Lecture 7: Electrical Activities of Cells

Comprehensive practice flashcards covering cellular membrane potentials, voltage- and stimulus-gated ion channels, electrochemical gradients, thermodynamics, the Nernst equation, and the maintenance of resting potential in excitable cells.

What are the five steps in the functional sequence describing how neurons and muscle cells work?

1. Perceive stimulation: changes in temperature, chemicals such as neurotransmitters, mechanical forces, and more.
2. Convert the stimulus into an electrical signal (a change in cellular membrane potential, $\Delta V_m$).
3. Decision-making process: whether to respond or not to respond.
4. Action potential: a huge change in cellular membrane potential (if deciding to respond).
5. Results: Neurotransmitter release in the neuron or contraction in the muscle fiber.

How is cellular membrane potential ($V_m$) physically established across the lipid bilayer?

Cells use selective ion channels and the cellular membrane to separate positive and negative charges. Unbalanced charges accumulate close to the cellular membrane, generating an electric field that is strongest across the lipid bilayer.

By definition, what energy change does the membrane potential ($V_m$) represent, and what does a negative value indicate?

$V_m$ represents the energy change for moving a $+1$ charge from outside to inside the cell. If $V_m$ is negative (such as $-70\,\text{mV}$), moving a positive charge inward releases energy, and the sign of $V_m$ aligns with the excess unbalanced negative charges inside the cell.

What mathematical equation determines the value of $V_m$ in terms of charge ($Q$) and membrane capacitance ($C$)?

$V_m = \frac{Q}{C} = \frac{Q}{\frac{\varepsilon_0 \varepsilon_r A}{d}}$, where $C$ denotes the capacitance of the membrane and tells how many charges are needed to create one unit of voltage across the membrane.

According to the table shown, what are the resting membrane potential ranges or values for bacteria, skeletal muscle cells, and neurons?

• Bacteria: $-100$ to $-120\,\text{mV}$
• Skeletal muscle cells: $-95\,\text{mV}$
• Neurons: $-60$ to $-70\,\text{mV}$

In an initially electroneutral cell, if the efflux of $10^6\,K^+$ ions establishes a $V_m$ of $-100\,\text{mV}$, what will $V_m$ become if another $10^6\,K^+$ ions leave the cell?

$V_m$ becomes $-200\,\text{mV}$, because membrane potential is directly proportional to the amount of separated net charge ($Q$).

What is the difference between depolarization and hyperpolarization (repolarization)?

Depolarization occurs when $V_m$ becomes more positive (the intracellular side becomes more positive), whereas repolarization/hyperpolarization occurs when $V_m$ becomes more negative (the intracellular side becomes more negative).

What three major classes of stimulus-gated ion channels are depicted here that convert physiological stimuli into electrical signals?

1. Chemically-gated (ligand-gated) channels (e.g., Acetylcholine receptor / ACh)
2. Mechanically-gated channels (e.g., stretch-activated channels responding to physical pressure)
3. Temperature-gated channels (e.g., TRP channels responding to heat or cold)

What structural element in the voltage-sensor domain of the channel shown detects changes in $V_m$ to regulate pore opening?

The transmembrane helix $S4$, which contains positively charged amino acids ($++++$). When $V_m$ changes, the $S4$ helix moves like a lever, mechanically transmitting movement to the pore domain ($S5$, $S6$, selectivity filter) to open or close the channel.

Based on the illustrated diagram, what criterion determines whether a voltage-gated channel transitions from a closed state to an open state?

The channel transitions to the open state if the stimulus-induced membrane potential change brings the potential to or above the threshold voltage ($\text{resting } V_m + \Delta V_m \ge \text{threshold}$, here $-55\,\text{mV}$). If the new $V_m$ is below threshold, it remains closed.

What biological factor inherently alters the threshold voltage of a voltage-gated $Na^+$ channel?

The number of charges in the $S4$ domain (an intrinsic protein property), rather than the resting $V_m$ of the cell or the $\Delta V_m$ induced by the stimulus.

In terms of kinetic molecular principles, what does it mean when ion movement is described as 'spontaneous'?

It means the movement occurs solely due to the innate kinetic energy and random walk (random thermal collisions) of the ions without requiring external driving machinery.

In the diffusion system shown, if $1/6$ of ions randomly move across the boundary in either direction, how do 6,000 ions on the left and 600 ions on the right establish net flow and equilibrium?

• Left side: $6{,}000 \times \frac{1}{6} = 1{,}000$ ions move right.
• Right side: $600 \times \frac{1}{6} = 100$ ions move left.
• Net flow: $1{,}000 - 100 = 900$ ions move from left to right.
• Movement continues until concentration is equalized at $3{,}300$ ions on each side ($\Delta G = 0$).

How does an electric gradient produce net directional movement from the random walk of ions?

The membrane potential creates an electric field within the membrane. This electric field exerts an electric force described by Coulomb's law that biases the ions' random motion toward the direction of the force, driving net movement.

