Not sure whether this question is well defined: is there a way to obtain a measure / estimate of the mutation rate for a specific gene? Does it make sense to ask this question (ie for a specific gene)? or is it more sensible to ask this question of a genomic region (say, the one that contains the gene of interest)?
Do you mean the rate of change for a given sequence in the germline of a population over many generations (or even between species), or the frequency of somatic alterations in a tumor? Do you want to consider non-coding changes in introns/UTR, or synonymous changes to codons?
For organisms where a selectable marker gene can be assayed (typically micro-organisms), yes, you can measure the per-gene mutation rate by selecting for "revertant" mutations on a medium that does not allow growth unless the revertant mutation is present. If you know the total target length of the gene, you can then scale the per-gene mutation rate to the per-base-pair mutation rate. A good discussion of per-gene mutation rate estimation and how to use it to find per-base-pair mutation rate cane be found in Lang and Murray (2008).
You also ask whether one should calculate the per-gene vs per-genomic-region mutation rate. This is the same as asking the question "what is a gene?", since in the revertant assay any nucleotide that could cause a change to the selected phenotype (coding, RNA, cis-regulatory, etc.) would be captured and included in the estimate. In my view, the total set of nucleotides that could revert at a locus to a selected phenotype defines the gene, so (though it is not usually framed this way) the per-genomic-region mutation rate is probably a better representation of the underlying biology.
You can calculate the mutation rate of each Amino-Acid/Nucleotide using Rate4Site and then average it along any region you choose whether it's a gene or a genomic region. You should have a phylogenetic tree and a multiple-sequence-alignment of your sequences.
So I know you wrote this awhile ago...so this thread may be dead, but I am also trying to figure out mutation rate per gene. How to do you take the score calculated by rate4site (ie. conservation score for each aa) and convert it to mutation rate?
Do you mean the rate of change for a given sequence in the germline of a population over many generations (or even between species), or the frequency of somatic alterations in a tumor? Do you want to consider non-coding changes in introns/UTR, or synonymous changes to codons?