Evolution of Microbial Growth Traits Under Serial Dilution

Grow now, pay later: When should a bacterium go into debt?

Microbes grow in a wide variety of environments and must balance growth and stress resistance. Despite the prevalence of such trade-offs, understanding of their role in nonsteady environments is limited. In this study, we introduce a mathematical model of "growth debt," where microbes grow rapidly initially, paying later with slower growth or heightened mortality. We first compare our model to a classical chemostat experiment, validating our proposed dynamics and quantifying Escherichia coli's stress resistance dynamics. Extending the chemostat theory to include serial-dilution cultures, we derive phase diagrams for the persistence of "debtor" microbes. We find that debtors cannot coexist with nondebtors if "payment" is increased mortality but can coexist if it lowers enzyme affinity. Surprisingly, weak noise considerably extends the persistence of resistance elements, pertinent for antibiotic resistance management. Our microbial debt theory, broadly applicable across many environments, bridges the gap between chemostat and serial dilution systems.

How microscopic epistasis and clonal interference shape the fitness trajectory in a spin glass model of microbial long-term evolution

The adaptive dynamics of evolving microbial populations takes place on a complex fitness landscape generated by epistatic interactions. The population generically consists of multiple competing strains, a phenomenon known as clonal interference. Microscopic epistasis and clonal interference are central aspects of evolution in microbes, but their combined effects on the functional form of the population's mean fitness are poorly understood. Here, we develop a computational method that resolves the full microscopic complexity of a simulated evolving population subject to a standard serial dilution protocol. Through extensive numerical experimentation, we find that stronger microscopic epistasis gives rise to fitness trajectories with slower growth independent of the number of competing strains, which we quantify with power-law fits and understand mechanistically via a random walk model that neglects dynamical correlations between genes. We show that increasing the level of clonal interference leads to fitness trajectories with faster growth (in functional form) without microscopic epistasis, but leaves the rate of growth invariant when epistasis is sufficiently strong, indicating that the role of clonal interference depends intimately on the underlying fitness landscape. The simulation package for this work may be found at https://github.com/nmboffi/spin_glass_evodyn.

Frequent asymmetric migrations suppress natural selection in spatially structured populations

Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, evolutionary graph theory has shown that some graphs can amplify or suppress natural selection, in a way that depends on microscopic update rules. We propose a model of spatially structured populations on graphs directly inspired by batch culture experiments, alternating within-deme growth on nodes and migration-dilution steps, and yielding successive bottlenecks. This setting bridges models from evolutionary graph theory with Wright-Fisher models. Using a branching process approach, we show that spatial structure with frequent migrations can only yield suppression of natural selection. More precisely, in this regime, circulation graphs, where the total incoming migration flow equals the total outgoing one in each deme, do not impact fixation probability, while all other graphs strictly suppress selection. Suppression becomes stronger as the asymmetry between incoming and outgoing migrations grows. Amplification of natural selection can nevertheless exist in a restricted regime of rare migrations and very small fitness advantages, where we recover the predictions of evolutionary graph theory for the star graph.

Studying Whole-Genome Duplication Using Experimental Evolution of Chlamydomonas

In this chapter, we present the use of Chlamydomonas reinhardtii in experiments designed to study the evolutionary impacts of whole genome duplication. We shortly introduce the algal species and depict why it is an excellent model for experimental evolution. Subsequently, we discuss the most relevant steps and methods in the design of a ploidy-related Chlamydomonas experiment. These steps include strain selection, ploidy determination, different methods of making diplo- and polyploid Chlamydomonas cells, replication, culturing conditions, preservation, and the ways to quantify phenotypic and genotypic change.

Microbial population dynamics decouple growth response from environmental nutrient concentration

How the growth rate of a microbial population responds to the environmental availability of chemical nutrients and other resources is a fundamental question in microbiology. Models of this response, such as the widely used Monod model, are generally characterized by a maximum growth rate and a half-saturation concentration of the resource. What values should we expect for these half-saturation concentrations, and how should they depend on the environmental concentration of the resource? We survey growth response data across a wide range of organisms and resources. We find that the half-saturation concentrations vary across orders of magnitude, even for the same organism and resource. To explain this variation, we develop an evolutionary model to show that demographic fluctuations (genetic drift) can constrain the adaptation of half-saturation concentrations. We find that this effect fundamentally differs depending on the type of population dynamics: Populations undergoing periodic bottlenecks of fixed size will adapt their half-saturation concentrations in proportion to the environmental resource concentrations, but populations undergoing periodic dilutions of fixed size will evolve half-saturation concentrations that are largely decoupled from the environmental concentrations. Our model not only provides testable predictions for laboratory evolution experiments, but it also reveals how an evolved half-saturation concentration may not reflect the organism's environment. In particular, this explains how organisms in resource-rich environments can still evolve fast growth at low resource concentrations. Altogether, our results demonstrate the critical role of population dynamics in shaping fundamental ecological traits.

The effect of weak clonal interference on average fitness trajectories in the presence of macroscopic epistasis

Adaptation dynamics on fitness landscapes is often studied theoretically in the strong-selection, weak-mutation regime. However, in a large population, multiple beneficial mutants can emerge before any of them fixes in the population. Competition between mutants is known as clonal interference, and while it is known to slow down the rate of adaptation (when compared to the strong-selection, weak-mutation model with the same parameters), how it affects the shape of long-term fitness trajectories in the presence of epistasis is an open question. Here, by considering how changes in fixation probabilities arising from weak clonal interference affect the dynamics of adaptation on fitness-parameterized landscapes, we find that the change in the shape of fitness trajectory arises only through changes in the supply of beneficial mutations (or equivalently, the beneficial mutation rate). Furthermore, a depletion of beneficial mutations as a population climbs up the fitness landscape can speed up the rescaled fitness trajectory (where adaptation speed is measured relative to its value at the start of the experiment), while an enhancement of the beneficial mutation rate does the opposite of slowing it down. Our findings suggest that by carrying out evolution experiments in both regimes (with and without clonal interference), one could potentially distinguish the different sources of macroscopic epistasis (fitness effect of mutations vs change in fraction of beneficial mutations).

Disentangling Intrinsic and Extrinsic Gene Expression Noise in Growing Cells

Gene expression is a stochastic process. Despite the increase of protein numbers in growing cells, the protein concentrations are often found to be confined within small ranges throughout the cell cycle. Generally, the noise in protein concentration can be decomposed into an intrinsic and an extrinsic component, where the former vanishes for high expression levels. Considering the time trajectory of protein concentration as a random walker in the concentration space, an effective restoring force (with a corresponding "spring constant") must exist to prevent the divergence of concentration due to random fluctuations. In this work, we prove that the magnitude of the effective spring constant is directly related to the fraction of intrinsic noise in the total protein concentration noise. We show that one can infer the magnitude of intrinsic, extrinsic, and measurement noises of gene expression solely based on time-resolved data of protein concentration, without any a priori knowledge of the underlying gene expression dynamics. We apply this method to experimental data of single-cell bacterial gene expression. The results allow us to estimate the average copy numbers and the translation burst parameters of the studied proteins.