Minimal frustration underlies the usefulness of incomplete regulatory network models in biology

Shubham Tripathi, David A. Kessler, Herbert Levine

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Regulatory networks as large and complex as those implicated in cell-fate choice are expected to exhibit intricate, very high-dimensional dynamics. Cell-fate choice, however, is a macroscopically simple process. Additionally, regulatory network models are almost always incomplete and/or inexact, and do not incorporate all the regulators and interactions that may be involved in cell-fate regulation. In spite of these issues, regulatory network models have proven to be incredibly effective tools for understanding cell-fate choice across contexts and for making useful predictions. Here, we show that minimal frustration-a feature of biological networks across contexts but not of random networks-can compel simple, low-dimensional steady-state behavior even in large and complex networks. Moreover, the steady-state behavior of minimally frustrated networks can be recapitulated by simpler networks such as those lacking many of the nodes and edges and those that treat multiple regulators as one. The present study provides a theoretical explanation for the success of network models in biology and for the challenges in network inference.

Original languageEnglish
Article numbere2216109120
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number1
StatePublished - 3 Jan 2023

Bibliographical note

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© 2022 the Author(s).


  • cell-fate choice
  • frustration
  • gene regulatory networks
  • network inference
  • sloppiness


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