Investigating octopus camouflage with ICA and hierarchical clustering

Each bag is attached all around by several muscles : if the muscles are relaxed, the bag will be small.

But if the animal contract these muscles, the bag will expand and the pigment will spread.

These muscles are controlled by some neurons, called “motoneurons”.

The whole goal of this study was to investigate neurons, even if indirectly !To better understand the camouflaging skill, the scientists figured that they had to pay a lot of attention to the size of these chromatophores.

Therefore, they designed an analysis pipeline to track them on the animal skin.

Developing a toolbox to track thousands of chromatophores and to extract their sizes while the animal is moving in a tank is already a huge achievement in itself.

However, I chose to focus on another result in this post.

So, I invite you to have a quick look at my first post here, which describes the principle of this pre-processing pipeline on another example (detecting neurons and extracting their activity from a video of a transparent fish brain).

I briefly summarize it in 3 steps :First, each image from the cuttlefish skin is aligned (rotated or translated) to match the orientation of a reference image.

Then, chromatophores are located.

Finally, the number of pixels within each chromatophore is extracted.

The (simplified) analysis pipeline to monitor the size of thousands of chromatophores in time.

Have a look at this post for more detailed explanations.

Image modified from Fig1 in the original publication.

This pre-processing step creates an exploitable data set from the cuttlefish images: a matrix [chromatophores x time], where each element is the size of one chromatophore at one time point.

Machine learning algorithms can then be easily applied to gain insights on the behavior of these thousands of pigment-filled bags.

(For example, Principal Component Analysis can be used to reduce the dimensionality of this data set from several thousands to 3, in order to plot the time evolution of this system in 3D.

This will be described in another post : “PCA and tSNE in Neurosciences : dimensionality reduction for visualization”)Let’s focus on the main goal : by studying the evolution of the chromatophore’s sizes, the neuroscientists actually wanted to assess the activity of the motoneurons controlling the muscles.

The size was just an indirect measurement.

However, things were not so simple (always in research) because it was quickly realised that:One motoneuron could control several chromatophores.

One chromatophore could be controlled by several neurons.

And this needed to be untangled first.

The issue here was to infer the value of the source signals (motoneurons activity) from the mixed signals (chromatophores activity) with no knowledge about the source signals or the mixing process.

This is a case of blind source separation and a good algorithm to use in this case is ICA : Independent Component Analysis.

The hypotheses of the ICA are the following :the source signals are statistically independentthe source signals are non-gaussianAccording to the Central Limit Theorem, if the source signals are independent (hyp1), their mixture will tend towards a gaussian distribution, even if the source signals are not gaussian themselves (Nice drawing to illustrate this theorem on the wikipedia page here).

If you add the hypothesis 2, this means that the distributions of the mixture signals will always be more gaussian than those of the source signals.

The goal is then to find a new space where the distributions are as far away from gaussian as possible, as illustrated in the following figure :If the source signals are independent and non-gaussian : a) the ICA algorithm can recover them from the mixed signals.

Adapted from an image found here.

and b) a new space can be found where the distributions are as far away from gaussian as possible.

Adapted from images found here.

There are many ways to implement ICA so, for this post, I prefer to leave you with the intuition and invite you to consult the many resources we can find on the web (like this website from a french neuroscientist or this website from the university of Helsinki).

Let’s go back to our cuttlefish : from the activity of the chromatophores, the ICA allows us to assess the activity of the motoneurons.

(Hyp 2 is quite easy to satisfy since most of the stuff we record in biology do not have a gaussian disctribution.

But Hyp1 is a bit more tricky : we cannot assume that each motoneuron is independent from the others, but we can accept that ICA will group together several motoneurons that are not independent).

Chromatophores will thus be grouped in “motor elements” : all the chromatophores in the same “motor element” are essentially controlled by the same motoneuron (or goup of motoneurons).

Reprinted by permission from Springer Nature : Nature, Elucidating the control and development of skin patterning in cuttlefish, Reiter et al (2018), License nb 4486000735048.

The result can be illustrated by this figure (from the original publication): the chromatophores circled in red have been found to be controlled by the same motoneuron (we can notice that they are all black), and the ones circled in blue by another one (they are all yellow, except one).

The first finidng is that one motoneuron essentially controls several chromatophores of identical colors !.The traces on the left represent the sizes of each chromatophore in time, let’s call that the “activity”.

Within the same motor element, the activity looks synchronized.

The average activity is then used to characterize the motor element.

Based on this result, the scientists used hierarchical clustering to group together motor elements with similar activity (one motor element = one group of chromatophores that represents one motoneuron.

).

Hierarchical clustering has already been nicely described in another “Towards Data Science” post that I invite you to read here.

(You can also watch this video to see how hierarchial clustering is used in biology to groupes genes with similar expression.

)Briefly, the algorithm computes the similarity between each motor element and creates a dendogram.

Then, a threshold is chosen and will create the clusters.

Here, the researchers used the “correlation distance ”as a similarity metric : d = 1 — r (r being the correlation coefficient).

if 2 motor elements are perfectly correlated, r = 1 and d = 0.

The distance between them is null : they are very close in space, since they are similar.

if there is no correlation, r = 0 and d = 1.

The distance between them increases.

if the 2 motor elements are anti-correlated, r = -1 and d = 2.

The results can be seen on the following figure: on the top left is an photography of a cuttlefish skin.

We will focus on the white patch delimited by the rectangle.

Reprinted by permission from Springer Nature : Nature, Elucidating the control and development of skin patterning in cuttlefish, Reiter et al (2018), License nb 4486000735048.

The image on the top right show the chromatophores grouped in motor elements in colored circles, empty or filled, as determined by the ICA.

This corresponds to the hierarchical clustering with a threshold of d = 0 (a maximum correlation of r = 1).

If the threshold is taken around d = 0.

4 (green arrow, bottom picture), we can see some motor elements being grouped together in a dozen of clusters.

If the threshold is taken near d = 2 (red arrow, middle picture), we can see clearly 2 clusters that are anti-correlated : the white patch and the dark edges.

This shows thatblack and yellow-ish chromatophores are controlled by different motoneurons.

the activity of these motoneurons is anti-corelated in time.

This makes sense : if the animal wants to disappear in a dark background, black chromatophores need to spread whereas yellow ones need to shrink.

So the “black-controlling” motoneurons will send the messsage to contract the muscles, while the “yellow-controlling” motoneurons will stay silent.

(If you are curious about the physiology underlying muscle contraction, you can have a look at this video to get an idea).

And, of course, vice versa if the animal wants to match a light backgroud, as illustrated by the following figure :In conclusion, using ICA and hierarchical clustering, scientists were able to describe how a cephalopod can camouflage in the backgroud.

And that’s inspiring !The study presented here has been performed by Sam Reiter, Philipp Hülsdunk, Theodosia Woo, Marcel A.

Lauterbach, Jessica S.

Eberle, Leyla Anne Akay, Amber Longo, Jakob Meier-Credo, Friedrich Kretschmer, Julian D.

Langer, Matthias Kaschube under the surpervision of Gilles Laurent in the Max Planck Institute for Brain Research, Frankfurt am Main, Germany.

All the figures have been reproduced with the permission of Springer Nature, License nb 4486000735048, from the orginal publication “Elucidating the control and development of skin patterning in cuttlefish”, Nature, Reiter et al (2018).

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