How Many Parameters Does It Take to Describe Disease Tolerance?

Abstract

The study of infectious disease has been aided by model organisms, which have helped to elucidate molecular mechanisms and contributed to the development of new treatments; however, the lack of a conceptual framework for unifying findings across models, combined with host variability, has impeded progress and translation. Here, we fill this gap with a simple graphical and mathematical framework to study disease tolerance, the dose response curve relating health to microbe load; this approach helped uncover parameters that were previously overlooked. Using a model experimental system in which we challenged Drosophila melanogaster with the pathogen Listeria monocytogenes, we tested this framework, finding that microbe growth, the immune response, and disease tolerance were all well represented by sigmoid models. As we altered the system by varying host or pathogen genetics, disease tolerance varied, as we would expect if it was indeed governed by parameters controlling the sensitivity of the system (the number of bacteria required to trigger a response) and maximal effect size according to a logistic equation. Though either the pathogen or host immune response or both together could theoretically be the proximal cause of pathology that killed the flies, we found that the pathogen, but not the immune response, drove damage in this model. With this new understanding of the circuitry controlling disease tolerance, we can now propose better ways of choosing, combining, and developing treatments.

Fig 1. Visualizing infections in individuals, in pure lines and diverse populations.

(A) A simple model in which microbes induce an immune response, which in turn limits microbe growth and kills the microbes. Both microbes and immune effectors can cause damage in this model.

Fig 2. Listeria monocytogenes growth characteristics in the fly.

(A) L. monocytogenes growth dynamics during infection. w¹¹¹⁸ flies were injected with 1,000 CFUs. Individual flies were homogenized and plated, and bacterial colonies were counted at each time point. The data are fit with a logistic curve with a maximal growth ceiling of approximately 17,000 bacteria and a growth rate of 0.1659/h. The dotted lines indicate the 95% confidence interval. (B) L. monocytogenes dynamics during antibiotic treatment. Flies were injected with 100 CFUs and treated with ampicillin. The data are fit with a plateau followed by a one-phase decay with a half-life of 2.4 d. The dotted lines indicate the 95% confidence interval. (C) Survival curves for treated and untreated flies demonstrate that antibiotic treatment led to recovery of the flies, which lived as long as wounding control flies. Data are reported in S1 Data.

Fig 3. Antimicrobial peptide expression dynamics.

(A) AMP dose response curve. Expression of AMPs was determined by microarray. Fold change is plotted relative to log microbe load (grey: uninfected control, black: infected, no treatment, red: infected, ampicillin treatment). The data are fit with a four-parameter sigmoid model. Adjusted r²: Drosomycin = 0.9521, Attacin A = 0.8509, Cecropin A = 0.8933. The dotted lines indicate the 95% confidence interval. (B) EC₅₀ of antimicrobial peptides. Error bars mark the 95% confidence interval. (C) Maximum expression level of antimicrobial peptides. Error bars mark the 95% confidence interval. (D) Relationship between Hill slope and EC₅₀. The data are fit with an exponential growth function with an adjusted r² = 0.5126. Data are reported in S1 Data.

Fig 4. Disease space analysis of infected and recovering flies.

(A) Infection map colored by treatment groups. The network was built using Ayasdi Core (data from S1 Table). Samples with similar expression patterns are binned together. Nodes are bins of individual samples. Bins containing the same sample are connected by edges. Cyan is the overlap of uninfected and no treatment groups, and orange is the overlap of ampicillin treatment and no treatment groups. (B) Infection map colored by CFU. The green arrow marks disease progression. Pathways of upregulated genes are numbered. Phases of infection are indicated by Roman numerals. (C) Infection map colored by heat shock protein 26. (D) Infection map colored by Attacin A. (E) Infection map colored by CG3117 (peptidase and death gene). (F) Infection map colored by CG32444 (aldose-1 epimerase and recovery gene).

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.

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.