Abstract
The authors develop a diagrammatic expansion to compute transfer entropy in stochastic Boolean networks analytically.
Highlights
In biological systems, signals from the environment are transmitted over large complex networks
This can be interpreted to mean that cooperative crosstalk between the two routes 0 → 1 → N and 0 → 1 → 2 → N increases transfer entropy (TE) in the coherent motif, while disruptive crosstalk decreases it in the incoherent motif
We can see that our method gives accurate results even for a large value of φ (i.e., φ 0.7), where the difference between the two motifs is quantitatively captured by the crosstalk term
Summary
Signals from the environment are transmitted over large complex networks. Biological networks often possess characteristic topology, such as small-world and scale-free properties [13,14] and motifs [15,16,17,18] They have regulatory functions that are highly biased, in favor of either high or low frequency in on-state outputs [19,20], and high frequency of canalizing inputs [21,22]. A Boolean function fi should satisfy the dependency on its input variables xIi , i.e., for any j ∈ Ii, fi(x j = 0, xIi\ j ) = fi(x j = 1, xIi\ j ) holds for at least one state of xIi\ j because network topology in our system Eq (1) is II. It is generally difficult to obtain the exact joint distribution, our method can estimate T0→N with arbitrary precision in a wide range of parameters φi
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