An information-theoretic perspective on feed-forward loop abundances in transcriptional networks
Abstract
In the transcriptional networks of \textit{Escherichia coli} and \textit{Saccharomyces cerevisiae}, the eight feed-forward loop (FFL) motifs occur at markedly different frequencies. Although previous studies have linked the abundant C1- and I1-FFLs to specific dynamical functions, a common account of the broader pattern is lacking. To address this gap, we adopt an information-theoretic approach. An FFL transmits information through two paths that share an input and converge on an output, suggesting that their interaction may contribute to differences among motifs. To investigate this, we decompose input-output mutual information (MI) into pathway MI and interference MI (IMI). Here, the pathway MI collects the contributions of individual pathways, whereas IMI identifies the contribution that arises from their interference. We find that within a representative parameter regime, IMI values of FFLs produce a hierarchy that closely resembles the abundance ordering in \textit{E. coli}, whereas total and pathway MIs do not. Motivated by this observation, we perform constrained optimization that identifies parameter regimes compatible with abundance-like targets for both \textit{S. cerevisiae} and \textit{E. coli}. We relate the optimized IMI hierarchy to pathway interference strength and local pathway sensitivities to understand the underlying biophysical origin. Our framework thus probes the correspondence between pathway interference, information transmission, and motif-abundance hierarchies.
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BibTeX
@misc{nandi2026informationtheoretic,
title = {{An information-theoretic perspective on feed-forward loop abundances in transcriptional networks}},
author = {Mintu Nandi and Sudip Chattopadhyay and Suman K Banik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.17699},
eprint = {2608.17699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17699},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An information-theoretic perspective on feed-forward loop abundances in transcriptional networks
AU - Mintu Nandi
AU - Sudip Chattopadhyay
AU - Suman K Banik
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2608.17699
UR - https://arxiv.org/abs/2608.17699
AB - In the transcriptional networks of \textit{Escherichia coli} and \textit{Saccharomyces cerevisiae}, the eight feed-forward loop (FFL) motifs occur at markedly different frequencies. Although previous studies have linked the abundant C1- and I1-FFLs to specific dynamical functions, a common account of the broader pattern is lacking. To address this gap, we adopt an information-theoretic approach. An FFL transmits information through two paths that share an input and converge on an output, suggesting that their interaction may contribute to differences among motifs. To investigate this, we decompose input-output mutual information (MI) into pathway MI and interference MI (IMI). Here, the pathway MI collects the contributions of individual pathways, whereas IMI identifies the contribution that arises from their interference. We find that within a representative parameter regime, IMI values of FFLs produce a hierarchy that closely resembles the abundance ordering in \textit{E. coli}, whereas total and pathway MIs do not. Motivated by this observation, we perform constrained optimization that identifies parameter regimes compatible with abundance-like targets for both \textit{S. cerevisiae} and \textit{E. coli}. We relate the optimized IMI hierarchy to pathway interference strength and local pathway sensitivities to understand the underlying biophysical origin. Our framework thus probes the correspondence between pathway interference, information transmission, and motif-abundance hierarchies.
ER -