Membrane Potential and Electrochemical Gradients (2A) - Bio & Biochem

1. What is the typical resting membrane potential magnitude for many neurons?

   Approximately $-70\ \text{mV}$. This value arises from the balance of ion concentrations and permeabilities, particularly high K$^+$ conductance.

2. What change in $V_m$ is called depolarization?

   $V_m$ becomes less negative (moves toward $0$). Reduction in negativity occurs when net positive charge enters, as in Na$^+$ influx during excitation.

3. If $V_m$ becomes more permeable to $Na^+$, which direction does $V_m$ shift?

   Toward $E_{Na}$ (depolarizes; becomes more positive). Increased Na$^+$ permeability allows influx, shifting potential toward Na$^+$'s positive equilibrium value.

4. What is the definition of an electrochemical gradient for an ion?

   Combined chemical gradient and electrical gradient. It integrates concentration differences and electrical potential to determine the direction and magnitude of ion flux.

5. What is the major extracellular cation in animal cells?

   $Na^+$. High extracellular Na$^+$ concentration is essential for osmotic balance and action potential generation.

6. Which direction does a cation move if $V_m - E_X$ is positive?

   Out of the cell (net outward cation flux). A positive driving force repels positively charged ions outward across the membrane.

7. Identify the sign of $E_X$ for an anion when $[X]_{out} > [X]_{in}$.

   Negative ($E_X<0$). Higher external concentration favors outward movement, but negative valence results in a negative equilibrium potential.

8. What condition defines electrochemical equilibrium for ion $X$ across a membrane?

   $V_m=E_X$ (no net driving force for $X$). At equilibrium, the membrane potential equals the ion's Nernst potential, resulting in zero net electrochemical force.

9. What does the valence term $z$ represent in the Nernst equation?

   Ion charge (e.g., $+1$, $-1$, $+2$). Valence indicates the ion's charge magnitude and sign, influencing the electrical force in the equilibrium calculation.

10. What is the primary active transporter that maintains $Na^+$ and $K^+$ gradients in animals?

    Na$^+$/K$^+$-ATPase. This pump actively maintains steep Na$^+$ and K$^+$ gradients essential for cellular function and excitability.

11. Identify the sign of $E_X$ for a cation when $[X]_{out} > [X]_{in}$.

    Positive ($E_X>0$). Higher external concentration creates an outward chemical gradient, yielding a positive equilibrium potential for cations.

12. What is the major extracellular anion in animal cells?

    $Cl^-$. Chloride's abundance extracellularly balances cationic charges and contributes to Donnan equilibrium.

13. What is the net charge moved per cycle by the Na$^+$/K$^+$-ATPase?

    Net $+1$ out (electrogenic pump). The unequal ion transport generates a net positive charge efflux, contributing to membrane hyperpolarization.

14. What does it mean for a membrane to be selectively permeable to $K^+$ at rest?

    $P_{K}$ is high; $V_m$ is driven toward $E_{K}$. High potassium permeability allows K$^+$ fluxes to dominate, pulling the membrane potential toward its equilibrium.

15. What is the definition of membrane potential ($V_m$) in a cell?

    Voltage across the membrane: $V_{in} - V_{out}$. Convention defines membrane potential as the difference between intracellular and extracellular voltages.

16. At $37^\circ\text{C}$, what is the common base-$10$ Nernst form for a monovalent ion?

    $E_X\approx\frac{61\ \text{mV}}{z}\log\left(\frac{[out]}{[in]}\right)$. At body temperature, the constant simplifies the natural log form to base-10 for easier physiological calculations.

17. Which direction does an anion move if $V_m - E_X$ is positive?

    Into the cell (net inward anion flux). A positive driving force attracts negatively charged ions inward across the membrane.

18. Which ion is closer to electrochemical equilibrium at rest if $V_m$ is near $-70\ \text{mV}$?

    $K^+$ (since $V_m$ is near $E_K$). At resting potential, the driving force for K$^+$ is smaller than for other ions due to high K$^+$ permeability.

19. What is the Na$^+$/K$^+$-ATPase transport stoichiometry per ATP hydrolyzed?

    $3\ Na^+$ out and $2\ K^+$ in. The unequal exchange creates concentration gradients crucial for resting potential and secondary transport.

20. What sign is the resting membrane potential of most neurons (inside relative to outside)?

    Negative (inside is negative relative to outside). Ion gradients and selective permeability result in a negatively charged interior relative to the exterior at rest.

21. What is the electrochemical driving force expression for ion $X$?

    $V_m - E_X$. This difference quantifies the net force driving ion movement away from its equilibrium potential.

22. What is the formula for the Nernst equilibrium potential for ion $X$?

    $E_X=\frac{RT}{zF}\ln\left(\frac{[X]_{out}}{[X]_{in}}\right)$. The equation balances the chemical concentration gradient with the electrical potential difference at equilibrium.

23. What is the major intracellular cation in animal cells?

    $K^+$. High intracellular K$^+$ concentration is maintained by active transport and supports resting membrane potential.

24. What change in $V_m$ is called hyperpolarization?

    $V_m$ becomes more negative. Increased negativity results from net positive charge efflux or negative charge influx, inhibiting excitability.

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