Modeling Growth-Mediated Dilution in Synthetic Circuits: Effects of Circuit Topology and Phase Separation

Growth-mediated dilution is a major source of variability and instability in synthetic gene circuits, influencing both expression dynamics and circuit memory. Our previous work demonstrated that circuit topology plays a critical role in determining how robustly a circuit maintains its function under changing growth conditions, and that phase separation can serve as a physical mechanism to buffer these perturbations. In this chapter, we present a comprehensive modeling framework that integrates deterministic gene regulation, stochastic gene expression, cell-volume growth and division, and condensate formation. We introduce two complementary stochastic simulation approaches. The first is a hybrid stochastic-deterministic population-level model that treats intracellular gene expression deterministically while modeling cell growth, division, and burden-dependent feedback stochastically to capture population-level dilution effects. The second is a single-cell, fully stochastic simulation that uses the Gillespie algorithm to model transcription, translation, and degradation reactions while continuously updating cell growth, dilution, division, and condensate size through a thermodynamic phase-separation model. The modeling frameworks presented here provide generalizable tools for analyzing growth-circuit interactions, evaluating robustness across parameter regimes, and guiding the design of synthetic circuits resilient to physiological fluctuations.