Abstract
Biological switches must sense changes in signal concentration and at the same time buffer against signal noise. While many studies have focused on the response of switching systems to noise in the ON state, how systems buffer noise at both ON and OFF states is poorly understood. Through analytical and computational approaches, we find that switching systems require different dynamics at the OFF state than at the ON state in order to have good noise buffering capability. Specifically, we introduce a quantity called the input-associated Signed Activation Time (iSAT) that concisely captures an intrinsic temporal property at either the ON or OFF state. We discover a trade-off between achieving good noise buffering in the ON versus the OFF states: a large iSAT corresponds to noise amplification in the OFF state in contrast to noise buffering in the ON state. To search for biological circuits that can buffer noise in both ON and OFF states, we systematically analyze all three-node circuits and identify mutual activation as a central motif. We also study connections among signal sensitivity, iSAT, and noise amplification. We find that a large iSAT at the ON state maintains signaling sensitivity while minimizing noise propagation. Taken together, the analysis of iSATs helps reveal the noise properties of biological networks and should aid in the design of robust switches that can both repress noise at the OFF state and maintain a reliable ON state.