0 ▁am ino ▁ac ids , ▁then ▁ ▁And ▁if ▁there ▁are ▁ ▁mut ated ▁am ino ▁ac ids ▁per ▁ 1 0 0 ▁am ino ▁ac ids , ▁then ▁it ▁is ▁approximately ▁equal ▁to ▁ ▁Now ▁ ▁and ▁ ▁can ▁be ▁related ▁by ▁ ▁For ▁large ▁values ▁of ▁, ▁an ▁assumption ▁that ▁can ▁be ▁reason ably ▁made ▁for ▁typical ▁prote ins , ▁this ▁expression ▁is ▁approximately ▁equal ▁to ▁ ▁| } ▁ ▁The ▁valid ity ▁of ▁these ▁estimates ▁can ▁be ▁verified ▁by ▁counting ▁the ▁number ▁of ▁am ino ▁ac ids ▁that ▁remain ▁un changed ▁under ▁the ▁action ▁of ▁the ▁matrix ▁. ▁The ▁total ▁number ▁of ▁un changed ▁am ino ▁ac ids ▁for ▁the ▁time ▁interval ▁of ▁the ▁P AM n ▁matrix ▁is ▁ ▁and ▁so ▁the ▁proportion ▁of ▁un changed ▁am ino ▁ac ids ▁is ▁ ▁An ▁example ▁- ▁P AM 2 5 0 ▁ ▁A ▁P AM 2 5 0 ▁is ▁a ▁commonly ▁used ▁scoring ▁matrix ▁for ▁sequence ▁comparison . ▁Only ▁the ▁lower ▁half ▁of ▁the ▁matrix ▁needs ▁to ▁be ▁computed , ▁since ▁by ▁their ▁construction , ▁P AM ▁matrices ▁are ▁required ▁to ▁be ▁symmetric . ▁Each ▁of ▁the ▁ 2 0 ▁am ino ▁acid ▁are ▁shown ▁down ▁the ▁top ▁and ▁side ▁of ▁the ▁matrix , ▁with ▁ 3 ▁additional ▁ambigu ous ▁am ino ▁ac ids . ▁The ▁am ino ▁ac ids ▁are ▁most ▁commonly ▁shown ▁listed ▁alphabet ically , ▁or ▁listed ▁in ▁groups . ▁These ▁groups ▁are ▁the ▁characteristics ▁shared ▁among ▁the ▁am ino ▁ac ids . ▁ ▁Us es