Identification of network motifs capable of frequency-tunable and robust oscillation

TL;DR

This study systematically analyzes 249 three-node network motifs to identify structural features that enable frequency-tunable and robust oscillations, revealing a tradeoff between tunability and robustness in biochemical networks.

Contribution

It introduces a comprehensive enumeration of network architectures and classifies them into functional groups based on oscillation properties, highlighting design principles for tunable and robust biochemical oscillators.

Findings

Most frequency-tunable networks are less robust.

Least frequency-tunable networks are less robust.

A tradeoff exists between frequency tunability and robustness.

Abstract

Oscillation has an important role in bio-dynamical systems such as circadian rhythms and eukaryotic cell cycle. John Tyson et. al. in Nature Review Mol Cell Biol 2008 examined a limited number of network topologies consisting of three nodes and four or fewer edges and identified the network design principles of biochemical oscillations. Tsai et. al. in Science 2008 studied three different network motifs, namely a negative feedback loop, coupled negative feedback loops, and coupled positive and negative feedback loops, and found that the interconnected positive and negative feedback loops are capable of generating frequency-tunable oscillations. We enumerate 249 topologically unique network architectures consisting of three nodes and at least three cyclic inhibitory edges, and identify network architectural commonalities among three functional groups: (1) most frequency-tunable yet less robust oscillators, (2) least frequency-tunable and least robust oscillators, and (3) less frequency-tunable yet most robust oscillators. We find that Frequency-tunable networks cannot simultaneously express high robustness, indicating a tradeoff between frequency tunability and robustness.