Figures and data in Linking functional and molecular mechanisms of host resilience to malaria infection

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10 figures, 1 table and 2 additional files

Figures

Figure 1

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Proportion of mice surviving over the course of infections initiated with 10⁵*P. chabaudi* AJ parasites.

Eight mouse strains are shown (with total sample sizes given in parentheses): WSB/EiJ (30), 129S1/SvImJ (10), NZO/HILtJ (10), C57BL/6 (20), CAST/EiJ (32), NOD/ShiLtJ (15), A/J (15), and PWK/PhJ (22). The dataset is a compilation of two experiments (Davis et al., 2021 and Gupta et al. unpublished). The lines for WSB/EiJ, 129S1/SvImJ and NZO/HILtJ are jittered as 100% of mice of each strain survived for 15 days.

Figure 2

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Longitudinal data of infection contain features of within-host ecology that influence infection outcomes.

In a phase plot bound by parasite burden and host health (i.e. disease space, sensu [Schneider, 2011; Torres et al., 2016]), infection progresses clockwise from the top-left corner (i.e. many RBCs, few iRBCs). Top left panel illustrates common trajectories. Following a rapid parasite growth phase (rightward movement along the x-axis), host health deteriorates (downward movement along the y-axis) during acute malaria infection. In the meantime, the parasite density starts to decline due to resource limitation and/or upregulated immunity. If a host is resilient, the trajectory tends towards the starting healthy state as parasites further decline and RBCs are replenished (path a, light grey). In contrast, the damage to host health may be irreparable in non-resilient hosts (path b, dark grey) (Schneider, 2011). The small, coloured plots at the bottom show the empirically observed trajectories of the first wave of malaria infection in 80 mice across eight strains in disease space, with the densities of iRBCs and RBCs on the x- and y-axis, respectively. The top right panel shows the median trajectory of the eight strains. Generally speaking, highly resilient strains (WSB/EiJ, 129S1/SvImJ, NZO/HILtJ, C57BL/6) follow path a, and less resilient strains (CAST/EiJ, NOD/ShiLtJ, A/J, PWK/PhJ) follow path b.

Figure 3

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Model schematics.

(a) A dynamical regulation model of host responses against blood-stage malaria. We condensed the complexity of the vertebrate acute innate response against malaria into two independent pathways responsible for general RBC clearance and targeted iRBC clearance (represented by the yellow and green block, respectively). Activation of each response occurs when the host detects the presence of pathogen-associated molecular patterns (PAMPs): f₁ and f₂ are linear functions of the iRBC density. For general RBC clearance, the activity resets daily. In contrast, the activity of the targeted responses against iRBCs accumulates over multiple days (see methods for further explanation). The output of each host response feeds back to influence the within-host infection dynamics (indicated by the coloured arrows in panel b). (b) Dynamics of RBCs and blood-stage malaria parasites within the host. Recruitment into and transitions among components of the asexual cycle are indicated with black arrows. Grey arrows indicate background mortality for different components. General clearance of RBCs and targeted clearance of iRBCs are marked with yellow and green arrows, respectively. Replenishment of RBCs (erythropoiesis) is indicated in blue.

Figure 4

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Differences in within-host ecological parameters reveal functional diversity linked to resilience to malaria infection.

(a) Strain-specific variation, $s$ , in each parameter of the set $θ ∋ (μ_{R}^{'}, μ_{R}^{''}, ρ, ψ_{N_{1}}, ψ_{N_{2}}, β)$ . The eight strains are ordered according to overall survival percentage from the top (see Figure 1). The average parameter value across the eight strains is indicated by $s = 0$ . (b) Ordered parameter stacks show functional similarities and differences between individual mice of different strains (indicated by colours). Each slice of a stack represents the median estimate for an individual mouse.

Figure 5

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Within-host ecological parameters differentiate mouse strains with varying degrees of resilience to malaria infection.

The PCA biplot displays the relationship between individual mice in the first two principal components, which collectively account for 66.7% of the total variance in parameters describing within-host malaria ecology, $θ ∋ (μ_{R}^{'}, μ_{R}^{''}, ρ, ψ_{N_{1}}, ψ_{N_{2}}, β)$ . The direction and length of the grey arrows indicate the contribution of each parameter to the principal components. Parameter descriptions are found in Table 1.

