  Fluctuations in intracellular reactions (intrinsic noise) reduce the
information transmitted from an extracellular input to a cellular response.
However, recent studies have demonstrated that the decrease in the transmitted
information with respect to extracellular input fluctuations (extrinsic noise)
is smaller when the intrinsic noise is larger. Therefore, it has been suggested
that robustness against extrinsic noise increases with the level of the
intrinsic noise. We call this phenomenon intrinsic noise-induced robustness
(INIR). As previous studies on this phenomenon have focused on complex
biochemical reactions, the relation between INIR and the input--output of a
system is unclear. Moreover, the mechanism of INIR remains elusive. In this
paper, we address these questions by analyzing simple models. We first analyze
a model in which the input--output relation is linear. We show that the
robustness against extrinsic noise increases with the intrinsic noise,
confirming the INIR phenomenon. Moreover, the robustness against the extrinsic
noise is more strongly dependent on the intrinsic noise when the variance of
the intrinsic noise is larger than that of the input distribution. Next, we
analyze a threshold model in which the output depends on whether the input
exceeds the threshold. When the threshold is equal to the mean of the input,
INIR is realized, but when the threshold is much larger than the mean, the
threshold model exhibits stochastic resonance, and INIR is not always apparent.
The robustness against extrinsic noise and the transmitted information can be
traded off against one another in the linear model and the threshold model
without stochastic resonance, whereas they can be simultaneously increased in
the threshold model with stochastic resonance.
