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E Pluribus Unum

Brian Hayes

How to Think Like a Slime Mold

The archetype of all StarLogo simulations is a model of cellular slime molds, such as Dictyostelium discoideum, creatures balanced on the borderline between protozoa and multicellular organisms. For most of its life, a slime mold is a single-celled amoeba, grazing in the soil or leaf litter for bacteria. But when food runs short, the slime mold undergoes a remarkable transformation. Thousands of cells stream toward gathering points, where they clump together to form a roving animal called a slug (though it is unrelated to the molluscan slugs); then the cells differentiate further into a more plantlike stalk structure, which finally emits spores that disperse and produce a new generation of amoebas.

It is the aggregation stage in this life cycle that lends itself to study by StarLogo simulation. The slime molds are summoned to the family reunion by a chemical cue, which in Dictyostelium is cyclic adenosine monophosphate (cAMP). An early hypothesis was that a few "founder" cells secrete the cAMP, becoming beacons for the assembly of the slug. But later experiments showed that all the cells secrete cAMP. It took some time to understand how the cells could assemble without leaders to rally around, but a StarLogo model readily reproduces the behavior.

In the model, the amoeboid cells are represented by turtles, which secrete cAMP into the underlying patches. The cAMP then diffuses into neighboring patches, and it also gradually loses its potency over time. The cells' movements are governed by a gradient-following rule: Each cell examines its immediate surroundings and generally moves toward the neighboring patch that has the highest concentration of cAMP, although there is a little randomness in the motion.

That's all there is to the model. The program includes no mechanism to decide where the cells will congregate, and there are no designated leaders or founders; all of the cells obey exactly the same rules. Nevertheless, cells scattered at random over the landscape soon clump together in colonies of 50 or 100. If the simulation is allowed to continue, some of these groups eventually coalesce into still larger aggregations. After many thousands of time steps, most of the amoebas are inside a few large and stable clusters.

Watching the model in action, it's easy to understand what's happening. Each cell exudes a halo of cAMP, which diffuses through the underlying patches and attracts other cells that happen to pass nearby. If two or three cells are close together, their pooled secretions produce a stronger chemical signal, which tends to hold the cells together and also attracts more passersby. Positive feedback keeps the process going: The more cells gather in a region, the more cAMP accumulates there to attract other cells.

Of course a model this simple can't capture all the details of slime-mold biology. For example, real slime-mold amoebas gather in waves or pulses, which have no counterpart in the simulation. But the computer model has an advantage when it comes to exploring hypothetical changes in the cells' behavior. Consider the gradient-following algorithm, which the program deliberately makes imperfect by adding a random "wiggle" to the cells' direction-finding procedure. A biological experiment to study this effect would be difficult to engineer, but in the computer model it's a matter of changing a couple of numbers. Adding more wiggle breaks up the clusters, which is not surprising since randomly wandering cells cannot respond reliably to a cAMP gradient. But what happens when you eliminate the randomness? I thought I knew the answer. I thought the random noise was needed to break out of local optima, and that without it the cells would get stuck in small clusters that never grew into big ones. The actual result is more interesting. With perfect gradient following you see not only stationary, disk-shaped clumps but also long trains of cells that march across the landscape as coherently moving clusters, maintaining their identity even when they collide and pass through one another. I'm not sure what to make of this observation. When I mentioned it to Resnick, he responded that it might possibly reveal something about the biology of slime molds, but it could also very well be an artifact of the StarLogo system.

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