To build an intuition about how genes code for an organism, one may visualize that DNA is an operating system within each cell, which can only divide, differentiate, regulate or die. Individual genes can be thought of as rules for a cellular automaton on an emergent 3D lattice.
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Yes, afaik the sequence of amino acids remains mostly unaffected. But it is not the point: the gene is a largely immutable subroutine, its activation state is a local parameterization.
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