Etiquette for contacting a corresponding author? I'm a 2nd year graduate student (biological sciences). I've been developing a new research tool, which builds upon a system developed by a different lab. However, I've had issues replicating the previous system, owing partly to a scarcity of certain details that would be useful for someone who is still new to most of the technical aspects of this type of research. 

I'm debating whether I should contact the corresponding author of the source literature to ask for clarification (e.g. if they could send me specific plasmid maps). However, based upon the research history of my lab, I'm concerned that the other lab may be able to deduce what enhancements I'd like to make to their system (since they've attempted to do similar things in the past). As such, I'm not sure if they would be willing to provide such information.

I've thought about discussing with my advisor. However, I also don't want to seem like I don't have the initiative/independence to seek out what I need myself. If general protocol is for students to directly contact corresponding authors, I'm wondering what is the best way for me to phrase this inquiry.

Thanks so much!
Ask your advisor. In this context I think it's more important to show you have some forethought to realize the situation could be potentially tricky and that you know when to ask for advice, versus showing your initiative/independence. You're a second year graduate student. 

There are several issues that your advisor will know more about than you regarding your relationship with this other lab, in terms of publication strategy, any personal contact they already have, avoiding your request sounding like an accusation or making you look foolish, etc. Your advisor might also know about the reputation of the other author: maybe this is someone who would be responsive to a student email, maybe it's someone who would ignore you and your advisor needs to intervene on your behalf. Your advisor can also give you recommendations on your own work and help you discover if there are other causes for your inability to replicate results so far, and save you both from some embarrassment if the problem is your own.