How is it that ionic diffusion is independent of other ions?
Most importantly, the whole Goldman-Hodgkin-Katz model is, well, a model. It is a way we would like to find and explain phenomena, given pen and paper.

Often, scientists build models in order to explain data in hand, but even then, they will have to add something from their imagination. For example, early astronomers saw planets moving differently from stars, and came up with the idea that, you know, planets do not circle the earth, but maybe around some points in space, which in turn circle the earth. That didn't work well, so they created the heliocentric model, where planets and the Earth circled the sun. That was still perfectible, and Newton suggested the planets do not move on circles, but on ellipses. Each generation of astronomers had almost the same data in hand, but chose to make some assumptions in their models.

The same goes with the lack of interaction between potassium and sodium ions: it is a theoretical assumption. As models go, the GHK model is quite good, because it fits experimental findings better than any other model. Its assumptions have a great chance of being true, of reflecting the physical world. I guess you really asked what are the physical facts that underlie the assumption of ion independence. The fact is, you are looking for explanations for a fact that may be or may not be - so any response you will receive is, to a degree, speculation.

My thought is that the number of water molecules (55 molar) that may collide with an ion is far greater than the number of cations (up to a few hundred nanomolar, about 100 million rarer). Perhaps the number of ion-ion collisions is negligible. There is one bottleneck, in the actual channels, but there different species do not meet, because each has its own channels.

Another, more factual, is that the model is imperfect, and independence is more of a wish than a complete truth. Quoting from http://books.google.com/books?id=SmJoSwnwSh0C&amp;lpg=PA353&amp;ots=3fvI19Sk5Q&amp;dq=ghk%20ion%20independence%20fails&amp;pg=PA353#v=onepage&amp;q&amp;f=false : "The rich literature on how ion channels fail to obey the independence principle is reviewed in Chapter 14 of Hille (1991), and some specific models will be studied in the following chapter."