Distributed majority consensus in synthetic microbial consortia with bursty gene expression.

Area of Science:

• Synthetic Biology
• Computational Biology
• Stochastic Processes

Background:

• Engineering microbial consortia for computation requires robust majority consensus mechanisms.
• Multiscale stochasticity, including gene expression noise and population dynamics, challenges reliable computation.
• Existing models often simplify complex intracellular and population-level interactions.

Purpose of the Study:

• To develop a hybrid mathematical framework coupling intracellular dynamics with population-level reactions for microbial consortia.
• To establish principled methods for achieving majority consensus in synthetic microbial systems.
• To analyze the impact of stochasticity and collision rules on computational robustness.

Main Methods:

• A hybrid framework coupling time-varying intracellular gene-expression dynamics (with jump noise) to population birth, death, and collision reactions via random time-change representation.
• Modeling intracellular states influencing birth/death hazards through bounded hazard maps.
• Analyzing two biologically motivated collision rules (Self-Destructive and Non-Self-Destructive) using instantaneous hazard integrals and martingale theory.

Main Results:

• Proved order-wise sufficient majority thresholds for both Self-Destructive (SD) and Non-Self-Destructive (NSD) collision rules under bounded-per-capita hazard assumptions.
• For SD collisions, established that O(log n) non-collision events suffice for consensus, requiring an Ω(log n) initial population gap.
• For NSD collisions, demonstrated that an Ω(n log n) initial gap suffices, contingent on neutral or favorable drift and O(n log n) reaction steps.

Conclusions:

• The developed framework provides an assumption-transparent mathematical and computational basis for majority-like decision-making in noisy synthetic microbial consortia.
• Heavy-tailed intracellular fluctuations affect timing but not the order-wise sufficient gap scales, provided hazard maps remain bounded.
• The study clarifies distinctions between the exact model and simulations, offering insights into computational robustness in engineered biological systems.