The Physical Chemistry of Self Organization

Self organization is a general phenomenon that occurs in many particle systems that are defined as active media. Such systems can be generally described by reaction-diffusion equations for their individual components i  

A catalytic example is provided by the autocatalytic reaction scheme in which x multiplies  

It provides a simple model case that illustrates formation of spatio-temporal patterns due to such finite-amplitude perturbations. 

In the Gray-Scott model PI of this system, both reactions are considered to be irreversible. This reaction scheme is a simplification of the autocatalytic model of the glycolysis cycle (see Chapter 7). A is a feed term and B an inert product. PearsonI °l has shown that as a function of kinetic and diffusion parameters this system leads to the formation of local regions of concentration defined by sharp boundaries. These local regions take on cell-like characteristics, thus undergoing multiplication and division behavior. We discuss some of the results in detail, also because of the discussion in the next chapter on self replication and the origin of protocellular systems. As a function of feed (F) and rate parameter (fc), a state phase diagram can be constructed (see Fig. 8.5). 

Two areas can be identified one with three steady states and another area to be characterized as excitable. At the boundary of the two time regimes transient patterns form in response to a small disturbance. In this unstable region a particularly interesting phenomenon is observed that behaves like cell multiphcation. Patterns occur with concentration profiles of cellular form that grow and rephcate. When these cells exceed a particular dimension, the interior destabilizes (in this case because a necessary concentration gradient is not maintained) and cells divide. 

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