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Screening of electrical interactions in salt solution (draft)

Page history last edited by Mark Eichenlaub 8 years, 2 months ago

So far we’ve considered two kinds of environments in which electrical interactions occur. We began with considering the electric forces and field produced by charged objects in vacuum. We found in this case that the electric field of a spherical charged object, such as an ion or a globular protein, depends on distance away according to 1/r2, and the corresponding electric potential depends on distance according to 1/r:

 

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(To obtain this expression for V, we choose the location of the zero of energy, which serves as the reference point for V, to be infinitely far away).

 

We also considered what happens to a very good conductor, such as a metal, placed in an external electric field (“external” just means its sources are outside the conductor). We reasoned there that charge will rearrange on the conductor so that the total electric field in the bulk of the object is zero — the field due to the rearranged charge perfectly cancels the external field. (“In the bulk” means everywhere in the material except right at the surface.) This happens because if there is a nonzero electric field in the bulk of the material, then that field exerts a force on the mobile charge carriers. These carriers therefore move until the external field and the field due to the rearranged mobile charge carriers add to zero everywhere inside the material. Once there is no field inside the material, and hence no force, there is no further rearrangement.

 

If instead we put a charged object into a metal — imagine embedding a positively charged particle right in the middle of a block of metal — then the electrons of the metal will cluster right around the positively charged particle in exactly the right amount and arrangement so that again there is no electric field on the metal. This will leave behind some positive charge on the surface of the metal, so there will be a field outside, but no field in the metal.

 

{Insert Picture}

 

Now in order to understand electrostatics at the molecular level in biology and biochemistry, we need to think about an intermediate situation between vacuum and a very good conductor. All of biochemistry and molecular biology takes place in salt water — water with a significant concentration of ions, but not nearly as high as the concentration of free electrons in metals.

 

In addition, in salt water, temperature matters. In metals, for reasons that require some pretty sophisticated physics to explain, we can ignore the thermal motion of electrons in conductors, and explain the electrical behavior of electrons in metals entirely in terms of electrical forces (later on when we study current flow through materials, we’ll find that the electrical resistance and conductance of metals does depend on temperature — but that is because of the thermal motion of the atomic nuclei, not the electrons). However, in salt water we have to take into account both the electrical forces on the dissolved ions, and the thermal energy that the water molecules and ions have that keeps them in steady motion. Even if two charged particles are attracted together electrically, thermal motion can separate them if the thermal energy is greater than the electric potential energy associated with keeping them together. In addition, we have to take into account effects of entropy.

 

Consequently, when a charged object, such as a protein (most proteins are negatively charged under physiological conditions) or a DNA molecule, is immersed in salt water, a process happens called screening or shielding. Let’s consider a negatively charged DNA molecule in salt solution. Without the DNA molecule, the salt solution will have equal concentrations of positive and negative ions everywhere, so that there are no electric fields. However, with the DNA molecule, positively charged ions are attracted to it and negatively charged ions repelled.

 

Without considering temperature and entropy, we’d expect the same scenario as with the charged object embedded in metal: positively charged ions would attach to the DNA molecule all along its length until it was electrically neutral. However, bringing these ions closer to the DNA molecule, we’ve eliminated the even distribution of positive and negative ions throughout the solution. That even distribution has the highest entropy and thus is the most entropically favored.

 

 

Consequently, what actually happens is shown in the figure (taken from Physical Biology of the Cell, p. 343). A “cloud” of positively charged ions clusters near the DNA, but there aren’t enough to completely neutralize the DNA. Thus outside the cloud, there is a weak electric field produced by the combination of the negatively charged DNA and this cloud of positively charged ions. This weak field in turn attracts in some more positively charged ions, and the field of these ions further reduces the electric field. The result is a high concentration of positively charged ions immediately adjacent to the DNA, and a decreasing concentration as distance from the DNA increases.

 

Not shown in the picture is that correspondingly, somewhere else there are extra negative ions. However, there is such an enormous volume of salt solution that can accommodate these extra negative ions that they can just spread out basically evenly and have very little effect.

This means that the electric field produced by a charged biological macromolecule in salt solution is VERY different from the electric field it would produce in vacuum. Instead of decreasing with distance according to 1/r2, we can see from this picture that the field should decrease more rapidly with distance, and at distances greater than the size of this collection of positive ions there should be no electric field at all.

 

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