Non-normality Can Facilitate Pulsing in Biomolecular Circuits
This work offers a new theoretical perspective for understanding pulse dynamics in biomolecular circuits, which is relevant for synthetic biology and systems biology.
The authors show that non-normality, a property from linear algebra, is present in standard models of biomolecular feedforward loops and correlates with pulsing dynamics, providing analytical tools for screening and design.
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.