Reaching Agreement in Competitive Microbial Systems
This addresses consensus challenges in synthetic biology applications, providing insights for designing robust microbial systems.
The paper tackles the problem of distributed agreement in microbial systems under competitive interactions, showing that direct competition enables majority consensus with high probability even with small initial gaps, while absence of competition requires large gaps.
We study distributed agreement in microbial distributed systems under stochastic population dynamics and competitive interactions. Motivated by recent applications in synthetic biology, we examine how the presence and absence of direct competition among microbial species influences their ability to reach majority consensus. In this problem, two species are designated as input species, and the goal is to guarantee that eventually only the input species which had the highest initial count prevails. We show that direct competition dynamics reach majority consensus with high probability even when the initial gap between the species is small, i.e., $Ω(\sqrt{n\log n})$, where $n$ is the initial population size. In contrast, we show that absence of direct competition is not robust: solving majority consensus with constant probability requires a large initial gap of $Ω(n)$. To corroborate our analytical results, we use simulations to show that these consensus dynamics occur within practical biological time scales.