PrP prions: Dose Response Models

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Prion

Author: Yin Huang
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General overview of prion and prion diseases

Scrapie is a prion agent. Prions are 'self-replicating' basic proteins of small molecular weight. Prions form a new class of infectious agents responsible for a number of slow degenerative central nervous system diseases of humans and other animal species. The transmissible spongiform encephalopathies (TSEs) are a group of progressive neurological prion diseases, including scrapie in sheep and goats, bovine spongiform encephalopathy (BSE) in cattle and Creutzfeldt-Jakob disease (CJD) in humans (Gale 2006).

Public awareness of prion diseases have been raised after an outbreak of BSE occurred among cattle in many European countries and scientific evidence indicated the foodborne transmission of BSE to humans (Will et al. 1996; Smith and Bradley 2003).

The disease is most easily transmitted to humans via consuming food contaminated with the brain or spinal cord of infected carcasses.



Summary Data

Diringer et al. (1998) inoculated outbred Syrian hamsters orally with graded doses of scrapie agent. The infectious agent was prepared from the brains of scrapied hamsters at the terminal stage of disease.

Jacquemot et al. (2005) exposed C57BL/6 mice to mouse-adapted scrapie strain C506M3 via the intraperitoneal route. The inoculum was a brain homogenate at 10% (wt/vol) in 5% glucose solution from a mouse with scrapie at the terminal stage of disease

Taylor et al. (1995) injected Weanling RIII/FaDk-ro mice with pooled BSE-infected brain. They measured the titer of infectivity by bioassay in mice. The infectious agent was prepared from the brains of 861cattle with suspected BSE obtained between August and November 1990 from five veterinary centers throughout England.


Table 1.1. Summary of the prion data and best fits

Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best-fit model Best-fit parameters LD50/ID50
1* Diringer et al. 1998 hamsters/scrapie strain 263K oral /5 LD50 i.c. Death beta-Poisson α = 1.76 N50 = 1.04E+05 1.04E+05
2 Jacquemot et al. 2005 mice/scrapie strain C506M3 intraperitoneal /3 LD50 i.c. Death exponential k = 2.40E-05 2.89E+04
3 Taylor et al. 1995 mice/BSE agent Unknown type of injection/4 ID50 unit Infection exponential k = 0.69 1.00

The data were not able to be statistically pooled.

*Recommended Model

It is recommended that experiment 1 should be used as the best dose response model. The exposure was oral route which is a better representation of an actual release scenario.

a:
Exponential and betapoisson model.jpg

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 1.2: hamsters/scrapie strain 263K model data
Dose Dead Survival Total
200 0 40 40
2000 1 79 80
20000 9 71 80
200000 58 22 80
2000000 29 1 30
Diringer et al. 1998


Table 1.3: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 14.54 12.62 4 3.84
4.00E-04
9.49
0.0058
Beta Poisson 1.92 3 7.81
0.589
Beta Poisson is best fitting model
Table 1.4 Optimized parameters for the best fitting (beta Poisson), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
α 1.76 -- -- -- -- -- --
N50 1.04E+05 -- -- -- -- -- --
LD50 1.04E+05 7.06E+04 7.83E+04 8.21E+04 1.33E+05 1.41E+05 1.54E+05


Figure 1.1 Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
Figure 1.2 beta Poisson model plot, with confidence bounds around optimized model


Optimization Output for experiment 2

Table 1.5: mice/ scrapie strain C506M3 model data
Dose Dead Survival Total
125 0 11 11
1250 1 9 10
12500 2 8 10
Jacquemot et al. 2005


Table 1.6: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.34 0.99 2 3.84
0.320
5.99
0.512
Beta Poisson 0.35 1 3.84
0.554
Exponential is best fitting model
Table 1.7 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 2.40E-05 1.00E-13 1.00E-13 7.23E-06 5.47E-05 5.81E-05 7.44E-05
LD50 (spores) 2.89E+04 9.32E+03 1.19E+04 1.27E+04 9.58E+04 6.92E+12 6.92E+12


Figure 1.3 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1.4 Exponential model plot, with confidence bounds around optimized model


Optimization Output for experiment 3

Table 1.8: mice/BSE agent model data
Dose Infected Non-infected Total
0.0186 0 13 13
0.186 4 12 16
1.856 9 5 14
18.56 13 0 13
Taylor et al. 1995


Table 1.9: Goodness of fit and model selection
Model Deviance Δ Degrees
of Freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 2.77 0.76 3 3.84
0.384
7.81
0.429
Beta Poisson 2.01 2 5.99
0.366
Exponential is best fitting model
Table 1.10 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations
Parameter MLE Estimate Percentiles
0.50% 2.5% 5% 95% 97.5% 99.5%
k 0.69 0.30 0.36 0.40 1.16 1.32 1.64
ID50 1.00 0.42 0.53 0.60 1.73 1.95 2.28


Figure 1.5 Parameter histogram for exponential model (uncertainty of the parameter)
Figure 1.6 Exponential model plot, with confidence bounds around optimized model

Summary

One should note that the dose unit in the literature was not given as organism number or cfu/pfu, so the relative units were presented.



References

Diringer, H., roehmel, J. and Beekes, M. (1998) Effect of repeated oral infection of hamsters with scrapie. Journal of General Virology 79, 609-612.

Gale, P. (2006) The infectivity of transmissible spongiform encephalopathy agent at low doses: The importance of phospholipid. Journal of Applied Microbiology 101, 261-274.

Jacquemot, C., Cuche, C., Dormont, D. and Lazarini, F. (2005) High incidence of scrapie induced by repeated injections of subinfectious prion doses. Journal of Virology, 8904–8908.

Smith, P. and Bradley, R. (2003) Bovine spongiform encephalopathy (bse) and its epidemiology. British Medical Bulletin 66, 185–198.

Taylor, D.M., Woodgate, S.L. and Atkinson, M.J. (1995) Inactivation of the bovine spongiform encephalopathy agent by rendering procedures. Veterinary Record 137, 605-610.

Will, R., Ironside, J., Zeidler, M., Cousens, S., Estibeiro, K., Alperovitch, A., Poser, S., Pocchiari, M., Hofman, A. and Smith, P. (1996) A new variant of creutzfeldt-jakob disease in the uk. Lancet 347, 921-925.