First there is bit of a snag in your terminology – “responsive” nowadays primarily refers to sites that adapt to screen sizes and is mostly unrelated to dynamically loaded content.
WordPress is not natively engineered for Ajax themes. It is of course possible and people do create such, but as percentage of overall theme building in ecosystem it’s tiny.
In a nutshell you will have to pick technology for implementation first and make it play with WordPress second.
The common starting point is general info on using Ajax in WordPress and you might or might not want to go with Backbone.js framework which is included in WP core.