Speaker of the Legislature

Something odd is occurring. Liberal MPPs are challenging Mike Brown to be Speaker of the Ontario Legislature. The two challenging are Steve Peters and David Zimmer. I find it odd that these two are challenging because both of them have a Parliamentary Assistant position that they would have to give up should they win. This would force a shuffle. I know cabinet ministers are not eligible to run for Speaker. Does this mean, however, that Parliamentary Assistants are allowed to run for Speaker?