Only women are capable of tetrachromacy because the gene that controls which wavelengths of light are detected by cones are on the X chromosome. Tetrachromat women have a mutation on one of their X chromosomes, and are heterozygous for "normal" cones (detect one wavelength) and "abnormal" ones (detect another wavelength). As it turns out, this means that some of their cones detect one wavelength of light, and others detect the other.
As men can not be heterozygous for traits on their X chromosomes, they can't express two cones simultaneously. They CAN have the mutation, but that means they see three colors that are somewhat different from the three colors that other men see, not that they see four colors.
All of the above as I understand it from a popular article on tetrachromacy. I am not a biologist.
The alleles being sex linked makes sense, although there are a couple of theoretical exceptions. One is the very rare male that has two X chromosomes because the SR-Y gene was transposed onto the X chromosome. The other would be having the reverse where the second gene is transposed onto the Y chromosome. The former are sterile while I would guess that the latter are not sterile, but unless they really do exist, are found and one that is found has the same combination as a tetrachromatic woman, there is no way to confirm that.
Genetics was one of my strong points when I was in school. I would have gone into bioinformatics if it were not for my poor performance in organic chemistry, which I felt crippled my ability to do the sort of work that I had wanted to do.
You don't need to be good at orgo to do informatics; I've worked with a number of very capable analysts who hadn't been anywhere near a lab since their undergrad days. (If you want to do lab work, things are different, but my experience is that it's kind of rare for informatic analysis and lab work to overlap.)
Another possibility for male tetrachromats would be people with the 47,XXY karyotype, who are phenotypically male but have the paired X chromosomes necessary to make tetrachromacy possible. Given the rarity of both variations, I can't imagine it being likely that any such person has been identified, but based on my (admittedly meager) knowledge of the subject, I don't see a theoretical barrier to such a person possibly existing.
While I call it bioinformatics because that is a handy umbrella term for biology and computers, what I really wanted to do was to figure out how to do in-Vivo gene splicing to correct genetic illnesses. Specifically, I wanted to build a compiler for generating gene sequences that could be synthesized and injected into bacteria to produce biological machines tailored to alter specific regions of a person's genome. You could call it a compiler for biological instances of sed commands on DNA. It would need to construct things that bypass with the immune system and two membranes with varying methods of entry and varying sized things permitted entry.
Others are making progress in that field, so I am hopeful that some day it will be a reality. The idea that molecular dynamics simulations are NP-complete is going to be a pain for anyone attempting to do that unless they are really clever in figuring out how to do construction like people were when they made the perfect ping. That should require Linus Pauling level or greater knowledge of chemistry, which I do not have. Building it would also produce an easy construction technique for a incredible number of biological weapons, so if it is never made, maybe it is for the best. Not to mention it would probably sow the seeds of the eugenics wars.
You are right about XXY. I had forgotten about it. I had no idea how to theoretically delete an entire chromosome without deleting all copies of it when I was studying with the goal of producing that tool, so it was easy for me to forget. Now that I think about it, it might be possible. Just append the entire chromosome in pieces to the end of another with the genes disabled and some trivial difference to enable final slicing into discrete chromsomes, delete all of the copies of the old trisomal/monosomal chromosomes and do final slicing and splicing to produce two new functioning chromosomes in what would hopefully be a large percentage of the cells while managing not to kill the organism in the process. It would need to be done when the organism is young to minimize negative impacts to its development and would be somewhat different when dealing with sex chromosomes. You would also need to be careful that genes that are needed for the procedure are not disabled by it (like not unlinking libc when trying to replace RHEL with Gentoo in in-place when using a script that calls commands that link to libc). If you manage to rewrite a sufficiently large enough percentage of the organism without killing it, that procedure should cure trisomy and monosomy conditions if done early enough in development. Doing it requires tools that we do not have though.
Anyway, that should make it clear why being bad at organic chemistry kept me from thinking that I could pursue this.
As men can not be heterozygous for traits on their X chromosomes, they can't express two cones simultaneously. They CAN have the mutation, but that means they see three colors that are somewhat different from the three colors that other men see, not that they see four colors.
All of the above as I understand it from a popular article on tetrachromacy. I am not a biologist.