Applying Machine learning in biological data
A simple starting point would be to apply a bag-of-words feature vector and try using a naive Bayes or logistic regression classifier.  You'll probably want to apply stemming and lemmatization and remove stop words.

Going based on this one example, determining which gene is regulated looks like it might be plausibly feasible, but determining whether it is up- or down-regulated might be pretty tough, especially given the limited training set you have.  Of course, it's hard to know without seeing more examples and without some domain knowledge in biology.

There are lots of techniques in the NLP literature, and probably your best bet is to start by reading up on standard NLP methods and start trying some of them, and see if that raises a more narrowly targeted question.  Machine learning often requires significant experimentation (try a bunch of things).  It's also helpful to know standard techniques so you can use your domain knowledge of these documents to help you brainstorm possible features.