I can speak with some direct experience, having applied to a PhD in one field but having a background in another (a little closer than biology vs computer science, but similar enough that the experience is relevant.)
In the context of a United States school, I think it is worth applying. I applied to an R1 school, was accepted, and completed the program.
When applying, my advice is to be open and transparent about your experience, and that you understand the challenge you are setting yourself up for. It's not terribly unusual to move from one field to a related one at this stage, and if your desire is to do research at the intersection of your old field and your new field, that is something to mention in any application statement, essay, etc.
My personal advice to you is this: You will have to pass whatever breadth requirement (often referred to as the qualifying exams, although they are not always exams, anymore) your chosen institute has, in your new field, and on their timetable.
These requirements are usually published, so you should absolutely take a look through those for your institute of choice, and make a plan for how you pass those requirements. It is not impossible. Anyone with the drive and intellect to complete a PhD can probably self-train up through those qualifying requirements. But it is significantly harder than just taking those equivalent courses during an undergraduate experience.