Supplementary Figure 1. Growth of E.coli strains with mutant DHFR genes as a function of trimethoprim concentration.

Transcription

1 Supplementary Figure 1. Growth of E.coli strains with mutant DHFR genes as a function of trimethoprim concentration. Growth of strains carrying all possible combinations of seven trimethoprim resistanceconferring mutations were measured across a range of trimethoprim concentrations. Each column presents a strain s triplicate growth measurements, quantified by the integral of optical density at 600nm from 0 to 30 hours, with that strain s mutations indicated in the color coded grid beneath the plot. Mutant strains are sorted by the overall number of mutations. A black to yellow heatmap indicates growth. Seven columns that are entirely black are genotypes that could not be successfully integrated into the chromosome of E.coli despite repeated attempts and might be non-viable mutation combinations.

2 Supplementary Figure 2. IC75 measurements are highly reproducible, and very little variance in IC75 is due to experimental noise. Here each strain is marked by a different random color. The individual and mean measurements of each mutant strain s log 10 (IC75) are highly correlated (r 2 =0.9924). The variance in each strain s individual log 10 (IC75) measurements around their mean log 10 (IC75) is only 0.76% of the full variance in the data set, that is, the sum of square differences between all measurements and their global errorweighted mean (gray horizontal line). The variance due to experimental error is thus remarkably small both because IC75 measurements are highly reproducible and because the variance in log(ic75) that is the signal (not noise) is very large.

3 Supplementary Figure 3. Multiple adaptive peaks in the landscape of trimethoprim resistance through DHFR mutations. Adaptive trajectories end at one of twelve genotypes that are locally optimal in trimethoprim IC75: all of their genetic neighbors have an IC75 that is lower or experimentally indistinguishable. Each of these peak genotypes are here marked by a black ring and are surrounded by their genetic neighbors. Arrows show the direction of favorable transitions, and are colored by the mutation changed in that transition. Dashed lines connect genotypes with indistinguishable IC75s.

4 Supplementary Figure 4. Pairwise and high-order genetic interactions are required to explain the adaptive landscape of trimethoprim resistance. a, A series of models of increasing complexity was constructed to fit the observed IC75 of each genotype and determine the relative contributions of mutation s individual effects and effects in combinations (Methods, Figure 2). As in Figure 2a, all possible genetic interaction terms are considered (Pairwise and high-order genetic interactions), which is contrasted with the results when only pairwise genetic interactions are considered, and when no genetic interactions are considered. b, The variance explained by each set of parameters (individual effects, pairwise and high-order interactions) was summed, for different models that do or do not consider pairwise or high-order genetic interaction terms. Without genetic interactions, 59% of variance in log(ic75) cannot be explained; without high-order genetic interactions, 25% of variance in log(ic75) cannot be explained, even though 27 parameters are available to describe all individual effects and pairwise interactions.

5 Supplementary Figure 5. High order genetic interactions between P21L and W30R. Growth as a function of increasing trimethoprim concentration (mean of triplicates) are shown for sets of strains that demonstrate the variable genetic interactions between P21L and W30R when acquired on different genetic backgrounds. In each graph, black represents the background (a strain with neither P21L nor W30R), red and green represent strains that have acquired either P21L or W30R, respectively, and brown represents a strain that has acquired both P21L and W30R. IC75 is determined from the intersection of these growth functions with a dotted line at 25% of the uninhibited wildtype growth.

6 Supplementary Figure 6. Estimates of the relative probabilities of evolutionary pathways to trimethoprim resistance. Previous studies that have reconstructed the intermediate genotypes between a drug-susceptible and a highly drug-resistant genotype have estimated the relative probabilities of different evolutionary pathways, and predicted that very few pathways have a significant probability of realization indeed, each such study predicted that the top one or two most probable pathways capture at least 50% of the probability of realization 1-4. Here, this method is applied to the landscape of trimethoprim resistance, using the equal fixation probability model (solid line; the probability of fixation of each beneficial mutation is equal) or a correlated fixation probability model (dashed line; the probability of fixation of each beneficial mutation is correlated with the magnitude of its effect) 1. In this multi-peaked landscape, the probability of realization is more distributed amongst many possible pathways under the equal fixation probability model, the 57 most probable pathways capture 50% of probability. Under the correlated fixation probability model, pathways that acquire the remarkably strong L28R mutation (77-fold increase in IC75 when acquired on a wildtype background) capture much of the probability density (45% chance of acquiring L28R first; 59% chance of acquiring L28R first or second); however, in the experimentally observed pathways L28R never occurred earlier than the third step 5. The probability that L28R would be observed in neither the first nor second step in any of five replicate evolution experiments is highly unlikely under the correlated fixation probability model (p = ( ) 5 = 0.01). This observation suggests that L28R arises with an unusually low probability, in contrast to the assumptions of the correlated fixation probability model. We therefore estimate that the true distribution of pathway probabilities may lie between the equal and correlated fixation probability models. In light of these models present inconsistency with experimental evolution studies, we purposefully avoid any further analyses based on predicted pathway probabilities.

