BLAST

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Sum Statistics and Sum Scores

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67

Note that the expected HSP (high scoring pair) length is dependent on the search

space (m*n) and the relative entropy of the scoring scheme, H, so it varies from

search to search.

To take edge effects into account when calculating an Expect, the expected HSP

length is subtracted from the actual length of the query, m, and the actual number of

residues in the database, n, to give their effective lengths, usually denoted by m´ and

n´, respectively (see Equations 4-12 and 4-13).

In a large search space, the expected HSP length may be greater than the length of

the query, resulting in a negative effective length, m´. In practice, if the effective

length is less than 1/k, it is set to 1/k, as doing so cancels the contribution of the

short sequence to the Expect; setting for example, gives , a for-

mulation independent of m’.

Unfortunately, effective lengths of less than aren’t uncommon today. Because

, the large size on many sequence databases can result in large expected HSP

lengths. In fact it’s not uncommon to see expected HSP lengths approaching 200

when searching some of the larger protein databases. Keep in mind that the average

protein is ~300 amino acids long; thus, for many searches, m´ is being set to 1/k rou-

tinely. Recent work by S.F. Altschul