Well protein production is regulated by other proteins that are indeed made from instructions encoded in the DNA. But you could imagine that a given cell has pr

Well protein production is regulated by other proteins that are indeed made from instructions encoded in the DNA. But you could imagine that a given cell has produced certain proteins that turn some genes on and others off. This pattern of control can be passed onto both daughter cells. This process is also somewhat stochastic, so not every cell in the population behaves exactly the same, so their daughters wouldn't either.