The Shape of a Disease Tolerance Curve

To measure a disease tolerance curve, we recorded the response of the host to a broad range of initial pathogen doses. We did this by injecting L. monocytogenes into flies over a range of ten to 100,000 bacteria and allowing the infected flies to die. We injected L. monocytogenes into the hemocoel of flies and monitored bacterial numbers 2 DPI to measure the ability of the fly to resist microbe growth when challenged with a range of infection intensities (Fig 5). We determined the median time to death (MTD) for each inoculum and used this time as a measurement of health (Fig 5B). Plotting microbe load versus MTD produced a curve that was readily fit by a four-parameter logistic sigmoid model (r² > 0.96) (Fig 5C).

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Fig 5. Disease-tolerance curves are sigmoid.

(A) Dose-dependent growth of L. monocytogenes during infection. Wild-type flies injected with 10–100,000 L. monocytogenes were homogenized and then plated 2 d post-infection to determine microbe loads. (B) Dose-dependent survival of L. monocytogenes-infected flies. Kaplan-Meier curves were plotted for flies injected with 10–100,000 L. monocytogenes. (C) Disease-tolerance curve. Pairs of microbe load and survival data for 63 microbe load/MTD pairs were plotted. This curve was fit with a four-parameter sigmoid model (r² > 0.96). (D) A cartoon showing the parameters used to describe a sigmoid disease-tolerance curve including vigor, slope, EC₅₀ (sensitivity), and maximal severity, as well as the measurement of phenotypic range. Data are reported in S2 Data.

https://doi.org/10.1371/journal.pbio.1002435.g005

Occasionally, tolerance curves are fit with mathematical functions, but the reason these functions are chosen is that they fit the data and not that they are dissected for further biological insights [5,30–32]. More typically, tolerance is visualized as a linear system, which requires just two parameters, vigor and slope [5,11]. In contrast, our sigmoid model provides four parameters (Fig 5D). In addition to vigor and slope used to describe a line, the sigmoid model adds the parameters of EC₅₀ and maximum effect. The EC₅₀ of the system is the number of microbes present at day 2 that cause a 50% change in MTD. Maximum effect is defined by the sigmoid’s asymptotic tail at high microbe loads. This defines a maximum death rate, suggesting that there is a previously unrecognized rate-limiting step for death.

In the model shown in Fig 1A, depletion of health could be induced either by bacterial damage effectors or indirectly by self-harm caused by the resistance response. We modeled the two possibilities by observing how the shape of the curve changed as we altered the model such that either the resistance response or bacteria were the sole cause of damage. We concentrated on changes in the rate that the immune response was turned on (τ), and the inflection points for the relationships between microbe density and the rates of immune induction and microbe-induced damage induction (σ_I and σ_M) (Fig 6A–6D, S4 Table). In the case in which resistance mechanisms drove damage (Fig 6A and 6C) and bacterial damage was set to zero, changes in τ or the inflection point for microbe-induced immunity caused shifts in both the EC₅₀ and microbe loads. The effect is more extreme when the inoculum is far below the microbial carrying capacity, as this gives the immune response an opportunity to control microbe loads. This results in a reciprocal mechanistic link between resistance and tolerance in which one is always high when the other is low. In the model in which bacteria drive damage, a loss of resistance results in high microbe loads and health pegged at maximum severity (Fig 6B). Shifts in the EC₅₀ of the bacterial damage-driven system, in which resistance-induced damage is set to zero, are caused by changes in the inflection point for bacterial-induced damage, as might be expected for differentially virulent strains of microbes or hosts that are better at neutralizing bacterial toxins (Fig 6D). In this second case, there is no mechanistic reciprocal link between resistance and tolerance, and the two vary independently of each other.

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Fig 6. Predicted and observed variation of tolerance curves.

