I use Mathematica to generate lists of genes from Saccharomyces Cerevisiae that I then throw into the GO enrichment analysis tool here: http://pantherdb.org/webservices/go/overrep.jsp. I know how to build and read from files in Mathematica, but I'm not sure how to approach automating the process of throwing the files with those lists of genes into the GO enrichment analysis tool with the desired options selected. Is there a good place to start looking? Thanks in advance!
This is more advice than an answer but here we go:
You start by investigating if this web analysis tool has an open API. If so, Mathematica has excellent support for using web services.
If there is no open API, then you can emulate the web request that is sent by the browser when you hit that submit button. If there is authentication involved, you will most likely need to capture the navigator cookie and include it as part of the request that you will send from Mathematica. Use you browser web inspector/development tool to find out the details about the web request sent.
If all else fails, you need to automate the GUI. Try to avoid this. On the Mac use AppleScript (which I know can be called from Mathematica) on Windows I would AutoHotKey (which I presume can be called from Mathematica).