Quantifying Selective Pressures Driving Bacterial Evolution Using Lineage Analysis

Organisms use a variety of strategies to adapt to their environments and maximize long-term growth potential, but quantitative characterization of the benefits conferred by the use of such strategies, as well as their impact on the whole population’s rate of growth, remains challenging. Here, we use a path-integral framework that describes how selection acts on lineages—i.e., the life histories of individuals and their ancestors—to demonstrate that lineage-based measurements can be used to quantify the selective pressures acting on a population. We apply this analysis to Escherichia coli bacteria exposed to cyclical treatments of carbenicillin, an antibiotic that interferes with cell-wall synthesis and affects cells in an age-dependent manner. While the extensive characterization of the life history of thousands of cells is necessary to accurately extract the age-dependent selective pressures caused by carbenicillin, the same measurement can be recapitulated using lineage-based statistics of a single surviving cell. Population-wide evolutionary pressures can be extracted from the properties of the surviving lineages within a population, providing an alternative and efficient procedure to quantify the evolutionary forces acting on a population. Importantly, this approach is not limited to age-dependent selection, and the framework can be generalized to detect signatures of other trait-specific selection using lineage-based measurements. Our results establish a powerful way to study the evolutionary dynamics of life under selection and may be broadly useful in elucidating selective pressures driving the emergence of antibiotic resistance and the evolution of survival strategies in biological systems.

Popular Summary

The theory of natural selection describes how an individual’s ability to produce viable offspring drives evolution: Organisms are in constant competition to transmit genetic information between generations. Obtaining a direct measurement of the selective pressures influencing this process requires monitoring every birth, death, or other life event within a population for extended periods of time, a challenging task for many biological systems. We use path integrals—a mathematical tool typically used in quantum physics—to describe evolving populations of bacteria and demonstrate how very accurate information about selection forces can be extracted from the lineage of a single individual. We focus on the survival function—the probability that an individual reaches a certain age—and the reproduction rate, the rate of producing offspring at a certain age.

By subjecting E. coli populations to cyclical antibiotic treatments in a lethal dose that interfere with how cell walls are synthesized, we first monitor and process thousands of division and lysis events to extract a comprehensive measure of selection forces acting on the population. We find that the probability of lysis is correlated with the time since the last cellular division. Parallel to this, we construct the complete pedigree of the population and show that a few surviving lineages are characterized by high fitness, which refers to their ability to generate offspring and survive each antibiotic treatment. We next demonstrate that the properties of these surviving lineages are a good approximation to the optimal lineage distribution—a distribution that emerges from the path integral formalism that maximizes the population’s growth rate. We use the statistics of individual ages along each surviving lineage to infer pressures that exist on the population, i.e., a higher probability of death above a certain age. A key relationship exists between this optimal lineage and the selection pressure acting on the population, and we demonstrate that the comprehensive and lineage measures of selection strongly agree with one another.

Our results demonstrate that precise information about the strength of selection and the forces driving evolution can be obtained by analyzing a single surviving lineage. Even though our analysis describes the survival of bacteria in response to cyclical antibiotic treatments, our framework can be generalized to detect signatures of trait-specific selection in other biological systems that include multicellular organisms and human populations. Additionally, we expect that our findings will inform the development of antibiotic resistance.

Figure 1

Strength of selection on life-history traits and the optimal lineage relation. (a) A behavioral change (e.g., a mutation, an epigenetic modification, or a different survival strategy) causes a small fitness increase $\delta h$ in a life-history trait $h(x)$ for cells at ages $x_1$ and $x_2$. (b) After a sufficiently long time, a population reaches steady-state growth and the population dynamics are dominated by cells whose ancestral lineage has an optimal age distribution ${\rho }_{*}(x)$. The distribution ${\rho }_{*}$ determines what portion of lineages benefit from the small boosts in fitness at ages $x_1$ and $x_2$: the change in growth rate $\delta \mathrm{\Lambda }$ resulting from the boost in fitness at age $x_i$ is precisely equal to $\delta h·{\rho }_{*}$ evaluated at $x_i$. (c) In this example, the change in growth rate is larger at age $x_1$ because it affects a larger fraction of the population’s lineage history.

Figure 2

Lytic response to carbenicillin antibiotics. (a) Schematic representation of the microfluidics device, where cells confined to growth chambers can be monitored for hundreds of generations. (b) The number of cells decreases sharply following each $100\mu \mathrm{g}/\mathrm{mL}$ carbenicillin treatment. The measured lysis rate is also in phase with the antibiotic treatments. (c) Average lysis rate in response to each 20-min treatment of carbenicillin (number of treatments is 25). The lysis rate peaks approximately 10 min after antibiotic removal. (d) The rate of cell lysis increases with cell age ($\mathrm{mean}\pm \mathrm{s}.\mathrm{d}.$, $n=3\min$).

Figure 3

Age-dependent growth and survival functions. (a) The age-dependent division probability obtained from life-history measurements of a population under cyclical carbenicillin treatments [$q(x)$, blue line] differs from a population grown under constant conditions (dashed line). Inset: The bimodal distribution of $q(x)$ is caused by the carbenicillin-dependent division rate, where cellular divisions are avoided during carbenicillin treatments. (b) Graph of the survival function $\ell (x)$ under carbenicillin treatments (blue line) as a function of the cell age. A non-negligible fraction of persister cells survive more than 2 h under carbenicillin treatments compared with a population grown in the absence of selection (dashed lines). Inset: Carbenicillin treatments decrease the survival probability for ages $\le 28\min$ (blue line) compared to an untreated population (dashed line). (c) The fraction of cellular deaths caused by lysis decreases once cells survive a single carbenicillin treatment cycle (dashed line at $t=90\min$). (d) An example of a persister cell that survives multiple antibiotic treatments but fails to revert to a proliferative state. (e) The average elongation rate decreases with increasing cell lifetime for cells under cyclical carbenicillin treatments (blue line) but remains constant for the untreated population (dashed line).

Figure 4

Lineage distribution and selection. (a) Bacterial pedigree of a population for $t=[0,20]$ h. The difference between lineage (teal) and population (orange) measurements is highlighted. The yellow bars denote antibiotic treatments. (b) Comparison between the average age of the population and surviving lineages during each treatment cycle. (c) The age distribution of population is underrepresented for ages between 25 and 50 min and enriched with younger cells. The different distributions reflect the age-dependent rate of lysis, whose effect is to remove older cells from the population but not from the surviving lineage. Inset: Lineage and population age distributions for cell populations grown in the absence of selection (i.e., constant conditions). (d) Comparison between the two measurements of the reproduction function, obtained using direct life-history measurements [$k(x)=b(x)\ell (x)$, dashed line] or extracted from the surviving lineage age distribution [$k_s(x)$ in Eq. (4), blue circles], is in very good agreement. Data are reported as the population $\mathrm{average}\pm \mathrm{s}.\mathrm{d}.$ ($n=18$ populations). Inset: Comparison between the rate of change of the reproduction function [$\kappa (x)\equiv k^{\prime }(x)/k(x)$] obtained from the life history and surviving lineage measurements ($\mathrm{mean}\pm \mathrm{s}.\mathrm{d}.$, $n=18$ populations).