▁the ▁distribution ▁of ▁the ▁un - g apped ▁local ▁alignment ▁scores , ▁of ▁the ▁query ▁sequence ▁and ▁a ▁lot ▁of ▁sh uff led ▁versions ▁( Global ▁or ▁local ▁sh uff ling ) ▁of ▁a ▁database ▁sequence , ▁to ▁the ▁G umb el ▁extreme ▁value ▁distribution . ▁Note ▁that ▁ ▁and ▁ ▁depend ▁upon ▁the ▁substitution ▁matrix , ▁gap ▁pen alt ies , ▁and ▁sequence ▁composition ▁( the ▁letter ▁frequencies ). ▁ ▁and ▁ ▁are ▁the ▁effective ▁lengths ▁of ▁the ▁query ▁and ▁database ▁sequences , ▁respectively . ▁The ▁original ▁sequence ▁length ▁is ▁short ened ▁to ▁the ▁effective ▁length ▁to ▁compens ate ▁for ▁the ▁edge ▁effect ▁( an ▁alignment ▁start ▁near ▁the ▁end ▁of ▁one ▁of ▁the ▁query ▁or ▁database ▁sequence ▁is ▁likely ▁not ▁to ▁have ▁enough ▁sequence ▁to ▁build ▁an ▁optimal ▁alignment ). ▁They ▁can ▁be ▁calculated ▁as ▁▁▁▁▁ ▁where ▁ ▁is ▁the ▁average ▁expected ▁score ▁per ▁aligned ▁pair ▁of ▁resid ues ▁in ▁an ▁alignment ▁of ▁two ▁random ▁sequences . ▁Alt sch ul ▁and ▁G ish ▁gave ▁the ▁typical ▁values , ▁, ▁, ▁and ▁, ▁for ▁un - g apped ▁local ▁alignment ▁using ▁B L OS UM 6 2 ▁as ▁the ▁substitution ▁matrix . ▁Using ▁the ▁typical ▁values ▁for ▁assess ing ▁the ▁significance ▁is ▁called ▁the ▁lookup ▁table ▁method ; ▁it ▁is ▁not ▁accurate . ▁The ▁expect ▁score ▁E ▁of ▁a ▁database ▁match ▁is ▁the ▁number ▁of ▁times ▁that ▁an ▁un related ▁database ▁sequence ▁would ▁obtain ▁a ▁score ▁S ▁higher ▁than ▁x ▁by ▁chance . ▁The ▁expectation ▁E ▁obtained ▁in ▁a ▁search ▁for ▁a