91Ó°ÊÓ

Resting Membrane Potential A variety of unusual invertebrates, including giant clams, mussels, and polychaete worms, live on the fringes of deep-sea hydrothermal vents, where the temperature is \(60^{\circ} \mathrm{C}\) (a) The adductor muscle of a giant clam has a resting membrane potential of \(-95 \mathrm{mV}\). Given the intracellular and extracellular ionic compositions shown below, would you have predicted this membrane potential? Why or why not? $$\begin{array}{lcc} & \multicolumn{2}{c} {\text { Concentration (mu) }} \\ \\)\cline { 2 - 3 }\\( \text { Ion } & \text { Intracellular } & \text { Extracellular } \\ \hline \mathrm{Na}^{+} & 50 & 440 \\ \mathrm{K}^{+} & 400 & 20 \\ \mathrm{Cl}^{-} & 21 & 560 \\ \mathrm{Ca}^{2+} & 0.4 & 10 \\ \hline \end{array}$$ (b) Assume that the adductor muscle membrane is permeable to only one of the ions listed above. Which ion could determine the \(V_{\mathrm{m}} ?\)

Step by step solution

01

Understanding the Nernst Equation

The Nernst equation helps predict the equilibrium potential for an ion based on its concentrations inside and outside the cell. It is given by:\[ E_\text{ion} = \frac{RT}{zF} \ln \left( \frac{[\text{ion}]_\text{outside}}{[\text{ion}]_\text{inside}} \right) \]At physiological temperature, this equation simplifies to:\[ E_\text{ion} = \frac{61}{z} \log \left( \frac{[\text{ion}]_\text{outside}}{[\text{ion}]_\text{inside}} \right) \]where:- \(R\) is the universal gas constant,- \(T\) is the temperature in Kelvin,- \(z\) is the charge of the ion,- \(F\) is the Faraday constant.

02

Calculate Membrane Potential for Each Ion

We need to calculate the membrane equilibrium potential for each ion using the Nernst equation at \(60^{\circ} C\). This temperature converts to \(333\) K in Kelvin. However, we will still use the simplified constant for physiological temperature (61 mV).### Potassium \( (K^+) \):\[ E_{K^+} = \frac{61}{+1} \cdot \log \left( \frac{20}{400} \right) \approx -91 \text{ mV} \]### Sodium \( (Na^+) \):\[ E_{Na^+} = \frac{61}{+1} \cdot \log \left( \frac{440}{50} \right) \approx +65 \text{ mV} \]### Chloride \( (Cl^-) \):\[ E_{Cl^-} = \frac{61}{-1} \cdot \log \left( \frac{560}{21} \right) \approx -89 \text{ mV} \]### Calcium \( (Ca^{2+}) \):\[ E_{Ca^{2+}} = \frac{61}{+2} \cdot \log \left( \frac{10}{0.4} \right) \approx +69 \text{ mV} \]

03

Analyzing the Results

From the calculations, the equilibrium potential closest to the given membrane potential of \(-95\) mV is for \(K^+\), which is \(-91\) mV. This suggests that the resting membrane potential (V_{m}) is predominantly determined by the permeability to \(K^+\).

04

Short Answer

The resting membrane potential of \(-95\) mV aligns with predictions based on potassium permeability, as \(E_{K^+}\) is \(-91\) mV.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nernst equation

The Nernst equation is a tool used in biology to determine the equilibrium potential of an ion across a membrane. It relies on the concentration difference of that particular ion inside and outside the cell. This equation helps explain the electrical potential needed to balance an ion's concentration gradient, thus preventing further net movement. The general form is: \[ E_{\text{ion}} = \frac{RT}{zF} \ln \left( \frac{[\text{ion}]_{\text{outside}}}{[\text{ion}]_{\text{inside}}} \right) \] Here,

• \( R \) is the universal gas constant.
• \( T \) is the temperature in kelvin.
• \( z \) is the charge of the ion.
• \( F \) is the Faraday constant.

At physiological temperatures, this equation simplifies to: \[ E_{\text{ion}} = \frac{61}{z} \log \left( \frac{[\text{ion}]_{\text{outside}}}{[\text{ion}]_{\text{inside}}} \right) \] Make sure to note that it's important for the ion distribution to maintain its gradient for proper cell function.

Membrane permeability

Membrane permeability refers to how easily ions can pass through the cell membrane. This concept plays a crucial role in determining the resting membrane potential. Although each ion has a specific equilibrium potential, the actual membrane potential depends on which ions the membrane is most permeable to. For example, if a membrane is mostly permeable to potassium ( \( K^+ \)), then the resting potential will be close to the equilibrium potential of \( K^+ \).Different factors affect membrane permeability:

• The specific ion channels present in the membrane.
• The number of ion channels open at any given time.
• The size and charge of the ion, as larger or charged ions need specific channels to pass through.

Understanding ion permeability ensures you know why certain ions dominate the resting membrane potential of a cell.

Ionic concentration gradients

Ionic concentration gradients refer to the difference in ion concentration across the membrane, typically with higher amounts of certain ions on one side compared to the other. Cells maintain these gradients using ion pumps and channels, which are vital for creating the cell's electrical potential. For instance:

• Sodium ( \( Na^+ \)) is usually more concentrated outside the cell.
• Potassium ( \( K^+ \)) is generally concentrated inside the cell.
• Chloride ( \( Cl^- \)) has a higher concentration outside the cell.
These gradients are important because they create an energy potential across the membrane. This potential is harnessed to transmit signals in nerve cells and drive active transport mechanisms in other cells. Maintaining these gradients is essential for processes like muscle contraction and neuron signaling.

Equilibrium potential

Equilibrium potential is the membrane potential at which there is no net movement of a particular ion in or out of the cell. This situation comes about when the electrical gradient (resulting from the charge difference across the membrane) exactly balances out the concentration gradient. The equilibrium potential for an ion is calculated using the Nernst equation. Let's explore why understanding equilibrium potential is important:

• It determines the charge the membrane must hold to stay at rest concerning that ion.
• It hints at which ion might dominate the resting membrane potential if other conditions are optimal.
• It helps in predicting how ions will move when channels open.

In practice, this means knowing the equilibrium potential helps explain what happens when a membrane suddenly becomes permeable to different ions, such as during a nerve impulse. Remember, only when the membrane's permeability to that specific ion predominates will the resting potential align closely with its equilibrium potential.