08:00:46 So good morning everyone and welcome to the KITP seminar on symmetries in morphogenesis.
08:00:52 Today we have with us Eran Sharon, who will give the fourth talk in the series and we're very happy to see that there is already a steady audience that enjoys the talks. For the new participants, I would like to say that the goal of the seminar is to
08:01:06 review physical aspects of morphogenesis, with a focus on how symmetry is broken during development and growth, meaning how do we begin with a spherical cell or a flat tissue and end up with a complex shaped animal or plant. We have so far seen multiple
08:01:22 mechanisms for for this from hydrodynamics and left right symmetry breaking to long range correlations in planners polarity. And I'm certain that we will learn something new today as well. Our objective is to try and look for general principles and
08:01:37 we aim to do so by inviting speakers with very scientific backgrounds, which worked on very different systems and, in fact, today we have our first talk on plants.
08:01:49 As usual, the talk will last for one hour, including questions and discussion and discussion is a very important part of the seminar. So we invite everyone was a question to just ask it during the talk, you can raise your hand in the zoom app or just unmute
08:02:04 unmute yourself and ask the question, also like to encourage everyone to keep their video on, I'm sure that will make the speaker much more comfortable, it will facilitate discussion.
08:02:16 So now, we're done with the technicalities I'd like to hand off the stage to Noah who will introduce the speaker.
08:02:24 Great. Thank you.
08:02:26 So I'm glad to see that one person has turned their video on I would encourage more people to do so. So that speakers, speaking to a real, real people.
08:02:37 Speaking to real, real people. Alright so today we have the pleasure of hosting Eran Sharon from Hebrew University in Jerusalem, and Eran and his group have produced beautiful science on a wide range of topics including pattern formation nonlinear
08:02:52 physics plasticity and growth phenomena, as well as fluid dynamics and turbulence.
08:02:59 And I actually encourage encountered rather Eran's runs work first through his early papers on fracture mechanics where he tested the standard limits are the limits of the standard theory rather a fracture.
08:03:14 The limits of the standard theory rather a fracture. And he explored fracture instabilities buckling cascades, thin sheets.
08:03:19 They.
08:03:21 Yeah, his group, or on and colleagues have beautiful papers formulating elasticity of non-euclidean plates and shells with residual stresses and related concepts which, which have generated, um,
08:03:36 I think a lot of application and engineered and, and biological contexts.
08:03:41 I think these, these ideas have really clarified some problems in morphogenesis as well.
08:03:47 So yeah, so his group is also studying morphogenesis and shape change in specific systems and plants, and this is in fact the topic that we will address today.
08:03:58 So without further ado, please welcome Eran Sharon. Thank you.
08:04:04 Thank you. And thank you for inviting me to talk about this fascinating topic in this fascinating, a program in, and it's good to talk you know after this last year.
08:04:26 I will not talk so much about symmetry breaking off morphogenesis, and it will be talking about perspective will have physicist, on a, on a growing leaf, maybe even more about how how symmetry is preserved or how growth is maintained, normal proper.
08:04:49 And it won't be biological talk. It will be kind of a mixture and collection of thumb, or version some suggestions for my experience, making a tiny reasonable reliable progress in working on these biological systems is so much more difficult in working
08:05:13 with synthetic systems.
08:05:16 And so I will present results. Some of them are nearly convincing some of them are suggestive, and the work was done at the Hebrew University rocket Institute of Physics and mainly by Shah have one with here in Spokane becomes a half.
08:05:34 And with my colleagues here.
08:05:36 And what we see here this field.
08:05:39 And this noisy will be ordered let's say it's not turbulence, it's a growth field of a small region in a leaf.
08:05:49 As the surface of the leaf.
08:05:53 And the. I will describe our attempt to understand.
08:06:00 Current first characterize understand the relation between what happens in the pixel level to the global shape. But then, to, to understand what actually controls, these pixels and look at it as kind of an adjective solid.
08:06:19 So, let's start.
08:06:21 So the general question is how such beautiful beings shape themselves.
08:06:28 And, and the approach. I will present today is of active matter. So very briefly, and just motivation. So I guess you you've heard already many talks about active matter active fluid fluids me, mainly, and he will see folks and earth, and even.
08:06:56 And as a sketch of an approach to describe this as a continuum active better you
08:07:03 can you.
08:07:04 What is your field, in this case it will be a velocity field, which is Victoria. And then there will be some constitutive relation between its elements, be some source terms.
08:07:19 And then this field exists in the three dimensional space so and you can see some constraints, it must are very tall, you can play the equations, etc.
