  Recent progress in experimental techniques has enabled us to quantitatively
study stochastic and flexible behavior of biological systems. For example, gene
regulatory networks perform stochastic information processing and their
functionalities have been extensively studied. In gene regulatory networks,
there are specific subgraphs called network motifs that occur at frequencies
much higher than those found in randomized networks. Further understanding of
the designing principle of such networks is highly desirable. In a different
context, information thermodynamics has been developed as a theoretical
framework that generalizes non-equilibrium thermodynamics to stochastically
fluctuating systems with information. Here we systematically characterize gene
regulatory networks on the basis of information thermodynamics. We model
three-node gene regulatory patterns by a stochastic Boolean model, which
receive one or two input signals that carry external information. For the case
of a single input, we found that all the three-node patterns are classified
into four types by using information-thermodynamic quantities such as
dissipation and mutual information, and reveal to which type each network motif
belongs. Next, we consider the case where there are two inputs, and evaluate
the capacity of logical operation of the three-node patterns by using
tripartite mutual information, and argue the reason why patterns with fewer
edges are preferred in natural selection. This result might also explain the
difference of the occurrence frequencies among different types of
feedforward-loop network motifs.
