YOU’RE SO VEIN: Beauty and Utility in a Leaf. You may have marveled at the intricate veins on a leaf, but did you know that the same pattern appears all over nature? The recursive looped network is found in neural nets, river deltas, insect wings and capillaries overlying a tumor.
• Inspired by leaf venation, mathematical physicists Marcelo Magnasco and Eleni Katifori of Rockefeller University wondered if there was an evolutionary basis for the selection of high density loops in networks. They digitally dissected the pattern and used complex algorithms to derive optimal solutions for two challenges facing any transport network: resilience to damage and fluctuations in load.
• The animated gif shows how flow of a fluorescent dye is routed around an injury (circular hole) in the main vein of a leaf, via closed loops, to reach the leaf tip. If the network had a simple tree-like branching pattern as is commonly assumed, then damage to any vein would result in tissue death downstream. Instead, the leaf is remarkably resilient to damage by insects, pathogens and the elements.
• Variations in load are also handled best by recursively nested loops. Some parts of the leaf may be lit by sunlight and exert greater demands on flow compared to shady parts. Again, hierarchically ordered trees are not as effective as topologically disordered networks seen in leaf vasculature. It took a unique partnership of physics and biology to reveal that Nature is a Master Engineer!
★★★ Many thanks to Kevin Staff for donating his time and skills in making the gif for ScienceSunday !
Watch: Lighting up Leaves
REF: Damage and Fluctuations Induce Loops in Optimal Transport Networks Eleni Katifori, Gergely J. Szollosi, and Marcelo O. Magnasco
DOI: 10.1103/PhysRevLett.104.048704
#sciencesunday
madame scientist's not-so-mad musings 
nice to see it growing…..
Gnotic Pasta , Kevin also made a gif of the Gingko leaf where the veins are not interconnected by loops. This is an example of a really ancient tree that did not “evolve” further as the dicots did. I didn’t load it for practical reasons..I’ll post it later, separately.
So cool. ‘Nuff said.
Cool! Is there any natural thing which is not fascinating?
Drew Sowersby , the authors did point out a similarity in street connections within cities. Their point is that “streets” of all sizes impinge on the larger arteries, so that it is not strictly a hierarchical set of large to medium to small connections. I guess the domains within a leaf would be like independent sections of connected “streets”. Cool gif!
The best gif I ever came across! 🙂
Wonderful post Rajini Rao 🙂
Thanks, Deeksha Tare . Thanks for that super interesting story and link, praveen kulkarni . Dicty is a great model organism too, has so much to teach us.
how can thats leaf glow?
mega ilham , a fluorescent dye was injected at the base of the leaf and then the leaf was imaged. If you look at the video in the link (see the post), you can watch them do it.
its so awesome.. (y)
Why only capillaries on a tumor? Do the capillaries throughout the rest of the human body not apply? What a cool GIF whatever the case.
Incidentally, today’s highlights on Answers.com is about who “You’re So Vain” might be about. The song is fun, but this is more interesting.^
The vagaries of writing for effect, Thomas Kang 🙂 The description applies to vasculature all over the body, as you note, but the reference to tumors alludes to potential practical applications of the work..in the event someone scoffs at the pointlessness of studying veins in leaves.
Carly Simon – You’re So Vain (with lyrics)
resilience to damage and fluctuations in load. > This is the most energy efficient way to construct a network that includes sufficient redundancy. It’s always possible to add more veins but the advantage of those probably doesn’t outweigh the energy cost required to construct them? From that point of view it’s not that remarkable* that this pattern seems to pop up everywhere and that networks have a tendency to grow into this shape. Making efficient use of energy seems to be what nature does best and with humans being as lazy as they are, it’s only natural that we are copying this aspect of nature. 🙂
*Note that when I say “not that remarkable”; it’s actually mindblowingly awesome but I mean that it makes sense unlike some other things that nature has produced… a platypus for example. 😉
The lyrics might be worth studying, too, but I find this so much more interesting. I mean leaf venation? C’mon.
I can see the city streets thing, but to me the Interwebs seems like a good illustration of this as well, as may be the universe. That’s why in the grand scheme of things if the LHC goes awry (or our Sun short circuits), it’ll only be a big deal for us, not for the rest of the universe.
It’s interesting that when I did a search for recursive looped networks I got a bunch of computing theory. Does anyone know if they are talking about the same topological ideas in an engineering/computer architectural sense?
Koen De Paus , it’s always about finding the optimum solution: balance between cost and performance. Never just about minimizing cost..something that people in business sometimes seem to miss?