(A–D) Predicted changes in infection tolerance curves as the rate of immune effector production (τ) and the inflection points for microbe-induced immunity or damage are altered in the immunological damage model (α only) and the bacterial damage model (ϕ only). Each line is the sigmoid fit of values computed by the model. The colors represent the value of the altered parameter, moving from violet to blue to green to red as the value increases. (E–H) Tolerance curve of a resistance-deficient fly strain (CG2247) infected with wild-type L. monocytogenes. (I–L) Tolerance curve of a natural variant D. melanogaster strain infected with wild-type L. monocytogenes. (M–P) Tolerance curve of L. monocytogenes ΔactA mutants injected into w¹¹¹⁸ control flies, (M–P). Microbe loads are recorded in (E), (I), and (M). Survival curves are recorded in (F), (J), and (N). Tolerance curves for the condition being tested are reported in (G), (K), and (O), with the corresponding data points in blue. The tolerance curve for w¹¹¹⁸ is shown in black without data points. Panels (H), (L), and (P) show illustrations of the changes in parameters seen in the tolerance curves. Data are reported in S2 Data.

https://doi.org/10.1371/journal.pbio.1002435.g006

Testing the Mathematical Model for Disease Tolerance

To test whether the shape of the disease tolerance curve in this host–pathogen pairing was driven by immunological damage or microbial damage, and to determine how the parameters of a sigmoid disease-tolerance curve varied, we measured the tolerance curves for a collection of Drosophila mutants that we previously showed differ in their resistance and tolerance defenses to L. monocytogenes [10–12]. We also tested natural variant flies from the Drosophila Genetics Reference Panel that were preselected because they showed extreme changes in their response to L. monocytogenes infections [33,34]. In addition, we tested L. monocytogenes mutants that altered pathogenesis in the fly [11]. These data supported the model in which bacteria caused damage in the system and did not support the immunological damage model.

A mutation in the D. melanogaster gene CG2247 was found previously to reduce the fly’s ability to both survive an infection and control L. monocytogenes growth [11]; here, we found that at 2 DPI, even CG2247 mutant flies injected with just ten bacteria had the same high microbe loads as flies injected with 100,000 bacteria, supporting the idea that these mutants alter resistance. This is visible in the tolerance curves, in which all of the points from infected mutant flies clustered on the bottom asymptote of the parental tolerance curve (Fig 6E–6H, S5 Table). An additional example of a fly strain with poor resistance is shown in the supplementary data (S3 Fig and S5 Table). Since flies suffering a loss of resistance showed no change in the maximum death rate of the infection, these results support the model in which bacteria are responsible for damage.

RNAseq analysis of CG2247 mutant flies suggests a molecular mechanism for the observed phenotype. We observed that in wild-type flies, the transcripts encoding the enzymes required to generate a reactive oxygen response against L. monocytogenes dropped over the course of the infection but recovered upon antibiotic treatment (S6 Fig) [11,35]. In contrast, these transcripts dropped to 10-fold lower levels in CG2247 mutants and did not recover to their original levels. We observed a reduction in the characteristic dark spots resulting from the action of this immune response (S6 Fig). We conclude that mutations in this gene disrupt the melanization immune response.

The disease-tolerance curve for the natural variant D. melanogaster strain, RAL 359, showed a reduction in the EC₅₀ of the system without a change in resistance [33]. RAL 359 was as capable as our lab control strain w¹¹¹⁸ in controlling L. monocytogenes growth; however, low doses of the microbe had a larger effect on health in this strain than in the control. This shifted the EC₅₀ from 922 to 83 colony-forming units per fly (Fig 6I–6L and S5 Table). The vigor and maximum death rate of these two strains was similar. This shift in EC₅₀ was a common phenotype, as shown in S4 and S5 Figs.

