The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the keys to solve this problem. We analyze a generic model to rigorously describe interactions dynamics of four bacterial strains: one fully sensitive to the drug, one with mutational resistance only, one with plasmidic resistance only and one with both resistances. By dening thresholds numbers (i.e. each strain's eective reproduction and each strain's transition thresholds numbers), we rst express conditions for the existence of non trivial stationary states. We nd that these thresholds mainly depend on bacteria quantitative traits such as nutrient consumption ability, growth conversion factor, death rate, mutation (forward or reverse) and segregational loss of plasmid probabilities (for plasmid-bearing strains). Next, with respect to the order in the set of strain's eective reproduction thresholds numbers, we show that the qualitative dynamics of the model range from the extinction of all strains, coexistence of sensitive and mutational resistance strains to the coexistence of all strains at equilibrium. Finally, we go through some applications of our general analysis depending on whether bacteria strains interact without or with drug action (either cytostatic or cytotoxic).
We study competition of two non-motile bacterial strains in a three-dimensional channel numerically, and analyze how their configuration evolves in space and time. We construct a lattice model that takes into account self-replication, mutation, and killing of bacteria. When mutation is not significant, the two strains segregate and form stripe patterns along the channel. The formed lanes are gradually rearranged, with increasing length scales in the two-dimensional cross-sectional plane. We characterize it in terms of coarsening and phase ordering in statistical physics. In particular, for the…
Levy flights in the space of mutations model time evolution of bacterial DNA. Parameters in the model are adjusted in order to fit observations coming from the Long Time Evolution Experiment with E. Coli.
Bacterial chemotaxis systems are as diverse as the environments that bacteria inhabit, but how much environmental variation can cells tolerate with a single system? Diversification of a single chemotaxis system could serve as an alternative, or even evolutionary stepping-stone, to switching between multiple systems. We hypothesized that mutations in gene regulation could lead to heritable control of chemotactic diversity. By simulating foraging and colonization of E. coli using a single-cell chemotaxis model, we found that different environments selected for different behaviors. The resulting …
Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. The selection-mutation model has unobservable fitness parameters and, to estimate them, we use an Approximate Bayesian Computation (ABC) algorithm. The algorithms are illustrated using in vitro data for phase variable genes of Campylobacter jejuni.
A number of studies have suggested using comparisons between DNA sequences of closely related bacterial isolates to estimate the relative rate of recombination to mutation for that bacterial species. We consider such an approach which uses single-locus variants: pairs of isolates whose DNA differ at a single gene locus. One way of deriving point estimates for the relative rate of recombination to mutation from such data is to use composite likelihood methods. We extend recent work in this area so as to be able to construct confidence intervals for our estimates, without needing to resort to co…
Metagenomics has revealed hundreds of bacterial species in almost all microbiota. In a few well-studied cases, bacterial communities have been observed to coordinate their metabolic fluxes. In principle, bacteria can divide tasks to reap the benefits of specialization, as in human economies. However, the benefits and stability of an economy of bacterial specialists are far from obvious. Here, we physically model the population dynamics of bacteria that compete for steadily supplied resources. Importantly, we explicitly model the metabolic fluxes yielding cellular biomass production under the c…
Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial colonies. Such sectors are spatially segregated sub-populations of mutants. The sectors can be seen both in disk-shaped colonies and in branching colonies. We study the sectors using two models we have used in the past to study bacterial colonies -- a continuous reaction-diffusion model with non-linear diffusion and a discrete ``Communicating Walkers'' model. We fi…
Mutation rate is a key determinant of the pace as well as outcome of evolution, and variability in this rate has been shown in different scenarios to play a key role in evolutionary adaptation and resistance evolution under stress caused by selective pressure. Here we investigate the dynamics of resistance fixation in a bacterial population with variable mutation rates and show that evolutionary outcomes are most sensitive to mutation rate variations when the population is subject to environmental and demographic conditions that suppress the evolutionary advantage of high-fitness subpopulation…
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grows stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild type population si…
Competition between random genetic drift and natural selection plays a central role in evolution: Whereas non-beneficial mutations often prevail in small populations by chance, mutations that sweep through large populations typically confer a selective advantage. Here, however, we observe chance effects during range expansions that dramatically alter the gene pool even in large microbial populations. Initially well-mixed populations of two fluorescently labeled strains of Escherichia coli develop well-defined, sector-like regions with fractal boundaries in expanding colonies. The formation of …
The differences between DNA-sequences within a population are the basis to infer the ancestral relationship of the individuals. Within the classical infinitely many sites model, it is possible to estimate the mutation rate based on the site frequency spectrum, which is comprised by the numbers $C_1,...,C_{n-1}$, where n is the sample size and $C_s$ is the number of site mutations (Single Nucleotide Polymorphisms, SNPs) which are seen in $s$ genomes. Classical results can be used to compare the observed site frequency spectrum with its neutral expectation, $E[C_s]= θ_2/s$, where $θ_2$ is the sc…
