Question

Suppose that the change in V\(_m\) was caused by the entry of Ca\(^{2+}\) instead of Na\(^+\). How many Ca\(^{2+}\) ions would have to enter the cell per unit membrane to produce the change? (a) Half as many as for Na\(^+\); (b) the same as for Na\(^+\); (c) twice as many as for Na\(^+\); (d) cannot say without knowing the inside and outside concentrations of Ca\(^{2+}\).

Short answer

(a) Half as many as for Na\(^+\).

Step-by-step solution

Understand the question

We need to determine how the entry of Ca\(^{2+}\) ions affects the change in membrane potential \(V_m\) in comparison to Na\(^+\) ions. Different options are given based on how many Ca\(^{2+}\) ions are needed relative to Na\(^+\).

Recall the charge difference

Ca\(^{2+}\) ions have a charge of +2, compared to Na\(^+\) ions which have a charge of +1. This means each Ca\(^{2+}\) ion carries double the charge compared to each Na\(^+\) ion.

Determine required ions

Since Ca\(^{2+}\) is doubly charged, the entry of one Ca\(^{2+}\) ion would produce the same charge difference as two Na\(^+\) ions. Therefore, half as many Ca\(^{2+}\) ions are needed to effect the same change in \(V_m\) as Na\(^+\) ions.

Key concepts

Calcium Ions

Calcium ions, denoted as Ca\(^{2+}\), are positively charged ions that play a crucial role in various cellular processes. These ions carry a positive charge of +2, which means they are doubly charged compared to other common cations like sodium ions. This double charge is significant in the context of membrane potential, as it impacts how these ions influence charge distribution and changes in potential.

In cellular environments, calcium ions are often found in low concentrations inside cells but higher concentrations outside. This gradient is essential for signal transduction and muscle contraction. When calcium ions enter a cell, they can trigger various responses, such as the release of neurotransmitters or the initiation of muscle contraction.

Sodium Ions

Sodium ions, or Na\(^+\), are fundamental to maintaining the cell's resting membrane potential and facilitating action potentials. With a single positive charge, sodium ions are involved in transporting other ions or molecules across cell membranes.

In neurons, the rapid influx of sodium ions during an action potential leads to depolarization, a critical step in the transmission of nerve impulses. Sodium-potassium pumps work to maintain a high concentration of sodium ions outside cells and potassium ions inside, which is vital for various cellular functions.

• Sodium ions have a +1 charge.
• Key players in nerve impulse transmission.
• Integral to maintaining balance in ion concentrations and membrane potential.

Ion Concentration

Ion concentration refers to the amount of specific ions present in and around a cell. This concentration plays a pivotal role in determining the membrane potential, which is essentially the voltage difference across a cell's membrane.

The membrane potential is influenced by the differential distribution of ions like calcium and sodium across the membrane, as quantified by the Nernst equation. This equation considers the intracellular and extracellular concentrations of ions to calculate the equilibrium potential.

Changes in ion concentration can lead to alterations in membrane potential, thereby impacting cellular activities such as muscle contraction, nerve firing, and the opening or closing of ion channels.

Electrochemical Gradient

The electrochemical gradient is a combination of two forces: the chemical gradient and the electrical gradient. It drives the movement of ions across membranes.

The chemical gradient refers to the difference in ion concentration between the inside and outside of the cell, whereas the electrical gradient is the difference in charge across the membrane.

• Driving force for ion movement.
• Maintains crucial cellular activities.
• Essential for establishing membrane potential.

These gradients are at the heart of many physiological processes, including the transmission of nerve impulses and the operation of cardiac muscles. By maintaining a balance between these gradients, cells can ensure proper function and responsiveness to external stimuli.