I'm not a molecular biologist, and some additional context would help, but it looks to me as if "determining" means "finding out" here. "Such that (+ clause)" is probably close to "in order to (+ base form) in meaning.

determining in this case is more like "choosing between". The repair process had to know normal DNA and mutant DNA and be able to know not only if the DNA is mutual, but how the repair should look. For example, you could have a DNA strand TTAAGGTTC. Let's say it is mutated to TTTAGGTTC. The repair process must (1) determine this second string is a "mutant" not "normal", and it must also know the third T should be repaired to an A. It must DETERMINE what the third base pair should be.

The problem with bidding on websites to take on a transliteration job or ghost writing someone else's thesis when one isn't qualified to do such a task (or whatever this is here- and there are many each day) can indeed lead to these types of incessantly enduring streams of decontextualised babble erroneously considered salvagable by sticking it in front of an empathetic teacher at italki. This is a worrying trend.

I completely understand the sentence, but you haven't actually phrased a question, and so I'm out, notwithstanding my lack of mind-reading capability.