Figure 6

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Distinct expression patterns of pro (TNF-α and IFN-γ) and anti-inflammatory cytokines (IL-10 and TGF-β) in eight mouse strains infected with *P. chabaudi* show that host resilience to malaria infection is linked to the strength and balance in cytokine expressions.

Raw temporal expression intensity in (a) uninfected control and (b) infected mice between day 3 and 9 post-infection. (c) The intensity of cytokine expression scaled by the median iRBC density of the strain per day. A higher value indicates higher propensity to express cytokines against the same density of parasites on a given day. (d) The ratio of pro- to anti-inflammatory cytokine expressions. Shown are additive expressions (i.e. TNF-α + IFN-γ and IL-10 + TGF-β), but multiplicative expression patterns (i.e. TNF-α × IFN-γ and IL-10 × TGF-β) were qualitatively identical (results not shown). The points and error bars are the means and standard deviations, respectively. For each day, the strains are ordered from left to right according to host survival as listed in Figure 1.

Appendix 1—figure 1

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The fit of the dynamical model to the density of RBCs (red) and iRBCs (blue).

Each column corresponds to a mouse strain. The crosses indicate data and grey bands correspond to 95% predictive intervals of the model, incorporating uncertainty in parameter estimation and sampling.

Appendix 1—figure 2

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Standardised model residuals of the dynamical model.

Crosses indicate residuals for individual time series, while red dots indicate the mean; blue dotted lines indicate the Bonferroni-corrected 95% confidence intervals. Poor fits are indicated by the mean residuals deviating from confidence intervals.

Appendix 2—figure 1

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Pairwise correlations of MCMC samples indicate that the parameter set $θ ∋ (μ_{R}^{'}, μ_{R}^{''}, ρ, ψ_{N_{1}}, ψ_{N_{2}}, β)$ is likely identifiable.

The highest correlation coefficient observed was 0.54 between $μ_{R}^{'}$ (daily background RBC mortality rate during infection) and $μ_{R}^{''}$ (density-independent RBC replenishment rate during infection).

Appendix 2—figure 2

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The model parameters were estimated with accuracy, precision and identifiability.

Posterior z-score (y-axis) measures how closely the posterior recovers the parameters of the true data generating process and posterior contraction (x-axis) evaluates the influence of the likelihood function over the prior, respectively. Smaller absolute posterior z-scores indicate that the posterior accurately recovers the parameters of the true data generating process: the absolute value beyond three to four may indicate substantial bias (Schad et al., 2021). The posterior contraction values close to one indicate that data are much more informative than the prior.

Tables

Table 1

Description of model parameters and their fixed values, or prior distributions used in Bayesian statistical inference.

Where parameters were estimated (indicated by $^{*}$ on the description), we assigned generic priors (for immune parameters, $ψ_{N_{1}}$ and $ψ_{N_{2}}$ , and hyperpriors $σ_{s}$ and $σ_{u}$ ) and weakly informative priors centred around specific estimates from previous studies for the rest.

Symbol	Description	Fixed value or prior	Source
Host responses
ρ	Proportion of deviation from $R_{c}$ restored per day *	$0.25 \times \exp (𝒩 (0, 1))$	Miller et al., 2010
$ψ_{N_{1}}$	Activation strength of indiscriminate RBC clearance *	$\exp (𝒩 (0, 1))$
$ψ_{N_{2}}$	Activation strength of targeted iRBC clearance *	$\exp (𝒩 (0, 1))$
Within-host infection dynamics
$R_{c}$	RBC density at homeostatic equilibrium	${RBC}_{(t = 0)}$	data
$I_{max}$	Maximum iRBC density observed	$2.65 \times 10^{6}$ per microliter	data
$μ_{R}$	Daily background RBC mortality rate	0.025	Miller et al., 2010
$μ_{R}^{'}$	Daily background RBC mortality rate (during infection) *	$0.025 \times \exp (𝒩 (0, 1))$	Miller et al., 2010
$μ_{R}^{''}$	Density-independent RBC replenishment rate (during infection) *	$0.025 \times \exp (𝒩 (0, 1))$	Miller et al., 2010
β	Parasite burst size *	$7 \times \exp (𝒩 (0, 1))$	Miller et al., 2010
$p$	Merozoite invasion rate	$1.5 \times 10^{- 5}$ per day	Mideo et al., 2011
$μ_{M}$	Merozoite mortality rate	48 per day	McAlister, 1977
Hyperpriors
$σ_{s}$	Standard deviations for strain-level variation	$\exp (𝒩 (0, 1))$
$σ_{u}$	Standard deviations for individual-level variation	$\exp (𝒩 (0, 1))$
Measurement errors
$σ_{RBC}$	Standard deviation for total RBC density *	$5 \times 10^{5} \times \exp (𝒩 (0, 1))$	Miller et al., 2010
$σ_{iRBC}$	Standard deviation for log₁₀ iRBC count *	$0.2 \times \exp (𝒩 (0, 1))$	Mideo et al., 2008b

