Gene regulatory networks (GRNs) control biological processes like pluripotency, differentiation, and apoptosis. Omics methods can identify a large number of putative network components (on the order of hundreds or thousands) but it is possible that in many cases a small subset of genes control the state of GRNs. Here, we explore how the topology of the interactions between network components may indicate whether the effective state of a GRN can be represented by a small subset of genes. We use methods from information theory to model the regulatory interactions in GRNs as cascading and superposing information channels. We propose an information loss function that enables identification of the conditions by which a small set of genes can represent the state of all the other genes in the network. This information-theoretic analysis extends to a measure of free energy change due to communication within the network, which provides a new perspective on the reducibility of GRNs. Both the information loss and relative free energy depend on the density of interactions and edge communication error in a network. Therefore, this work indicates that a loss in mutual information between genes in a GRN is directly coupled to a thermodynamic cost, i.e., a reduction of relative free energy, of the system.
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