Representing charges in computer programming

I'm preparing for a thesis in computer science on calculations based on concepts from Neuroelectrodynamics.

In short this theory states, that information transfer is not done by spike time coding, but by movement of electric charges. Also this charges affect (and get affected by) proteins in the brain cells, so the cells can act as a kind of memory

How can electric charges be represented in terms of programming? Do you have to simulate each and every ion or are there overall principles so you can calculate with "whole" charges? I could imagine Circuit simulations already implement some calculations with electrodynamics.

I assume there are already computation systems, but I didn't know what to look for.

Also, I'm quite new to the field of electrodynamic. Which book can you recommend on this topic?

• is there a pre-existing model you're looking to implement, or are you developing a model of your own? certainly if you want to model ions/charges moving around, there must be some kind of structural constraints. the particulars of that structure may steer your implementation one way or another. (the maxwells-equations tag seems like a shot in the dark) – JustJeff Dec 16 '11 at 0:45
• No, not really. I want to take a look at particle swarm optimization and see if I can modify it for my purposes. My ultimate goal would be to prove that a computational unit based on the new findings outperforms Integrate&Fire + STDP – user390 Dec 16 '11 at 19:39

As a general rule, when dealing with "big" things like cells, you shouldn't simulate the individual charged particles. A useful abstraction is charge density, the charge per unit volume, usually denoted $\rho$. The equations of electrodynamics can be formulated in terms of this charge density $\rho$ and the current density ${\bf J}$.