With regards to a "Confused mathematicians" question about LTP:
Cells may be depolarized without reaching threshold for action potential
generation, indeed it has been demonstrated that intacellular application
of the local anaesthetic QX314 which blocks action potentials still allows
the cell to undergo potentiation. In other words, LTP does not actually
require a postsynaptic action potential merely sufficient depolarization to
relieve Mg2+ blockade of the NMDA receptor.
Hoping this helps,
John H. Williams & David B. Wheeler
Dept. Molecular & Cellular Physiology
Beckman Center B103
Stanford University Medical School
Stanford, CA 94305
