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Figure 1 | BMC Systems Biology

Figure 1

From: Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks

Figure 1

Yeast cell cycle signed network of [19]. The undirected graph shown is a symmetrization of the one in [19], in which we also dropped the self-loops. In (a) the application of a gauge transformation to the three nodes in black reduces the number of negative edges (in red) and s σ = 1 becomes a ground state. In (b) a typical response to a perturbation is shown for the yeast cell cycle network and for a monotone network on the same graph: in the second system the order is always maintained in the response (blue trajectories are monotone states). In (c) the probability of being in the ground state p(s ground ) (upper plot) and the internal energy (h) (lower plot) are shown for the yeast cell cycle network (red) and for the monotone network (blue) as a function of β. As the dimension of the system is small, no mean field approximation is necessary in these calculation. The monotone network achieves order (here p(s ground ) > 0.8) earlier with growing β and the energy minimum reached is lower. The color bands are meant to highlight the values of β for which this happens

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