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

Arman Ferdowsi1

  • 1Faculty of Computer Science, University of Vienna, Vienna, Austria.

Mathematical Biosciences
|July 9, 2026
PubMed
Summary

We developed a hybrid framework for engineering microbial consortia to achieve robust population-level computations. Our model ensures majority consensus despite biological noise, providing a mathematical basis for synthetic biology decision-making.

Keywords:
Distributed computingMajority consensusMicrobial consortiaStochastic differential equationsStochastic gene expressionSynthetic biology

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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.