PrP prions: Dose Response Models

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Prion

(Scrapie, BSE, CJD)
Author: Yin Huang


General overview of prion and prion diseases

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 transmitted to humans via meats contaminated with the brain or spinal cords of infected carcasses.


http://www.cdc.gov/ncidod/dvrd/prions/




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.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
250* [1] hamsters scrapie strain 263k oral 5 LD50 i.c. death beta-Poisson α = 1.76E+00 , N50 = 1.04E+05 1.04E+05
251 [2] mice scrapie strain C506M3 intraperitoneal 3 LD50 i.c. death exponential k = 2.4E-05 2.89E+04
252 [3] mice BSE agent unknown type of injection 4 ID50 unit infection exponential k = 6.93E-01 1E+00
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

*Recommended Model

It is recommended that experiment 250 should be used as the best dose response model. The exposure was oral route which is a better representation of an actual release scenario.

Exponential and betapoisson model.jpg

Optimization Output for experiment 250 (Prion/scrapie)

hamsters/scrapie strain 263K model data [1]
Dose Dead Survived Total
200 0 40 40
2000 1 79 80
2E+04 9 71 80
2E+05 58 22 80
2E+06 29 1 30


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 14.5 12.6 4 3.84
0.000382
9.49
0.00576
Beta Poisson 1.92 3 7.81
0.589
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.


Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.76E+00 7.48E-01 8.76E-01 9.66E-01 1.44E+04 1.73E+04 2.08E+04
N50 1.04E+05 7.05E+04 7.83E+04 8.22E+04 1.34E+05 1.40E+05 1.55E+05


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


Optimization Output for experiment 251 (Prion/scrapie)

mice/ scrapie strain C506M3 model data [2]
Dose Dead Survived Total
125 0 11 11
1250 1 9 10
12500 2 8 10


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
0.32
5.99
0.512
Beta Poisson 0.35 1 3.84
0.554
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.


Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 2.4E-05 1.00E-13 1.00E-13 7.23E-06 5.47E-05 5.81E-05 7.44E-05
ID50/LD50/ETC* 2.89E+04 9.32E+03 1.19E+04 1.27E+04 9.58E+04 6.92E+12 6.92E+12
*Not a parameter of the exponential model; however, it facilitates comparison with other models.


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


Optimization Output for experiment 252 (Prion/BSE)

mice/BSE agent model data [3]
Dose Infected Non-infected Total
0.0186 0 13 13
0.186 4 12 16
1.86 9 5 14
18.6 13 0 13


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 2.78 0.763 3 3.84
0.382
7.81
0.427
Beta Poisson 2.01 2 5.99
0.365
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.


Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 6.93E-01 3.03E-01 3.69E-01 4.16E-01 1.14E+00 1.32E+00 1.70E+00
ID50/LD50/ETC* 1E+00 4.08E-01 5.27E-01 6.08E-01 1.67E+00 1.88E+00 2.29E+00
*Not a parameter of the exponential model; however, it facilitates comparison with other models.


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





References

  1. 1.0 1.1 Diringer, H., roehmel, J. and Beekes, M. (1998) Effect of repeated oral infection of hamsters with scrapie. Journal of General Virology 79, 609-612.
  2. 2.0 2.1 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.
  3. 3.0 3.1 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.

Diringer H, Roehmel J and Beekes M (1998) Effect of repeated oral infection of hamsters with scrapie. Journal of General Virology 79(3), 609-612.

Gale P (2006) The infectivity of transmissible spongiform encephalopathy agent at low doses: the importance of phospholipid. Journal of Applied Microbiology 101(2), 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 79(14), 8904-8908.

Smith PG and Bradley R (2003) Bovine spongiform encephalopathy (BSE) and its epidemiology. British Medical Bulletin 66(1), 185-198.

Taylor D, Woodgate S and Atkinson M (1995) Inactivation of the bovine spongiform encephalopathy agent by rendering procedures. Veterinary Record 137(24), 605-610.

Will RG IJ, Zeidler M, Cousens SN, Estibeiro K, Alperovitch A, Poser S, Pocchiari M, Hofman A, Smith PG. (1996) A new variant of Creutzfeldt-Jakob disease in the UK. Lancet 47(9006), 921-925.