The Life & Mind Seminar Network

Seminar #40: Reaction-Diffusion systems and Models of Autopoiesis

Posted in Seminars by Tom Froese on October 21, 2008

This week there will be two consecutive sessions on Wed 22 Oct in room ARUNDEL-401 — come to one or both:

(1) ARUN-401 4pm-4:30pm ALERGIC Introductory meeting
(2) ARUN-401 4:30pm: Nathaniel Virgo on “Reaction-Diffusion systems and Models of Autopoiesis”

(1) 4pm:
Alergic originally stands for Artificial LifE Reading Group In Cogs, but includes all sorts of interests around Evolutionary and Adaptive Systems, Creative Systems, and beyond. This 30-minute introduction is for both new and old participants, and is an opportunity to announce the variety of relevant discussion groups (…some new ones promised…) and other events

(2) 4:30pm. As a joint Alergic/Life & Mind talk, Nathaniel Virgo (CCNR) will present

Reaction-Diffusion systems and Models of Autopoiesis

This talk is an expanded version of one I gave at the Artificial Life conference this year. In addition to the discussion and visual demonstrations of reaction-diffusion models I will also talk about some of the discussion that took place in the Life and Mind seminars and blog last term, concerning the role of boundaries and spatial structure in the definition of autopoiesis. The abstract for the original talk is as follows:

We analyse pattern formation in reaction-diffusion systems from an autopoietic point of view, emphasising the commonalities between living organisms and a certain class of so-called dissipative structures, namely those (such as spot patterns or hurricanes) in which there are more-or-less clearly defined unities, or individuals, which arise from the system’s dynamics.

Previous authors have used cellular automata as a basis for studying the emergence of autonomous agent-like structures, but the continuous nature of reaction-diffusion systems gives them a substantial advantage over discrete cellular automata as it enables systems to be perturbed by an arbitrarily small amount. Since reaction-diffusion systems are simulations of physical/chemical systems the resulting model agents must obey the relevant thermodynamic constraints, an aspect of living systems that has generated a lot of recent discussion in the autopoietic literature.

The Gray-Scott model is perhaps the simplest reaction-diffusion system that can create complex patterns; it models a single type of autocatalyst feeding on a ‘food’ chemical that is continually added to the system; both are able to diffuse on a two-dimensional surface. One of the patterns that can be formed consists of blurred but individuated “spots” of autocatalyst separated by regions in which the autocatalyst is absent. We take a single spot as the basis for our model agent.

With the autopoietic description in mind we perform three experiments. Firstly, we put these spots into situations where there is a spatial gradient of the food molecule and find that they tend to move along it, usually away from areas where the level of food is too low for their survival. The relationship between constitution and behaviour is fundamental to the autopoietic theory, and this result opens the possibility of studying the interface between the two empirically.

Secondly we vary the rules of the system, allowing a different set of chemical reactions, which can result in agents with a more complex anatomy than just a single spot, and even a very limited form of heredity.

Finally we find that individuated spots are very likely to arise when there is a negative feedback between the whole system’s activity and its overall supply of food. This situation is common in natural systems, and our result suggests a direction for further research into the conditions under which individuated unities are likely to occur in general.


2 Responses

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  1. Tom Froese said, on October 23, 2008 at 2:56 pm

    Thanks, Nathaniel, for a great seminar to continue the debate of last term.

    I’m not sure about the proposal to extend the notion of autopoiesis beyond the organism and into the environment, but I have a feeling that we are definitely achieving some clarity on the role of the boundary.

    As it was already shown in the diagram of Matt’s earlier post to this blog, the boundary of a single-cell organism is a special kind of process. And as Nathaniel again pointed out, perhaps it is best described as a process which enables and is enabled by all other processes of the autopoietic (or more generally: living) system.

    I really like this more general way of understanding the role of the boundary for the single-cell organism. Could we perhaps use this special kind of process in order to distinguish between living and non-living organizationally closed systems as such?

    I think we need to accept the fact that autonomous (organizationally closed) systems pretty much exist everywhere in all shapes and sizes. This is interesting in itself and shows us that we need to be careful when we attempt to analyze phenomena in systemic terms which do not respect this special kind of relational inter-connectivity.

    But this prevalence of autonomous systems also means that we need to find more precise ways of distinguishing those autonomous systems which are also living systems. Perhaps the wholistic enabling process, exemplified by the single-cell boundary, could be one such indicator? Can anyone think of an operationally closed system which includes such a process but which we do not want to call living?

    Can we derive a definition of life based on this? Here is my first rough attempt:

    A living system is an organizationally closed system of processes, where one of those processes enables and is enabled by all other processes of that system which exist at the same level of description.

  2. Nathaniel Virgo said, on October 26, 2008 at 7:54 pm

    Hi Tom, thanks for your comments. I have a response to the point about extending the boundary, which I’ve put at the bottom of this comment because I’d like to address a point about defining life first.

    I think there is one problem with your tentative definition of life, which is that it seems it would apply to reaction-diffusion spots, as I showed in my talk. Or is the “same level of description” qualifier meant to prevent that? If that is the case, would your definition apply to a model with a more explicit boundary mechanism, such as ones based on the Varela et at tesselation model?

    Personally I think it would not be wise to call such things “alive.” I think we might argue that they are autopoietic, and accept that autopoietic (not just operationally closed) systems are common in the non-living world. Defining life against that background is obviously very difficult. My own approach is not to try. When I talk about living organisms I mean only to refer to the large class of examples that biologists call alive: the eucaryotes, procaryotes and archea. It might turn out that one day we will have a definition of life that satisfies us all, but I suspect it will not happen until we have a much wider set of examples to choose from. For example, we probably need to examine organisms from other planets (do all forms of life have DNA/RNA and proteins, or is there something more subtle that their organisations share? We cannot answer this question with essentially only one example) as well as many more natural and artificial examples of things like our model organisms which share some properties with living organisms but which we do not want to call alive.

    Finally, back to your first point. I can see that the extension of autopoiesis will be a tricky issue for some, but my opinion is that it is unavoidable: I don’t think it really makes sense to talk about a “closed” network of processes whose operational limits are coincident with the organism’s boundary, and I don’t think it was what Maturana and Varela meant, as I explained in my post last term. Luckily I also think it’s desirable to conceptualise autopoiesis in an extended way. It is precisely this extended view of life which allows us to see the true role of the environment in the process of living. If we try to ignore the extended network of constitutive processes we end up with a view of an organism as something that must continually monitor its environment and then choose an appropriate reaction.

    This is the very mistake that the GOFAI programme made with cognition, which is only now being un-made. Taking this brain-centric viewpoint obscured many of the simplest mechanisms by which regulation can occur and resulted in people building insanely complicated machines like ASIMO to perform a task like walking that can actually be performed by a few hinged pieces of wood if the design takes proper advantage of the dynamical relationship between the walker and its environment.

    Taking a similar organism-centric approach to life creates a similar kind of over-complication where we convince ourselves that organisms must be doing something very difficult and clever in order to maintain themselves in the face of a changing environment when in fact all that is needed is for the organism+environment system to result in a dynamically stable entity. Ultimately I believe this is the most important thing that my reaction-diffusion spot model shows.

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