My wife is a microbiology PhD. student. Does the copyright to her work and lab notebooks belong to her, or the University/her Principal Investigator?

The answer is "it depends." There are several principles that may control here. First, as a general matter, the work of an employee belongs to the employer, if there is a traditional employee-employer relationship. That means, generally, that a work of authorship written by an employee of a university belongs to the university. Whether an employee-employer relationship exists may depend on numerous facts, including whether your wife receives a stipend and whether that stipend is reported on Form W-2. The latter fact would nearly certainly establish the existence of the required relationship and render the work the property of the employer. It is also possible that your wife has impliedly assented to the university's policies regarding this issue by accepting the benefits of her arrangements (whatever those benefits might be).