Evolutionary speaking, some mutations lead to better fitness of an organism and its adaptation to the environment changes, but I was wondering if there are some constraints on having new mutations. For example, if a gene is needed for survival, I expect to see it more resistant to having new mutations. So, my question is what are these constraints, especially for bacteria?
This is an undergraduate/graduate lecture type question and the answer varies: traditional Darwinists believed a reasonable proportion of mutations would result in beneficial adaptation, neutral theory however would state the vast majority of mutations have no effect on phenotype and only an absolute minority result in beneficial adaptation. It depends on which bacteria are the focus of investigation and the selective constraint (I would assume its antibiotics).
Once the bacterial species and selective constraint are described its a straight-forward empirical investigation using molecular mathematics because the mutations driving antibiotic resistance are all known.