I’ve made a short movie showing autocatalytic sets arising in a dynamical simulation of a simple polymer model. It shows how autocatalytic subsets appear, one after another, and then grow in concentration. This provides a nice visual and dynamical example of our usually more graph-theoretical analyses.
For a gentle (but fairly complete) introduction to autocatalytic sets, please see my pop-sci article in The Scientist from last year. In that article, the phenomenon that autocatalytic sets often consist of a hierarchical structure of autocatalytic subsets was illustrated with an image adapted from our original publication in the Journal of Systems Chemistry (2012):
This image shows an autocatalytic set (or RAF set, in our formal terminology) that was found by our RAF detection algorithm in an instance of a simple binary polymer model. This RAF set consists of several smaller subsets which themselves are RAF sets, indicated by the different colored outlines. For example, the purple one is a subset of the red one, which itself is a subset of the full RAF set, and the green one is an “extension” of the blue one (i.e., it can only exist once the blue one exists). In our original publication, we also presented the results of a dynamical simulation of this RAF set, showing how the different RAF subsets come into existence over time, starting with just food molecules, and then grow in concentration of their constituent molecules.
I’ve now made a short movie based on these results, which shows these RAF subsets arising and growing in “real time”. In this movie, the thickness of the colored outlines represents the concentration of the molecules in the different RAF subsets. The system is fed by a small but steady supply of food molecules (in this case bit strings of lengths one and two), and the Gillespie algorithm is used to simulate the reaction dynamics.
Initially, only the purple and yellow subsets exist in small concentrations (all reactants and catalysts of these RAF subsets are in the food set, so they arise immediately). For the first 17 seconds or so, not much happens other than these two subsets slowly growing in concentration. Then at 0:18 the blue subset comes into existence. This subset needs a spontaneous (uncatalyzed) reaction to happen before it can be instantiated, but spontaneous reactions only happen at a low rate (compared to catalyzed reactions). But once the blue subset exists, it slowly starts growing in concentration. Then at 0:28 the green subset comes into existence as well. As mentioned above, the green subset can only exist once the blue subset exists, but it still needs one spontaneous reaction to happen, hence the delay in its appearance after the blue one has arisen. Finally, at 0:34 the red subset also comes into existence (it needs one reaction to happen spontaneously as well). Note that once the blue and red subsets have arisen, the purple subset eventually decreases in concentration again, as its product molecule (100) is used as a reactant again in the (larger) red subset, and its reactants (0 and 10) are now also used in the blue subset (i.e., they “compete” for resources).
Because of the need for spontaneous reactions for several of the RAF subsets to arise, in a different simulation they may arise in a different order (e.g., the red subset may appear before the blue one does). In this particular simulation, the rates of spontaneous reactions are still relatively high, just to show all RAF subsets arising in a short enough time-span. However, in reality these spontaneous rates are much lower (compared to catalyzed reactions), and it could be that not all RAF subsets will actually arise. Moreover, imagine that we have several compartments with initially just food molecules present, it may very well be the case that in one of them only the red subset arises but not the blue one, and vice versa in another compartment, giving rise to two different protocells (or phenotypes)!
Food for thought, while pondering the origin of life…