The body is home to a diverse microbiota, mainly in the gut. Resistant bacteria are selected for by antibiotic treatments, and once resistance becomes widespread in a population of hosts, antibiotics become useless. Here, we develop a multiscale model of the interaction between antibiotic use and resistance spread in a host population, focusing on an important aspect of within-host immunity. Antibodies secreted in the gut enchain bacteria upon division, yielding clonal clusters of bacteria. We demonstrate that immunity-driven bacteria clustering can hinder the spread of a novel resistant bacte…
Unraveling the evolutionary forces shaping bacterial diversity can today be tackled using a growing amount of genomic data. While the genome of eukaryotes is highly stable, bacterial genomes from cells of the same species highly vary in gene content. This huge variation in gene content led to the concepts of the distributed genome of bacteria and their pangenome (Tettelin et al.,2005; Ehrlich et al.,2005). We present a population genetic model for gene content evolution which accounts for several mechanisms. Gene uptake from the environment is modeled by events of gene gain along the genealogi…
The current picture of bacterial evolution is based largely on studies of 16S rRNA. However, this is just one gene. It is known that horizontal gene transfer can occur between bacterial species, although the frequency and implications of this are not fully understood. If horizontal transfer were frequent, there would be no single evolutionary tree for bacteria because each gene would follow a different tree. We carried out phylogenetic analyses of rRNA and tRNA genes from Proteobacteria (a diverse group for which many complete genome sequences are available) using RNA-specific phylogenetic met…
This paper develops a mathematical model describing the influence that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant in order to survive. We analyze the behavior of the model in the limit of low and high antibiotic-induced first-order death rate constants, and find that the highest mean fitness is obtained …
Recent studies have shown that packings of cells, both eukaryotic cellular tissues and growing or swarming bacterial colonies, can often be understood as active nematic fluids. A key property of volume-conserving active nematic model systems is chaotic self-mixing characterized by motile topological defects. However, for active nematics driven by growth rather than motility, less is understood about mixing and defect motion. Mixing could affect evolutionary outcomes in bacterial colonies by counteracting the tendency to spatially segregate into monoclonal sectors, which reduces the local genet…
Recent studies have revealed effects of various tree species on soil physical and chemical properties. However, effects of various tree species on composition and activity of soil microbiota and the relevant controls remain poorly understood. We evaluated the influence of tree species associated with two different mycorrhizal types, ectomycorrhiza (EcM) and arbuscular mycorrhiza (AM), on growth, biomass and metabolic activity of soil fungal and bacterial communities using common garden tree species experiments throughout Denmark. The soil microbial communities differed between six European tre…
The cell invasion mechanism of Trypanosoma cruzi has similarities with some intracellular bacterial taxa especially regarding calcium mobilization. This mechanism is not observed in other trypanosomatids, suggesting that the molecules involved in this type of cell invasion were a product of (1) acquired by horizontal gene transfer; (2) secondary loss in the other trypanosomatid lineages of the mechanism inherited since the bifurcation Bacteria-Neomura (1.9 billion to 900 million years ago) or (3) de novo evolution from non-homologous proteins via convergent evolution. Similar to T. cruzi, seve…
The fruit fly Drosophila is a classic model organism to study adaptation as well as the relationship between genetic variation and phenotypes. Although associated bacterial communities might be important for many aspects of Drosophila biology, knowledge about their diversity, composition, and factors shaping them is limited. We used 454-based sequencing of a variable region of the bacterial 16S ribosomal RNA gene to characterize the bacterial communities associated with wild and laboratory Drosophila isolates. In order to specifically investigate effects of food source and host species on bact…
We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [Chavanis & Sire, PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index $n$ similar to polytropic stars in astrophysics. At the critical index $n_{3}=d/(d-2)$ (where $d\ge 2$ is the dimension of space), there exists a critical temperature $Θ_{c}$ (for a given m…
Conjugation is the primary mechanism of horizontal gene transfer that spreads antibiotic resistance among bacteria. Although conjugation normally occurs in surface-associated growth (e.g., biofilms), it has been traditionally studied in well-mixed liquid cultures lacking spatial structure, which is known to affect many evolutionary and ecological processes. Here we visualize spatial patterns of gene transfer mediated by F plasmid conjugation in a colony of Escherichia coli growing on solid agar, and we develop a quantitative understanding by spatial extension of traditional mass-action models.…
Aalto University（阿尔托大学）；Broad Institute（博德研究所）；Harbor-UCLA Medical Center（港城加州大学洛杉矶分校医疗中心）
Bacterial populations that colonize a host play important roles in host health, including serving as a reservoir that transmits to other hosts and from which invasive strains emerge, thus emphasizing the importance of understanding rates of acquisition and clearance of colonizing populations. Studies of colonization dynamics have been based on assessment of whether serial samples represent a single population or distinct colonization events. A common solution to estimate acquisition and clearance rates is to use a fixed genetic distance threshold. However, this approach is often inadequate to …
Dispersal of species is a fundamental ecological process in the evolution and maintenance of biodiversity. Limited control over ecological parameters has hindered progress in understanding of what enables species to colonise new area, as well as the importance of inter-species interactions. Such control is necessary to construct reliable mathematical models of ecosystems. In our work, we studied dispersal in the context of bacterial range expansions and identified the major determinants of species coexistence for a bacterial model system of three Escherichia coli strains (toxin producing, sens…
