Of note, the use of bifurcation theory for classification and categorization of the dynamics of species in a reaction mechanism, initiated in, is now commonly adopted for the construction and fine-tuning of synthetic networks. In particular, the aim is to understand if and how IRMA can be turned into a robust and tunable synthetic oscillator or a bistable switch. Oscillations have a crucial role in cell behaviour: the circadian clock and the cell cycle are common examples. Currently, the interest of many researchers is focused on the properties of cellular oscillations that only depend on the topology of the reaction network, transcending the individual species involved. In the case of IRMA, the goal is challenging, both in terms of the mathematical analysis and in terms of the in vivo implementation. Up to now, only small topologies have been analyzed, and the synthetic oscillators experimentally built consist of a few genes. Moreover, to our knowledge, Ruscogenin numerical continuation techniques for DDEs model have not been applied to the analysis of synthetic gene networks up to now. We found that multi-step processing of gene products in the negative feedback loop and strong cooperativity in gene regulation are the ingredients to elicit robust oscillations. With the aim of tuning the dynamics of IRMA and turning it into an autonomous biochemical oscillator, we shall seek to achieve the desired dynamic behaviour by appropriately varying the model parameters. In so doing it is obviously fundamental both to remain inside the physically feasible range and to minimize the number of changes to the existing network topology and nominal parameter values, in order to speed up the Hapepunine experimental implementation. In our specific case, the number of physical parameters is quite high, thus an exhaustive exploration of the parameter space would be excessively complicated and time consuming. On the other hand, from the analytical view point it is cumbersome to get any results about the structural stability of equilibria under parameters variations since the system is time-delayed and highly non-linear, due to the large value that the Hill coefficients can assume.
The aim is to understand if and how IRMA can be turned into a robust
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