Re: How does mRNA know when to stop making copies of DNA?

To understand what stops mRNA production, we first have to look at what starts
it.  In a eukaryotic cell, most of the genes are turned off.  To be turned on,
an activator molecule must be present.  An activator is a molecular signal in the
cell telling the cell it needs to make a protein.  It could be a metabolic
product, a protein, an RNA , or some molecule from the environment.  There are
an enormous number of processes going on in a cell and all need to be monitored.
The activator starts the process of specific proteins (called DNA-binding
proteins) binding to the promoter region of the gene, opening this area for the
RNA polymerase to begin transcribing a particular gene or set of genes to meet
the needs of the cell.  These gene products may be activators for other genes
which results in a cascade of gene activities.  

Eventually the conditions which caused the need for the gene activity are no
longer present (the food has been metabolized, the waste has been disposed of,
the cell has moved to another stage of its life, etc) and the activator is no
longer present.  The protein complex which is unfolding the DNA becomes unstable
and the RNA polymerase no longer has a place to bind for that gene.  Until this
happens the RNA polymerases have been transcribing the gene over and over.  Now
the RNA polymerases go off in search of another gene to transcribe.  Thousands
of copies of a messenger RNA can be made in the time it takes you to read this
in a process which is still under much study.  For genetic engineering to be
successful, transcription must be at the right time, in the right place, in the
right amount.