Dielectric constant and plasma membrane

[nobahar]

Hello!

Electric force is inversely proportional to the dielectric constant. In a textbook, this is said to be forty-fold greater for water than the phospholipid membrane. As such, ions are unlikely to cross the plasmamembrane. I assume this has something to do with preferring to stay in water. Here's the thing, this is force, and not energy. Okay, the two are related (from my limited understanding), but not the same. Why would a reduced force between ions lead to the inability of ions to cross the membrane? If the dielectric constant is lower in the plasmamembrane, then the force is greater between ions. I am guessing an increased force means that like charges trying to accumulate to interact ith opposite charges will be unstable? Or something...
There's something obvious I'm missing here.
Maybe its that to separate charges to partition the ion into the membrane would require more energy than is available?
Any help appreciated.

 

[mishrashubham]

Okay, the two are related (from my limited understanding), but not the same. Why would a reduced force between ions lead to the inability of ions to cross the membrane?

It doesn't. You are right, it has got to do with hydrophobicity and hydrophilicity. The selectively permeable nature of the cell membrane arises because of this property. Small hydrophobic substances get through relatively easily while charged ones like ions can only enter through channels.

I am guessing an increased force means that like charges trying to accumulate to interact ith opposite charges will be unstable?

That does happen. You can think of accumulation of the plasma membrane as similar to a capacitor. Connecting a capacitor to a cell causes a buildup of charge on the plates although the rate of addition keeps decreasing due to increase in voltage between the plates.

Similarly the positively charged ions pass through ion specific channels on the membrane that causes charge to buildup on either side of the membrane gradually increasing the voltage until it stops entirely. The graph looks something like this


http://www.kpsec.freeuk.com/images/charge.gif

 

[atyy]

The dielectric constant is a measure of how polarizable a substance is: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html.

An ionic substance tends to dissolve better in a polar substance, because the local charge of the polar substance can substitute for one of the opposite charges in the ionic substance, making it easier for a charge to move through the polar substance.

The lipid bilayer is polar. However, the hydrocarbon tail which a charge has to cross first is very non-polar, and so ions don't readily dissolve in it.

 

[Andy Resnick]

The OP's post is very confusing- ions do not passively diffuse though the cell membrane- there are channel and transporter proteins to control the flow of material. Ion channels can be selective by using the hydration radius: for example, Na+ and K+ have different hydration radii, and so a channel can pass one but not the other. Paracellular transport is passive diffusion, but the OP does not seem to be talking about that.

There are also water channels, glucose transporters, and the whole endocytosis/exocytosis mechanism.

 

[nobahar]

Thanks for the responses. Atyy's repsonse makes sense to me: the ions have a shell of hydration, and would have to shed this shell in order to partition into the membrane. The hydrocarbon chains, however, cannot substitute fore the electrostaticc interactions between the ions and water, and so energy would be needed to put into shed the shell of hydration with nothing to replace this interaction. This would cost energy.
My issue is with what the textbook says about force. It says that force is inversly proportional to the dielectric constant. As such, water, which has a higher dielectric constant, would mean a lower force than a membrane, which has a lower dielectric constant. So the ions express a higher electric force in the membrane. Why then, is it not able to parition into the membrane. What is the connection here? Perhaps it is the extra force means a higher energy state: is there a need to put energy in in order to generate an increase force of attraction (and repulsion) between ions? This would certainly link the two concepts.

 

[atyy]

The force that is being talked about is the force between the two oppositely charged plates of a capacitor. If the intervening medium has a large dielectric constant, it is highly polarizable, and the induced polarization can partially "cancel" the local charge on the capacitor plates. Since the local charge is effectively reduced, the effective field and force between the capacitor plates is also reduced. The link in post #3 explains this in more detail.

So the relationship between the dielectric constant and force reduction between capacitor plates and low ionic solubility are both explained by the idea that the dielectric constant is related to a material's polarizability.

 

[mishrashubham]

So the ions express a higher electric force in the membrane. Why then, is it not able to parition into the membrane.

No, the force is not inside the membrane. Like atyy said, it is the force between the two plates of a charged capacitor. The two sides of a plasma membrane can act like the two plates of a capacitor.

What happens when we insert a dielectric between the plates is something like this.

The polarization of the dielectric generates an opposing electric field causes the net field to be less than what it would have been, had it not been there at all. The dielectric constant can be in fact expressed as the ratio of the field before to the field after inserting the dielectric.

 

[nobahar]

Thanks!
I have posted yet another question on cell membranes and circuits...