Culturing Science – biology as relevant to us earthly beings

Nature-inspired network design: recent studies in slime mold and leaf veins

This post was chosen as an Editor's Selection for Nature-inspired design:  this phrase makes me think of shark-skin swimsuits, velcro, and an endless assortment of coffee tables using natural knots and tree branches.  There is logic behind design reliant upon natural elements.  After all, organisms have been undergoing evolution for millions of years for the sake of efficiency.  If anyone knows how to cut through the water cleanly, it would be a shark, wouldn’t it?

When thinking about designing human networks, it thus seems “natural” to turn to nature, which certainly has expertise in the subject.  Every organism has to have a way of transporting nutrients and water around its body, systems which become more complicated as the organisms do.  Think about your circulatory system: all those veins and arteries and capillaries seemingly spread through your skin and innards at random.  But this network of transport tubes has gone through great evolution in order to be so intricate that it seems random to us.

Three recent papers have highlighted the use of organisms to help plan civilized networks: that is, highways and train systems.  The first two papers feature one of my father’s favorite organisms, the slime mold, while the third looks at leaf vein systems.  (For my post on leaf veins as drivers of plant evolution, click here.)

Slime molds are plasmodial protists — their cellular structure is undefinable.  While a slime mold can live as a unicellular and uninuclear organism, if it runs into another of its own species, the two will join by their cellular membranes.  If there are many around, the organism can potentially become a huge amorphous sac with many nuclei, spreading over a surface foraging for food.  (The question is: is it the singular cell membrane or the singular nucleus that makes an organism “unicellular?”)  Here’s a quick video by John Bonner, a Princeton slime mold specialist, showing the beauty of this unfortunately-named creature:

Edit: A commenter pointed out that John Bonner’s “slime molds” are different than the ones used in the research discussed below.  The slime molds in this video, Dictyostelium discoideum, do in fact form a multicellular organism and don’t exhibit the same sort of networking behavior.  The video is still worth watching, but be aware of these differences!  (Thanks, Iain and class!)

When foraging, the blob spreads over a surface looking for sugar.  Once food is located, it will redirect most of its mass elsewhere, leaving a vein behind leading to the food source.  After millions of years of evolution, one would expect that this vein would be the most efficient path between the two points.

Independently, two groups of researchers took advantage of this assumption to use slime mold to compare its foraging network between food sources to our networks connecting cities.  (For the record: one of the papers was published in the International Journal of Bifurcation and Chaos, which is an obsession-worthy title.)  Each team laid out oat flakes simulating the layout of major cities (one oat flake each!) in their region of choice – the UK and Tokyo metro areas.  The question: will the slime mold trails emulate our own systems, thought out by our grand human brains for efficiency?

Slime mold networks compared to actual city planning. Image maniputed; see papers for original figures

The answer: for the most part, yes!  As you can see in the above figures, the authors of each paper saw very similar networks to our own.  However, the slime mold lacked a more circular structure, connecting the outer hotspots to one another.  And why would it have these:  due to its impermanent nature, a slime mold does not need the forethought to create multiple connections to the same spot.  If one is broken, they can simply create a new line leading straight through.

If we’re trying to use these organisms to help us plan transportation networks, obviously this is not a perfect fit, as weather and technical problems cause blocked lines frequently.  We do need this sort of forethought when laying out our cities!  But we are not the only ones.  A paper published last week in Physical Review Letters (open access here) looked at branching patterns in leaf venation.

Just like in our own circulatory system, the network of veins bringing nutrients and water throughout a leaf cannot be simply retracted and reformed, but is a permanent structure.  With herbivores knawing holes all the time, you betcha that plants have evolved “looping networks,” as the authors put it, to ensure that a blockage in one pathway doesn’t deprive the entire leaf of nutrients.  Traditionally modelling has shown these looping networks to be inefficient compared to non-circular, tree-like networks.  Do you think these authors believed that?

As support for their premise, they punched a hole through the central vein of a lemon leaf (see image above) and injected fluorescent dye below.  And behold!  The dye was able to spread throughout the leaf despite this disruption.  They then created a model that incorporated the network’s (a) resilience to damage and (b) variation in load.  Separately and together, the models agreed: looping networks are actually more efficient in the long run.

What do these studies put together show us?  That neither alone is good enough.  We need our slime-mold, treelike networks for basic structure, with some excess leaf-vein looping for support during damage control and tourist influx.  (You never know when you’ll host the Olympics.)  The circularity might seem excessive, but when bad times hit, it will be worth it.  (The citizens will appreciate it too.)

This may seem like second nature to many of you.  But sometimes it’s nice to get some support from “first nature,” amiright?

(Endnote:  I really am curious about the grammar for slime mold.  Are slime mold(s) awesome or is a slime mold awesome?  Guesses/answers in the comments, if you are so inclined.)

Andrew Adamatzky, & Jeff Jones (2009). Road planning with slime mould: If Physarum built motorways it would
route M6/M74 through Newcastle International Journal of Bifurcation and Chaos arXiv: 0912.3967v1

Katifori, E., Szöllősi, G., & Magnasco, M. (2010). Damage and Fluctuations Induce Loops in Optimal Transport Networks Physical Review Letters, 104 (4) DOI: 10.1103/PhysRevLett.104.048704

Tero A, Takagi S, Saigusa T, Ito K, Bebber DP, Fricker MD, Yumiki K, Kobayashi R, & Nakagaki T (2010). Rules for biologically inspired adaptive network design. Science (New York, N.Y.), 327 (5964), 439-42 PMID: 20093467

Written by Hanner

February 11, 2010 at 5:55 am

13 Responses

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  1. IMHO, it is quite unfortunate that the human networks chosen to compare are transport networks. There is a fundamental difference between the goal of a transport network and the two examples studied. The circular paths do not exist because slime molds and plants do need to care about the travelling distance between two adjacent leaf nodes. Try telling a resident of city A that to go to city B which is 20km away she needs to pass through city C, adding 50km to her trip! Her rage will have absolutely nothing to do with redundancy.

