We performed theoretical analysis of a gene network sub-system, containing a feed forward loop (FFL) mediated by transcription factor (TF) and miRNA. We shown that mechanisms of miRNA action lead to various dynamical behaviour of FFL during cell cycle, essentially, at early stages, and govern their ability to dampen noise caused by TF fluctuations.

The molecular mechanisms of miRNA action are not clear so far, and we investigate three mathematical models [1], that describe the gene expression in miRNA-mediated FFL and are based on the 1st order non-linear coupled O.D.E. We solved in closed form the equations with regulation terms containing the Hill functions. The solutions provide a genuine 'check point' for numerical simulations, and we studied their dependence on variations in time, initial conditions, coefficients etc .

We rigorously proven the uniqueness of solutions, i.e., in the models there is the one-to-one correspondence between the given parameter set and the solution, describing temporal dynamics of target protein production in FFL. In addition to qualitative consideration [1] based on steady state data only, we first examined the FFL temporal dynamics quantitatively and at the whole time interval of cell cycle. We show [2] that FFLs mediated by miRNA and TF may have many possible outcomes, depending on interaction between the loop elements. The target protein profiles can take different forms uniquely defined by initial conditions and model coefficients.

FFLs show distinctive ability to dampen the TF fluctuations, depending on the mechanism of miRNA action. Analytical results show that one may predicate that a noise arisen at early stage in TF production in all loops and models will be translated into miRNA and target protein in alignment with the Hill functions in a model. For example, we found that when the noise amplitude is high, but the total amount (the regular one plus noise fluctuations) of miRNA is intermediate (the Hill function is far from limits), then the noise is

translated directly into the protein production and will not be suppressed by a loop. When the noise amplitude is still high, however, the total amount of miRNA is sufficiently high, too (the Hill function is close to any of limits), then the noise level is relatively small to disturb the protein production and will be suppressed by a loop.

To sum up, the analysis of temporal behaviour of the FFL together with the ability to find out a unique solution for any set of parameters may help a biologist to select the most feasible mechanism of miRNA action for the type of FFL given.

References

1. M.Osella et al. PLoS Computational Biology, 7, 3, e1001101 (2011).

2. Duk M.A., Samsonov A.M., Samsonova M.G. in: Proc. DD-2013, p 42-46. ISBN 978-1-4799-1037-3.