Schematic representation of a host population models that includes the possibility of resistance loss.

<p>A modified implementation of a previous host population model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-Bonhoeffer1" target="_blank">[40]</a> under a combination of two drugs <i>a</i> and <i>b</i> (Equation S6 and S7 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775.s005" target="_blank">File S1</a>) takes into account the possibility of resistance loss. Hosts can be infected by pathogens of four different types: wild type, a-resistant, b-resistant and a,b-resistant. The numbers of individuals infected are correspondingly represented by variables <i>y_w</i>, <i>y_a</i>, <i>y_b</i>, and <i>y_a,b</i>. The original model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-Bonhoeffer1" target="_blank">[40]</a> considered only the possibility of acquiring resistance (black arrows). In our modified host population model, motivated by our findings in the single host model, we assume that a nonzero resistance-decaying rate can cause loss of resistance (red arrows).</p

Illustration of the infection dynamics model and of a novel strategy to fight resistance.

<p>(<i>A</i>) Schematic representation of the main dynamical transitions based on the model from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-DAgata1" target="_blank">[42]</a>. The arrows represent the possible fates of the populations of sensitive and resistant pathogen strains. Horizontal gene transfer (rate <i>τ</i>) and plasmid loss (rate <i>ρ</i>) are the mechanisms responsible for interconverting between sensitive and resistant strains. The use of an antibiotic can reduce the sensitive population, but is not effective against the resistant one. Conversely, the cost of carrying a plasmid causes a reduction of the resistant population in the absence of antibiotic use. Also, both strains are susceptible to immune system killing. This model of infection dynamics can be used to search for optimal treatments. <i>(B)</i> Schematic representation of the current state of an infection and its treatment. Regular antibiotic is effective against an infection caused by the sensitive strain, but is not effective against an infection with high abundance of resistant pathogens (<i>B-top</i>). Here we show that an effective control of the infection can be obtained by initially treating against the resistant strain (antiR condition) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-Chait1" target="_blank">[33]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-Palmer1" target="_blank">[34]</a> and subsequently applying antibiotic treatment (<i>B-bottom</i>).</p

Resistance attenuation occurs in the in the absence of antibiotic treatment when the abundance of sensitive pathogen is saturated.

<p>The resistant and sensitive strains have to compete for resources when the bacterial population approaches carrying capacity. This competition reduces the abundance of resistant strains due to the cost of resistance. Under this saturated conditions, both the probability of plasmid loss <i>(A)</i> and the growth rate <i>(B)</i> affect resistance attenuation. (<i>A</i>) The intensity of resistance attenuation increases with the probability of plasmid loss (<i>ρ</i>). (<i>B</i>) The intensity of resistance attenuation increases with the difference in growth rate between both strains. In this analysis, we set up the probability of resistance loss to be equal to zero to highlight only the effects of growth rate. The left panel shows a case in which both sensitive and resistant strains have the same growth rate. In this case, both strains can coexist with high population abundance. In the right panel, we assume that a plasmid cost reduces resistance growth rate from 2.77 to 2 day⁻¹. The abundance of the resistant pathogen decreases over time when the abundance of the sensitive pathogen is saturated. The intensity of resistance attenuation is proportional to the difference in growth rate. Unless otherwise mentioned, all parameters used in this analysis correspond to the default values described in Table S1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775.s005" target="_blank">File S1</a> for no treatment condition. Initial abundances of sensitive and resistant pathogens are 10⁸ and 10⁹ cells respectively.</p

Resistance attenuation is influenced by the nature of antiR treatment and by the plasmid loss rate.

<p>The nature of the antiR treatment (whether bactericidal or bacteriostatic, see Text S1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775.s005" target="_blank">File S1</a>) and the rate of plasmid loss influence the dynamics of resistance attenuation. We illustrate the resistance decaying rate (<i>A</i>) and <i>t_clear</i> (<i>B</i>) as a function of the rate of plasmid loss and the nature of treatment. At low rates of plasmid loss (<i>ρ≈0</i>), antiR treatment increases the resistance attenuation by a factor ∼15, independently of the nature of antiR treatment. Values are estimated according to data published in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0080775#pone.0080775-Chait1" target="_blank">[33]</a>.</p

Resistance attenuation is boosted when the population of sensitive pathogens approaches carrying capacity.

