Single subscription for multiple sites

I would like to run several sites (different themes, different content) from a single drupal installation

mainsite.com - to login and manage user registration and subscriptions
site1.mainsite.com
site2.mainsite.com
site3.mainsite.com

The sites are for health professionals who may be interested in one or more of the areas of special interest.

Is it possible to have a single user registration process through the default site, and single login for one or more of the subdomains, so that users can be members of one or more of the sites? This user registration / subscription process would allow restrictions around which sites the user has access to.

Any ideas how this could be done / whether it could be done?

Thanks