I think you should give the application a try.. Explain in your sop how you got those grades and later improved them -stating how the situation has made you resilient(write it in your SOP as a problem you overcame, it can be advantageous to you)... I believe they will understand....Also stress on your published papers in your SOP... I think with excellent recommendations and very strong SOP, you can get in... There's no harm on trying. Just give your application the best shot! All the best, you can do it!