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If I want to study, say, gustatory response of salmons to a bile acid, I need to mutagenize a sample of salmon males. However, given that there are many genes involved in this response, what is minimum no. of salmons I should mutagenize, such that ALL the genes involved have some mutations?

I have searched quite a lot for some statistical method that tells me this, but to my surprise I haven't found any.

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Don't think about mutagenized animals, think about mutagenized genomes. Depending on when the mutagenesis is carried out, and how efficient it is, a very small number of males could give rise to thousands of mutagenized F1 progeny, each carrying a uniquely mutagenized genome. That is the number to focus on. Typically, in fruit flies and soil nematodes the animals are hit "pretty hard" such that each F1 is carrying hundreds, if not thousands, of mutated sites, randomly throughout the genome. The trade-off is to not mutagenize them so much that they suffer a drastic decrease in fertility or viability, while at the same time minimizing the number of F2 homozygotes you have to screen for phenotypes.

In C. elegans exposed to 50 mM ethylmethane sulfonate for 4 hr, you might reasonably hope to recover 1 loss-of-function mutation after screening 2,000 mutagenized F1 genomes.

Are there good genetic markers along all of the salmon chromosomes? If you are only interested in recovering dominant mutations then you can screen the F1 directly (however dominant alleles tend to be much rarer than recessive alleles, and interpretation of dominant phenotypes is challenging without lots of good genetic tools, like duplications and deficiencies). Otherwise you will have to mate the F1 to obtain male and female F2 and then set up brother-sister matings so that you can score the F3 for phenotypes of interest.

None of these numbers would apply to salmon because the genome is much larger, and unless someone has already done a dose-response curve on the optimal mutagenic dose for salmon, you would need to do that first.

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