Feedback modules, which appear ubiquitously in biological regulations, are often subject to disturbances from the input, leading to fluctuations in the output. Thus, the question becomes how a feedback system can produce a faithful response with a noisy input. We employed multiple time scale analysis, Fluctuation Dissipation Theorem, linear stability, and numerical simulations to investigate a module with one positive feedback loop driven by an external stimulus, and we obtained a critical quantity in noise attenuation, termed as "signed activation time". We then studied the signed activation time for a system of two positive feedback loops, a system of one positive feedback loop and one negative feedback loop, and six other existing biological models consisting of multiple components along with positive and negative feedback loops. An inverse relationship is found between the noise amplification rate and the signed activation time, defined as the difference between the deactivation and activation time scales of the noise-free system, normalized by the frequency of noises presented in the input. Thus, the combination of fast activation and slow deactivation provides the best noise attenuation, and it can be attained in a single positive feedback loop system. An additional positive feedback loop often leads to a marked decrease in activation time, decrease or slight increase of deactivation time and allows larger kinetic rate variations for slow deactivation and fast activation. On the other hand, a negative feedback loop may increase the activation and deactivation times. The negative relationship between the noise amplification rate and the signed activation time also holds for the six other biological models with multiple components and feedback loops. This principle may be applicable to other feedback systems.
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| Evidence ID | Analyze ID | Gene/Complex | Systematic Name/Complex Accession | Qualifier | Gene Ontology Term ID | Gene Ontology Term | Aspect | Annotation Extension | Evidence | Method | Source | Assigned On | Reference |
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| Evidence ID | Analyze ID | Gene | Gene Systematic Name | Phenotype | Experiment Type | Experiment Type Category | Mutant Information | Strain Background | Chemical | Details | Reference |
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| Evidence ID | Analyze ID | Gene | Gene Systematic Name | Disease Ontology Term | Disease Ontology Term ID | Qualifier | Evidence | Method | Source | Assigned On | Reference |
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| Evidence ID | Analyze ID | Regulator | Regulator Systematic Name | Target | Target Systematic Name | Direction | Regulation of | Happens During | Regulator Type | Direction | Regulation Of | Happens During | Method | Evidence | Strain Background | Reference |
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| Site | Modification | Modifier | Source | Reference |
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| Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Allele | Assay | Annotation | Action | Phenotype | SGA score | P-value | Source | Reference | Note |
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| Evidence ID | Analyze ID | Interactor | Interactor Systematic Name | Interactor | Interactor Systematic Name | Assay | Annotation | Action | Modification | Source | Reference | Note |
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| Complement ID | Locus ID | Gene | Species | Gene ID | Strain background | Direction | Details | Source | Reference |
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| Evidence ID | Analyze ID | Dataset | Description | Keywords | Number of Conditions | Reference |
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| Evidence ID | Analyze ID | File | Description |
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