Conventional wisdom holds that the best way to treat infection with antibiotics is to ‘hit early and hit hard’. A favoured strategy is to deploy two antibiotics that produce a stronger effect in combination than if either drug were used alone. But are such synergistic combinations necessarily optimal? We combine mathematical modelling, evolution experiments, whole genome sequencing and genetic manipulation of a resistance mechanism to demonstrate that deploying synergistic antibiotics can, in practice, be the worst strategy if bacterial clearance is not achieved after the first treatment phase. As treatment proceeds, it is only to be expected that the strength of antibiotic synergy will diminish as the frequency of drug-resistant bacteria increases. Indeed, antibiotic efficacy decays exponentially in our five-day evolution experiments. However, as the theory of competitive release predicts, drug-resistant bacteria replicate fastest when their drug-susceptible competitors are eliminated by overly-aggressive treatment. Here, synergy exerts such strong selection for resistance that an antagonism consistently emerges by day 1 and the initially most aggressive treatment produces the greatest bacterial load, a fortiori greater than if just one drug were given. Whole genome sequencing reveals that such rapid evolution is the result of the amplification of a genomic region containing four drug-resistance mechanisms, including the acrAB efflux operon. When this operon is deleted in genetically manipulated mutants and the evolution experiment repeated, antagonism fails to emerge in five days and antibiotic synergy is maintained for longer. We therefore conclude that unless super-inhibitory doses are achieved and maintained until the pathogen is successfully cleared, synergistic antibiotics can have the opposite effect to that intended by helping to increase pathogen load where, and when, the drugs are found at sub-inhibitory concentrations.

We take an evolutionary approach to a problem from the medical sciences in seeking to understand how our knowledge of rapid bacterial evolution should shape the way we treat pathogens with antibiotic drugs. We pay particular attention to combinations of different drugs that are purposefully used to produce potent therapies. Textbook orthodoxy in medicine and pharmacology states one should hit the pathogen hard with the drug and then prolong the treatment to be certain of clearing it from the host; how effective this approach is remains the subject of discussion. If the textbooks are correct, a combination of two antibiotics that prevents bacterial growth more than if just one drug were used should provide a better treatment strategy. Testing alternatives like these, however, is difficult to do in vivo or in the clinic, so we examined these ideas in laboratory conditions where treatments can be carefully controlled and the optimal combination therapy easily determined by measuring bacterial densities at every moment for each treatment trialled. Studying drug concentrations where antibiotic synergy can be guaranteed, we found that treatment duration was crucial. The most potent combination therapy on day 1 turned out to be the worst of all the therapies we tested by the middle of day 2, and by day 5 it barely inhibited bacterial growth; by contrast, the drugs did continue to impair growth if administered individually.

Funding: Structural funding by the DFG Excellence Clusters Inflammation at Interfaces and Future Ocean. REB and RPM were funded by EPSRC grants EP/I00503X/1 and EP/I018263/1 ( http://www.epsrc.ac.uk/Pages/default.aspx ). AFH was funded by an Exeter University CLES award (no grant number). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Introduction

Our arsenal of antimicrobials boasts a wide diversity of drugs and we continue to invest in the search for new ones [1]. Yet bacteria adapt so readily to their ambient environment that all antibiotics in clinical use have bacteria that resist them [2],[3]. A Staphylococcus aureus infection traced in vivo yielded over thirty de novo mutations from a 12-week therapy, each mutation conferring an increase in drug resistance [4]. With such a rapidly evolving foe and antibiotic discovery programmes waning substantially [3], determining optimisation principles that maintain the efficacy of the antibiotic repertoire already in our possession represents one of the keenest challenges confronting the scientific community.

And yet drug-resistance evolution has been called ‘conceptually uninteresting’ [5]. This view is the result of assuming a fixed timeline: a pathogen is treated with antibiotics, resistance traits emerge, sweep through the population and fix. The more efficient the drug, the greater selection for resistance and the sooner resistance fixes. The only mitigating action we can take is hit early, hit hard and kill drug-susceptible cells before they accumulate, so the old argument goes [6].

Bacteria are hardest hit by multi-drug combinations. Developed for over 70 years [1],[7],[8], combinations are key in our fight against microbes [9], viruses [10] and cancers [11]. Combinations said to be synergistic, where two drugs hit the pathogen much harder than each drug alone, are highly prized [1],[12],[13]. Indeed, the rapid deployment of synergistic antibiotics should, according to the same logic, be the fastest way of clearing a bacterium.