Changing the virulence of the L. monocytogenes also altered the EC₅₀ of the system. Mutant L. monocytogenes lacking the virulence factors actin assembly-inducing protein (ActA) or listeriolysin O (LLO) had previously been shown to kill flies more slowly than wild-type L. monocytogenes (Fig 5C versus Fig 6O) [11]. The tolerance curves for flies infected with an ΔactA mutant showed a shift in the EC₅₀ from 922 to 5,753 (Fig 6M–6P and S5 Table). We observed a ceiling for the number of L. monocytogenes that can be maintained in a wild-type infected fly (Figs 2A and 5A) and hypothesize that this is defined by the number of phagocytes in the fly that provide a niche for L. monocytogenes growth [13]. The ΔactA mutant bacteria approached this limit before they induced maximal pathology and, thus, we did not observe a low asymptotic tail. Δhly mutants produced a similar result to ΔactA mutants, only more extreme (S4 Fig).

Disease Spaces

The disease space analysis of recovering and dying flies reveals that far more is going on in these sick animals than AMP gene expression, and it lets us organize these events with a simple map. A commonly used time point for gene expression studies in Drosophila is 6 h post infection [44,45]; this is a particularly problematic time point because it combines transient expression of heat shock genes with expression of antimicrobials. Flies fated to die have a progressing gene signature in which a set of transcripts is increased without a corresponding increase in microbe load. We anticipate that one will need to measure the course of pathogenic infections to identify these genes, rather than follow microbes that simply elicit an immune response but do not kill wild-type flies (for example Escherichia coli or Micrococcus luteus [40,46]. Just as each pathogen causes a different disease in humans, we expect that there will be a range of pathologies caused by insect pathogens and do not assume that these L. monocytogenes-induced genes are the only morbidity genes in the fly. The nature of this particular death response is unclear, as the identity of the genes does not provide obvious clues. In contrast, recovering flies have a unique gene expression signature that suggests function; for example, enzymes in biosynthesis and energy metabolism are repressed during infection but pop up hysteretically as microbes are removed, suggesting the induction of a recovery response that rebuilds damaged tissues.

Why Does Shape Matter?

The shapes of tolerance curves are important because they will define which medications can be used to improve the health of an infected patient depending upon their position on the sigmoid curve. Here is a concrete example: If we think about the dose response curve to sepsis in humans as a linear response, then any drug that limits damage will help every patient. We come to a different conclusion if we consider a sigmoid relationship. Humans suffer from sepsis when relatively small numbers of microbes enter the blood, and very sick patients can have much higher levels of microbes. This suggests the sickest patients will be found on the asymptote of a sigmoid curve, where they will be suffering maximum pathological effects. Drugs that change the basal level of a response, EC₅₀, or slope will not help these patients; they will only respond to drugs that manipulate maximal response levels. Thus, we need to understand the shape of these tolerance curves and where the patients lie on the curves to select appropriate treatments.

The discussion of tolerance in patients raises a tricky point. We’ve shown it is possible to measure a disease tolerance curve in a model system; this demonstrated the nonlinear nature of tolerance and suggested the existence of new dimensions we should follow when measuring disease outcomes. The problem is that this approach requires us to perform many more experiments than we do currently when analyzing phenotypes, and this approach is likely impossible to apply to most human infections for the following two reasons: First, disease tolerance is plotted using summary characteristics of an infection. For example, one might measure the maximum parasite load and minimum health for an infection [5]. This is accessible experimentally, but it is unethical to gather these data from a patient, as you need to treat the patient when they enter the clinic. In one rare case of HIV, infected patients’ tolerance curves have been recorded because these chronically infected patients are followed for years, but that approach isn’t going to be useful for acute infections [47]. Second, disease tolerance is a measurement of the behavior of a population and not an individual. The information we gather about an individual allows us to place a datum on a health by microbe graph, but we don’t know the shape of the curve that should be fit through that individual [9]; thus, we can’t easily determine which parameters need fixing in the sick patient. What we learn from model systems is that there are underlying rules that can be used to explain disease outcomes, and that these rules are nonlinear. By studying these rules in models, we can identify the molecular mechanisms corresponding to the mathematical parameters and then apply this knowledge to human biology by analogy. If we want to measure changes directly in human immune infections, we need to rely on descriptions of disease space, which are described in the accompanying paper [48].

