▁of ▁each ▁of ▁the ▁ 1 9 ▁mut ations ▁are ▁known , ▁and ▁the ▁sum ▁of ▁the ▁prob abilities ▁of ▁these ▁twenty ▁out comes ▁must ▁be ▁ 1 , ▁this ▁last ▁probability ▁can ▁be ▁calculated ▁by ▁ ▁which ▁simpl ifies ▁to ▁ ▁{ | ▁class =" to cc ol ours ▁col laps ible ▁col lapsed " ▁width =" 6 0 %" ▁style =" text - align : left " ▁! Calcul ation ▁of ▁the ▁diagonal ▁entries ▁| - ▁| ▁ ▁Sub st itut ing ▁in ▁the ▁expression ▁for ▁the ▁non - di ag onal ▁entries ▁mut ation ▁matrix : ▁ ▁Since ▁the ▁values ▁of ▁ ▁and ▁ ▁are ▁constants ▁that ▁don ' t ▁change ▁with ▁the ▁value ▁of ▁▁ ▁And ▁thus ▁can cellation ▁reve als ▁that ▁ ▁| } ▁ ▁A ▁result ▁of ▁particular ▁significance ▁is ▁that ▁for ▁the ▁non - di ag onal ▁entries ▁ ▁Which ▁means ▁that ▁for ▁all ▁entries ▁in ▁the ▁mut ation ▁matrix ▁ ▁Cho ice ▁of ▁the ▁constant ▁of ▁proportional ity ▁The ▁prob abilities ▁contained ▁in ▁ ▁vary ▁as ▁some ▁unknown ▁function ▁of ▁the ▁amount ▁of ▁time ▁that ▁a ▁protein ▁sequence ▁is ▁allowed ▁to ▁mut ate ▁for . ▁Instead ▁of ▁attempting ▁to ▁determine ▁this ▁relationship , ▁the ▁values ▁of ▁ ▁are ▁calculated ▁for ▁a ▁short ▁time ▁frame , ▁and ▁the ▁matrices ▁for ▁longer ▁periods ▁of ▁time ▁are ▁calculated ▁by ▁assuming ▁mut ations ▁follow ▁a ▁Mark ov ▁chain ▁model . ▁The ▁base ▁unit ▁of ▁time ▁for ▁the ▁P AM ▁matrices ▁is ▁the ▁time ▁required ▁for ▁ 1 ▁mut ation