On the Robustness of Biomolecular Systems to Perturbations in Translational Resources

The reliable operation of biomolecular circuits depends on the availability of shared cellular resources such as ribosomes, whose levels can vary substantially across growth conditions and cellular contexts. Although resource competition among co-expressed genes is well recognized, the relationship between resource variation and the robustness of circuit dynamics has not been characterized quantitatively. This paper integrates a resource-aware gene expression model, contraction theory-based analytical bounds, and experimental validation to study the effect of translational resource variation on constitutive gene expression and its mitigation through feedback. We show that the constitutive circuit exhibits sensitivity to resource perturbations, and that redesigning it with negative autoregulatory feedback enhances the contraction rate and reduces the steady-state deviation bound, though at lower expression levels. Experiments in E. coli using both plasmid copy number variation and a ribosome sequestration module are consistent with these predictions, confirming that the feedback circuit maintains relatively stable expression under conditions where the constitutive circuit shows large changes. These findings offer a systematic approach for analyzing and improving the robustness of biomolecular circuits operating under variable resource conditions.