7 Supplementary Figure 7. Conversion and reversion of mutations allows escape from evolutionary 'dead-ends'. a, For each genotype, the best accessible improvement in IC75 by gaining a new mutation is shown as a function of that genotype s IC genotypes appear to be local optima as the best gain of mutation is deleterious (gray region below 1 change in IC75). b, For each genotype, the best accessible improvement in IC75 by gaining, converting, or reverting a mutation is shown as a function of that genotype s IC75. Points are color-coded by the nature of the best step: black for gain of mutation; orange for mutation conversion; blue for mutation loss. The only local optima remaining are all strongly trimethoprim resistant (Supplementary Figure 3).

8 Supplementary Figure 8. Indirect evolutionary paths increase the connectivity of genotypes to peaks with few additional steps. a, A histogram of path length in direct and indirect evolutionary pathways. Direct paths are up to 5 steps long, and they are outnumbered by the indirect paths of only 5 or 6 steps. Yet more indirect pathways are of length 7, but few are any longer. b, The number of genotypes that can trace an accessible evolutionary path to each peak genotype is greatly expanded by the consideration of indirect paths. c, Equivalently, the number of peaks that can be reached from each given genotype is on average greater when considering indirect paths. This is demonstrated by a histogram of how many genotypes can trace an accessible evolutionary path to a given number of peaks. For example, considering direct paths there is only one genotype (wildtype) that can reach all eleven peaks, but considering indirect paths there are four genotypes can reach all eleven peaks.

9 Supplementary Figure 9. Fast commitment to evolutionary fate in a multi-peaked landscape created by Diminishing Returns or Decompensatory epistasis. An adaptive landscape can contain multiple peaks from an edge case of 'diminishing returns' epistasis or from decompensatory epistasis 6, that is, if each successive mutation confers a smaller advantage and a peak is reached when additional mutations confer no further advantage (diminishing) or even a disadvantage (decompensatory). In the diminishing returns case, peaks are neutrally connected, and in the decompensatory case, they are separated by a fitness valley; though these differences have no impact on the feasible evolutionary trajectories. (The observed DHFR landscape contains some of each class: some peaks are neutrally connected peaks and some are separated from all others by a valley). To construct a landscape shaped by diminishing returns or decompensatory epistasis, that is comparable in structure to the observed DHFR landscape, a peak is composed of an always beneficial promoter mutation plus any combination of three amino-acid mutations chosen from a set of five. As in Figure 4a, the fraction of adaptive peaks that are potentially accessible from different genotypes along evolutionary trajectories are shown for trajectories in the observed DHFR landscape (blue) and the diminishing returns model landscape (orange). Similar to the pairwise epistasis model (Figure 4a), the diminishing returns landscape shows rapid commitment to fate.

10 Supplementary Figure 10. Genetic interactions expand the number of adaptive trajectories and postpone commitment to fate in the evolution of cycloguanil resistance. The analyses presented in Figures 3 and 4 are here applied to a 3-peaked adaptive landscape of cycloguanil resistance, measured in Saccharomyces cerevisiae that carry DHFR from Plasmodium falciparum 4. Analyses are applied to the majority consensus adaptive trajectories, being those found in more than half of the simulated landscapes (from Table S5 of Ref. 4 ). a, Adaptive trajectories were analyzed to determine how often each type of cycloguanil-resistance mutation was gained and kept (black) or gained and later lost (gray). b, The number of direct (black) and indirect (gray) pathways to each of the three peaks were calculated, and contrasted with the maximum number of direct paths (dashed lines; 2! = 2 for the 2-mutation peak, 3! = 6 for the 3 mutation peak). As the 5-mutation peak contained mutations at every site examined in that study, indirect paths containing mutations absent from the final genotype cannot be identified from the scope of this data set. c, The number of accessible adaptive peaks was determined at every step along each adaptive trajectory, as in Figure 4a but applied the landscape of cycloguanil resistance.