<p>This figure shows the infection dynamics of both resistant (dashed red line) and sensitive (solid blue line) pathogens under antiR treatment (purple shade). The decrease in the abundance of resistant pathogen is relatively small when the sensitive strain is far from carrying capacity (time t<8 days), but is strengthened when the sensitive population reaches carrying capacity. The initial abundances of sensitive and resistant pathogens are 10⁸ and 10⁹ cells respectively.</p

AntiR treatment boosts resistance attenuation and leads to total healing.

<p>Both antibiotic suspension (no treatment) and antiR treatment can reduce the abundance of resistant pathogens. However, this reduction is greater under antiR treatment. This figures illustrates the potential advantage of an antiR treatment in fighting a resistant infection. When no treatment is applied, the fraction of resistant population decreases slowly (<i>A</i> and <i>B</i>, time window between 16 and 36 hours) and it is followed by an ineffective antibiotic treatment. In (<i>B</i>), the resistance attenuation is faster due to treatment against resistance (antiR, purple-shaded area), and leads to an effective antibiotic treatment (t>36h). The black dashed horizontal line marks a single cell, i.e. the level below which the infection is healed. The initial abundance of both sensitive and resistant pathogens is 10⁹ cells. Note that the period of antibiotic suspension preceding an antiR treatment is not necessary for an optimal therapy and is shown in this figure only for highlighting the different slopes.</p

Relative biomass production for matching versus non-matching expression.

<p>Relative biomass production for matching versus non-matching expression.</p

The principles of our method illustrated using a simple metabolic network.

<p>Flux limits in this figure are represented by a thin black outline. Reaction fluxes are represented as shaded regions with flux magnitude proportional to <i>thickness</i>. Flux direction is not indicated. <b>Panel A</b>. Creation of the baseline flux limits (corresponding to in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036947#pone-0036947-g002" target="_blank">Figure 2</a>, Panel A)<b>.</b> Each reaction is given a flux limit corresponding to the maximum optimal flux solution over the two <i>in silico</i> nutrient uptake conditions. The shading is orange for <i>in silico</i> glucose growth, blue for <i>in silico</i> acetate and grey where the two solutions overlap. <b>Panel B.</b> Creation of the glucose expression-derived flux limits (corresponding to in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036947#pone-0036947-g002" target="_blank">Figure 2</a>, Panel B). Each flux limit shown in Panel A has been scaled by the level of gene expression for <i>in vivo</i> growth on glucose relative to the maximum gene expression for that reaction over both nutrient conditions. The arrows indicate two reactions for which gene expression was significantly lower on glucose than on acetate, resulting in significantly reduced flux limits. <b>Panel C</b>. Effect of the glucose expression-derived flux limits of Panel B on <i>in silico</i> glucose growth. The glucose optimal flux from Panel A (orange region) lies within the limits; biomass production is not changed. <b>Panel D.</b> Effect of the glucose expression-derived flux limits of Panel B on <i>in silico</i> acetate growth. The acetate optimal flux from Panel A (blue region) exceeds the flux limits for several reactions. (This is analogous to the optimal flux vector lying outside the flux cone in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036947#pone-0036947-g002" target="_blank">Figure 2</a>, Panel B.) Hence the flux limits will lead to smaller optimal fluxes for these reactions and reduced biomass production. Relative biomass production is therefore smaller for <i>in silico</i> acetate than for <i>in silico</i> glucose, and we conclude that glucose is the more likely carbon source for the expression data.</p

Ranking of the six challenge nutrients.

<p>Ranking of the six challenge nutrients.</p

Constituents removed from <i>i</i>AF1260 biomass.

<p>Constituents removed from <i>i</i>AF1260 biomass.</p