A "toxin" is something which is toxic to a system. But our knowledge of the brain is so primitive that we can't reasonably claim to know which chemicals are toxic at tiny, long-term dosage levels, unless it leads to death. There is no evidence that it's possible to die directly from sleep deprivation. Therefore this seems a dubious headline.
If you don't sleep for long enough (about 7 days), you'll start to have visual and auditory hallucinations and also delusional thinking. You'll also experience severely reduced effectiveness of just about every system in your body. You might not die if you don't sleep for a year (say), but you'll probably get permanent brain damage.
http://www.amsciepub.com/doi/abs/10.2466/pms.1989.68.3.787?j...
I have no idea where you get 7 days from, I'm not sure its possible to stay awake for 7 days.