[Paper Review] A simple model for the distribution of plasmid lengths

Alice Ledda, Luca Ferretti|arXiv (Cornell University)|Nov 2, 2014

Bacteriophages and microbial interactions17 references3 citations

TL;DR

This paper proposes a fitness-based evolutionary model linking plasmid length to gene redundancy and conjugation efficiency, showing that diminishing returns from redundant genes create an 'insertion load' that limits plasmid stability. The model predicts a positive correlation between conjugative machinery and plasmid length, explains plasmid prevalence without fixation, and links rising antibiotic stress to increased plasmid length and resistance gene content.

ABSTRACT

Plasmids are major players in Horizontal Gene Transfer mechanisms, hence they are highly variable in their gene content and length. We propose a model for the fitness of a plasmid as a function of its length, which predicts diminishing returns. We infer the distribution of plasmid lengths by a simple evolutionary model and we show that there is a positive correlation between the presence and efficiency of the conjugation machinery and the length of the plasmid. The model predicts an "insertion load" on plasmids, which could explain also the fact that plasmids are widespread in bacterial populations but rarely established. Finally we discuss how the typical length of plasmids increases with the amount of stress in the environment, focusing on the recent human-driven increase in antibiotic concentrations.

Motivation & Objective

• To understand the evolutionary forces shaping plasmid length distribution in bacterial populations.
• To model how gene redundancy and fitness costs influence plasmid persistence and transmission.
• To investigate the role of conjugation machinery in determining plasmid length and stability.
• To explore how environmental stress, particularly increasing antibiotic concentrations, affects plasmid length evolution.
• To explain the paradox of widespread plasmid presence without stable fixation in bacterial populations.

Proposed method

• Models plasmid fitness as a function of length using a continuous approximation of gene function acquisition, assuming random sampling from a finite set of n*f functions.
• Uses the equation Δf(l) = s* (1 − e^(-kl)) to represent the cumulative fitness advantage, where k = 1/(n*f * l_gene), capturing diminishing returns from added genes.
• Integrates length-dependent fitness into a simple evolutionary model to infer the equilibrium distribution of plasmid lengths.
• Analyzes the impact of conjugation rate and plasmid cost on the stability and length of plasmids, particularly under environmental stress.
• Considers the 'insertion load' from redundant genes as a key factor limiting plasmid establishment and promoting loss in the absence of selective pressure.
• Simulates the transient fitness response to sudden environmental stress (e.g., antibiotic exposure), showing temporary fitness gains before load effects dominate.

Experimental results

Research questions

• RQ1 What drives the observed distribution of plasmid lengths across bacterial populations?
• RQ2 How does gene redundancy affect plasmid fitness and evolutionary stability?
• RQ3 What is the relationship between conjugation machinery and plasmid length?
• RQ4 Why are plasmids widespread but rarely fixed in bacterial populations?
• RQ5 How does increasing environmental antibiotic stress influence plasmid length and resistance gene accumulation?

Key findings

• The model predicts that plasmid fitness increases with length but with diminishing returns due to gene redundancy, creating a fitness cost known as the 'insertion load'.
• There is a positive correlation between the presence and efficiency of conjugation machinery and the length of the plasmid, as conjugative plasmids can tolerate more non-conjugative genes.
• Plasmids are maintained near the 'border of stability' due to insertion load, making them prone to loss or fixation under small environmental perturbations.
• The model explains why plasmids are widespread but rarely fixed: they persist under stress but are lost when selection pressure drops.
• Increased environmental antibiotic concentrations lead to a transient fitness advantage for longer plasmids, accelerating their spread and increasing their average length over time.
• Conjugative plasmids are predicted to carry more non-conjugative genes than mobilizable plasmids, consistent with empirical observations of plasmid length variation.