consider PDB ID 1a13 which has only 1 chain A

Its sequence is INWKGIAAMAKKLL

1st step: Calculate the original secondary structure states using DSSP. DSSP is a software which takes PDB file of original secondary structure and assigns actual secondary structure of all the residues in the sequence.

So using DSSP we got original secondary structure as "CCCCCHHHHHCCCC"

i.e. first 5 residues fall in coil, next 5 residues fall in helix while after that all residues fall in coil.

2nd step: predict the secondary structure of the protein with sequence INWKGIAAMAKKLL with your own method (or with existing methods like PSIPRED).

Suppose we got predicted structure of the above sequence as "CCCCCHHHHHEEEE"

3rd step: Now calculate Q3 which is defined as number of correctly predicted secondary structure states divided by total number of residues in a protein.

Therefore in the above example Q3 = (10/14)x100 (first 10 residues are correctly predicted).

Similarly Q3H (Q3 for helix) can be calculated as number of correctly predicted helix secondary structure states divided by total number of helix residues in a protein

In the above example Q3H = (5/5)x100 = 100% while Q3C = (5/9)x100

Hope this helps.

Dear Prithvi Singh,

I totally agree with you that it is very difficult to predict secondary structure of proteins due to the large size of the Protein Data Bank (>35,000 sequences). However, the accuracy of protein secondary structure prediction has steadily improved over the past 30 years.

Herein some publications that describe the prediction methods for secondary structure of proteins:

1-Improving the accuracy of protein secondary structure prediction using structural alignment

Scott Montgomerie, Shan Sundararaj, Warren J Gallin and David S Wishart 

BMC Bioinformatics20067:301

DOI: 10.1186/1471-2105-7-301

Abstract

Background

The accuracy of protein secondary structure prediction has steadily improved over the past 30 years. Now many secondary structure prediction methods routinely achieve an accuracy (Q3) of about 75%. We believe this accuracy could be further improved by including structure (as opposed to sequence) database comparisons as part of the prediction process. Indeed, given the large size of the Protein Data Bank (>35,000 sequences), the probability of a newly identified sequence having a structural homologue is actually quite high.

Results

We have developed a method that performs structure-based sequence alignments as part of the secondary structure prediction process. By mapping the structure of a known homologue (sequence ID >25%) onto the query protein's sequence, it is possible to predict at least a portion of that query protein's secondary structure. By integrating this structural alignment approach with conventional (sequence-based) secondary structure methods and then combining it with a "jury-of-experts" system to generate a consensus result, it is possible to attain very high prediction accuracy. Using a sequence-unique test set of 1644 proteins from EVA, this new method achieves an average Q3 score of 81.3%. Extensive testing indicates this is approximately 4–5% better than any other method currently available. Assessments using non sequence-unique test sets (typical of those used in proteome annotation or structural genomics) indicate that this new method can achieve a Q3 score approaching 88%.

Conclusion

By using both sequence and structure databases and by exploiting the latest techniques in machine learning it is possible to routinely predict protein secondary structure with an accuracy well above 80%. A program and web server, called PROTEUS, that performs these secondary structure predictions is accessible at http://wishart.biology.ualberta.ca/proteus. For high throughput or batch sequence analyses, the PROTEUS programs, databases (and server) can be downloaded and run locally.

http://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-7-301

2-Protein Sci. 2003 Feb; 12(2): 288–295.

doi:  10.1110/ps.0222303

PMCID: PMC2312422

Accurate and automated classification of protein secondary structure with PsiCSI

Ling-Hong Hung and Ram Samudrala

Author information ► Article notes ► Copyright and License information ►

This article has been cited by other articles in PMC.

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Abstract

PsiCSI is a highly accurate and automated method of assigning secondary structure from NMR data, which is a useful intermediate step in the determination of tertiary structures. The method combines information from chemical shifts and protein sequence using three layers of neural networks. Training and testing was performed on a suite of 92 proteins (9437 residues) with known secondary and tertiary structure. Using a stringent cross-validation procedure in which the target and homologous proteins were removed from the databases used for training the neural networks, an average 89% Q3 accuracy (per residue) was observed. This is an increase of 6.2% and 5.5% (representing 36% and 33% fewer errors) over methods that use chemical shifts (CSI) or sequence information (Psipred) alone. In addition, PsiCSI improves upon the translation of chemical shift information to secondary structure (Q3 = 87.4%) and is able to use sequence information as an effective substitute for sparse NMR data (Q3 = 86.9% without 13C shifts and Q3 = 86.8% with only Hα shifts available). Finally, errors made by PsiCSI almost exclusively involve the interchange of helix or strand with coil and not helix with strand (

The prediction is run on proteins of known  structure from the PDB. The exact secondary structure classification from the PDB can be gotten from STRIDE or DSSP.

It is not possible to get a true (not estimated) Q3 value on a protein of unknown structure

   The answer lies in your question itself. You said that the text's numerator is a predicted value. That in itself means that your query is being run through a series of protein structures whose conformation is already annotated in PDB.

  You can't prove anything with bioinformatics alone. Yes, it reduces costs and analyzable data sets thus saving time. But at the end of the day, it all lies in the mathematical algorithms that govern it; which if I may daresay are questionable.

   In anycase, to conclude the answer to your question, the query is sieved through algorithms that perform the analysis on proteins of known structure already in the database. Hopefully with the advancement in neural networks, the 'prediction' will get better, but at the moment, it is fairly hard to get the actual score.

consider PDB ID 1a13 which has only 1 chain A

Its sequence is INWKGIAAMAKKLL

1st step: Calculate the original secondary structure states using DSSP. DSSP is a software which takes PDB file of original secondary structure and assigns actual secondary structure of all the residues in the sequence.

So using DSSP we got original secondary structure as "CCCCCHHHHHCCCC"

i.e. first 5 residues fall in coil, next 5 residues fall in helix while after that all residues fall in coil.

2nd step: predict the secondary structure of the protein with sequence INWKGIAAMAKKLL with your own method (or with existing methods like PSIPRED).

Suppose we got predicted structure of the above sequence as "CCCCCHHHHHEEEE"

3rd step: Now calculate Q3 which is defined as number of correctly predicted secondary structure states divided by total number of residues in a protein.

Therefore in the above example Q3 = (10/14)x100 (first 10 residues are correctly predicted).

Similarly Q3H (Q3 for helix) can be calculated as number of correctly predicted helix secondary structure states divided by total number of helix residues in a protein

In the above example Q3H = (5/5)x100 = 100% while Q3C = (5/9)x100

Hope this helps.