Fly Stocks and Husbandry

Flies were maintained on standard dextrose fly media (129.4 g dextrose, 7.4 g agar, 61.2 g corn meal, 32.4 g yeast, and 2.7 g tegosept per liter) at 25°C with 65% humidity and 12 h light/dark cycles. Shortly after eclosion, adult flies were collected into bottles containing dextrose fly media. At least 24 h post eclosion, adult flies were anesthetized with carbon dioxide, and males were sorted into groups of 20 and placed into vials containing standard dextrose fly media. Experiments were performed on flies 5–7 d post eclosion unless otherwise indicated. CG2247 piggybac allele (BL18050), Pcmt piggybac allele (BL18398), kenny piggyback allele (BL11044), CG7408 piggyback allele (BL19305), piggybac allele parental strain w¹¹¹⁸ (BL6326), RAL 359 (BL28179), RAL 787 (BL28231), RAL 375 (BL25188), RAL 309 (BL28166), RAL 73 (BL28131), RAL 380 (BL25190), and RAL 821 (BL28243) strains were obtained from the Bloomington stock center.

Injection

Bacteria were injected into flies essentially as described previously [10,12,14,49]. Flies were anaesthetized with carbon dioxide. A drawn glass needle carrying L. monocytogenes was used to pierce the cuticle on the ventrolateral side of the abdomen. A picospritzer III was used to inject 50 nl of liquid into the fly. Bacteria were delivered at different concentrations to produce injections of approximately 10, 100, 1,000, 10,000 or 100,000 CFU. Infectious doses were determined for each experiment by plating a subset of flies at time zero. Approximately 200–400 flies were used for each dose in the experiment to measure survival and to count colonies.

Bacterial Strains and Culturing Conditions

All L. monocytogenes stocks: Wild type/mutant parental strain (10403S), Δhly (DP-L2161) [50], and ΔactA (DP-L3078) [51] were stored at -80°C in brain and heart infusion (BHI) broth containing 25% glycerol. To prepare L. monocytogenes for injection, bacteria were streaked onto Luria Bertani (LB) agar plates containing 100 ug/mL streptomycin and incubated at 37°C overnight. Single colonies of L. monocytogenes from the LB agar plate were used to inoculate 4 mL of brain and heart infusion (BHI) broth and incubated overnight at 37°C without shaking. Bacteria were removed from the incubator at log growth phase. Prior to injection, L. monocytogenes cultures were diluted to the desired optical density (OD) 600 in phosphate buffered saline (PBS) and stored on ice.

Bacterial Plating

Single flies were homogenized in PBS using a motorized plastic pestle in 1.5 ml tubes. The supernatants were plated using an Autoplate spiral plater and counted using a Qcount automated counter. At least six samples were counted to determine the median number of bacteria for each inoculum. Bacteria were plated onto LB medium and incubated overnight at 37°C before counting.

Survival Curve Analysis

200–400 flies were injected and checked daily to measure mortality for each inoculum. Flies were housed in vials containing 20–25 flies each.

Repetitions

Each set of conditions was repeated at least three times; for example, an experiment for a mutant fly line would be set up independently on three different days to gather microbe load and survival data. Pairs of plating and survival data from these multiple experiments were all plotted on the same tolerance curve.

