When I see a cake, I head straight towards it and help myself to a slice. And when I see a large cloud of fume rising up from a smoker, I make a little detour, so my baby doesn’t have to inhale the toxic fumes.

All this gets a little bit more complicated, when someone turns off the lights. Some animals have very good night vision (like lions) or use echo location (need I mention the bats?) to gain the advantage over us in the dark. (More on how animals see the environment and how we know about it, can be found in another blogpost here.) On the smaller scale of life bacteria, nematodes and amoeba have neither eyes nor ears, and have to navigate their environment using other cues.

Let us call this a highly developed sense of smell. Chemotaxis is a way of navigating the environment using chemical gradients as a cue. Animals who rely on chemotaxis can register many different molecules and are very sensitive to changes in concentration. For my friend Caenorhabditis elegans the response to more than 100 chemicals has already been measured [1, 2]. And these measurements show that C. elegans can distinguish between the chemicals, and respond to each of them individually.

Broadly speaking chemical cues fall into one of two categories: attractive and repelant. Whether they are one or the other depends on whether they signal the presence of food or danger. Some animals, like C. elegans, can also adapt their response based on previous experience.

Looking at the movement of small creatures in the lab, it all seems straight forward enough: there is a gradient of some attractive chemical, and up it they go. There are even mathematical descriptions linking the gradient and the base speed of the creature with the progress they will make. However, for the little guy we are observing all looks a bit different: They can’t see the total chemical gradient, they don’t know, where the highest concentration is. All they know is the chemical concentration at the point where they are. And we must call it a point, while we are long enough to notice, whether our feet are colder than our head, the bacteria are so small, that the environment is the same in all directions. However, they have one more clue, they also remember the chemical concentration from the point where they have just been. So this is how they know whether they are generally going in the right direction. Now all you need to throw in is a little bit of random sampling, and the bacteria very reliably end up at the point of highest concentration of attractant.

This mixture of random sampling and directed motion makes chemotaxis so powerful. It is also known as a biased random walk. Bacteria do so by the run and tumble mechanism. If there are no stimuli, bacteria swim around and change direction about once a second. If there are chemical stimuli they will modify how often they change direction depending on whether they are currently heading the right way. Chemotaxis in C. elegans works similarly, with one of the differences being that it is called swim and pirouette. Being endowed with a small nervous system, the nematode can also orient itself in a targeted manner during a pirouette, while a bacterium will always change direction randomly.

Chemotaxis is one of the favourite things among mathematicians to model. This is due to the wealth of experimental data available and the relatively small set of parameters necessary to describe the process. This is one of the showcase systems, where the interplay between mathematical simulation and experimental design and interpretation has lead to great advances in the field.



[1] Ardiel, Evan L., and Catharine H. Rankin. “An elegant mind: learning and memory in Caenorhabditis elegans.” Learning & Memory 17.4 (2010): 191-201.

[2] Coburn, Cara M., and Cornelia I. Bargmann. “A putative cyclic nucleotide–gated channel is required for sensory development and function in C. elegans.” Neuron 17.4 (1996): 695-706.

feature image: By Chrstphr.jones – Own work, CC BY-SA 4.0,

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