shows discrete transitions between 0 and 1 molecules. By contrast, the deterministic simulation shows unrealistic continuous transitions. The time evolution of 
shows that the gene is activated most of the time (K and L).
doi: https://doi.org/10.1371/journal.pone.0027414.g003