Setting ToolTip for DataGridView automatically created columns

Setting ToolTip for DataGridView automatically created columns

I would like to programatically set tooltips to automatically generated
columns in a DataGridView. I was trying to use AutoGeneratingColumn event
(http://msdn.microsoft.com/en-us/library/cc903950%28VS.95%29.aspx), but
that in fact can only access DataGridColumn, not DataGridViewColumn, and
the former doesn't have ToolTipText property.
Or if I could bind the ToolTips to a source that would also be great. The
goal is to have the ability to manipulate/set tooltips in the same place
where I set the columns for the underlying DataTable.