Converting Date to Unix Time

Dear All,
I am struggling with a simple problem. I did some online research, but
I am still banging my head against the floor.
I read a csv file into a data frame and I have a columns with entries like

2012-04-13 00:23:45
2012-04-22 07:53:09


etc..
Each line posted above is the content of a single cell.
How can I convert that into Unix time?
Many thanks

Lorenzo