The network model used in this work consists of 130 internal nodes and 9 input nodes, which represent protein species being either active (1) or inactive (0), connected through 542 interactions. Input signals (top) and output nodes (bottom) are labeled with abbreviations that are defined in the text.
Dynamics of the system for constant inputs. (a) Dynamic evolution of the network nodes for random initial conditions and a fixed combination of input states (stress, IL1/TNF, ECM, and are inactive, while pump, EGF, , , and are active). White (black) regions correspond to active (inactive) states. After some initial transient, the network reaches a limit cycle attractor where the activity of some of nodes oscillate periodically, while that of the others is fixed to either the active or inactive state. (b) Histogram of the transient lengths for different random initial conditions (see main text). Transient lengths were computed by first finding the attractors and then identifying the iteration at which the attractor is reached. The inset in (b) shows the histogram in doubly logarithmic axes, which reveals that the tail of the histogram follows a power law (red dashed line) with scaling exponent 2.4. Note that the data shown in the inset has not been divided by .
Population dynamics of the system for constant inputs. (a) Population average for output nodes obtained from 3000 realizations of the network dynamics with different initial conditions and the same fixed combination of input states as in Fig. 2(a). Different combinations of fixed inputs lead to different population averages of the outputs. (b) Histogram of the transient lengths of the population dynamics for the 512 possible combinations of input states. Transients for the population dynamics are computed as the maximum transient lengths of the average activities of single nodes. These node-specific transients were calculated by first establishing the range of values of the stationary state (within a certain tolerance) and then finding the iteration at which the node’s average activity value enters this range and never leaves it again. The population relaxation durations are close to the median transient lengths of individual realizations of the network dynamics [cf. Fig. 2(b)]. As in Fig. 2(b), the inset in plot (b) depicts the histogram in doubly logarithmic scale. The plot indicates that this histogram has again a fat tail, although in this case the number of data points is too small to reveal a clear-cut power law.
Effects of stochastic chatter acting upon the input nodes. (a) Dynamic evolution of the network nodes for a given realization of chatter affecting all input nodes. In this case, the evolution of the network is erratic and does not reach stable or periodic attractors [compare the evolution shown here with that presented in Fig. 2(a)]. (b) Population average for the output nodes [color coding as in Fig. 3(a)] obtained from the 3000 realizations of the network dynamics for a fixed value of chatter for all input states.
Response of the network to periodic driving. Power spectrum of the average activity of an output node (Akt) vs stimulation frequency, , being applied to a given input node (stress), while the other input nodes are subject to a fixed chatter level .
Frequency filtering of the network. Power spectral density of the average output-node activity at the input frequency , normalized to the power of the input signal, as a function of , for one input node and fixed chatter level for the rest of inputs. The periodic driving is applied to (a) stress and (b) EGF input nodes.
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