How to update controller options and re-render element?

I'm writing a component which is instantiated on an element inside a "wrapper" controller.

e.g.

2. this.element.find('table').components_table({
3.             headers: {
4.                 name: "Name"
5.             },
6.             rows: new $.Model.List([ 
7.                 new $.Model({ name: "Chris" }), 
8.                 new $.Model({ name: "Dave" })
9.             ])
10. });

This works fine but I don't know how to re-draw the component when the models change? I'm not going off server-synchronised events here. Effectively I want to provide the result of a search component as the new options to the table component...and automatically re-draw the table component.

Any ideas? I hope I'm missing something blatantly obvious!