EXPLORABLES

by Dirk Brockmann

This explorable illustrates how simple, single-cell organisms can manage to aggregate into multi-cellular structures by emitting and responding to chemical signals. Individual cells respond by orienting towards a chemical signal and moving up its gradient, a process known as chemotaxis. The combination of synchronized signal emission and chemotaxis yields collective behavior with beautiful spatial branching patterns during the aggregation process.

This type of behavior is observed in organisms like Dictyostelium discoideum, a famous critter that dwells as a single-cell organism but self-assembles into a multi-cellular "slug" when food is scarce (Here's a great video of this transition). "Dicty" uses the chemical cyclic AMP (cAMP) as a signaling molecule.

This explorable is a variation of the original model introduced by David Kessler and Herbert Levine in their 1993 paper "Pattern formation in Dictyostelium via the dynamics of cooperative biological entities", the paper that inspired this explorable.

This explorable is also Hiroki Sayama's favorite.

Press Play and keep on reading....

This is how it works

The model has two dynamic components: 1. the dots in the display represent individual cells that can move around and 2. the spatial concentration of cAMP (blue). Initially 3000 cells are scattered randomly in the system and the cAMP concentration is zero.

When not responding to signals, cells move around randomly, the wiggling motion that you can see (and control using the random movement slider).

A special pace-maker cell (red dot) in the center emits spiked doses of cAMP into the system at a regular frequency. The cAMP then diffuses concentrically into the system. When other cells detect cAMP above an activation threshold, they become active, too. They then respond by emitting a cAMP pulse as well, yielding a cAMP pulse cascade. The strength of individual pulses can be changed with the cAMP pulse strength slider. Once a cell emits a pulse, it needs to recover for some time before it can become activated again. You can control this recovery time with one of the sliders.

Cells also respond to the chemical signal by directed movements. When the cAMP-concentration near a cell is above a movement threshold and the cell is still active it starts moving towards higher concentrations of cAMP. The amount of directed movement is controlled with the responsiveness slider.

For the default settings, you should see that very quickly blue concentric cAMP waves go through the system and that branches emerge along which the cells move towards the center.

Switches

You can use the switches to hide the cells or the cAMP concentration to focus on the patterns of one or the other. When you turn on the cell state toggle on, cells are colored according to their state: gray: inactive, red: active, black: recovering. By default the pace-maker cell is always active. Once the system is activated and for the right parameter settings, you can turn the pace-maker off and the system will remain activated.

Advanced settings

This model has a number of parameters. With the advanced settings turned on, you have access to more parameter sliders. You can change the diffusion constant of the cAMP and the life-time of signaling molecules, so how quickly cAMP degregates. You can also change the movement threshold and the activation threshold.

Further information


Related Explorables:

Particularly Stuck

Diffusion Limited Aggregation

Cycledelic

The spatial rock-paper-scissors game

Janus Bunch

Dynamics of two-phase coupled oscillators

Hopfed Turingles

Pattern Formation in a simple reaction-diffusion system

Critically Inflammatory

A forrest fire model

Dr. Fibryll & Mr. Glyde

Pulse-coupled oscillators