Clear contact->org association via Connect for PHP

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I know how to create a new org object.  I know how to associate an existing org object to the contact record.

I know I'm forgetting something that I'll be kicking myself for once someone points me in the right direction, but ...

How do I CLEAR the contact->organization association?  A contact tells me that she is no longer a member of a particular company, so I want to clear that association.  Easy to do in the console, but I want to set up a page where customer's can clear that association themselves.