What type of traffic do you currently get because of those articles?
What quantity/quality of links do you get because of those articles?
Is it possible for you to recreate the content (in your own words), and just replace the articles?
If it is good content and its generating traffic, you should try to find a way to recreate original content to replace what is there. At the very least, you should put some 301 redirects in place to the most similar content that will remain on your site.
Corollary question: Will there be any way that a human visitor and/or a search engine can tell that you've deleted all articles from a particular source? If yes, you need to make it look as if you made the decision yourself for the benefit of your site, rather than that the contributor decided there's something wrong with you. ("I quit" vs. "You're fired".) But resist the temptation to imply there is something wrong with the contributor. It doesn't sound as if you really think there is-- and that kind of thing can come back and bite you.