In my never-ending struggle to solve the problem of strings binding at the nut, I experimented with teflon tape and found it to be far superior to graphite or some of the other materials commonly used to solve this problem. It leaves no mess, and does not interfere with the tone of the string.
Teflon tape or sometimes called 'plumbers tape', is very inexpensive and works great to alleviate strings getting hung-up in the nut when tuning or bending notes.
You simply lay a piece of the teflon tape over the nut or your bridge, place the strings over the top and tune up!