Question

Ion Channel Selectivity Potassium channels consist of four subunits that form a channel just wide enough for \(\mathrm{K}^{+}\) ions to pass through. Although \(\mathrm{Na}^{+}\)ions are smaller \(\left(M_{z} 23\right.\), radius \(0.95 \AA\) ) than \(K^{+}\)ions \(\left(M_{\mathrm{r}} 39\right.\), radius \(\left.1.33 \bar{A}\right)\), the potassium channels in the bacterium Streptomyces Lividans transport 104 times more \(\mathrm{K}^{+}\)ions than \(\mathrm{Na}^{+}\)ions. What prevents \(\mathrm{Na}^{+}\)ions from passing through potassium channels?

Short answer

\(\mathrm{Na}^+\) ions are not efficiently dehydrated within the channel, making their passage energetically unfavorable.

Step-by-step solution

Understanding the Ion Properties

Begin by examining the properties of the sodium (\(\mathrm{Na}^+\)) and potassium (\(\mathrm{K}^+\)) ions. The sodium ion has a molar mass \(M_r\) of 23 and a radius of 0.95 \(\text{Å}\), whereas the potassium ion has a molar mass \(M_r\) of 39 and a radius of 1.33 \(\text{Å}\). Despite \(\mathrm{Na}^+\) ions being smaller, they are not favored for transport through potassium channels.

Discussing the Potassium Channel Structure

Potassium channels comprise four subunits that form a narrow opening. This channel is specifically sized to accommodate the \(\mathrm{K}^+\) ions. The size and shape of this opening are crucial because they play a significant role in the selectivity against smaller \(\mathrm{Na}^+\) ions.

Analyzing Ion Selectivity Mechanism

Ion selectivity is often due to the energetic cost of dehydration and rehydration of ions. \(\mathrm{K}^+\) fits perfectly within the channel, allowing it to be efficiently dehydrated and then rehydrated after passing through. \(\mathrm{Na}^+\), though smaller, does not fit well due to its different radius and charge density, making dehydration and rehydration inefficient and energetically unfavorable.

Drawing Conclusion from Selectivity

The inability of \(\mathrm{Na}^+\) ions to pass through the potassium channels is primarily due to the channel's specific structural compatibility with \(\mathrm{K}^+\) ions. An energetic barrier prevents \(\mathrm{Na}^+\) from efficiently passing through due to the high energetic cost of removing its hydration shell fully within the channel confines.

Key concepts

Understanding Potassium Channels

Potassium channels are fascinating structures that form pathways for \(\mathrm{K}^{+}\) ions to traverse cell membranes. These channels are unique because they consist of four protein subunits, which collectively create a pore just the right size for potassium ions. This precise size is crucial because it ensures the selectivity of the channel, allowing mainly \(\mathrm{K}^{+}\) ions to pass through while excluding others.

What's truly remarkable is that even though \(\mathrm{Na}^{+}\) ions are smaller than \(\mathrm{K}^{+}\) ions, the channel's specialized structure is adept at preventing them from passing. Think of it like a lock designed to fit only one particular key. It demonstrates the channel's innate ability to discriminate precisely based on ion size and the chemical characteristics of the channel walls.

Potassium channels showcase the principle of form follows function. Their exact architecture and size are vital for maintaining cellular function and signaling.

Ion Properties and Selectivity

The properties of ions play a crucial role in determining which can pass through specific channels. In our scenario, the potassium ion \(\mathrm{K}^{+}\) is larger, with a radius of 1.33 Processes dependent on these properties include the dehydration and rehydration that ions undergo when they pass through a channel.

The sodium ion \(\mathrm{Na}^+\) is smaller, with a radius of 0.95 Yet, this smaller size doesn't equate to easier passage through the potassium channel. There's more to the story than mere size. The charge density and how easily their hydration shells can be removed and replaced as they move through the channel also matter. This plays a significant role in whether ions can pass through channels efficiently and accurately.

Understanding these properties helps explain why \(\mathrm{K}^{+}\) ions are preferentially transported over \(\mathrm{Na}^{+}\) ions despite size differences.

Energetic Cost of Dehydration

A vital concept in ion selectivity is the energetic cost of dehydration. Ions in solution don't move naked; they are surrounded by water molecules. These water molecules must be stripped away—a process known as dehydration—before the ion can enter the channel.

For \(\mathrm{K}^{+}\) ions, this dehydration is energetically more favorable compared to \(\mathrm{Na}^+\). The potassium channel's architecture supports this by providing an environment that fits the dehydrated \(\mathrm{K}^{+}\) ion perfectly. On the other hand, the smaller \(\mathrm{Na}^+\) ions can't achieve this favorable interaction due to their size and a higher charge density that requires a larger energy input for dehydration.

This higher energy cost makes \(\mathrm{Na}^{+}\) ions less likely to pass through the channel effectively. Thus, the energetic cost of dehydration is a critical factor that influences the selectivity of potassium channels.

Mechanisms of Ion Selectivity

Ion selectivity in channels is a brilliant biological mechanism that ensures cells only let in what they need. For potassium channels, this selectivity is achieved through a combination of mechanisms.

Firstly, the specific size of the channel pore matches the dehydrated size of \(\mathrm{K}^{+}\) ions, allowing them to move with minimal resistance. Secondly, the channel has a specific lining that interacts favorably with \(\mathrm{K}^{+}\) ions once they're inside, supporting their movement through.

• Size compatibility: The channel only fits \(\mathrm{K}^{+}\), effectively excluding \(\mathrm{Na}^{+}\).
• Charge distribution: The charge and orientation within the channel make it energetically favorable for \(\mathrm{K}^{+}\) to pass through.
• Energy efficiency: The dehydration and subsequent rehydration are energetically efficient for \(\mathrm{K}^{+}\), but not for \(\mathrm{Na}^{+}\).

By combining these features, potassium channels ensure that \(\mathrm{K}^{+}\) ions are favored over \(\mathrm{Na}^{+}\), illustrating a highly selective biological process that balances structural fit with energetic considerations.