Drupal using panels with ajax
For this to work you might have to restructure some of your blocks into mini panels but you could implement this module, Panels Ajax Tabs. Ajax can now be used when loading content via panels, either as a tab or container.


  Provides the ability to have a tabbed panel-pane that displays mini-panels within it.


If you require more control; instead you could utilize Ctools AJAX. Of course this is a much more hands on approach.

Hope this helps,