Interpreting phenotypic antibiotic tolerance and persister cells as evolution via epigenetic inheritance

Abstract

Epigenetic inheritance is the transmission of nongenetic material such as gene expression levels, RNA and other biomolecules from parents to offspring. There is a growing realization that such forms of inheritance can play an important role in evolution. Bacteria represent a prime example of epigenetic inheritance because a large array of cellular components is transmitted to offspring, in addition to genetic material. Interestingly, there is an extensive and growing empirical literature showing that many bacteria can form 'persister' cells that are phenotypically resistant or tolerant to antibiotics, but most of these results are not interpreted within the context of epigenetic inheritance. Instead, persister cells are usually viewed as a genetically encoded bet-hedging strategy that has evolved in response to a fluctuating environment. Here I show, using a relatively simple model, that many of these empirical findings can be more simply understood as arising from a combination of epigenetic inheritance and cellular noise. I therefore suggest that phenotypic drug tolerance in bacteria might represent one of the best-studied examples of evolution under epigenetic inheritance.

Keywords: antibiotic resistance; dormancy; drug resistance; infectious disease; nongenetic; transgenerational inheritance.

Figure 1

Schematic of model assumptions. The constants α and β are the lower and upper bounds on expression level. Expression level x* is the value above which a cell becomes a persister. Grey shading indicates expression levels for which persister formation occurs. (a) Density of cells with different expression levels, n(x, t). Green area represents total number of non-persister cells. Red area represents total number of persister cells. (b) Qualitative form of function v(x), giving the within-generation rate of directional change in expression level as result of physiological homeostasis within a cell. The constant γ is the homeostatic set point expression level. (c) Birth and death rates, b(x, t) and d(x, t), as a function of expression level.

Figure 2

Processes embodied by equation (1). The constants α and β are the lower and upper bounds on expression level. Expression level x* is the value above which a cell becomes a persister. Grey shading indicates expression levels for which persister formation occurs. All plots show density of cells with different expression levels at three different time points. (a) When resources are abundant reproduction increases the density of non-persister cells only. (b) Between-generation change/noise tends to equalize the density across expression levels. (c) Homeostasis tends to concentrate expression levels around the set point γ.

Figure 3

Density of cells with different expression levels over time, n(x, t). Each curve represents a particular point in time. Expression levels are arbitrarily bound between α = −0.9 and β = 0.1 with x* = 0 being the threshold for persister formation. Grey shading indicates expression levels for which persister formation occurs. (a) Initial density is n(x, 0) = 1 (i.e., uniform across all expression levels). (b) Initial density is n(x, 0) = 1 if x > x* and n(x, 0) = 0 otherwise (i.e., only persister cells present). Parameter values: θ = 100, η = 1, ϵ = 0.1, m = 0.001, σ = 0.0015, μ = 0.00075, γ = −0.5, v(x) = 0.5(x − α)(x − β)(x − γ), a = 0.15, d = 0.1. Model solved numerically for 200 time units using Mathematica.

Figure 4

(a) and (b). Density of cells with different expression levels over time, n(x, t). Each curve represents a particular point in time. Expression levels are arbitrarily bound between α = −0.9 and β = 0.1 with x* = 0 being the threshold for persister formation. Grey shading indicates expression levels for which persister formation occurs. (a) Between-generation change/noise and homeostasis are weak relative to reproduction when resources are abundant (m = 0.00025, v(x) = 0.075(x − α)(x − β)(x − γ)). Phenotypic distribution (i.e., the shape of the density curve) equalizes slowly (particularly for values of x > x*), and not until after carrying capacity is approached. (b) Between-generation change/noise and homeostasis are strong relative to reproduction when resources are abundant (m = 0.05, v(x) = 15(x − α)(x − β)(x − γ)). Phenotypic distribution equalizes quickly and then simply increases until carrying capacity is reached. (c) Total population size of non-persister (black) and persister (red) cells over time for the numerical results in panels (a) and (b). (d) Fraction of population consisting of persister cells as a function of time for the numerical results in panels (a) and (b). All other parameter values: θ = 100, η = 1, ϵ = 0.1, σ = 0.00015, μ = 0.000075, γ = −0.5, a = 0.15, d = 0.1. Model solved numerically for 500 time units using Mathematica.

Figure 5

Asymptotic probability density of cells with different expression levels during exponential population growth (i.e., the area under the curve is 1). Curves correspond to different exponential growth rates (i.e., resource abundances). Expression levels are arbitrarily bound between α = −0.9 and β = 0.1 with x* = 0 being the threshold for persister formation. Grey shading indicates expression levels for which persister formation occurs. Parameter values: m = 0.01, σ = 0.0015, μ = 0, γ = −0.5, v(x) = 0.5(x − α)(x − β)(x − γ), d = 0.1. Birth rate for non-persister cells was set to a constant value of either b = 0.15 (low), b = 1 (medium), or b = 10 (high) to generate different exponential growth rates.

Figure 6

Density of cells with different expression levels over time, n(x, t). Curves correspond to different levels of within-generation noise in expression level. Expression levels are arbitrarily bound between α = −0.9 and β = 0.1 with x* = 0 being the threshold for persister formation. Grey shading indicates expression levels for which persister formation occurs. Parameter values: σ = 0.0015, μ = 0, γ = −0.5, v(x) = 5(x − α)(x − β)(x − γ), d = 0.1, and birth rate for non-persister cells set to balance death rate (i.e., b = 0.1). Noise levels are m = 0.01 (low) and m = 0.02 (high).