Additional files

Supplementary file 1 Data and modelling, analysis and visualisation programs.: https://cdn.elifesciences.org/articles/65846/elife-65846-supp1-v1.zip
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Tsukushi Kamiya
Nicole M Davis
Megan A Greischar
David Schneider
Nicole Mideo

(2021)

Linking functional and molecular mechanisms of host resilience to malaria infection

eLife 10:e65846.

https://doi.org/10.7554/eLife.65846

Figures

Proportion of mice surviving over the course of infections initiated with 10⁵P. chabaudi AJ parasites.

Longitudinal data of infection contain features of within-host ecology that influence infection outcomes.

Model schematics.

Differences in within-host ecological parameters reveal functional diversity linked to resilience to malaria infection.

Within-host ecological parameters differentiate mouse strains with varying degrees of resilience to malaria infection.

Distinct expression patterns of pro (TNF-α and IFN-γ) and anti-inflammatory cytokines (IL-10 and TGF-β) in eight mouse strains infected with P. chabaudi show that host resilience to malaria infection is linked to the strength and balance in cytokine expressions.

The fit of the dynamical model to the density of RBCs (red) and iRBCs (blue).

Standardised model residuals of the dynamical model.

Pairwise correlations of MCMC samples indicate that the parameter set $θ ∋ (μ_{R}^{'}, μ_{R}^{''}, ρ, ψ_{N_{1}}, ψ_{N_{2}}, β)$ is likely identifiable.

The model parameters were estimated with accuracy, precision and identifiability.

Tables

Description of model parameters and their fixed values, or prior distributions used in Bayesian statistical inference.

Additional files

Supplementary file 1

Transparent reporting form

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Downloads (link to download the article as PDF)

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Proportion of mice surviving over the course of infections initiated with 105P. chabaudi AJ parasites.

Longitudinal data of infection contain features of within-host ecology that influence infection outcomes.

Model schematics.

Differences in within-host ecological parameters reveal functional diversity linked to resilience to malaria infection.

Within-host ecological parameters differentiate mouse strains with varying degrees of resilience to malaria infection.

Distinct expression patterns of pro (TNF-α and IFN-γ) and anti-inflammatory cytokines (IL-10 and TGF-β) in eight mouse strains infected with P. chabaudi show that host resilience to malaria infection is linked to the strength and balance in cytokine expressions.

The fit of the dynamical model to the density of RBCs (red) and iRBCs (blue).

Standardised model residuals of the dynamical model.

Pairwise correlations of MCMC samples indicate that the parameter set θ∋(μR′,μR′′,ρ,ψN1,ψN2,β) is likely identifiable.

The model parameters were estimated with accuracy, precision and identifiability.

Description of model parameters and their fixed values, or prior distributions used in Bayesian statistical inference.

Supplementary file 1

Transparent reporting form

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

Proportion of mice surviving over the course of infections initiated with 10⁵P. chabaudi AJ parasites.

Pairwise correlations of MCMC samples indicate that the parameter set $θ ∋ (μ_{R}^{'}, μ_{R}^{''}, ρ, ψ_{N_{1}}, ψ_{N_{2}}, β)$ is likely identifiable.