Question

Compare the resting membrane potential of a neuron with the potassium and sodium equilibrium potentials. Explain how this comparison relates to the relative permeabilities of the resting plasma membrane to these two ions.

Short answer

The resting membrane potential is the voltage difference across the neuronal cell membrane at rest and is typically around -70 mV. It arises due to the unequal distribution of ions across the membrane and selective permeability to different ions. The potassium (E_K) and sodium (E_Na) equilibrium potentials are the membrane potentials at which the net flow of each ion across the plasma membrane is zero. The resting membrane potential is closer to E_K (-80 mV) as compared to E_Na (+60 mV), indicating that the resting plasma membrane is more permeable to potassium ions than sodium ions. This difference in permeabilities is due to a higher number of open potassium ion channels compared to sodium ion channels at rest, which contributes to the maintenance of the resting potential and the generation of action potentials when the cell is activated.

Step-by-step solution

Define resting membrane potential and equilibrium potentials

Resting membrane potential is the voltage difference across the neuronal cell membrane at rest, which is typically around -70 mV. This potential arises due to the unequal distribution of ions across the membrane and the selective permeability of the membrane to different ions. Potassium (K+) and sodium (Na+) equilibrium potentials refer to the membrane potentials at which the net flow of each ion (K+ and Na+, respectively) across the plasma membrane is zero. This is achieved by balancing the electrochemical driving forces for each ion across the membrane.

Determine the potassium and sodium equilibrium potentials

The equilibrium potentials for potassium (E_K) and sodium (E_Na) can be calculated using the Nernst equation: \[E_{ion} = \frac{RT}{zF} \ln\frac{[ion]_{out}}{[ion]_{in}}\] where R is the gas constant, T is the temperature, z is the charge of the ion, F is Faraday's constant, and [ion]_out and [ion]_in represent the extracellular and intracellular ion concentrations, respectively. For K+ ions, z = +1 and the typical concentrations are [K+]_out = 5 mM and [K+]_in = 140 mM. For Na+ ions, z = +1 with typical concentrations being [Na+]_out = 145 mM and [Na+]_in = 12 mM. Plugging these values into the Nernst equation, we can compute E_K and E_Na.

Compare the resting membrane potential with equilibrium potentials

The resting membrane potential is typically around -70 mV, while the calculated equilibrium potentials for potassium and sodium ions are around -80 mV and +60 mV, respectively. The resting membrane potential is closer to the potassium equilibrium potential (E_K) as compared to the sodium equilibrium potential (E_Na). This observation indicates that the resting plasma membrane is more permeable to potassium ions than sodium ions.

Relate the comparison to the relative permeabilities of the plasma membrane to potassium and sodium ions

The reason why the resting membrane potential is closer to E_K than E_Na is due to the permeabilities of the plasma membrane to these ions. The selective permeability of the plasma membrane to different ions is primarily determined by ion channels present in the membrane. At rest, there are more potassium ion channels open than sodium ion channels, leading to higher permeability to potassium ions than sodium ions. Consequently, the resting membrane potential is close to the potassium equilibrium potential. This difference in permeabilities contributes to the maintenance of the resting potential and the generation of action potentials when the cell is activated.