Chapter 19, Problem 104FP

Interpretation Introduction

(a)

Interpretation:

The capacitance of the membrane for the typical cell needs to be described.

Concept introduction:

The capacitance can be calculated as follows:

$C=\frac{{\epsilon }_0\epsilon A}{I}$

Here,

C − capacitance

e₀ − dielectric constant of a vacuum

e₀ e− dielectric constant of the membrane

A- Surface area of the membrane

I − membrane thickness

Interpretation Introduction

(b)

Interpretation:

The net charge required to maintain the observed membrane potential should be determined.

Concept introduction:

The observed Nernst potential across the cell wall is 0.085 V.

Interpretation Introduction

(c)

Interpretation:

Number of K⁺ ions must flow through the cell membrane to produce the membrane potential should be determined.

Concept introduction:

In most cells K⁺ concentration inside the cell is greater than the outside. Therefore, there is a stable concentration gradient across the cell membrane. If potassium channels open, K⁺ starts to diffuse to outside because of concentration gradient. As a result, excess of positive charge on the outside of the cell is built up and inside of the cell become more negative relative to outside. This sets up a electric potential difference across the membrane. This electric potential difference makes the remaining K⁺ to leave the cell. Finally, the electric potential difference across the membrane achieve a maximum level where the electric force driving K⁺ back to the cell is equal to the chemical force on K⁺ towards outside of the cell. At this point there is no net movement of K⁺.

Interpretation Introduction

(d)

Interpretation:

Number of K⁺ ions in the typical cell should be determined.

Concept introduction:

In most cells K⁺ concentration inside the cell is greater than the outside. Therefore, there is a stable concentration gradient across the cell membrane. If potassium channels open, K⁺ starts to diffuse to outside because of concentration gradient. As a result, excess of positive charge on the outside of the cell is built up and inside of the cell become more negative relative to outside. This sets up an electric potential difference across the membrane. This electric potential difference makes the remaining K⁺ to leave the cell. Finally, the electric potential difference across the membrane achieve a maximum level where the electric force driving K⁺ back to the cell is equal to the chemical force on K⁺ towards outside of the cell. At this point there is no net movement of K⁺.

Interpretation Introduction

(e)

Interpretation:

It should be shown that the fraction of the intracellular K⁺ ions transferred through the cell membrane to produce the membrane potential is so small and it does not change K⁺ concentration within the cell.

Concept introduction:

In most cells K⁺ concentration inside the cell is greater than the outside. Therefore, there is a stable concentration gradient across the cell membrane. If potassium channels open, K⁺ starts to diffuse to outside because of concentration gradient. As a result, excess of positive charge on the outside of the cell is built up and inside of the cell become more negative relative to outside. This sets up an electric potential difference across the membrane. This electric potential difference makes the remaining K⁺ to leave the cell. Finally, the electric potential difference across the membrane achieve a maximum level where the electric force driving K⁺ back to the cell is equal to the chemical force on K⁺ towards outside of the cell. At this point there is no net movement of K⁺.