3 The Minimal Model

The original computational model of autopoiesis was presented in the form of a detailed, natural language, algorithm [46, Appendix]. This algorithm is reviewed and critiqued, in detail, in [27]. I will return to that critique in due course, but first it is important to have a general, qualitative, view of the model, and the phenomenology it is intended to exhibit.

The chemistry takes places in a discrete, two dimensional, space. Each position in the space is either empty or occupied by a single particle. Particles generally move in random walks in the space. There are three distinct particle types, engaging in three distinct reactions (see Figure 1):

Production: Two substrate (S) particles may react, in the presence of a catalyst (K) particle to form a link (L) particle.
Bonding: L particles may bond to other L particles. Each L particle can form (at most) two bonds, thus allowing the formation of indefinitely long chains, which may close to form membranes. Bonded L particles become immobile.
Disintegration: An L particle may spontaneously disintegrate, yielding two S particles. When this occurs any bonds associated with the L particle are destroyed also.

Chains of L particles are permeable to S particles but impermeable to K and L particles. Thus a closed chain, or membrane, which encloses K or L particles effectively traps such particles.

The basic autopoietic phenomenon predicted for this system is the possibility of realising dynamic cell-like structures which, on an ongoing basis, produce the conditions for their own maintenance. Such a system would consist of a closed chain (membrane) of L particles enclosing one or more K particles. Because S particles can permeate through the membrane, there can be ongoing production of L particles. Since these cannot escape from the membrane, this will result in the build up of a relatively high concentration of L particles. On an ongoing basis, the membrane will rupture as a result of disintegration of component L particles. Because of the high concentration of L particles inside the membrane, there should be a high probability that one of these will drift to the rupture site and effect a repair, before the K particle(s) escape, thus re-establishing precisely the conditions allowing the build up and maintenance of that high concentration of L particles.

A secondary phenomenon which may arise is the spontaneous establishment of an autopoietic system from a randomised initial arrangement of the particles.

Both these phenomena were reported and illustrated in the original paper.

One specific weakness of this original model deserves mention here. This is that the K component is not itself produced by any reaction in the putatively autopoietic system. Prima facie this appears to violate the demand for closure in the processes of production. The paper itself is somewhat confusing on this point. A ``six-point key'' is provided for determining whether any given entity is autopoietic. Point 6 of this first appears to require that all components should, indeed, be produced by interactions among the components; but immediately equivocates by allowing some exceptions to this if the relevant components ``participate as necessary permanent constitutive components in the production of other components'' [46, p. 193]. This does appear somewhat clumsy. On the other hand, there must surely be some exceptions allowed (specifically, covering the case of the S particles which are simply harvested from the environment). In any case, as will be discussed later, more recent elaborations of this original model have specifically allowed for production of the K particles [1], so there is no fundamental difficulty here.

Barry.McMullin@dcu.ie