What formula defines the electrochemical gradient ($\Delta G$) for net movement of an ion from outside to inside a cell?

$\Delta G = RT \ln\left(\frac{C_{in}}{C_{out}}\right) + z F V_m$, where the first term is the chemical gradient and the second term is the electric gradient.

According to the second law of thermodynamics, what do negative, positive, and zero values of $\Delta G$ indicate for ion movement?

• $\Delta G < 0$: Occurs spontaneously because the process releases free energy from the system.
• $\Delta G > 0$: Cannot occur spontaneously because the process requires energy input.
• $\Delta G = 0$: The system is at equilibrium; forward and reverse processes occur at equal rates with no net driving force.

What are the three core thermodynamic insights regarding spontaneous ion movement and equilibrium?

1. Insight-1: Spontaneous ion movement always leads to a decrease of the system's free energy ($G$), continuing as long as it can decrease $G$.
2. Insight-2: Equilibrium is reached when the system's free energy is at its lowest under the specified condition.
3. Insight-3: Equilibrium is the ultimate outcome of spontaneous ion movement.

What does Insight-4 state regarding ion concentrations during changes in $V_m$?

Only a tiny fraction of ions (approximately $0.001\%$ or $10^6$ out of $10^{11}$ ions) crosses the membrane to establish a large voltage change (such as $-100\,\text{mV}$). Therefore, bulk ion concentrations change minimally ($C_{e,in} \approx C_{0,in}$ and $C_{e,out} \approx C_{0,out}$) while $V_m$ undergoes significant alterations.

True or False: During an action potential, the influx of $Na^+$ driving $V_m$ from $-70\,\text{mV}$ to $+30\,\text{mV}$ significantly increases the intracellular $Na^+$ concentration.

False. Only a negligible fraction of ions crosses the membrane to charge the capacitance, leaving the bulk intracellular $Na^+$ concentration virtually unchanged.

How is the Nernst equation derived from the electrochemical gradient equation at equilibrium ($\Delta G = 0$)?

At equilibrium, $\Delta G = 0 = z F V_{e,m} + RT \ln\left(\frac{C_{0,in}}{C_{0,out}}\right)$. Solving for $V_{e,m}$ ($E_{ion}$) gives the Nernst equation: $E_{ion} = -\frac{RT}{zF} \ln\left(\frac{C_{0,in}}{C_{0,out}}\right)$

Based on the resting neuron model shown, what are the intracellular and extracellular concentrations and relative permeabilities for $K^+$, $Na^+$, $Cl^-$, and $Ca^{2+}$?

• $K^+$: Intracellular $140\,\text{mM}$, Extracellular $4\,\text{mM}$, Permeability $1$
• $Na^+$: Intracellular $15\,\text{mM}$, Extracellular $145\,\text{mM}$, Permeability $0.05$
• $Cl^-$: Intracellular $4\,\text{mM}$, Extracellular $110\,\text{mM}$, Permeability $0.1$
• $Ca^{2+}$: Intracellular $0.0001\,\text{mM}$, Extracellular $5\,\text{mM}$, Permeability $0$

What are the equilibrium potentials ($E_{ion}$) for $Cl^-$, $K^+$, $Na^+$, and $Ca^{2+}$ in a neuron, and which ion is at equilibrium at a resting $V_m$ of $-70\,\text{mV}$?

• $E_{Cl} = -70\,\text{mV}$
• $E_K = -90\,\text{mV}$
• $E_{Na} = +50\,\text{mV}$
• $E_{Ca} = +137\,\text{mV}$ Only $Cl^-$ is at equilibrium because its Nernst potential equals the resting membrane potential ($-70\,\text{mV}$). All other ions are NOT at equilibrium.

What two mechanisms do cells use to balance ion movement and maintain a stable resting potential despite non-equilibrium conditions?

1. Make ion permeability zero ($0$) by closing channels (e.g., $Ca^{2+}$).
2. If permeability is not zero, invest metabolic energy to intervene via active transport (e.g., $Na^+/K^+$ ATPase using 1 ATP to export $3\,Na^+$ and import $2\,K^+$ against their electrochemical gradients so that ion influx equals ion efflux).

In a resting neuron with a resting potential of $-70\,\text{mV}$, in which directions do the chemical and electric gradients drive $K^+$?

The concentration (chemical) gradient drives $K^+$ out of the cell ($140\,\text{mM}$ inside vs. $4\,\text{mM}$ outside), while the electric gradient drives $K^+$ into the cell (negative interior attracts positive ions). Because $E_K = -90\,\text{mV}$, the chemical outward drive exceeds the electrical inward drive, causing net outward movement.

What occurs if additional $Na^+$ channels open in a resting neuron?

Additional $Na^+$ ions rush into the cell driven by both their inward chemical and electrical gradients, thereby depolarizing the membrane (making $V_m$ more positive).