Non-normality can underlie pulse dynamics in  engineering contexts. However, its role in pulses generated in biological contexts is generally unclear. Here, we address this issue using  tools of linear algebra and control 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 pseudosepctrum analysis to identify non-normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics. Finally, we find that the interplay of non-normality and zero dynamics of the system is important in determining the pulse characteristics in response to an input. These results should be useful in analysis, to screen for pulsed dynamics in biomolecular circuits, and in design, by highlighting tunable system properties .
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 .
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many
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biological
biomolecular
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the mathematical
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control
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pseudosepctrum
pseudospectrum
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find that the interplay of non-normality and zero dynamics of the system is important in determining the pulse characteristics in response to an input. These results should be useful in analysis, to screen for pulsed dynamics in biomolecular circuits, and in design, by highlighting tunable system properties
illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design