We don't have non-protected/private methods in controllers, or in other words, all non-action methods in a controller are support methods for actions in that same controller.
For shared methods, we either use separate helper classes, usually with a static interface, or more recently traits if we want them available in multiple controllers.
p.s. for new apps, I suggest not using the underscore naming method anymore, but use namespaces, so \Controller\Base\Backend instead of Controller_Base_Backend. The first one is PSR compliant, the second one will be deprecated with the release of 1.9 in a preparation to move fully to PSR-4 and composer.