To make our discussion more precise we say that a pair of bacteriostatic antibiotics of equal efficacy is synergistic if a 50-50 weighted combination of both drugs inhibits growth more than the two single-drug treatments when measured over one day of bacterial growth [8],[14]–[16]. (Strictly speaking, we ask this for all (θ,(1−θ))-combinations where θ is any value between 0 and 100%, not just 50-50, as shown in Figure 1.) With this definition we can formulate a null hypothesis, H 0 : a synergistic drug combination also inhibits growth synergistically if the treatment lasts longer than a day. Put differently, if the 50-50 combination treatment is more efficient than both single-drug monotherapies on the first day of treatment, it should also be more efficient on subsequent days to be deemed synergistic.

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larger image TIFF original image Download: Figure 1. The drug interaction profile, i(θ), as defined in The drug interaction profile, i(θ), as defined in Materials and Methods The drug interaction profile is closely related to the two ‘checkerboard’ diagrams shown in (a) and (c). In a checkerboard, the concentration of both drugs is given on the x and y axes, bacterial growth inhibition (or population density or some other fitness measure) is then plotted on the z axis. The contour of all concentrations that reduce this measure by half is an isobole here denoted IC 50 and figures (a) and (c) show two checkerboard plots viewed from above. Basal concentrations of both drugs that achieve the same inhibitory effect in this illustration are D 50 and E 50 , θ then parameterises the equidosage line between these two values. The fitness measure evaluated along this line is shown in (b) and (d) and we define the degree of interaction based on this curve, this is i(θ). We say the interaction is synergistic when the drug proportion that minimises i(θ) satisfies 0<θ<1 as in (b), we denote the resulting value by θ syn . In (d) we observe θ syn = 0 or θ syn = 1, in this case the drugs are said to be antagonistic as i(θ) is maximised by some drug combination and minimised by the monotherapies. https://doi.org/10.1371/journal.pbio.1001540.g001

Any in vitro test of H 0 necessitates the use of antibiotic concentrations that support measurable population densities, the treatments we can use to test it are, as a result, necessarily constrained to a sub-inhibitory dosing regime. We must therefore question how relevant this study can be to antibiotic use in vivo, we argue that it is relevant for the following reasons. Drug interactions are often determined by one-day checkerboards and isoboles [17], like those illustrated in Figure 1, but by their very nature checkerboards only provide insight into the interaction inside the sub-inhibitory regime as isoboles can only be calculated if cells grow. Moreover, drug concentrations can sweep downwards from their highest values to sub-inhibitory concentrations during treatment ([18], Figure 1), repeatedly so for intermittent dosing regimens [19],[20]. The different diffusivities small antibiotic molecules exhibit in different tissue can create substantial inhomogeneities in concentration [21] resulting in a potential spatiotemporal mosaic of selection for resistance [18],[22] whereby treatment can reduce pathogen load in some, but not all, organs [23]. Indeed, spatial diffusion itself creates concentration gradients with rapid, super-exponential decay away from a point source. It is therefore essential to understand how antibiotic combinations mediate resistance at all dosages within this mosaic, including sub-inhibitory, particularly as resistance is known to be selected for at very low concentrations, well below the minimal inhibitory concentration [24].

Now, we argue that treatments with the greatest short-term efficacy do not necessarily lead to the lowest bacterial densities later. A simple construction accounting for both density-dependent and frequency-dependent selection on drug resistance suffices to explain why. Consider three scenarios with two drugs, ‘A’ and ‘B’. A bacterium is either unchallenged by antibiotics, challenged with drug A only (or drug B only) or else treated with the optimally synergistic combination of both, as in Figure 2(a). The no-drug treatment sees the cells grow, to carrying capacity say, without selecting for drug-resistant phenotypes. The synergistic combination inhibits drug-susceptible cells optimally, better than the two monotherapies, and so, by the end of day 1, the lowest bacterial load of all is observed in this treatment. However, suppose some cells exhibit genetic or epigenetic adaptation conferring resistance; such cells may even have been present in low frequencies at the start of treatment. It is now in the synergistic line that drug-resistant phenotypes fare best as they have fewer competitors for the extracellular metabolites needed for growth.

