Reaction, Diffusion and Dimensionality

As we have seen so far, biological cells are complex systems containing many different molecular species that interact with one another to form molecular complexes or entirely different molecular species. Biomolecular interactions may be conveniently described as chemical reactions, and, in fact, the cell itself can be regarded as a complex biochemical reactor, in which many reactions occur simultaneously. Some examples have already been introduced in previous chapters (see, e.g., the self-association of amphiphiles into micelles and membranes), with others yet to follow.

In the next section, we will lay down the classical framework for describing reaction kinetics. We will first consider that biochemical reactions take place in an aqueous solution (e.g., the cell cytosol), assumed to be homogenous, and that the chemical reaction of interest does not interfere with others taking place simultaneously in the same cellular volume. Many of these approximations do seem to break down under most circumstances in biological cells. In the second part of this chapter, therefore, we will relax some of the approximations, and will make use of fractal concepts to incorporate deviations of biological systems from the Euclidian geometry of smooth objects, which may impinge on the reaction kinetics inside the cell.