The fluctuation of intracellular biochemical reactions (intrinsic noise) reduces the information transmitted from an extracellular input to a cellular response. On the other hand , recent studies  demonstrated that the transmitted information hardly decreases against the extracellular input fluctuation (extrinsic noise) when the intrinsic noise is large. Therefore, it has been suggested that larger intrinsic noise enables more robust information transmission against the extrinsic noise, which is called `` intrinsic noise-induced robustness (INIR) '' . However,  it is unclear whether INIR universally appears in various biochemical reactionsbecause previous studies focused on the specific biochemical reactions . Moreover, its mechanism remains elusive. In this paper, we address these questions by analyzing the simple models. We first analyze the linear model , whose input-output relation is linear. We show that the robustness against the extrinsic noise increases with the intrinsic noise in the linear model, and therefore , INIR is realized in this simple model . Moreover, we demonstrate that INIR strongly appears when the variance of the intrinsic noise is larger than that of the input distribution. Next, we analyze the threshold model , whose output depends on whether the input exceeds the threshold or not . When the threshold is equal to the mean of the input, INIR is also realizedin the threshold model. On the other hand, when the threshold is much larger than the mean of the input , the threshold model shows the stochastic resonance(SR), and the INIR is not always realized . However, the robustness against the extrinsic noise and the transmitted information are trade-off in the linear model and in the threshold model without SR , whereas they can be simultaneously increased in the threshold model with SR .
Fluctuations of intracellular biochemical reactions (intrinsic noise) reduce the information transmitted from an extracellular input to a cellular response. However , recent studies have demonstrated that the transmitted information barely decreases with respect to extracellular input fluctuations (extrinsic noise) when the intrinsic noise is large. Therefore, it has been suggested that larger intrinsic noise enables more robust information transmission in the presence of extrinsic noise, which is called intrinsic noise-induced robustness (INIR) . However, because previous studies have focused on specific scenarios, it is unclear whether INIR appears universally in biochemical reactions . 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 , therefore realizing the INIR phenomenon . Moreover, INIR is particularly strong 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 . However, 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 .
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