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. 2014;15 Suppl 12(Suppl 12):S9.
doi: 10.1186/1471-2164-15-S12-S9. Epub 2014 Dec 19.

Dynamics of miRNA driven feed-forward loop depends upon miRNA action mechanisms

Maria A Duk, Maria G Samsonova, Alexander M Samsonov

Dynamics of miRNA driven feed-forward loop depends upon miRNA action mechanisms

Maria A Duk et al. BMC Genomics. 2014.

Abstract

Background: We perform the theoretical analysis of a gene network sub-system, composed of a feed-forward loop, in which the upstream transcription factor regulates the target gene via two parallel pathways: directly, and via interaction with miRNA.

Results: As the molecular mechanisms of miRNA action are not clear so far, we elaborate three mathematical models, in which miRNA either represses translation of its target or promotes target mRNA degradation, or is not re-used, but degrades along with target mRNA. We examine the feed-forward loop dynamics quantitatively at the whole time interval of cell cycle. We rigorously proof the uniqueness of solutions to the models and obtain the exact solutions in one of them analytically.

Conclusions: We have shown that different mechanisms of miRNA action lead to a variety of types of dynamical behavior of feed-forward loops. In particular, we found that the ability of feed-forward loop to dampen fluctuations introduced by transcription factor is the model and parameter dependent feature. We also discuss how our results could help a biologist to infer the mechanism of miRNA action.

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Figures

Figure 1
Figure 1
The incoherent and coherent feed-forward loops. Arrows mean activation, the turned over T-bars indicate repression. TF-transcription factor, miR-miRNA, Target - target protein. A: 1In - type 1 incoherent FFL, TF activates both target mRNA and miRNA synthesis. B: 1C - type 1 coherent FFL, TF represses traget mRNA and activates miRNA synthesis. C: 2In - type 2 incoherent FFL, TF represses both target mRNA and miRNA synthesis. D: 2C - type 2 coherent FFL, TF activates target mRNA and represses miRNA synthesis.
Figure 2
Figure 2
The solutions to the Stop model in various FFLs. 1In - type 1 incoherent FFL, 1C-type 1 coherent FFL, 2In - type 2 incoherent FFL, 2C - type 2 coherent FFL; w, q, s, r and p denote graphs of solutions for TF mRNA, TF, miRNA, target mRNA and target protein, resp. A - D: temporal dynamics of absolute number of each molecule species is presented. E - H: the molecules numbers for each species are normalized on steady state values to better visualize the behaviour of RNA species.
Figure 3
Figure 3
The solutions to the Target degradation model in various FFLs. 1In - type 1 incoherent FFL, 1C-type 1 coherent FFL, 2In - type 2 incoherent FFL, 2C - type 2 coherent FFL; w, q, s, r and p denote graphs of solutions for TF mRNA, TF, miRNA, target mRNA and target protein correspondingly. A - D: the temporal dynamics of absolute number of each molecule species is presented, E - H: molecules numbers for each species are normalized on steady state values to better visualize the behaviour of RNA species.
Figure 4
Figure 4
The variation of target protein quantities in different models of 1In loop in response to variation of hs, kq and initial miRNA molecules numbers. The values of hs coefficient defining the amount of TFs, at which the transcription rate of miRNA gene is half of its maximum value, were within 0 - 400 mol. interval, the translation rates kq for TF were taken from 0 - 0.16sec−1 interval, initial quantities of miRNA were changed as described in section. Left column - Stop model, central column - Target degradation model, right column - Dual degradation model. A - C: In all models the quantity of target protein increases as hs rise. D: In the Stop model the largest number of target protein molecules is observed at intermediate values of the kq coefficient. E-F: In the Target and Dual degradation models kq increase leads to increase of target protein quantity. G and I: In both Stop and Dual degradation models the form of target protein profile changes from the bell-shaped to the U-shaped one as the initial number of miRNA molecules rises. H: In the Target degradation model all profiles show moderate dependence on the change of the initial number of miRNA molecules.
Figure 5
Figure 5
The variation of target protein quantities in different models of 1C loop in response to variation of hs, kq and initial miRNA quantities. The parameter values are the same as of Fig. Left column - Stop model, central column - Target degradation model, right column - Dual degradation model. A-C: The dependence of target protein profiles on hs variation. D - F: The dependence of target protein profiles on kq variation. G - I: The dependence of target protein profiles on initial miRNA quantities. Initial quantities of miRNA were changed as described in section.
Figure 6
Figure 6
The variation of target protein quantities in different models of 2C loop in response to variation of hp, hg, krs and hs coefficients, and initial miRNA and TF quantities. Parameters hp, hg, krs define the action of miRNA on target mRNA, hs is the dissociation coefficient. The miRNA and TF initial quantities were changed as described in section. Left column - Stop model, central column - Target degradation model, right column - Dual degradation model. A: In the Stop model the quantity of target protein increases as the value of hp increases from 0 to 240 molecules. B: In the Target degradation model the quantity of target protein increases as the value of hg increases from 0 to 240 molecules. C: The increase of the krs coefficient value from 0 to 8 × 10−5 mol−1sec−1 results in the fall of the target protein quantity in the Dual degradation model. D - F: In all models the increase of hs from 0 to 400 leads to decrease in target protein quantities. textbfG - I: The dependence of target protein quantities on initial miRNA molecules number in the models. J - L: The patterns of dependence of target protein quantities on initial TF quantities in the models.
Figure 7
Figure 7
The ability of FFLs to buffer noise introduced by TF in frame of different models. In each panel the values of parameter ε calculated in 100 experiments are shown as narrow vertical lines. ε < 0 means that the noise is buffered in a loop, ε > 0 means non-ability of the loop to dampen noise. The coefficients and initial conditions for each experiment are given in section. A-C: Type 1 incoherent loop is able to buffer noise introduced by TF in all models. D - F: Type 2 incoherent loop buffers TF noise in all models. G: Type 1 coherent loop is a bad buffer in frame of the Stop model. I, H: Type 1 coherent loop is able to dampen TF noise in frame of the Target and Dual degradation models. J: Type 2 coherent loop is a bad buffer in frame of the Stop model. K, L: Type 2 coherent loop is able to buffer TF noise under the Target and Dual degradation models.
Figure 8
Figure 8
The target protein profiles in 1C FFL are shown in different models for identical both initial conditions and the steady state level of a target protein. Solid line - Stop model, dashed line-Target degradation model, dotted line - Dual degradation model.
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