East Pakistan or Bangladesh was created after separation from their original motherland India on the basis of extreme religious intolerance and bigotry that was strong enough to tear apart a nation, cause death to millions, and making many more millions homeless refugees. Later the eastern part of Pakistan understood that the religion islam that prompted the creation of this new nation after so much bloodbath and misery, wasn't constructive enough to bind the two parts of Pakistan together to build a strong and united nation, and the 'control of power' was a stronger desire than the bond of Islam. Hence, a new idea of intolerance in the name of ethnicity and language was fanned that caused another fresh series of bloodbath and misery, and Bangladesh was created.
And no, there is nothing like 'Bangladeshi gene', it is a false country created based on religion where Hindu Bengalis have no place.