Depolarizing local potentials sum together, and if the voltage reaches the threshold potential, an action potential occurs in that cell.

What potentials cause summation?

Temporal summation occurs when a high frequency of action potentials in the presynaptic neuron elicits postsynaptic potentials that summate with each other. The duration of a postsynaptic potential is longer than the interval between incoming action potentials.

What do local potentials do?

The stimuli open ion channels in the membrane, which allows specific ions to flow in or out of the cell. This ion movement produces a change in the membrane voltage around the area of the open channels. These local shifts in membrane potential are called graded (or local) potentials.