action potential and heart rhythmic conduction system

I'm not sure how much detail you need but here it is in short:

The resting membrane potential for a neuron is -70mV, due to the Na+/K+ ATPase that brings 2 K+ in and 3 Na+ out (which creates the electrochemical gradient).  Its -70mV because more K+ is in the cell, bringing it closer to K+'s equilibrium potential.

Auto-rhythmic cells have an unstable resting potential due to three ionic events:
1) Gradual decreasing permeability to K+ (keeping more inside the cell)
2) Funny Na+ (leaky Na+) channels, allow Na+ to move in >> This point here is what I've seen in the majority of my courses!
3) Transient (T-type) Ca2+ channels open, Ca2+ starts to enter the cell (Ca2+ is what causes depolarization but that occurs when L-type channels open)
The membrane potential before these events is ~ -60mV (but since it is unstable it doesn't stay at this value, it is constantly rising until it reaches threshold, depolarizes, repolarizes, the cycle repeats).

I attached two diagrams for you to compare.

Hope this helps!