You really should go up to a science professor that gave you an A and ask for a letter. I did that with a professor I didn't know. He told me to come by in the morning one day and hang out with him for a few hours. I ended up helping him in his lab and for like 5 hours. We mostly talked about football and other non-dental stuff. He then wrote an amazing letter for me. We still keep in touch.
Many professors will want to talk to for a while. Others will want you to print out your aadsas ap and give a copy to them to look over. Others will want to read your PS. Others want your resume. Just suck it up and go to their office IN PERSON and speak with them. Do not ask by email, especially if they head large classes.
Moral of the story. Just go up the professor and ask. All they can say is no.
@op you can have more than 4 letters if you want. i sent 4 to AADSAS. the extra ones i just sent separately
i dont think it really matters what kind of professor you get to write the letter? if your engineering professor taught a bio class or chem class, then i would consider them a "bio" or "chem" professor. if your engineering didn't teach any bio or chem class, then i wouldn't consider him a "bio" or "chem" professor.
i would just recommend choosing professors you are comfortable with. only you will know what type of relationship you have with the professor. i wouldnt really want to help you choose which professors to ask. i don't think it will make too big of a difference between the professors you choose.
as a generaly rule and this is in almost every thread. submit your application as early as possible and send in your dat scores later.