After HGP, we are not having many databases which consist of several notepad files of ATCG....
Can we distinguish quantitatively a given A,T,C and G stretch as DNA or Gene?
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I interpret your question as: Given a stretch of DNA sequence, can we determine if it encodes a gene? My summary of the answer would be: "Sometimes".
The problem you ask about is called "Gene prediction" and is described in some detail by Wikipedia: http://en.wikipedia.org/wiki/Gene_prediction
The most basic indication that a gene may exist is the presence of an "Open Reading Frame" (ORF). An ORF is a stretch of DNA from which a single protein may be produced. However, an ORF is not strictly required for a gene (as not all genes encode proteins), and not all ORFs are genes. There are many software tools for gene prediction available which use different rules to predict if a given region of DNA is functional (contains a gene or a regulatory element). They may be usable on any kind of DNA sequence, or on sequences from certain organisms only, depending on the program.
Two commmonly used gene prediction tool are GLIMMER (http://www.ncbi.nlm.nih.gov/genomes/MICROBES/glimmer_3.cgi, used for microbial genomes) and GeneMark (http://opal.biology.gatech.edu/gmhmm2_prok.cgi). See also http://en.wikipedia.org/wiki/Gene_prediction
As a quick check, you may also use NCBI BLAST (http://blast.ncbi.nlm.nih.gov/Blast.cgi) to see if your sequence aligns to a known gene.
This is possible and is an important topic in bioinformatics. Lots of tools have been written and papers have been published, most important
.. and so on. Try GenScan, for instance.
My conviction is that genes are not randomly arranged as a finite string. There must be a beautiful organization.
In bacteria, you will have a whole series of genes required for a pathway all next to each other, so that their expression can all be controlled from one point upstream of them. We call that whole suite of genes and the upstream binding site an operon.
But in eukaryotes, there is no grand organization of genes with regard to their position on the chromosomes, in general. Regardless of what you think they should look like, we don't observe a wonderful organization. Evolution results in things looking pretty haphazard. Go browse ensembl.org if you want to see for yourself.