Dynamic analysis of sequestration-based feedbacks in cellular and biomolecular circuits

Nonlinear feedback controllers are ubiquitous features of biological systems at different scales. A key motif arising in these systems is a sequestration-based feedback. As a physiological example of this type of feedback architecture, platelets (specialized cells involved in blood clotting) differentiate from stem cells, and this process is activated by a protein called Thrombopoietin (TPO). Platelets actively sequester and degrade TPO, creating negative feedback whereby any depletion of platelets increases the levels of freely available TPO that upregulates platelet production. We show similar examples of sequestration-based feedback in intracellular biomolecular circuits involved in heat-shock response and microRNA regulation. Our systematic analysis of this feedback motif reveals that platelets induced degradation of TPO is critical in enhancing system robustness to external disturbances. In contrast, reversible sequestration of TPO without degradation results in poor robustness to disturbances. We develop exact analytical results quantifying the limits to which the sensitivity to disturbances can be attenuated by sequestration-based feedback. Next, we consider the stochastic formulation of the circuit that takes into account low-copy number fluctuations in feedback components. Interestingly, our results show that the extent of random fluctuations are enhanced with increasing feedback strength, but can exhibit local maxima and minima across parameter regimes. In summary, our systematic analysis highlights design principles for enhancing the robustness of sequestration-based feedback mechanisms to external disturbances and inherent noise in molecular counts. ### Competing Interest Statement The authors have declared no competing interest.