====== Compare Identification Summaries with Spectral Count ======

===== Definition =====

  * The ''peptide spectral count'' consist in counting the number of spectra which matches the current peptide. Thus, it's equal to the number of peptide spectrum matches (PSM).
  * ''Protein basic spectral count'' (BSC) is equal to the sum of the ''peptide spectral count'' for all peptides which identify the protein.
  * ''Protein specific spectral count'' (SSC) is equal to the sum of the ''peptide spectral count'' for specific peptide only. A specific peptide, is a peptide which does not identify any other protein (or more precisely protein in other protein sets) in the context of the identification summaries.
  *  ''Protein weighted spectral count'' (WSC) is the ''Protein specific spectral count'' + sharing-weighted spectral count of shared peptide. 

|{{ :prolineconcepts:scdef.png?500 |}}|
^ Example calculation of spectral count ^

===== Specificity and weight reference =====

The peptide specificity and the spectral count weight could be defined in the context of the ''Identification Summary'' where the spectral count is calculated as shown in previous schema. 
It could also could be done using another ''Identification Summary'' as reference, like using the common parent ''Identification Summary''. This allow to consider only identified and validated protein in the merge context.
 
If we consider the following case, where //Sample1// ''Identification Summary'' is the merge of //Replicat1// and //Replicat2//.

{{:prolineconcepts:scmerge.png?500|}}


If the spectral count calculation is done at each child level, aligning protein sets identified in parent to protein sets in child, we get the following result:

|^ Sample1 ProteinSets ^Replicat1 |||^Replicat2 ||||
| | Ref Prot. | BSC | SSC | WSC | Ref Prot. | BSC | SSC | WSC|
|P2 | P2 | 5 | 2| 4| P3 | 7| 7| 7|
|P3 | P3 | 4 | 1| 2| P3 | 7| 7| 7|


We can see that when different parent protein sets are seen as one protein set in a child, the spectral count is biased. **This calculation was not retain!**

Now, if we align on child protein rather than protein sets, we get the following result :

|^ Sample1 ProteinSets ^Replicat1 |||^Replicat2 ||||
| | Ref Prot. | BSC | SSC | WSC | Ref Prot. | BSC | SSC | WSC |
|P2 | P2 | 5 | 2| 4| P2 | 2| 0| 0|
|P3 | P3 | 4 | 1| 2| P3 | 7| 7| 7 |

Again, when considering specificity at child level, the result of spectral count in Replicat2 is not representative, as it has a null SSC and WSC. **This calculation was not retain!**

A way to make some correction is to define the specificity of the peptide and their weight at the parent level, and apply it at the child level. Therefore, specific peptides for P2 is pe8 and for P3 it is pe6 and pe7.
For peptide weight, if we consider pe4 for example, it will be define as follow:
  * Weight pe4 for P2 = 2/8  => P2 has 1 specific peptide with 2 PSM for a total of 8 PSM (if we consider P2 and P3 (6 specific PSM) which are proteins identified by pe4)
  * Weight pe4 for P3 = 6/8  => P3 has 6 specific PSMs for a total of 8 ...

The spectral count result will thus be: 

|^ Sample1 ProteinSets ^Replicat1 |||^Replicat2 ||||
| | Ref Prot. | BSC | SSC | WSC | Ref Prot. | BSC | SSC | WSC |
|P2 | P2 | 5 | 2| 2.75| P2 | 2| 0| 0.5|
|P3 | P3 | 4 | 1| 3.25| P3 | 7| 5| 6.5 |

__NOTE__:

In case of multiple level hierarchy (Sample -> Condition1 vs Condition2 -> 3 replicates by conditions), it could make sense to calculate the spectral count weight at "Condition1" and "Condition2" levels rather than "Sample" level to keep the difference involved by the experiment condition.


===== In Proline =====

Actually, spectral count is calculated for a set of hierarchy related ''Identification Summaries''. In other words, this means that ''Identification Summaries'' should have a common parent. The list of protein to compare or to consider is created at the parent level as the peptide specificity. User can select the dataset where the shared peptides spectral count weight will be calculated. (See previous chapter)

Firstly, the ''peptide spectral count'' is calculated using following rules
  * Equal to Peptide Spectrum Matches Count if Identification Summaries is a leaf (not issued from a merge)
  * Sum of child ''peptide spectral count''  in case of identification Summaries merge
  * Sum of validated child ''peptide spectral count'' in case of Search Result merge. Validated child PSMs are PSMs which satisfy validation applied to parent ''Identification Summaries''.

Once, ''peptide spectral count'' is known for each peptide, protein spectral count is calculated using following rules 
  * Protein BSC  = sum of ''peptide spectral count'' 
  * Protein SSC = sum of ''peptide spectral count'' for specific peptide only 
  * Protein WSC = SSC + weighted ''peptide spectral count'' for shared peptides. The weight of a peptide for a given protein (P1) =  peptide SC  x (number of specific PSM of P1 /number of specific PSMs of all protein identified by the peptide). See explanation in previous chapter