A Model for Designing Adaptive Laboratory Evolution Experiments

Abstract

The occurrence of mutations is a cornerstone of the evolutionary theory of adaptation, capitalizing on the rare chance that a mutation confers a fitness benefit. Natural selection is increasingly being leveraged in laboratory settings for industrial and basic science applications. Despite increasing deployment, there are no standardized procedures available for designing and performing adaptive laboratory evolution (ALE) experiments. Thus, there is a need to optimize the experimental design, specifically for determining when to consider an experiment complete and for balancing outcomes with available resources (i.e., laboratory supplies, personnel, and time). To design and to better understand ALE experiments, a simulator, ALEsim, was developed, validated, and applied to the optimization of ALE experiments. The effects of various passage sizes were experimentally determined and subsequently evaluated with ALEsim, to explain differences in experimental outcomes. Furthermore, a beneficial mutation rate of 10^-6.9 to 10^-8.4 mutations per cell division was derived. A retrospective analysis of ALE experiments revealed that passage sizes typically employed in serial passage batch culture ALE experiments led to inefficient production and fixation of beneficial mutations. ALEsim and the results described here will aid in the design of ALE experiments to fit the exact needs of a project while taking into account the resources required and will lower the barriers to entry for this experimental technique.IMPORTANCE ALE is a widely used scientific technique to increase scientific understanding, as well as to create industrially relevant organisms. The manner in which ALE experiments are conducted is highly manual and uniform, with little optimization for efficiency. Such inefficiencies result in suboptimal experiments that can take multiple months to complete. With the availability of automation and computer simulations, we can now perform these experiments in an optimized fashion and can design experiments to generate greater fitness in an accelerated time frame, thereby pushing the limits of what adaptive laboratory evolution can achieve.

Keywords: Escherichia coli; adaptive evolution; evolutionary biology.

FIG 1

ALEsim flow chart. A workflow outlining the logical steps the simulator takes when performing a single simulated ALE experiment is presented. Due to the stochastic nature of ALE experiments (in vivo and in silico), multiple experiments are averaged together to identify general trends.

FIG 2

Governing equations, assumptions, and parameters for ALEsim. (a) Microbe growth occurs according to an exponential growth curve, where μ is the growth rate, t is the time elapsed, N₀ is the initial cell count at t = 0, and N(t) is the cell count at the given time t. No lag phase or stationary phase is modeled. The total cell count, N(t), is determined by summation of exponential growth curves for all individual cell lines. (b) Favorable mutations occur during cell growth according to a binomial distribution, where each cell division represents one Bernoulli trial with a probability of success equal to the beneficial mutation rate (BMR). (c) Each flask is modeled as a completely homogeneous culture. (d) The number of cells represented for each cell line in each inoculum (N_Green^Inoculum and N_Other^Inoculum) is randomly chosen according to a normal distribution with a mean and variance equal to the number of cells represented in the flask (N_Green^Flask) times the ratio of the flask volume (V_flask) to the inoculum volume (V_inoculum). (e to g) The volume of medium per flask (e), the inoculum volume (f), and the passage optical density (g) can be altered. (h) The simulated ALE experiment can be stopped after a specified amount of time or a maximum number of flasks. (i) Based on the relative growth rate increases seen in ALE experiments, a range of allowable growth rate increases is determined. (j) Based on matching the evolution trajectory (plot of growth rate versus flask number) with various beneficial mutation rates (BMRs), the probability of a favorable mutation is obtained. (k) Since each ALE is based on randomly generated mutations, multiple ALE simulations are averaged together to obtain repeatable results from the same parameters. The number of simulations is controlled by the user.

FIG 3

Fitness trajectories of E. coli evolved on glycerol. The absolute growth rates of independently evolved cultures of E. coli, as fitted by a cubic spline for all ALE experiments, are indicated for different passage sizes. Dashed lines represent regions where the spline fit is based on sparse data and therefore is not considered accurate. The small upturn in growth rates at the endpoint is an artifact of the spline interpolation and is ignored in determinations of endpoint growth rates. All except five ALE experiments reached fitness state 3. The rates at which the final growth rate was achieved varied. The hypermutating strain with a passage size of 10% reached state 3 significantly faster than all others (it possessed a mutation in mutY). The purple hypermutating strain was identified as a potential hypermutating strain based on the number of mutations fixed (P = 0.003; false discovery rate, 0.087) and the presence of a frameshift insertion in mutL.

FIG 4

Distribution of fitness increases in glycerol ALE experiments. A histogram of the normalized increases in growth rate (μ_max = 0.64 h⁻¹) attributed to each jump for the different experiments is presented. The fitness increases were categorized according to which state transition was made. The different passage sizes (indicated by different colors) did not show any significant variance in the ability to fix distinct increases in growth rates. A few small jumps not shown were small observed increases in fitness that did not jump between any of the identified states.

FIG 5

Simulated versus experimental results with large and small passage sizes. Two ALE experiments with E. coli MG1655 in M9 glucose minimal medium were simulated using ALEsim. The strain and medium conditions were identical in the two experiments. The only differences were in the culture volume (25 ml versus 250 ml), the optical density when passaged (variable versus OD₆₀₀ of 1.2), and the passage volume (variable versus 800 μl) (experiment 1 had the 25-ml culture volume, OD₆₀₀ of 1.2, and 800-μl passage volume, while experiment 2 had the 250-ml culture volume, variable OD₆₀₀, and variable passage volume). The variable nature of the optical density when passaged and the passage size in the latter experiment was a consequence of manually passaging the culture each day. The former experiment employed an automated system for monitoring and passaging the culture, to maintain consistency. Although the same strain and conditions were used, the final fitness levels achieved in the two experiments were quite different. ALEsim was used to simulate these experiments, with the only differences being the three aforementioned parameters. The ALEsim results showed that the differences in these parameters were sufficient to explain why the final growth rates achieved were different, further highlighting the importance of choosing the parameters properly. The simulated results are represented by a 95% confidence interval. The confidence interval for experiment 2 is too small to be visible.

FIG 6

Upper bound on possible jumps in growth rates. (A) Upper bounds on possible jumps in growth rates are shown. At a given point in time, a jump that reaches above the upper bound from a single mutation is statistically infeasible (95% confidence limit), whereas jumps that stay below the line are possible. (B) The upper bounds on jumps for different passage sizes are shown. These experiments were simulated with parameters that matched the experimental parameters used. Increasing the passage size can have a significant impact on the upper bound. Consequently, the time required to eliminate jumps of certain magnitudes can be much longer. As the passage size increases, however, there comes a point at which the returns begin to diminish, such that passage sizes between 0.1% and 10% do not show a large difference in the time required to find a given jump. (C) Relative amounts of resources needed to perform an ALE experiment were normalized to the smallest passage size. As the passage size is increased, the resource usage begins to increase greatly.

FIG 7

Genetic analysis by passage size. The bar chart presents the observed fraction of mutations at a given passage volume. As a general trend, the larger the passage size is, the greater the probability is of a mutation in a given allele being fixed in the population. Data for a key mutation in the glpK gene and for all mutations are indicated. The ordinal rank of passage size was compared to the observed fraction of mutations using a Wilcoxon rank test, which resulted in P values of 0.008 and 0.024 for all mutations and glpK mutations, respectively.