Scaling of Noise Under Resource Constraints in Gene Regulatory Motifs

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Understanding noise propagation in gene regulatory circuits requires accounting for both model and resource constraints. In this work, we investigated the role of model order in influencing stochastic behaviour by deriving and analytically comparing reduced protein-only models with higher-order models that include mRNA and molecular complexes, and found that protein-based models can exhibit higher noise levels in the gene expression. Through frequency-response analysis, we explained that the higher-order models provide additional noise-filtering effects. We also analyzed a one-dimensional constrained model and showed that the Fano factor decreases as the strength of resource constraint increases. Finally, we considered larger circuit motifs, such as toggle switches and incoherent feed-forward loops, and found that resource limitations can minimise stochastic switching in a bistable circuit, whereas in an incoherent feed-forward loop, resource constraints can make the adaptation faster. Our results highlight that both mechanistic detail and shared resource constraints play a central role in determining fluctuation levels in biomolecular circuits.