Maze-solving by chemotaxis

Here, we report on numerical simulations showing that chemotaxis will take a body through a maze via the shortest possible route to the source of a chemoattractant. This is a robust finding that does not depend on the geometrical makeup of the maze. The predictions are supported by recent experimental studies which have shown that by moving down gradients in $p\text{H}$, a droplet of organic solvent can find the shortest of multiple possible paths through a maze to an acid-soaked exit. They are also consistent with numerical and experimental evidence that plant-parasitic nematodes take the shortest route through the labyrinth of air-filled pores within soil to preferred host plants that produce volatile chemoattractants. The predictions support the view that maze-solving is a robust property of chemotaxis and is not specific to particular kinds of maze or to the fractal structure of air-filled channels within soils.

Figure 1

(Color online) Examples of mazes produced by a randomized version of the depth-first search algorithm. The directions, up (U), down (D), right (R), and left (L), in which chemotaxis will take a droplet of organic solvent or a biological organism in response to a chemoattractant are indicated. Overall movement tracks from arbitrarily chosen starting locations can be seen by moving through the mazes in the directions indicated. Irrespective of their starting location, droplets and organisms always take the shortest most direct route to the source of the chemoattractant (●). In these simulations the chemoattractants have not yet diffused throughout the mazes entirely.

Figure 2

(Color online) Examples of mazes produced by a recursive division method. The directions, up (U), down (D), right (R), and left (L), in which chemotaxis will take a droplet of organic solvent or a biological organism in response to a chemoattractant are indicated. Overall movement tracks from arbitrarily chosen starting locations can be seen by moving through the mazes in the directions indicated. Irrespective of their starting location, droplets and organisms always take the shortest most direct route to the source of the chemoattractant (●).