Figures and data in Gastrointestinal helminths increase Bordetella bronchiseptica shedding and host variation in supershedding

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Nhat TD Nguyen

Ashutosh K Pathak

Isabella M Cattadori

(2022)
Gastrointestinal helminths increase Bordetella bronchiseptica shedding and host variation in supershedding

eLife 11:e70347.

https://doi.org/10.7554/eLife.70347
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Figures
Tables
Additional files

21 figures, 4 tables and 1 additional file

Figures

Figure 1

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Observed levels of B. *bronchiseptica* shedding by contact of infected rabbits with a Bordet-Gengou agar petri dish.

Rabbits (infected shedders and non-shedders) from the four types of infection are reported, *B. bronchiseptica* (B), *B. bronchiseptica-G. strigosum* (BG), *B. bronchiseptica-T. retortaeformis* (BT) and *B.…*

Figure 2

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Observed level of B.bronchiseptica shedding by days post infection (Dpi) and type of infection.

Shedding events (points), host individual trajectories (thin lines) and median population trend (smoothed thick lines) with 95% CI (blue shadows) are reported. The trajectories of few individuals …

Figure 3

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Frequency of observed B.bronchiseptica shedding events for the four types of infection.

Events have been grouped by shedding level using 0.5 CFU/s unit intervals, the first interval represents events with zero shedding. Red lines indicate the 95^th and 99^th percentile thresholds, …

Figure 4

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B. *bronchiseptica* shedding on BG-blood agar petri dishes.

Examples of A: supershedding event and B: average shedding event.

Figure 5

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Estimated immune responses in the blood by time and type of infection.

Empirical longitudinal data (points) with estimated trajectories (black lines) for every individual rabbit, and group means (blue lines) with 95% CIs (blue shadows) are reported. The abrupt …

Figure 6

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Estimated rates of infection in the whole respiratory tract and immune response in the blood by time and type of infection.

Means (continuous lines) and 95% CIs (shaded areas) are reported for neutrophils (black), IgA (blue), IgG (red), and *B. bronchiseptica* infection (green). Individual trends (dotted lines) have been …

Figure 7

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Estimated dynamics of B. *bronchiseptica* shedding by time and type of infection.

The empirical shedding events (gray points), the estimated individual trajectories (smoothed thin black lines) and the estimated median group trends (blue lines), with the related 95%CIs (blue …

Appendix 1—figure 1

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Parameter estimates from posterior distribution for BG.

Individual average (black points) with 95% CIs (black segments), and group average (named ’Pop’, red points) with 95% CIs (red segments), are reported. X-axis lists the rabbit’s ID every 5 animals …

Appendix 1—figure 2

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Parameter estimates from posterior distribution for BT.

Full details in Appendix 1—figure 1.

Appendix 1—figure 3

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Parameter estimates from posterior distribution for BTG.

Full details in Appendix 1—figure 1.

Appendix 2—figure 1

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Relationship between B.bronchiseptica peak of shedding and percentile changes in neutrophils, IgA, and IgG.

The growth a, and neutralizing c, rates of neutrophils (subscript 1), IgA (subscript 2) and IgG (subscript 3), including bacterial growth rate r, are reported by group. Mean estimates with 95% CIs …

Appendix 2—figure 2

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Relationship between B.bronchiseptica time to peak of shedding and percentile changes in neutrophils, IgA, and IgG.

Full details in Appendix 2—figure 1.

Appendix 3—figure 1

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MCMC trace plot for B.

Different colors represent the four chains.

Appendix 3—figure 2

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MCMC trace plot for BG.

Different colors represent the four chains.

Appendix 3—figure 3

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MCMC trace plot for BT.

Different colors represent the four chains.

Appendix 3—figure 4

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MCMC trace plot for BTG.

Different colors represent the four chains.

Appendix 3—figure 5

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MCMC posteriors from B.

Histograms (diagonal), pair-wise scatterplots (upper right) and related correlations (lower left) from the parameter posteriors.

Appendix 3—figure 6

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MCMC posteriors from BG.

Histograms (diagonal), pair-wise scatterplots (upper right) and related correlations (lower left) from the parameter posteriors.

Appendix 3—figure 7

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MCMC posteriors from BT.

Histograms (diagonal), pair-wise scatterplots (upper right) and related correlations (lower left) from the parameter posteriors.

Appendix 3—figure 8

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MCMC posteriors from BTG.

Histograms (diagonal), pair-wise scatterplots (upper right) and related correlations (lower left) from the parameter posteriors.

Appendix 4—figure 1

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Model validation using group-level parameters.

The vertical lines represent the true parameters that were used to simulate the datasets.

Tables

Table 1

Description and unit of parameters and variables used in the dynamical and observed models.