RNA Isolation for Microarray

Flies were injected with 50 nl of Listeria (OD₆₀₀ = 0.001, or approximately 100 CFUs) or left manipulated. Following injection, flies were placed in vials containing dextrose fly media and incubated at 29°C. Samples were separated into three groups: Moribund, recovering, and uninfected control. Moribund flies were infected, and samples were collected on the following DPI: 0.25, 1, 2, 2.25, 3, 4, 5, and 6. Recovering flies were infected and flipped onto dextrose fly media containing 1 mg/ml ampicillin 2 DPI. Recovering samples were collected on the following DPI: 2.25, 3, 4, 5, 6, 7, 9, and 16. Uninfected control flies were not infected but were flipped onto dextrose fly media containing 1 mg/ml ampicillin 2 dpi. Uninfected control samples were collected on the following dpi: 2.25, 3, and 9. At each of the indicated time points, groups of 20 flies were homogenized in TRIzol, and RNA was isolated using a standard TRIzol preparation. Additional flies were used to determine CFUs and monitor survival. Biological triplicates were obtained from three independent experiments. Quality of RNA was determined using a BioAnalyzer 2100. Samples were labeled using the Quick Amp Labeling Kit, One-Color (Agilent), and hybridized to 4x44K (V2) Drosophila Gene Expression Microarray (Agilent) using the Agilent Gene Expression Hybridization kit following the manufacturer’s protocol. Microarrays were scanned using an Agilent Technologies Scanner, and processed signal intensities were determined using Agilent’s Feature Extraction software. RNA quality assessment, labeling, hybridization, and microarray feature extraction were performed at the Stanford Functional Genomics Facility.

Microarray Analysis

The microarray data were analyzed using Genespring v12.1 (Agilent). Microarrays were normalized to the 75th percentile. The median expression level on 0 dpi was set as the baseline. Prior to statistical analysis, low-quality spots were removed based on flag calls. To determine differential gene expression, one-way ANOVA was performed comparing all samples to 0 dpi. P-values were corrected by the Benjamini-Hochberg method. Genes with p-values <0.05 at any time point with a fold-change greater than 2 were categorized as differentially expressed. Differentially expressed genes were then clustered using Mfuzz [52].

Topological Data Analysis

Only genes that were differentially expressed in moribund and recovering but not in uninfected control were used in the topological data analysis using the Ayasdi 3.0 software platform (ayasdi.com, Ayasdi Inc., Menlo Park, California). Nodes in the network represent clusters of samples of infected flies, and edges connect nodes that contain samples in common. Nodes are colored by the average value of their samples for the variables listed in the figure legends. TDA was used to map the way hosts loop through the disease space in an unsupervised fashion. Two types of parameters are needed to generate a topological analysis. First is a measurement/notion of similarity, called a metric, which measures the distance between two points in some space (usually between rows in the data). Second are lenses, which are real valued functions on the data points. Lenses are used to create overlapping bins in the dataset. Overlapping families of intervals are used to create overlapping bins in the data. Metrics are used with lenses to construct the Ayasdi 3.0 output. Multiple lenses can be used in each analysis. There are two parameters used in defining the bins. One is resolution, which determines the number of bins; higher resolution means more bins. The second is gain, which determines the degree of overlap of the intervals. Once the bins are constructed, we perform a clustering step on each bin, using single linkage clustering with a fixed heuristic for the choice of the scale parameter. This heuristic is described in [26]. This gives a family of clusters within the data, which may overlap. We built a network with one node for each such cluster and where we connect two nodes, if the corresponding clusters contain a data point in common. We used two types of lenses. The first type was lenses based on dimension reduction algorithms such as multidimensional scaling and nearest neighbor analyses; these helped analyze the data in an unsupervised manner. The second type was lenses based on the data alone, for example, the levels of antimicrobial gene expression or recovery gene expression. The gene expression markers helped us dissect the graphs using knowledge about the biology of the system. To build our map, we analyzed our dataset with samples as rows and genes as columns. We used the Variance Normalized Euclidean metric. We used the PCA coord1 and PCA coord2 lens as well as two data lenses: CG32373 and Fuca (Resolution = 19, Gain = 6, and equalized was used for all lenses).

