Why is search no longer working after changing service application app pool account?

Last night I tried changing the application pool that the SharePoint service accounts use to be a lesser privileged account (it had been originally set up to use the farm account!).  I added a new managed account and updated the IIS service applications app pool to use this new account via Central Admin.  Most everything worked fine, all the other service apps with the exception of the search service.  When searching for sites or people, the results page would not load and the error in the ULS logs was:

CoreResultsWebPart::OnInit: Exception initializing: System.NullReferenceException: Object reference not set to an instance of an object

Are there other permissions that need to be set somewhere in order for the search to work?  Do the search databases need special permissions?