I am a mathematician started learning system biology - so I have a couple of questions.
Alleles are different forms of the one gene. How could we understand that A1 and A2 are alleles of the same gene but not two different genes?
The genes are translated into proteins through RNAs. How this translation is often? And how does it happen? Suppose that for simplicity there are only 3 genes in DNA: G1,G2,G3. What determines times when each of the genes will be translated?
(1) The definition of an allele requires that they are from the same gene. The formal proof that two mutations are alleles of the same gene requires a complementation test.
(2) Since translation is temporally downstream of transcription, the primary determinant of when a gene is translated is when it is transcribed. Understanding what determines transcription is one of thethe holy grails of genomics.
I don't define a gene as a (set of) transcript(s) but rather as a complementation unit (a la Seymour Benzer), i.e. all of the functional sequences associated with a mappable functional locus (=gene) in a genome. This locus-based definition of a gene (the classical genetic perspective) therefore includes all regulatory and transcribed sequences. Also, alleles are not strictly defined by being variants per se, but by being functionally/positionally equivalent loci. In fact most alleles are identical by descent or state.
I think you meant to say "since translation is temporally downstream from transcription" (You first transcribe the DNA to mRNA and then the mRNA is translated to protein).
Your first statement is actually too narrow: alleles are loci that vary in a population, but they do not have to be located in genes. Polymorphic ncRNA variants or enhancer regions that are far from coding DNA would be distinct alleles. The 8q24 cancer suscptibility allele is not in a gene, for example.
I don't define a gene as a (set of) transcript(s) but rather as a complementation unit (a la Seymour Benzer), i.e. all of the functional sequences associated with a mappable functional locus (=gene) in a genome. This locus-based definition of a gene (the classical genetic perspective) therefore includes all regulatory and transcribed sequences.
Nature. 2006 May 25;441(7092):398-401. Genetics: what is a gene? "A locatable region of genomic sequence, corresponding to a unit of inheritance, which is associated with regulatory regions, transcribed regions and/or other functional
sequence regions."
2) it is a complex question. Many, many, many (and still unknown) factors can modulate the gene expression. For example see the WP category Category:Gene_expression.
So you mean that if we have a DNA sequence we just can realize that e.g. A1 and A2 are on the same location in the DNA of different cells, but they are different - hence a) they are the same gene since the location is the same b) they are different alleles of this gene?
a) short answer: yes. More complex answer with 2 'genes' at the same location see this question. Again, it depends of your definition of "what is a gene ?".
But DNA then have to me similar in some sense? I mean if we take DNAa and DNAb from different types of cells - then if on location LOCa of DNAa there is a gene - it doesn't mean that on the very same location of DNAb have to be a gene. On the other hand - if there will be a gene - will it be another gene or an allele of the first gene?
Just to remember: similarity isn't homology. A gene could have very dissimilar homologs at non-homologous location in different organisms or even in the same species. The only safe way to tell who is who about genes is by reconstructing its history. This is the correct way to separate alleles, parologs and homoplastic sequences.
Very basically in every cell you have two copies of every chromosome (the story gets more complicated for the sex chromosomes, but I will ignore that here). The copies are different, meaning they contain different versions of the same gene at the same location of the different chromosomes. Originally one of the copies comes from the paternal and the other one from the maternal DNA. The two alleles for a given gene thus reside on the two different copies of the same chromosome. I hope that clears up some of the confusion.
You are right though that if you also have multiple copies of the same gene (which according to the definition would be different genes, but for practical reasons you would indeed consider them as copies of the same gene) it is hard to decide what sequence comes from the other allele and what sequence comes from the copy.
A classic to read: http://www.ncbi.nlm.nih.gov/books/NBK21054/