Quantifying Dynamic Stability of Genetic Memory Circuits

Bistability/Multistability has been found in many biological systems including genetic memory circuits. Proper characterization of system stability helps to understand biological functions and has potential applications in fields such as synthetic biology. Existing methods of analyzing bistability are either qualitative or in a static way. Assuming the circuit is in a steady state, the latter can only reveal the susceptibility of the stability to injected DC noises. However, this can be inappropriate and inadequate as dynamics are crucial for many biological networks. In this paper, we quantitatively characterize the dynamic stability of a genetic conditional memory circuit by developing new dynamic noise margin (DNM) concepts and associated algorithms based on system theory. Taking into account the duration of the noisy perturbation, the DNMs are more general cases of their static counterparts. Using our techniques, we analyze the noise immunity of the memory circuit and derive insights on dynamic hold and write operations. Considering cell-to-cell variations, our parametric analysis reveals that the dynamic stability of the memory circuit has significantly varying sensitivities to underlying biochemical reactions attributable to differences in structure, time scales, and nonlinear interactions between reactions. With proper extensions, our techniques are broadly applicable to other multistable biological systems.