How to let users edit one specific custom post

Hi,

I’m looking for any tips or advice for the following situation:

I’m currently developing a website that shows profile pages for some of the members of a community (it’s a paid feature). I’ve created the profile page as a custom post with custom fields to have total control about the look and feel of the profile page.

Want would be nice is that the member can edit his/her own profile page. But how can this be achieved? I’ve already been looking at the Members plugin but that once doesn’t support custom fields afaik. It’s of course possible to site the role of the members with a profile page to editor but that way they’re able to edit all profile pages.

So in shrot: How can I create a role that one specific member can edit one specific custom post?