Parameters/	Descriptions	Unit	Value
Variables
Rabbit i^th specific parameters
$a_{1, i}, b_{1, i}, c_{1, i}$	Growth, decay and B. bronchiseptica neutralization rates of neutrophils	day^-1	Estimated
$a_{2, i}, b_{2}, c_{2, i}$	Growth, decay and B. bronchiseptica neutralization rates of IgA	day^-1	Estimated
$a_{3, i}, b_{3}, c_{3, i}$	Growth, decay and B. bronchiseptica neutralization rates of IgG	day^-1	Estimated
r_i	Per capita B. bronchiseptica replication rate	day^-1	Estimated
$x_{1, i} (t)$	Time-dependent neutrophil response	cells/ml	Calculated
$x_{2, i} (t)$	Time-dependent IgA response	O.D. index	Calculated
$x_{3, i} (t)$	Time-dependent IgG response	O.D. index	Calculated
$y_{i} (t)$	Time-dependent B. bronchiseptica infection intensity	CFU/g count	Calculated
Group parameters
$μ_{a_{1}}, μ_{b_{1}}, μ_{c_{1}}$	Mean of neutrophil growth, decay and neutralization rates	day^-1	Estimated
$σ_{a_{1}}, σ_{b_{1}}, σ_{c_{1}}$	Standard deviation (S.D.) of neutrophil growth, decay and neutralization rates	day^-1	Estimated
$μ_{a_{2}}, μ_{c_{2}}$	Mean of IgA growth, and neutralization rates	day^-1	Estimated
$σ_{a_{2}}, σ_{c_{2}}$	Standard deviation (S.D.) of IgA growth, and neutralization rates	day^-1	Estimated
$μ_{a_{3}}, μ_{c_{3}}$	Mean of IgG growth, and neutralization rates	day^-1	Estimated
$σ_{a_{3}}, σ_{c_{3}}$	Standard deviation (S.D.) of IgG growth, and neutralization rates	day^-1	Estimated
$μ_{r}, σ_{r}$	Mean and S.D. of B. bronchiseptica replication rates	day^-1	Estimated
$x_{1}^{*}$	Neutrophils level at equilibrium	cells/ml	Observed
$μ_{y_{0}}$	B. bronchiseptica infection intensity at time t=0	CFU/g count	Estimated

Table 2

Model prior and posterior parameters for the immune response and B. bronchiseptica infection.

We report: mean and S.D. of priors, and mean, 95% CI and S.D. from posterior distributions for each group. The complete description of the parameters is provided in Table 1.

Parameters	Priors	Posteriors B	Posteriors BG	Posteriors BT	Posteriors BTG
$μ_{a_{1}} * 10^{- 4}$	0.10 (0.05)	2.89 (1.17–4.61)	1.08 (0.31–1.85)	3.32 (1.73–4.90)	0.93 (0.35–1.50)
$μ_{a_{2}} * 10^{- 5}$	1.10 (0.20)	2.00 (1.65–2.35)	0.81 (0.51–1.11)	0.99 (0.61–1.36)	1.36 (0.91–1.81)
$μ_{a_{3}} * 10^{- 5}$	0.30 (0.10)	1.51 (1.27–1.75)	0.66 (0.43–0.89)	0.78 (0.49–1.36)	0.86 (0.59–1.81)
$μ_{b_{1}}$	0.50 (0.10)	1.20 (0.83–1.57)	0.54 (0.37–0.71)	0.86 (0.61–1.11)	0.58 (0.40–0.77)
$b_{2} * 10^{- 3}$	0.30 (0.10)	7.07 (5.55–8.59)	3.10 (2.4–3.80)	5.57 (4.97–6.16)	7.43 (6.50–8.36)
$b_{3} * 10^{- 4}$	0.10 (0.07)	0.93 (0.03–1.83)	0.66 (0.02–1.30)	0.39 (0.01–0.77)	0.49 (0.01–0.97)
$μ_{c_{1}}$	0.20 (0.05)	0.11 (0.06–0.16)	0.13 (0.06–0.20)	0.05 (0.03–0.07)	0.30 (0.19–0.42)
$μ_{c_{2}}$	0.12 (0.02)	0.044 (0.003–0.085)	0.13 (0.03–0.22)	0.22 (0.16–0.27)	0.01 (.0004–0.02)
$μ_{c_{3}}$	0.10 (0.07)	0.042 (0.002–0.083)	0.29 (0.18–0.40)	0.33 (0.25–0.42)	0.32 (0.23–0.42)
$r$	1.70 (0.30)	0.06 (0.01–0.12)	1.18 (0.83–1.54)	1.01 (0.83–1.18)	1.47 (1.10–1.83)
$μ_{y_{0}} * 10^{3}$		0.68 (0.68–0.68)	0.71 (0.35–1.07)	0.68 (0.36–1.01)	0.82 (0.46–1.18)
$x^{*}$		0.05	1.89	1.93	2.75
$σ_{x_{1}}$		0.45	0.38	0.53	0.70
$σ_{x_{2}}$		0.22	0.40	0.33	0.22
$σ_{x_{3}}$		0.08	0.10	0.15	0.15
$σ_{y}$		1.00	6.02	4.50	4.01

Appendix 3—table 1

Scale reduction factors for each parameter of the four types of infection.

