First Steps Toward Emergence of Life Theory

By Stephen Sadler

What turned a primordial mixture of amino acids and proteins into the first organized, self-replicating unit? What was it that breathed the vital breath into a collection of inanimate chemical building blocks, giving rise to an unbroken chain of evolution stretching three and a half billion years into the future and culminating in us?

For many years Kauffman has studied the mathematics behind groups of molecules known as ‘autocatalytic sets’. These sets of molecules and their associated chemical reactions are special because they form self-sustaining systems which, given a ‘food source’ of simple molecules, are able to form more complex molecules which themselves catalyse, or speed up, reactions which give rise to other molecules in the set. In this way, they form “functionally closed” structures (see Figure 1) that speed up the production of the members of the set, promoting the existence of the set as a whole.

Figure 1: an example of an autocatalytic set. Black dots represent molecules in the set, whilst white boxes represent reactions. Solid arrows stand for reaction inputs and outputs, and dashed arrows indicate catalysis. Because each arrow ends on a molecule in the group, the group is said to be “functionally closed”.

To see what all this has to do with life, we must define what we mean by “life”. Whilst definitions vary, most share some common themes, for example: self-organisation, self-replication, and the ability to evolve with successive generations. Kauffman himself has defined a living organism as “an autonomous agent or a multi-agent system capable of reproducing itself or themselves, and of completing at least one thermodynamic work cycle” [1].

So could autocatalytic sets fulfil these criteria? Almost by definition their existence promotes the proliferation of their constituents, which sounds remarkably like self-replication. Their closed structure and well-defined flow of reactants and catalysts through reactions also sounds like it might fulfil the self-organisation criterion. But can they evolve? It is this question that Kauffman’s latest work addresses.

The group studied the mathematical properties of autocatalytic sets and made the remarkable discovery that any given set can be decomposed into so-called ‘irreducible autocatalytic sets’. What’s more, the number of irreducible autocatalytic sets that any larger autocatalytic set can be decomposed into rises exponentially with the size of the larger set. Since these sets overlap to some degree, they can be said to be mutually dependent, and it is not too much of a leap of faith to imagine them beginning to behave as the elements of a ‘meta autocatalytic set’.

“In other words, self-sustaining, functionally closed structures can arise at a higher level (an autocatalytic set of autocatalytic sets), i.e., true emergence,” the group say.

The combining and splitting of these functionally-closed, self-replicating entities can, according to the group’s paper, give rise to inheritance, mutation and competition. In other words: evolvability.

However, the authors don’t stop there. Is it too far fetched, they ask, to “consider a complete cell as an (emergent) autocatalytic set?” And if not, then why not think “of the collection of bacterial species in your gut (several hundreds of them) as one big autocatalytic set”? Going one step further, could the theory not be applied to ecology to describe any mutually dependent set of organisms, they ask? Could the economy not be viewed as an autocatalytic set, with its processes (reactions) assembling complex structures out of more simple ones (reactants), facilitated by tools, factory production lines and humans (catalysts)?

These are big ideas and, by the authors’ own admission, rather speculative, but with the tantalising possibility of a single theory to explain the phenomena of emergence, functional organisation and the origin of life, it seems difficult to disagree with them when they conclude: “we believe that these ideas are worth pursuing and developing further”.

A preprint version of the group’s paper can be found at

[1] 2004, “Autonomous Agents”, in John D. Barrow, P.C.W. Davies, and C.L. Harper Jr., eds., Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity, Cambridge University Press.