As of 15 March 2015, I’m taking a 3 year stint on the editorial board of PNAS. Right now there are ten of us in the evolution section, so I’m likely to handle a lot of papers. What we do is read the paper and then decide whether to forward it to a handling editor. That person will also decide if the paper is worth reviewing and if it is choose reviewers and make a decision. We have been encouraged to reject without further review about two thirds of the papers we receive. Since the editor that agrees to actually handle the paper also has this option, you have two hurdles to actually having your paper go to reviewers.
This does not mean your paper has not been reviewed. I will be reading every paper I receive, though if the paper does not go out for review, I will not be sending you detailed comments. When I read your paper, I will be using the same kinds of criteria an actual reviewer will use, but there are some important differences. First of all, I see a lot of papers, so I’m developing a sense of what is likely to make it further through the review process. I want to save time for everyone by not sending on papers that are likely to fail. Second, I am usually likely to be more distant from your field than an assigned reviewer would be. Therefore you will have to be really good at framing your work. Of course you have to do this anyway before the work can be published in a general journal like PNAS.
If the work is in a more distant field, I’m likely to get a quick sense of the importance of your paper by going to Google Scholar and typing in a few key words from your work. I’ll look at abstracts of papers that come up first to see some history. Then I’ll restrict the search to the last five years to see what the current excitement is. I realize this will sound very inadequate to really understanding a field, but it is what I do.
What does it take to convince me that your paper is important, well-framed, and likely to excite the impatient readers of PNAS? Soon I’ll be posting a check list on this. But for now know that the most important thing is that you frame your paper well. Don’t just tell your story, but put it in context of what else has been done in the field. This should happen in the introduction and also in the discussion. The broader you make these perspectives, the more likely you are to convince me of the importance of your work.
The other thing I’ve noticed about successful work for PNAS is that the papers tell a fairly complete story. They do not make a small advance, but pursue the first results with follow-up experiments so they have a full story. I’ve been really surprised at the number of times I am entranced by a topic that seems really cool only to discover from a little digging that you have already published a close variant of the story somewhere else. This version probably seems more different to you than it does to me.
I’m guessing you already think your work is important and complete or you wouldn’t be sending it to PNAS, so maybe your biggest challenge is to understand that others also do great work. Put your results in the context of what went before so we have an even more complete story, not just your own new nugget. I’ll be writing more on this interesting process. It is important to add, of course, that these are my opinions, and mine alone. They have not been endorsed by PNAS, NAS, or anyone else.
Sociobiology 
Joan – congratulations on that appointment! My experience (principally at the American Naturalist) has been similar. I decline quite a few papers (not quite 2/3, though), because I anticipate that they won’t fare well in review, and the authors might as well know that quickly. I do tend to provide fairly extensive comments when I do an editorial decline – but then, I deal with fewer papers than you’re likely to (I’d say I handle about 15 a year). Somewhat to my surprise, authors don’t seem unusually upset by editorial declines (a few have even thanked me by e-mail).
Does this mean that cover letters to PNAS should explicitly mention any recent high profile papers related to the submitted manuscript?
I suppose it can’t hurt to have a paragraph on why the field is exciting and to show that you are aware of where your paper fits in the broader field. People use cover letters differently. I think the best cover letter is short but makes the importance of the paper really clear, perhaps in more layman’s terms than the actual paper does. I tend to rely on the paper itself, not on the cover letter. Editors may differ on this. I don’t like cover letters that tell me repeatedly that the paper is important, using bolded text without clearly showing me why.
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