When SharePoint User Profile service application connects to Active Directory to synchronize user profiles, it uses user account provided in Connection Setting page in Central Administration, Manage Profile Service page. This account requires special permissions: http://technet.microsoft.com/en-us/library/hh296982.aspx
The next code shows how to get this account name from your code:
SPServiceContext serviceContext = SPServiceContext.GetContext(currentWeb.Site);
UserProfileConfigManager config = new UserProfileConfigManager(serviceContext);
DirectoryServiceConnection conn = config.ConnectionManager.OfType<DirectoryServiceConnection>().FirstOrDefault(x => x.DisplayName == "Connection Name");
if (conn!=null)
{
string accountName = conn.AccountUsername;
}