Leaving aside the issues that may be exacerbated by her sisters' departure - this is perfectly normal for a teenager! You can expect mood swings, silences, grumps, temper tantrums, and so on, because it's all part of growing up.
Your yongest may feel left out if her sisters used to spend time with her - have a word with them, and see if they can give her a call, or arrange to meet up for a girly day out from time to time.
You need to make time for her as well. Set aside a Saturday when you can take her out for lunch and a bit of shopping - just something simple like a new top - and then a MacDonalds for tea, and pictures. This will give her your undivided attention for a few hours, and she may open up to you about antying that is distressing her.
She may want to be the 'young lady' but all girls at that age revert to childhood at bedtime. Make sure you look in on her before she goes to sleep, give her a good night kiss and tell her you love her, and you are there for her always if she needs to talk, but don't press the issue - she will when she wants to.
Get Dad involved as well - girls are often closer to their Dads at this time, so make sure Dad makes some time to be with her - even if it's just watching TV.
This is a horrible time for everyone, but it passes, and your understanding and support is what she needs, even though she will work really hard at convincing you that she doesn't!