11 Supplementary Figure 11. Postponed commitment to evolutionary fate depends on adaptive loss of mutations. a, The fraction of adaptive peaks that are potentially accessible from different genotypes along evolutionary trajectories, as in Figure 4a. The observed data is contrasted with models of 'pairwise incompatibility' and 'diminishing returns', as presented in Figure 4a and Supplementary Figure 9. b, As for panel a, but excluding the possibility of adaptive mutation loss. This has two effects: firstly, the only trajectories considered are those that consist exclusively of gaining mutations, and secondly, the fraction of accessible peaks along that limited set of trajectories also changes because peaks are only considered accessible if they can be reached exclusively by gaining mutations. In this scenario, there is no postponement of commitment to evolutionary fate relative to the 'pairwise incompatibility' and 'diminishing returns' models (which are themselves unchanged as they never include adaptive mutation loss).

12 Supplementary Figure 12. Adding random high-order genetic interactions to an adaptive landscape increases the number of feasible evolutionary trajectories and postpones commitment to evolutionary fate. a, From the range of simulated adaptive landscapes described in Figure 4b, adding random second, third, fourth, and fifth order genetic interactions increases both the number of mutation events until half or fewer adaptive peaks remain accessible, and the number of feasible evolutionary pathways from the wildtype genotype to an adaptive peak. Consistent with the hypothesis that genetic interactions postpone commitment to fate by increasing peak accessibility via an expanded number of feasible evolutionary pathways, across these thousands of landscapes a strong correlation is observed between the log of the number of evolutionary pathways and the number of mutational steps taken until fate commitment (r 2 =0.79, p< ). b, In the style of Figure 4a, the fraction of adaptive peaks that remain accessible along an evolutionary trajectory is plotted for trajectories on simulated adaptive landscapes with variable numbers of random genetic interactions (blue; from Figure 4b), and contrasted with the pairwise incompatibility landscape that contains only three second-order genetic interactions (purple; as described in Figure 4a). As more random genetic interactions are added, evolutionary trajectories grow in maximum possible length, and options amongst different adaptive peaks are narrowed much later along these evolutionary trajectories.

13 Supplementary Note 1: Quantification of growth. When microbial growth is measured by optical density, the resulting data can be quantified by the rate of division (the slope of log(optical density) over some timespan or some number of doublings), or by integrating optical density over time (also known as 'area under the growth curve'). In analyzing this data set, integrating optical density was preferred primarily for showing superior experimental reproducibility compared to measurements of growth rate. Of secondary consideration is that the integral of optical density is sensitive to the observed effects of trimethoprim not only on the division rate, but also on yield and the duration of lag phase; a strain which grows only after a substantial delay to a reduced final density should be considered less competitively fit. The observation that the integral of optical density shows superior experimental reproducibility is consistent with other large-scale studies of microbial responses to antibiotics 7,8. These effects are illustrated below by the response of DHFR mutant L28R to trimethoprim, when quantified by division rate (panel a) and by the integral of optical density (panel b). Here three experimental replicates of optical density measurements are shown in different colors. When measuring division rate, a solid line marks the fastest doubling observed at OD For any choice of a minimum OD at which division rate can be quantified, there occurred reproducibility problems on account of this threshold, where some replicates were considered 'growing' while others were not; by contrast, integrating OD has no such problem. a. Growth quantified by division rate (fastest doubling at OD 0.05) b. Growth quantified by the integral of optical density

14 Supplementary Note 2: Comparison between empirical DHFR landscape and forward evolution of trimethoprim resistance. The set of trimethoprim resistance conferring mutations studied here were selected from those that occurred in replicate experimental evolution studies in a modified tubidostat, the 'morbidostat' 5. The adaptive steps observed in the morbidostat always ended at a fourmutation peak. In all replicate evolution experiments the adaptive steps up to at least the third mutation are consistent with the empirical DHFR landscape profiled here: they correspond to an increase in trimethoprim resistance. The fourth mutations acquired in the morbidostat always conferred only a minor increase in trimethoprim resistance, and sometimes appear in the present landscape to be neutral steps, rather than beneficial. A number of differences in conditions between the morbidostat and the experiments conducted here exist which may explain these subtle differences, including: (1) growth in glass flasks with magnetic stirring versus growth in microtiter plates with shaking, (2) growth in dynamically fluctuating trimethoprim concentrations versus static trimethoprim concentrations, (3) competitive growth and clonal interference versus growth of a single strain quantified by integrating optical density over time, (4) differences in the chromosomal context of DHFR - the strains in this study contain DHFR flanked by selective markers that may alter the wildtype expression level, and (5) differences in the exact identity of mutations: in the morbidostat there were two different types of promoter mutations (-35C>T, -9G>A), 3 different amino acid substitutions at A26 (A26T, A26V, A26S) 3 different amino acid substitutions at W30 (W30R, W30G, W30C), and in one evolving population, mutations elsewhere in the chromosome (acra, acrb, rpob).

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