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.
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
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.