Can a mallet toe cause a plantar plate injury?

I just did a web-cam call with a runner who had a thing called a "mallet toe" deformity. He had pain in the ball of the foot when running.

He said he was reading about plantar plate sprains, and thought, "Maybe I have a plantar plate sprain because I got this funky toe."

He wanted to know if a mallet toe could cause a plantar plate injury. 

Can a mallet toe cause a plantar plate injury?

Well, that's what we're talking about today on the Doc On The Run podcast.