Phenotypic Switching Can Speed up Microbial Evolution

Abstract

Stochastic phenotype switching has been suggested to play a beneficial role in microbial populations by leading to the division of labour among cells, or ensuring that at least some of the population survives an unexpected change in environmental conditions. Here we use a computational model to investigate an alternative possible function of stochastic phenotype switching: as a way to adapt more quickly even in a static environment. We show that when a genetic mutation causes a population to become less fit, switching to an alternative phenotype with higher fitness (growth rate) may give the population enough time to develop compensatory mutations that increase the fitness again. The possibility of switching phenotypes can reduce the time to adaptation by orders of magnitude if the "fitness valley" caused by the deleterious mutation is deep enough. Our work has important implications for the emergence of antibiotic-resistant bacteria. In line with recent experimental findings, we hypothesise that switching to a slower growing - but less sensitive - phenotype helps bacteria to develop resistance by providing alternative, faster evolutionary routes to resistance.

Figure 1

The model. (A) Diagram showing the six possible states of a cell and the available transitions between them. The genotypes are labelled 1, 2 and 3, the phenotypic states are labelled A and B. Transitions between genotypes/phenotypes occur at rates μ and α, respectively. All cells are initially in state 1A. Evolution continues until a single cell reaches the target state 3A. (B) Each cell can replicate, switch phenotype, or die with rates r, α and d respectively. Upon replication a cell has the probability μ of producing a mutant of each neighbouring genotype. (C) The fitness landscapes for both phenotypes. Phenotype A has a fitness valley at 2A while phenotype B has uniform fitness across all genotypes.

Figure 2

Mean adaptation time T for different scenarios – note logarithmic scale. (A) A bar chart comparing pairs of T values with and without switching phenotypes (α = 10⁻⁵ and α = 0 respectively) for different parameter values. Left-most pair of bars: K = 100, μ = 10⁻⁵, δ = 0.4 and d = 0.1. A label underneath each pair of bars indicates which variable has been changed compared to the left-most pair. (B) T as a function of the switching rate α for a range of mutation probabilities μ. Parameters as in (A). For small enough μ an optimal (minimizing T) switching rate can be seen.

Figure 3

Trajectories of successful cells in genotype/phenotype space. (A) Diagram showing how different trajectories that go through the same set of states are grouped together into the same trajectory class. This class is represented as a symbol in which blue lines correspond to transitions made by the successful cell. (B) The most probable trajectory class as a function of μ and α, for K = 100, δ = 0.4 and d = 0.1. Three regions labelled 1, 2, 3 can be distinguished. (C) Comparison between analytic formula for the mean adaptation time (lines) and computer simulations (blue points). Parameters: K = 100, μ = 10⁻⁵, d = 0.1, δ = 0.4. Black curve corresponds to T = T_AT_B/(T_A + T_B) (see SI Sec. X for explanation) with T_A given by Eq. (1) and T_B by Eq. (2). Red curve is from Eq. (3).

Figure 4

(A) Trajectories of successful cells can be grouped regarding whether they avoid (trajectory “u”) or visit (trajectory “v”) the fitness valley at state 2A. (B) The most common trajectory group and the probability of a trajectory visiting state 2A (colours, see the colour bar) as a function of switching rate α and carrying capacity K, for μ = 10⁻⁶. In all simulations δ = 0.4 and d = 0.1.

Figure 5

Mean adaptation time T plotted versus the switching rate α, for different fitness costs c = {0, 0.01, 0.02, 0.05, 0.1} of phenotype B and for parameters K = 100, μ = 10⁻⁵, δ = 0.9 and d = 0.1.

Figure 6

Evolution selects switching rates within the optimal range. (A) Left: examples of evolutionary trajectories in the extended model in which the stochastic phenotype switching (SPS) rate α also evolves. (A) Right: trajectories are used to calculate transition probabilities between the states of the system, which are then represented by the thickness of links connecting the states. Red links correspond to mutations in phenotype A, green links to mutations phenotype B and purple links to switching between phenotypes. (B) Graph of transition probabilities where line thicknesses are proportional to the probability that a successful trajectory will take that step. The parameters are K = 100, μ = 10⁻⁵, δ = 0.4 and d = 0.1, the same that were used in Fig. 2B (blue line). The population begins at the wild-type 1A with α = 2.56 × 10⁻¹⁰ and evolves until a cell in state 3A is produced. (C) The probability that genotype space is crossed at a given α in either phenotype A or B. The probability has a maximum where the mean adaptation time T for fixed α (plot from Fig. 2B superimposed on the same graph) has its minimum.