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larger image TIFF original image Download: Figure 2. Smile-frown transition: a verbal argument and a toy mathematical model. (a) Synergistic drugs suppress drug-susceptible sub-populations (yellow cells) more than single-drug therapies however, this eliminates competitors of the drug-resistant red cells who grow more rapidly than the yellow cells would have done at weaker synergies. Thus greater synergy can increase population densities. (b) Solving Equation 1a–b and plotting population density against drug proportion shows that a short-term synergistic combination (blue) can maximise densities later (red). The red dots show the path of the optimal combination, note this idealised model is symmetric about θ = 1/2 but empirical data will not be. (c and d) The densities of drug-susceptible cells (S on the vertical axis in (c)) and resistants (R on the vertical axis in (d)) are shown at different times where, again, the blue line denotes a treatment of short duration and the red line denotes a longer treatment. The arrow in (c) represents the loss of S that occurs because of the drug whereas the arrow in (d) represents the analogous gain in R. For longer treatments the latter more than compensates for the former and by summing the red and blue lines in (b) and (c), respectively, we obtain the red and blue curves showing population density, Δ = S+R, in (a). https://doi.org/10.1371/journal.pbio.1001540.g002

To clarify how this might arise, imagine a population of bacteria with two subpopulations of drug-susceptible and resistant cells and suppose extracellular metabolites are shared equally among all the growing cells. As the growth of susceptibles is suppressed more at greater synergies, more metabolites become available for resistant cells in those treatments. However, resistant cells necessarily grow faster than susceptible cells do when the drugs are present, with a greater fitness difference at greater synergies. Thus the total population density can be increased by the synergy even when the number of drug-susceptible cells present is reduced. Now, if resistant cells are absent or at low frequencies at the beginning of treatment, the exposure to antibiotics must be long enough to allow the resistants to achieve densities comparable to the susceptibles and so the treatment duration then needs to be long enough for the claim in the previous sentence to be true. This process is illustrated in Figure 2.

This idea, known as ‘competitive release’ [25] has been tested in treatments of malaria in vivo using mice [5] where higher drug concentrations have been shown to select for higher parasite load but competitive release makes new predictions for antibiotic therapy, for combinations in particular. First, the optimal combination is not robust: the best way of deploying a drug pair depends on how long the treatment lasts. Second, and as a result, the favoured property of antibiotic synergy is not necessarily robust to adaptations that confer drug resistance. Not only will synergy decay with time, it can be lost completely and replaced with an antagonism because more potent combinations have paradoxically selected for larger bacterial load. Thus the theory of competitive release is not consistent with our null hypothesis and provides an evolutionary rationale for rejecting it.

A toy mathematical model captures the verbal argument completely and shows that synergy loss can be viewed as a form of tipping point. Imagine a bacterial population consisting of cells susceptible to both antibiotics at density S(t), where t is time. Suppose there is a completely resistant phenotype, R(t), and μ is the mean rate in a random Poisson process by which susceptible cells gain resistance. The dimensionless variable θ between zero and one controls the drug combination and k(θ) = 1+θ(1−θ) measures the efficiency of each combination at drug concentrations (A,B) = (A 0 θ, B 0 (1−θ)). Here A 0 and B 0 are normalising concentrations, chosen so that each drug achieves equal inhibitory effect at a defined time. Note that k(θ)is maximised when θ = 1/2. This value represents a 50-50 combination therapy whereby (A,B) = (A 0 /2, B 0 /2).

The toy model is the following logistic growth equation modified to include antibiotics: (1a) (1b)where and R(0) = 0. We therefore begin with susceptible cells but no resistant ones. Figure 2(b) shows the population densities that result from this model, Δ t (θ) = S(θ,t)+R(θ,t), plotted as a function of θ for increasing values of time t.

For short times (Equation 1a–b) exhibits synergy because density is suppressed most by the combination where θ = 1/2, so the plot of Δ t (θ) has the convex, U-shaped ‘smile’ shown in blue in Figure 2(b). At later times, but only provided μ>0, the shape of the density profile changes and now density is greatest for the 50-50 combination and lowest for the ‘monotherapies’, where θ = 0 and θ = 1. So the plot of Δ t (θ) now exhibits a near-concave, W-shaped ‘frown’ consistent with antagonism having its maximal value at θ = 1/2, as shown in red in Figure 2(b). Density is now maximised where before it was minimised. We call the resulting passage from synergy to antagonism the ‘smile-frown transition’, referring to it on occasion as ‘synergy inversion’ because the convex, synergistic profile is inverted to form a near-concave, antagonistic one; this is a different notion of synergy inversion to the one in [26].

If we set μ = 0, thus preventing the modelled population from adapting to the drug, it then follows that Δ t (θ) has a synergistic profile at all times. In this case the 50-50 combination, represented by the value θ = 1/2, is the optimal combination for all times as it minimises population density, irrespective of treatment duration.

We tested the veracity of these theoretical predictions using an evolutionary functional genomics approach that combined evolution experiments using Escherichia coli, a genomic analysis, the genetic manipulation of an identified candidate resistance mechanism and quantitative mathematical modelling. This approach highlights the molecular mechanism that causes the synergy loss predicted by theory, whereas the theory alludes to the generality of the empirical results that we now describe.