Non-normality Can Facilitate Pulsing in Biomolecular Circuits

TL;DR

This paper investigates how non-normality in biomolecular circuits can facilitate pulsing behavior, using mathematical tools to analyze simple and complex models, and providing insights for design and analysis.

Contribution

It demonstrates that non-normality is present in standard biomolecular models and correlates with pulsing, offering a framework for analysis and design of such circuits.

Findings

Non-normality is present in standard feedforward loop models.

Non-normality correlates with pulsing dynamics in larger models.

Methods can guide design and analysis of biomolecular circuits.

Abstract

Non-normality can underlie pulse dynamics in many engineering contexts. However, its role in pulses generated in biomolecular contexts is generally unclear. Here, we address this issue using the mathematical tools of linear algebra and systems theory on simple computational models of biomolecular circuits. We find that non-normality is present in standard models of feedforward loops. We used a generalized framework and pseudospectrum analysis to identify non-normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics. Finally, we illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design.