# Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty

### Shaunak Sen and Richard M. Murray

Submitted, 2015 Conference on Decision and Control (CDC)

Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncer- tainty and bound the variation in the magnitude of the input- output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers.

- Conference Paper: http://www.cds.caltech.edu/~murray/preprints/sm15-cdc_s.pdf
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