Final answer:
Both calcium channels and funny channels contribute to the spontaneous depolarization of pacemaker cells, with funny channels causing a slow depolarization and calcium channels causing a faster depolarization leading up to the action potential.
Step-by-step explanation:
The opening of both calcium channels and funny channels contributes to the spontaneous depolarization of pacemaker cells. The funny channels, which are also known as hyperpolarization-activated cyclic nucleotide-gated channels, allow a slow influx of Na+ ions after repolarization, which gradually depolarizes the cell membrane. As the membrane potential reaches about -40 mV, calcium ion channels open and Ca2+ enters the cell, further depolarizing the membrane at a more rapid rate until an action potential is initiated. Therefore, the correct answer to the question is E) both calcium channels and funny channels.
It is important to note that potassium channels are more involved in repolarizing the cell membrane after the action potential has peaked, not in the spontaneous depolarization leading up to the action potential. Thus, they do not contribute directly to the prepotential depolarization but rather to the process of bringing the membrane potential back down to initiate the next cycle.