When a reply is made to a comment, a twitter notification (@twittername) will be sent to the original comment author to notify him/her of the reply. The notification will be sent from your Twitteraccount. 
This will allow the users to follow up on the comment and expand the conversation if desired.

CommentTweets

When a reply is made to a comment, a twitter notification (@twittername) will be sent to the original comment author to notify him/her of the reply.

This is a plugin that adds a twitter link to comments if the comment author uses an email connected to a twitter account.

Add Twitter Link to Comments

This is a plugin that adds a twitter link to comments if the comment author uses an email connected to a twitter account.

CommentTweets vs Add Twitter Link to Comments