    The slime’s problem is akin to the travelling salesman problem (need to visit all the nodes, minimizing the covered distance).

    The leaf’s problem has some similarities with communication networks (especially for multicasting). Small fiber optics networks with a single central hub would probably fit very well and display more remarkable similarities.

    I wonder how these researchers managed to miss these points.

    C. Akritidis

    February 11, 2010 at 10:00 am

    • I feel confident that both researchers were aware of the limitations of their own systems. Neither claimed to have the answer to solve all transportation system design issues — simply a new way to look at them.

      And you are right. I like your description of the slime mold as a traveling salesman. And the leaf is trying to get water EVERYWHERE, with the points very close to one another, which would not be an ideal system for us.

      But is there not something emotionally fulfilling about these studies? I think that modern transportation is one of the major institutions that separates us from “nature” per se, or makes us feel unnatural. Instead of just relying on our bodies to get us around, we have all these abiotic machines that we ourselves have built, and we can go anywhere in the world!

      And then we get a lil gross slime mold to emulate it. Maybe we’ve still got a little bit of nature left in us.

      (I personally believe that we are still very much a part of “nature,” but there are many who disagree.)

      Best, and thanks for reading,


      February 11, 2010 at 10:14 am

      • Well, the subject is very interesting, but I will follow the tangent you took. I don’t care much for the words ‘natural’ and ‘unnatural’. I agree with you and believe that it is impossible for us to do anything ‘unnatural’, since we are part of nature.
        It’s just that the natural path we have chosen to follow seems to be unsustainable in the long run.
        Whether we choose to ignore the risks of obliterating the rest of our ecosystem, is up to us. We will inevitably have to adapt the new situation or perish, just like all our predecessors. If we end up thriving in a world completely devoid of other complex lifeforms, it will still be natural. But do we really want to get there?

        C. Akritidis

        February 12, 2010 at 10:06 am

      • Hey, C,

        I agree. Natural and unnatural are incredibly tricky words. Partially because “nature” has many meanings – whether referring to the environment or some innate tendency of our biology.

        I like to try and not refer to humans as “unnatural” because I don’t want to align myself with the sort of environmentalist who thinks that because we’re not wearing animal skins and living in caves we are somehow no longer natural beings. We evolved the ability to reason through innate processes, and we use it to help our species succeed.

        All organisms exploit their environment to a certain extent for the things that they need. But we are taking it way too far. When a species goes so far as to actually destroy its environment in the process of utilizing it, we definitely have a problem.

        I am more than a little into the apocalypse, so my thoughts are skewed, but sometimes I think that the only way for the planet to recover is for us to kill ourselves off. A great extinction event for the planet. Earth will rehab herself for several million years and then new life will be reborn.

        I hate the thought that we are not meant for this planetand that we can’t find a way to make it work. I do think that something serious and major will need to happen environmentally before politicians and higher-ups take notice. When the scientists are made out to be conspiracy theorists, how else can we be noticed?

        So, in short, human abilities are natural, but when we use them to destroy nature, our actions are not natural.

        Best to you,


        February 15, 2010 at 5:02 pm

    • PS: I wish I knew more about fiber optics! If what you say is true, I bet the researchers do too.


      February 11, 2010 at 10:16 am

    • -C. Akritidis
      Although your points are well noted, these concerns highligted are issues easily solved through a holistic approach in the practice. You could go through city B more effectively by perhaps isolating the main roads from the local roads/streets,and public transport If you are looking at the midrib of the leaf analogous to where the a central city B would be situated, then you separate the transportation into two levels, these could be a highway more direct route through the city, and the second one perhaps a lower level could be the local network. The same could be done for all its rooting networks, yes! its economically demanding, but sustainable, stable and efficient in the long run.

      S. M

      July 6, 2013 at 1:36 pm

  2. […] posted here: Nature-inspired network design: recent studies in slime mold and … Share and […]

  3. Hannah —

    remind me to tell you about similar ideas in river networks…


    February 12, 2010 at 9:10 am

  4. […] little something about network design in slime mold and leaf […]

  5. interesting enough to those who think this is a hoot… there is a new disease running around the world called Morgellons and it is also caused by a slime mold nano version and people are suffering. It would be amazing if someone could figure out how to kill this in human hosts.

    After thought

    March 23, 2010 at 10:26 pm

  6. Great article. I was teaching this to my class this very week and will send it on to them. However they and I would have to point out a wee mistake – and one commonly made. John’s Dictyostelium and Toshi’s Physarum are both known as ‘slime molds’, but the former (that is in the embedded video) is multi-cellular when it aggregates in response to food scarcity, and does not exhibit the behavior discussed here of forming a network among resources. It is also fascinating but a very different organism.
    Ants, however, do this rather well.


    October 1, 2010 at 6:10 am

    • Thanks for your comment, Iain! I added a note in the article to clarify. I really appreciate your help!
      I hope your class enjoys it.

      Do you know if there is any research on ant networking? I used to study leaf-cutters but don’t remember any papers on their network efficiency.

      Hannah Waters

      October 1, 2010 at 10:33 am

  7. thanks for the comment!

    I love leaf venation in particular and plant geometry in general. Have you encountered L-systems by any chance? They are amazing.


    December 13, 2010 at 8:32 pm

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