Bacterial persistence: a model of survival in changing environments

Abstract

The persistence phenotype is an epigenetic trait exhibited by a subpopulation of bacteria, characterized by slow growth coupled with an ability to survive antibiotic treatment. The phenotype is acquired via a spontaneous, reversible switch between normal and persister cells. These observations suggest that clonal bacterial populations may use persister cells, whose slow division rate under growth conditions leads to lower population fitness, as an "insurance policy" against antibiotic encounters. We present a model of Escherichia coli persistence, and using experimentally derived parameters for both wild type and a mutant strain (hipQ) with markedly different switching rates, we show how fitness loss due to slow persister growth pays off as a risk-reducing strategy. We demonstrate that wild-type persistence is suited for environments in which antibiotic stress is a rare event. The optimal rate of switching between normal and persister cells is found to depend strongly on the frequency of environmental changes and only weakly on the selective pressures of any given environment. In contrast to typical examples of adaptations to features of a single environment, persistence appears to constitute an adaptation that is tuned to the distribution of environmental change.

Figure 1.—

Phase diagram for competition between wild type and hipQ in periodic environments. Growth and stress durations in hours are given by t_g and t_s, respectively. The strain with the higher fitness is indicated in each of the two regions. All parameter values used for this computation are given in Table 1. Extreme possible values of the switching parameter b of the hipQ mutant were considered: main figure uses b_hip = 10⁻⁴; inset uses b_hip = 10⁻⁶.

Figure 2.—

Ratio of growth rates of hipQ to wild type in the (t_g, t_s) plane. Time is given in hours. (A) b_hip = 10⁻⁴; (B) b_hip = 10⁻⁶. The black line in A and B is the curve of equal fitness, shown in Figure 1, along which the z-coordinate is identically zero.

Figure 3.—

Competition of wild type against hipQ at (t_g, t_s) = (20, 2.5), starting from 50,000 wild-type and 50,000 hipQ cells: (A) stochastic dynamics; (B) deterministic dynamics. Gray bars indicate periods of growth, while spaces between bars are periods of antibiotic stress. When the red and blue lines overlap completely, we use a dashed line to resolve them. Circled events are as follows: a is the formation of a single wild-type persister cell, which dies soon after; b is the complete extinction of normal cells of both wild type and hipQ; and c is the switch of a single hipQ persister cell to the normal type. In these simulations, N_max = 110,000 and N_i = 100,000. Parameter values are given in Table 1, taking b_hip = 10⁻⁴. Deterministic dynamics correspond to numerical solution of Equations 1, with population size rescaling, as in the stochastic simulation.

Figure 4.—

Stochastic competitions between wild type and hipQ at t_g = 20 for various values of t_s. For each data point, 100 simulations were run, starting from a 1:1 ratio of wild type to mutant. N_i was taken to be the given population size, while N_max was set to 1.1 N_i. Due to long simulation times for N = 10⁶, the points on this curve for t_s < 3 are averages over 20 runs. The dotted line indicates the result in the large population (deterministic) limit.