The Autocell model
The autocell is a simple autocatalytic set (see diagram). A, B, D and E are the basic substrates. A and B combine together to form catalyst C, this relation is catalysed by F, where the synthesis of catalyst F by substrate D and E is catalysed by C. 12 F molecules can join together to form a polyhedral autocell. The autocell can enclose catalysts C and F.
In Deacon's original proposal, autocells occasionally break open, releasing catalyst molecules. If the other substrates are present, further autocells will be made.
We have shown that an autocell that had evolved the ability to break open in response to a molecule X, a sign of the presence of substrate, would reproduce more rapidly than a non-interpreting autocell.
We set up a system that contains both species of autocells. One has the ability to interpret the environment, the other does not.
The two types of autocells share one common substrate A. Since both species of autocells require substrate A, there is a competition between the two species. The non-interpretative Autocell is labelled as Fcell, and interpretative Autocell is labelled as Mcell.
We have modelled this competition in a pulsed system (see graph right), with substrates entering every 15s. Each pulse has a probability p(A) of containing A, and p(X) of containing X. The probabilities are not independent, i.e. P(A&X)≠P(A)P(X).
In order to enhance the competition, substrate A is designed to be limiting. All other substrates are at the same concentration in the pulse. The molecules constantly leave the system by diffusion. We asked how the competition between interpreting and non-interpreting autocells is affected by the relation between the sign X and the limiting substrate A.
Click following the link to see the equations used to model the interpretative autocell: Autocell_equations.pdf
Results
There are four possible scenarios for each cycle:
i) the pulse contains both A and X (first pulse, far left)
ii) the pulse contains X but no A (second pulse, left of centre)
iii) only A and no X (third pulse, right of centre)
iv) neither of the two (fourth pulse, far right).
The benefit of the interpretation depends on the "quality of the sign" - how reliable an indication of the presence of A is the presence of X. In our model is expressed as p(A|X). The figure on the right shows the invasion exponent (a measure of the efficiency of the mutated species at invading the resident population) of M as a function of p(A|X) for two different settings.
KcatX indicates how sensitive the interpretative autocell is to substrate X. At low KcatX competition by interpretative autocells (M) is weakly dependent of the quality of the sign. In sensitive autocells, the invasion exponent rises steeply with the quality of the sign, p(A|X).
These results confirm that acquisition of a capacity for responsiveness to a sign, X, that is probabilisitcally correlated with a particular state of the environment (in this case, presence of substrate) would offer a selective advantage to a simple proto-biotic entity.
In further research, Professor Niles Lehman and colleagues (see Investigators page) are attempting to synthesise a ribozyme capable of similarly interpreting its environment. Results of that investigation will be reported when available.
