We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . We use a Boolean model for the regulation dynamics and comment on the impact of various Boolean function classes that have been suggested to better represent in vivo regulatory interactions. In addition to an exceptionally large dynamical core network and an excess of self-intercting genes, we find that , even when these differences are eliminated, the Yeastaccommodates more dynamical attractors than best matching model networks which typically come with a single dominant attractor. We further investigate the robustness of the networks under minor perturbations. We find that , requiring all inputs of the Boolean functions to be nonredundant squeezes the stability of the system to a narrower band near the order-chaos boundary, while the network stability still depends strongly on the used function class. The  difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core .
We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare it with two unbiased ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first -by construction- exactly and the second approximately) , degree-degree correlations and the k-core structure observed in Yeast . An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a URLanization which is achieved by subtle modifications in the network's degree distributions . We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behaviour, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast 's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network .
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them with a previously proposed ensemble of networks
it with two unbiased ensembles: one obtained by reshuffling the edges and the other
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Even though the model ensemble successfully reproduces the degree distributions
Both ensembles reproduce the degree distributions (the first -by construction- exactly and the second approximately)
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, we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes
. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a URLanization which is achieved by subtle modifications in the network's degree distributions
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for the regulation dynamics and comment on the impact of various Boolean function classes that have been suggested to better
of regulatory dynamics with various classes of update functions to
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In addition to an exceptionally large dynamical core network and an excess of self-intercting genes, we find that , even when these differences are eliminated, the Yeastaccommodates more dynamical attractors than best matching model networks which typically come with
We find that the Yeast's core network has a qualitatively different behaviour, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to
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We further
Finally, we
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under minor perturbations. We find that , requiring all inputs of the Boolean functions to be nonredundant squeezes the stability of the system to a narrower band near the order-chaos boundary, while the network stability still
and find that the stability
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robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the
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model
reference models
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in terms of stability
's core
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which is consistent with the type of statistically outlier motifs found in the core
suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network