So how exactly do you interact with your audience? Talk to your followers. If someone follows you, they obviously respect you enough to have done so. Give them credit and shoot them a "Thanks for the follow" tweet every once in a while. You'll be amazed at how much less often you'll lose followers if you interact with them. Someone responds to your tweet? Tweet back. By creating engaging conversations and interactions with your audience, people won't just pass by your Twitter handle, they'll remember you, and they probably won't unfollow you. Trust me, there's nothing worse than gaining a few hundred followers in a day, and then losing fifty the next week because you didn't interact with any of them.
Some people that are great examples of public figures that interact with their audience, and that I've been able to interact with, are Eric Hutchinson, Raviv Ullman, and Gary Vaynerchuk. Give them all a follow, because they post great content.
In summary, don't just float in Twitter cyberspace with a profile that just sits and does nothing. Take advantage of the great social media tool that Twitter is, interact with people, get to know them, and in turn, you and your brand will benefit from it. Plus, it's pretty neat to know people all over the world through 140 characters. Have a good night, and have fun tweeting!