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I am studying mathematical models of transcription and translation and I am wondering:

In a particular genome, how many copies of a gene coding for one particular protein should one expect? Are they all transcribed at the same rate?

I know humans have two copies of each chromosome, so the answer would be at least 2 in humans. But I wonder if one particular gene coding for a protein we need in abundance might be present in many copies in the genome to increase expression.

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Remi.b talked at great length in his answer about copy-number variation and the generation of new genes. However, I don't think he quite answered what I think is a pretty basic question:

How many copies of any particular gene are there in (a human) genome?

The answer to that question is also simple: two - one on the chromosome from the mother, and one from the father. The exception is genes on the X and Y chromosomes, but that's complicated so I'll ignore it :)

Now, that's not to say that there might be several versions of any particular gene, having arisen through such mutational events as Remi.b explained. So, in antiquity, gene ABC123 might have been duplicated, leading to today's genes ABC123a and ABC123b, which may or may not have different functions. But, for ABC123a, there are only two copies per (normal) cell, and the same is true for ABC123b and all the rest.

Are they all transcribed at the same rate?

But I wonder if one particular gene coding for a protein we need in abundance might be present in many copies in the genome to increase expression.

The regulation of gene expression is quite complex. However, the cell (I'm referring to eukaryotes here, I don't know how different prokaryotes and Archaea are) has mechanisms to ensure that the products of so-called housekeeping genes, which are needed in great abundance, are available to the cell. One method is to attract and keep the RNA polymerases (which transcribe the gene into messenger RNA (mRNA), which is the template for translation into a protein - the actual gene product) bound to the gene sequence through a variety of DNA "promoter" and "enhancer" sequences, which other proteins called transcription factors bind to and recruit the polymerase to the gene. These polymerases are kept active for as long as the cell needs the gene's protein product, churning out copy after copy of mRNA. There are many other mechanisms as well, ranging from how the core histone proteins that give chromosomes their shape bind near the gene, to the manner in which the translation machinery (ribosomes) bind to the mRNA and produce multiple protein molecules per mRNA copy. So, even though we may only have two copies of a particularly vital gene, the cell has evolved ways of meeting demand for its product.

Are they all transcribed at the same rate?

No, they are not. This all depends on the number, kind, and placement of transcription factor binding sequences in the DNA surrounding and within a gene, as well as the exact identity of the transcription factor(s) recruited. Some keep the polymerase machinery very tightly bound, ensuring quick and accurate transcription, while others don't bind tightly at all, allowing the polymerase to "fall off" the DNA and/or work more slowly. Each gene is uniquely and exquisitely regulated to be transcribed where, when, and in the quantity needed.

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Cell cycle

Talking about physical copies of gene, we would indeed have at least 1 copy during the haploid phase, 2 copies during the diploid phase and 4 copies during the mitosis (and during the first phase of the meiosis). Of course, species having mitosis during the haploid phase would have 2 copies of the gene during the mitosis. I am not talking about polyploid species and am not talking about some fungi and other things that have all kind of crazy reproductions system. I am not talking about mtDNA either. Finally, I am not addressing the case of specialized cells that lose part of their genome or the case of tissues that are basically cells who merged together, so that the concept of cell does not even hold any more such as the Syncytiotrophoblast (in the placenta) (see also cell fusion and syncytium).

In short, the variation in the number of copies during the life-cycle is very dependent on the species of interest, the sequence of interest and may also fall under some semantic issue about what is a cell. Note another potential semantic issue result from the question "how similar two genes have to be to still be called copies?".

Mutations and polymorphism

Now, some genes can be found in several copies. When, in a given population the number of copies of a given gene varies from one individual to another, we talk about Copy-Number Variation (CNV). The increase in the number of copies is called gene duplication (or gene amplification or chromosomal duplication when a very big chunk of DNA gets duplicated). The decrease in the number of copies is called gene deletion. There are a diversity of processes that can cause deletions and duplications such as homologous recombination, retrotransposition event, aneuploidy, polyploidy, and replication slippage.

Evolution of CNV

What mutation is likely to occur first

Gene duplication does not necessarily yield to an increase in the protein concentration (but it can as it is the case for the Pelizaeus–Merzbacher disease for example). If higher expression is selected for, it "feels more likely to me" that the first mutation(s) allowing for this increased expression will affect the regulatory sequences and will not increase the number of gene copies.

Consequences of gene duplications

Gene duplication (if not loss) can yield to subfunctionalization or neofunctionalization. From wikipedia:

Subfunctionalization [is a process] in which pairs of genes that originate from duplication, or paralogs, take on separate functions

...In others words, copies are free to accumulate mutations as long as the other copy is still doing its job

Neofunctionalization, one of the possible outcomes of functional divergence, occurs when one gene copy, or paralog, takes on a totally new function after a gene duplication event

...Basically, one copy gets a totally new function... that can yield to very interesting innovations such as anti-freeze proteins (ref) or snake venom (ref).

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