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@@ -72,7 +72,7 @@ The relative time/space efficiencies of BiGpairSEQ when backed by different MWM
2. Pre-filter the sequence data to reduce error and minimize the size of the necessary graph. 2. Pre-filter the sequence data to reduce error and minimize the size of the necessary graph.
1. *Saturating sequence filter*: remove any sequences present in all wells on the sample plate, as there is no signal in the occupancy data of saturating sequences (and each saturating sequence will have an edge to every vertex on the opposite side of the graph, vastly increasing the total graph size). 1. *Saturating sequence filter*: remove any sequences present in all wells on the sample plate, as there is no signal in the occupancy data of saturating sequences (and each saturating sequence will have an edge to every vertex on the opposite side of the graph, vastly increasing the total graph size).
2. *Non-existent sequence filter*: sequencing misreads can pollute the data from the sample plate with non-existent sequences. These can be identified by the discrepancy between their occupancy and their total read count. Assuming sequences are read correctly at least half the time, then a sequence's total read count (R) should be at least half the well occupancy of that sequence (O) times the read depth of the sequencing run (D). Remove any sequences for which R < (O * D) / 2. 2. *Non-existent sequence filter*: sequencing misreads can pollute the data from the sample plate with non-existent sequences. These can be identified by the discrepancy between their occupancy and their total read count. Assuming sequences are read correctly at least half the time, then a sequence's total read count (R) should be at least half the well occupancy of that sequence (O) times the read depth of the sequencing run (D). Remove any sequences for which R < (O * D) / 2.
3. *Misidentified sequence filter*: sequencing misreads can cause one real sequence to be misidentified as a different real sequence. This should be fairly infrequent, but is a problem if it skews a sequence's overall occupancy pattering by causing the sequence to seem to be in a well where it is not, in fact, present. This can be detected by looking at discrepancies in a sequence's per-well read count. On average, the read count for a sequence in an individual well (r) should be equal to its total read count (R) divided by its total well occupancy (O). Remove from the list of wells occupied by a sequence any wells for which r < R / (2 * O). 3. *Misidentified sequence filter*: sequencing misreads can cause one real sequence to be misidentified as a different real sequence. This should be fairly infrequent, but is a problem if it skews a sequence's overall occupancy pattern by causing the sequence to seem to be in a well where it is not, in fact, present. This can be detected by looking at discrepancies in a sequence's per-well read count. On average, the read count for a sequence in an individual well (r) should be equal to its total read count (R) divided by its total well occupancy (O). Remove from the list of wells occupied by a sequence any wells for which r < R / (2 * O).
3. Encode the occupancy data from the sample plate as a weighted bipartite graph, where one set of vertices represent the distinct TCRAs and the other set represents distinct TCRBs. Between any TCRA and TCRB that share a well, draw an edge. Assign that edge a weight equal to the total number of wells shared by both sequences. 3. Encode the occupancy data from the sample plate as a weighted bipartite graph, where one set of vertices represent the distinct TCRAs and the other set represents distinct TCRBs. Between any TCRA and TCRB that share a well, draw an edge. Assign that edge a weight equal to the total number of wells shared by both sequences.
4. Find a maximum weight matching of the bipartite graph, using any [MWM algorithm](https://en.wikipedia.org/wiki/Assignment_problem#Algorithms) that produces a provably optimal result. 4. Find a maximum weight matching of the bipartite graph, using any [MWM algorithm](https://en.wikipedia.org/wiki/Assignment_problem#Algorithms) that produces a provably optimal result.
* If desired, restrict the matching to a subset of the graph. (Example: restricting matching attempts to cases where the occupancy overlap is 4 or more wells--that is, edges with weight >= 4.0.) See below for discussion of why this might be desirable. * If desired, restrict the matching to a subset of the graph. (Example: restricting matching attempts to cases where the occupancy overlap is 4 or more wells--that is, edges with weight >= 4.0.) See below for discussion of why this might be desirable.