To determine which action would cause hyperpolarization in a postsynaptic cell, we need to analyze the role of each type of ion channel.
1. Opening of Na[tex]\(^+\)[/tex] Channels:
- When Na[tex]\(^+\)[/tex] channels open, sodium ions (Na[tex]\(^+\)[/tex]) flow into the cell due to their higher concentration outside the cell.
- This inflow of positive ions (Na[tex]\(^+\)[/tex]) decreases the internal negativity of the cell, causing depolarization.
- Therefore, opening Na[tex]\(^+\)[/tex] channels results in depolarization, not hyperpolarization.
2. Opening of Ca[tex]\(^{2+}\)[/tex] Channels:
- Similar to Na[tex]\(^+\)[/tex], calcium ions (Ca[tex]\(^{2+}\)[/tex]) have a higher concentration outside the cell.
- When Ca[tex]\(^{2+}\)[/tex] channels open, Ca[tex]\(^{2+}\)[/tex] ions flow into the cell, bringing positive charge inside.
- This also reduces the internal negativity of the cell and leads to depolarization.
- Thus, opening Ca[tex]\(^{2+}\)[/tex] channels also results in depolarization, not hyperpolarization.
3. Opening of K[tex]\(^+\)[/tex] Channels:
- Potassium ions (K[tex]\(^+\)[/tex]) are more concentrated inside the cell than outside.
- When K[tex]\(^+\)[/tex] channels open, K[tex]\(^+\)[/tex] ions move out of the cell, taking positive charge with them.
- This increases the internal negativity of the cell, leading to hyperpolarization.
- Therefore, opening K[tex]\(^+\)[/tex] channels results in hyperpolarization.
Based on the analysis:
- Opening of Na[tex]\(^+\)[/tex] channels causes depolarization.
- Opening of Ca[tex]\(^{2+}\)[/tex] channels causes depolarization.
- Opening of K[tex]\(^+\)[/tex] channels causes hyperpolarization.
Thus, the correct answer is the opening of K[tex]\(^+\)[/tex] channels, which is option 3.
