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Little odd question here. I was told that DNA was read in groups of three.
Assuming this, my question is: Which way would better describe how the DNA is read.
(123)456789 to 123(456)789 to 123456(789) or (123)456789 to 1(234)56789 to 12(345)6789
Assuming that the string of numbers 123456789 represents a DNA sequence.
DNA codes for proteins via codons. A codon is a combination of three nucleotides. As there are 4 different nucleotides available in DNA, there are 64 permutations possible. These 64 codons code for the 20 amino acids and 3 stop codons. Hence, many amino acids are coded by several different codons - the genetic code is said to be redundant.
Typically DNA sequences have a single reading frame (but see @user3790338's answer for an interesting exception to this rule). The reading frame is, basically, defined by the first amino acid of the protein that it decodes. Thereafter, each subsequent triplet is one codon, in a non-overlapping way (123 - 456 - 789 - etc.). Note that DNA sequences contain so-called introns that intervene the coding DNA. These regions are eliminated post-transcriptionally. For clarity-sake I have disregarded them in my answer.
However, one has to realize that this coding of DNA is only important phsyiologically during translation, i.e., when mRNA is being translated into a protein. It is the ribosome that actually reads the codons and stop codons to determines which amino acid is to be incorporated in the growing protein and when to stop translation. Hence, although we read DNA sequences in terms of codons, the cellular machinery doesn't read DNA, it reads mRNA.
Assuming the first coding position is 1, the DNA will be read as: (123)456789 to 123(456)789 to 123456(789). There are fairly few exceptions to this, e.g. some viruses (e.g. http://www.ncbi.nlm.nih.gov/pubmed/1966841), where reading frames overlap like in your second example. This is because the viral genome is much smaller and needs to code all of its proteins into as little nucleic acid as possible. Note that there is more than one way for frames to overlap.
