python - Get the vertices on a LineString either side of a Point

I have a shapely LineString and defined a shapely Point which lies along the LineString.

How can I find the vertices of the LineString which lie either side of the point? (split the line in two).

This is very similar to this blog post by the author: http://sgillies.net/blog/1040/shapely-recipes/

Except, instead of cutting by distance along the line, I want to cut given a point that lies along the line.