ABSTRACT
In the next two chapters, we take a much closer look at mathematical modelling of a particular biological system. The system we choose to examine is perhaps the most basic of all such systems – a single cell. In this chapter we will focus on the necessary physiological background; in the next we turn to the mathematical models. A cell basically consists of three parts: inside (intracellular), boundary (the membrane) and outside (extracellular). Both the intracellular and extracellular media are fluids with many free ions (i.e. electrically charged particles). The cell membrane is selectively permeable, with varying degrees of permeability to some of these ions, and so an electrical potential difference across the cell membrane will be established, as some of these positively or negatively charged particles are allowed to move across the boundary. By convention, the extracellular fluid is electrical ground (i.e. it has a potential of 0 V) and the intracellular medium will typically have a potential (relative to extracellular) of up to ±100 mV. The basic system is depicted in Fig. 5.1. Hence, the cell is essentially an imperfect boundary separating two sepa-
rate collections of chemicals such that these chemicals can pass across that boundary via various mechanisms. The net effect of these chemicals moving about is that, because of the electrical charges associated with the chemical species (these are ions and cations, rather than complete molecules), there is a net movement of charge across the cell boundary and the electrical balance between the inside and the outside of the cell is affected by this redistribution of chemical species. Of course, the human body, along with every living organism, is made up
of various different sorts of cells. For the sake of definiteness, we will focus on one particular type of cells: neuron. The brain consists of a very large (about 1012) number of cells of a very large (about 103) number of different types, Nonetheless, the cells in the human brain fall into two basic types: neuroglial cells and neurons. Neuroglial cells (as far as we are concerned here) have no significant function. Despite making up about one-third of the cells in the brain there is no definitive description of their functional role. Neurons, on the other hand, are the stuff that makes us us. These are the
Figure 5.1: A model cell. Basic caricature of the structure of a cell.