Model Rationale and Methods

To evaluate the impact of within-host infection dynamics on host health curves, we created a compartmental model consisting of four ordinary differential equations for microbes (M), immune effectors (I), microbial damage effectors (D), and health (H).

Microbes grow in a sigmoid fashion at rate r as they deplete the host substrate, and immune effectors can either kill microbes outright at rate ε per effector or inhibit microbial growth at rate η. In these simulations, growth rate limitation was used as the main immune response. Two mechanisms contribute to immune effector production. Reflecting the sigmoid relationship between microbe density and AMP levels, immune effectors can increase in proportion to microbe density up to a maximal rate of τ*k_M until effector levels saturate immune pathway machinery (k_I). The parameter σ_I reflects the microbe concentration at the inflection point for immune induction. Immune effectors decay at rate μ. Microbes secrete virulence factors and toxins at a maximal rate φ*k_D, modulated by a sigmoidal relationship between damage factor production and microbe density to reflect a process like quorum sensing controls on virulence factor production. As with immunity, there is a carrying capacity imposed on damage effectors. This could reflect either negative feedbacks on further effector production at high effector densities or a bottleneck limiting flux through the system. The parameter σ_D reflects the microbe density that produces a half-maximal induction rate. Damage effectors degrade at rate ρ. Immunopathology and damage effectors deplete health (H) at rates γ and α, respectively, while hosts can recover health according to a sigmoidal relationship with current health (reflecting the difficulty of achieving recovery at low health due to organ failure and other catastrophe) at rate z. “Death” is called when health dips below 10% of maximum (k_H). All simulations were conducted within a parameter space outlined in S4 Table and run in Matlab (v. 7.11.0) using the ode45 solver.

Curve Fitting

The sigmoidal curves were fit using the four-parameter method in Prism. We tested several models (linear, exponential, logistic, and sigmoid) and picked the model that gave the best adjusted r². We used the adjusted r² to account for overfitting. When the curve-fitting program suggested a clearly erroneous result, such as an extremely high top or low bottom, we fixed the top or bottom at the average level for the vigor or for the average of the last three points for the bottom.

RNAseq

Flies were injected with 50 nL of 0.01 OD600 (1000 CFUs) of L. monocytogenes resuspended in PBS. Flies were placed in vials containing dextrose fly media and incubated at 29°C. 3 DPI flies were flipped onto dextrose fly media containing 1 mg/mL ampicillin. Groups of 20 flies were homogenized in TRIzol for RNA extraction on the following DPI: 0, 1, 2, 3, 4, 6, 8, 10, 12, 14, 16, and 18. Additional flies were used to determine CFU and monitor survival. We tested w¹¹¹⁸, CG2247, Pcmt, and RAL359 strains. As a control, additional sets of w¹¹¹⁸ were left uninfected and flipped onto dextrose fly media containing 1 mg/mL ampicillin 3 dpi, and samples for RNAseq were collected at the indicated time points. RNA was isolated using standard TRIzol preparation. Library preparation and sequencing was performed by the Duke Center for Genomic and Computational Biology. Briefly, quality of RNA was assessed by Bioanalyzer 2100. Polyadenylated RNA was enriched from total RNA. Barcoded TruSeq cDNA Libraries were constructed and quality was assessed by Qubit and Agilent Tapestation. 50 bp single end reads were obtained by sequencing the libraries on an Illumina HiSeq 2000 using a full flow cell. Reads were mapped using STAR, and RPKM for each gene was determined by Cufflinks.

Melanization Assay

Groups of 20 female flies were anesthetized with carbon dioxide and injected with 50 nl of 0.01 OD600 (~1,000 CFUs) of L. monocytogenes resuspended in PBS. After injection, flies were flipped onto dextrose fly media and incubated at 29°C. At 2 dpi, the percent melanized for each group was determined by anesthetizing the flies with carbon dioxide and scoring each abdomen for presence of melanization spots. For each genotype, eight groups of flies were scored.