Parameters	B	BG	BT	BTG
$μ_{a 1}$	1.000234	1.000103	1.000252	1.000047
$μ_{b 1}$	1.000166	1.000205	1.000122	1.000073
$μ_{c 1}$	1.000053	1.000047	0.999977	1.000423
$μ_{a 2}$	1.000120	1.000174	1.000285	0.999986
$μ_{b 2}$	1.000043	1.000049	1.000051	1.000128
$μ_{c 2}$	1.000060	0.999973	1.000240	1.000316
$μ_{a 3}$	1.000068	1.000166	1.000027	1.000059
$μ_{b 3}$	1.000013	0.999927	0.999919	1.000089
$μ_{c 3}$	0.999967	1.000016	1.000224	1.000204
$μ_{r}$	0.999972	0.999961	1.000139	1.000517
log(LLH)	1.000650	1.000406	1.000521	1.000401

Appendix 5—table 1

Bayesian Information Criterion (BIC) and level of model complexity (N), including pair-wise Δ BIC with the best fitted model.

Models	BIC-ΔBIC	B	BG	BT	BTG	N
Neutrophils+IgA+IgG	BIC	-652.9	-351.2	594.8	-610.5	12
Neutrophils+IgA	BIC	-251.3	-302.2	-570.9	-507.7	9
Neutrophils+IgA	ΔBIC	401.5	48.9	23.9	102.8
Neutrophils+IgG	BIC	-314.8	-105.6	-442.0	-423.9	9
Neutrophils+IgG	ΔBIC	338.1	245.6	152.7	186.5

Additional files

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Figures

Observed levels of B. bronchiseptica shedding by contact of infected rabbits with a Bordet-Gengou agar petri dish.

Observed level of B.bronchiseptica shedding by days post infection (Dpi) and type of infection.

Frequency of observed B.bronchiseptica shedding events for the four types of infection.

B. bronchiseptica shedding on BG-blood agar petri dishes.

Estimated immune responses in the blood by time and type of infection.

Estimated rates of infection in the whole respiratory tract and immune response in the blood by time and type of infection.

Estimated dynamics of B. bronchiseptica shedding by time and type of infection.

Parameter estimates from posterior distribution for BG.

Parameter estimates from posterior distribution for BT.

Parameter estimates from posterior distribution for BTG.

Relationship between B.bronchiseptica peak of shedding and percentile changes in neutrophils, IgA, and IgG.

Relationship between B.bronchiseptica time to peak of shedding and percentile changes in neutrophils, IgA, and IgG.

MCMC trace plot for B.

MCMC trace plot for BG.

MCMC trace plot for BT.

MCMC trace plot for BTG.

MCMC posteriors from B.

MCMC posteriors from BG.

MCMC posteriors from BT.

MCMC posteriors from BTG.

Model validation using group-level parameters.

Tables

Description and unit of parameters and variables used in the dynamical and observed models.

Model prior and posterior parameters for the immune response and B. bronchiseptica infection.

Scale reduction factors for each parameter of the four types of infection.

Bayesian Information Criterion (BIC) and level of model complexity (N), including pair-wise Δ BIC with the best fitted model.

Additional files

Transparent reporting form

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Observed levels of B. bronchiseptica shedding by contact of infected rabbits with a Bordet-Gengou agar petri dish.

Observed level of B.bronchiseptica shedding by days post infection (Dpi) and type of infection.

Frequency of observed B.bronchiseptica shedding events for the four types of infection.

B. bronchiseptica shedding on BG-blood agar petri dishes.

Estimated immune responses in the blood by time and type of infection.

Estimated rates of infection in the whole respiratory tract and immune response in the blood by time and type of infection.

Estimated dynamics of B. bronchiseptica shedding by time and type of infection.

Parameter estimates from posterior distribution for BG.

Parameter estimates from posterior distribution for BT.

Parameter estimates from posterior distribution for BTG.

Relationship between B.bronchiseptica peak of shedding and percentile changes in neutrophils, IgA, and IgG.

Relationship between B.bronchiseptica time to peak of shedding and percentile changes in neutrophils, IgA, and IgG.

MCMC trace plot for B.

MCMC trace plot for BG.

MCMC trace plot for BT.

MCMC trace plot for BTG.

MCMC posteriors from B.

MCMC posteriors from BG.

MCMC posteriors from BT.

MCMC posteriors from BTG.

Model validation using group-level parameters.

Description and unit of parameters and variables used in the dynamical and observed models.

Model prior and posterior parameters for the immune response and B. bronchiseptica infection.

Scale reduction factors for each parameter of the four types of infection.

Bayesian Information Criterion (BIC) and level of model complexity (N), including pair-wise Δ BIC with the best fitted model.

Transparent reporting form