Rajini Rao They very much are. Our computer networks are complete crap when compared to those found in nature. A single machine causing problems (accidentally through errors or purposefully through malicious intent) can shut down entire networks. Mostly because our networks are designed to make it easy on network engineers to fix problems if they pop up. There is a new school looking at letting networks emerge naturally, to let them grow themselves by letting machines talk to each other and figure out the optimum solution you just described. Network virtualization is getting more attention every year and is a requirement before such techniques can be implemented in a practical manner.
It’s interesting to think about the constant pressure that the organism’s environment puts on the organism, for instance, with respect to optimal size. Dinosaurs won’t survive in the desert, nor will most other large animals. Constant environmental pressures on organisms, starting with the supply of potential energy that the environment provides, selects out for organisms that best balance cost and performance, a good part of which is determined by size.
Now you’ve got me wondering . . . what makes leaves recursive loops? I guess the circulation takes place on a molecular level, with water and minerals flowing outward from the stem to the leaves and throughout the leaf, and carbon dioxide making the return trip? I guess I still don’t fully understand what the tree does with the carbon dioxide once it comes in, aside from spitting out oxygen (and even that I don’t fully understand why).
Thank you for the non-biological insights which were missing in this post, Prabat Parmal , Thomas Kang and Koen De Paus . Check out Koen’s new post on this topic: https://plus.google.com/u/0/108487783243149848473/posts/Fo7gzT6pSZT
There you go, Peter Lindelauf , planting a seed for a future G+ post. I even have a handy image to go along 🙂
Light is the energy source, Peter. I’ll work on it being somewhat comprehensible 🙂
Oh yes, I love that one from Tennyson! Gives me chills.
Battle of Balaclava, in Crimean War. A doomed charge based on miscommunication. It’s a very poignant poem, short and bittersweet: http://poetry.eserver.org/light-brigade.html
I love this one!
This is awesome! and do some people really assume its just a branching pattern?? wow. I forgot most people (as in the sane ones lol) dont spend hours staring at leaves and such like i do XD. Whats really fascinating is watching leaves repair themselves. its super awesome!
Im looking forward to seeing the flourescent dye get to work in the palmate venation of the ginko leaf! :DD
oh, and Peter Lindelauf , to be simple, Sunlight fuels the reaction that takes H2O and NADP+ and turns it into O2, H+ and NADPH in Photosystem II.
Margaret Ross , I edited my post to add the reference and a link to a cool video on this that does show linear leaves (they too, have closed loops). I forgot to transfer the links because G+ ate up my post the first time and I had to redo it
There was another vid showing a variety of leaf shapes lit up with this technique, let me look for the link.
AWESOME! thx! ^^
Wow! that’s all I am going to say.
Margaret Ross , this two min vid may have a few more shapes:Science Nation – Revealing Nature’s Mathematical Formula for Survival
Tom Lee , you’re always posting these beautiful images of trees 🙂
Good Monday to you, Feisal Kamil ! Thanks, lovely leaf networks! I don’t know if they would be described as fractal, but they are nested loops. If you look at each section, it is divided into further sections and so on. Err, that does sound like fractals, doesn’t it?
Catch up with you later, then. #sciencesunday was trending all day, so your curator friends are happy (but tired) 🙂
For better or worse, the trending thing brought out my competitive instincts, LOL! I think I’ve switched off now 🙂
hi
Exactly, Mark Bruce!
I have no idea whether it’s God or Nature, but whoever it is they apparently have a much better interleaf service provider.
God is creature and every thing in the world is create on the order of Holy God.
yes creator.
No No you don’t understand my words. i mean that God is creator of every thing and we have to investigate all creation of God. creation is wonderful lovely like milk, honey etc.
awesome!
Rajini Rao Thanks for the great visualization!
I understand this phenemenom as an instance of a small world network, which are commonly found in nature (brain, rivers, food chains, social graphs, roads…) and allow for a relatively short distance between any two nodes via central hubs. This structure is common in social, the web & nature due to a rich get richer type effect (it’s muched more nuanced than that of course). In biology it is effective and likely evolved since it is robust to damage, as most paths are routed through a relatively small number of hubs the probability of a particular node taking the network down is low. This is why you can take relatively large pieces of the brain out with little effect but at the same time a small important area being damaged can have debilitating effects. The internet is often argued to be a scale free network which is actually an extreme version of a small world network, with massive hubs and even slower growth of diameter with respect to the number of nodes.
Also btw, wise people in business take a leaf from nature and try to find pareto optimal solutions.
Feisal Kamil It’s not a fractal but such networks do share a certain property of fractals of being self similar and scale invariant. Small world networks can also form fractals under the correct condition.
Very cool parallels to the internet. Thanks for the many insights and comment on fractals, Deen Abiola .
beautifully illustrated.
And for some reason..insects..Wasps,hornets, ect like feeding on the underside of leaves
The ribs are more prominent, RJ Matlock , perhaps they have easier access to the sap from the underside.
It runs in the veins of nature, I guess.