I have a different spin on socially enabled communication than most probably. I look at the concept of trying to deliver your message through more channels. Email is a channel, Twitter is a channel, Facebook, and LinkedIn are also channels. What you really want to do is start to expand your definition of subscribers to include friends, followers, colleagues…etc.
Then use the mechanisms provided by the other channels to drive that traffic to click to your communications landing page.
Promote your Twitter address on your weekly publication, use Twitter updates to highlight stories. Ask for email addresses on your landing page that people may be directed to from Twitter, ask for followers of your Twitter page on your landing page from your newsletter. Combine the mediums; let them interact with one another.
An example of integrating the communications could be responses that you illicit through the social networks can be highlighted in the weekly publication.