Hi,
As far as I understand it, the TPP uses a mixture model-based approach to 
determine posterior probabilities and it then uses these probabilities to 
estimate the FDR. This can be done with or without the use of a decoy 
database. However, when using some of the more sophisticated options (like 
non-parametric modelling), you will need a decoy database to help the 
modelling algorithms pin down the negative distribution. Also, when the 
data is of not so excellent quality, the decoys can help make a better 
distinction between good and bad identifications.

After the analysis with ProteinProphet, you get something like this in the 
ProteinProphet window:

Prob Sens FPER Corr  Incorr
0.00 1.000 0.930 217 2874
0.10 1.000 0.337 217 110
0.20 1.000 0.337 217 110
0.30 0.915 0.216 198 55
0.40 0.865 0.152 187 34
0.50 0.816 0.102 177 20
0.60 0.777 0.074 168 14
0.70 0.747 0.058 162 10
0.80 0.647 0.019 140 3
0.90 0.608 0.010 132 1
0.95 0.569 0.005 123 1
0.96 0.547 0.004 119 0
0.97 0.529 0.003 115 0
0.98 0.507 0.002 110 0
0.99 0.470 0.001 102 0
1.00 0.152 0.000 33 0

The FPER is your FDR, so if you decide to set it at 1%, you notice that 
this corresponds with a probability cut off of 0.90. Now, in your protein 
list, you accept all proteins with a prob. of 0.09 or higher, which is 
estimated to be 132 correct ones and 1 incorrect protein. Everything below 
is discarded.

I found lots of info in the following papers (esp. the last paper). 
Hope this helps!
Cheers,
Bjorn

[1] Choi, H., Fermin, D., and Nesvizhskii, A. I. Significance analysis of 
spectral count data in label-free shotgun proteomics. Mol. Cell. Proteomics 
7, 12 (2008), 2373–2385.

[2] Choi, H., Ghosh, D., and Nesvizhskii, A. I. Statistical validation of 
peptide identifications in large-scale proteomics using the target-decoy 
database search strategy and flexible mixture modeling. J. Proteome Res. 7, 
1 (2008), 286–292.

[3] Choi, H., and Nesvizhskii, A. I. False discovery rates and related 
statistical concepts in mass spectrometry-based proteomics. J. Proteome 
Res. 7, 1 (2008), 47–50.

[4] Choi, H., and Nesvizhskii, A. I. Semisupervised model-based validation 
of peptide identifications in mass spectrometry-based proteomics. J. 
Proteome Res. 7, 1 (2008), 254–265.

[5] Deutsch, E. W., Mendoza, L., Shteynberg, D., Farrah, T., Lam, H., 
Tasman, N., Sun, Z., Nilsson, E., Pratt, B., Prazen, B., Eng, J. K., 
Martin, D. B., Nesvizhskii, A. I., and Aebersold, R. A guided tour of the 
Trans-Proteomic Pipeline. Proteomics 10, 6 (2010), 1150–1159.

[6] Keller, A., Nesvizhskii, A. I., Kolker, E., and Aebersold, R. Empirical 
statistical model to estimate the accuracy of peptide identifications made 
by MS/MS and database search. Anal. Chem. 74, 20 (2002), 5383–5392.

[7] Nesvizhskii, A. I. A survey of computational methods and error rate 
estimation procedures for peptide and protein identification in shotgun 
proteomics. J. Proteomics 73, 11 (2010), 2092–2123.

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