08:07:33 Now, here what we see is a growing leaf it's a tobacco leaf. It grows slowly in these markers, I will. You will be back to them in this case we stretch the leaf between these two points and these are just references to other side of the leaf, and it grows,
08:07:53 and again it is made of pixels of elements, sales, like those elements here on Earth beach.
08:08:04 And it is active, it's not a passive system, and it evolved as dynamics. So, if we want to make the power loud, so there is a field, the field here it's a growth field, it's in your feet in front of Victoria.
08:08:21 And there is some constitutive relation which I will try to describe it as radiology of this material connections relations between a response, and the strain of the growth to the
08:08:41 neighbors.
08:08:44 And in this case of a leaf, it is a two dimensional surface. So, it must obey. It must be a two dimensional surface for, in a way, these compatibility equations have described the surface as hold, and they actually link between the shape of the leaf,
08:08:59 and, and, and this say growth field.
08:09:12 Okay, so this is roughly the framework, and the structure will be that.
08:09:21 Again, it will catch a global view and structure of how I want to present a problem.
08:09:32 Separation to mechanics and to biological parts that interact.
08:09:40 I will spend few few, few slides about the mechanical problem, and of again how shape is linked to a growth let's call it in this talk, inelastic different information.
08:09:55 And then I will stop it this will be a good time for question, then I will discard three main parts of experiment in the first week exceed the both of a normal, normal growth of belief is far from being a water balloon like inflation.
08:10:15 It's a very rough, a field in the other parts, we will see that the material the active material of the leaf is visco elastic with clear indication for response to external stress.
08:10:37 The change material properties, and it's further evolution.
08:10:43 And in the last part, I will present some very dramatic changes in normal leaf growth response to illuminate and changes, day or night or light and dark, which lead us to some suggest that the stomach stomata activity in the leaf are very central element
08:11:10 in growth over the great regulation, but it's not an artifact it's not.
08:11:28 Okay.
08:11:32 So schematics say we, how can we view leaf growth.
08:11:33 It's tomatoes are not just for breathing, probably very important elements in this active method.
08:11:37 So there's an active process.
08:11:42 And a lot of biology in a.
08:11:46 And it dictates some growth. The field of growth.
08:11:53 And as a result, shape is selected.
08:11:58 And then everything would be updated mechanical state of all these elements is updated, and probably some going biological process updates, the active, out of equilibrium processes and and the thing is that all this part is hidden.
08:12:19 We don't see it and we have observed that the shape of the leaf.
08:12:25 And we must spend a lot of work in order to guess what's going on in this part. So, this part is basically mechanical once the actual attempted extension of the self is determined by need some material and it must obey the of the most of mechanics and
08:12:59 is a theme sheet of material and updates the stresses within it after relaxation. Then, this is a biological part which responses and closes the loop and let the system evolved in.
08:13:09 Let's start with the building block. Again, very schematic view of the building block.
08:13:17 Clinton which is not like an animal film, and I go back to an old model of by Lockhart.
08:13:33 We see the volume, changing the volume of the cell vs is around parameters, basically, we have pressure to lower pressure inside.
08:13:39 Em, and basically it's a visco elastic in the in of the cell wall.
08:13:44 And there is a yielding of the Federal wall, which allows increase or change in the volume of the.
08:13:54 Now, just as what these equations are in the context of our problem. So, they are without arguing, how accurate they are but what are they. Therefore, in a pixel an isolated element.
08:14:12 It's not a field.
08:14:15 These are not feel the equations.
08:14:18 And these are all scarves color variable the pressure and all the parameters.
08:14:24 And normally you would assume that these are fixed numbers.
08:14:30 And that's it.
08:14:31 Now, what actually in a in a in a growing belief, you talk about a field of, of these of all of these guys, and they can change in time and space. So, these equations are actually very far from describing a leaf growth on this bass information is not
08:14:53 Information is not here and all the variability of space comes from space and time is not encoded here.
08:15:00 So, this is our starting point, and we will see that actually the evidence is the, This is a good
08:15:19 And let's say just a give this notion that growth must be regulated, especially if you think about it being sheets material, if it doesn't grow properly.
08:15:36 Very quickly, it will buckle and crinkled and crumble and this actually happens.
08:15:40 If you manipulate some jeans. In the leaves that are normally flat, this beautiful work but truly almost 20 years old.
08:15:53 You can see how a flat leaf become crinkled and crumpled.
08:15:58 These are other examples from Enrico coins law.
08:16:01 Here are examples from normally always lobbying the Faculty of Agriculture and you validation from the Weizmann Institute, these are two new terms of rabid dog says, and you see how leaves becomes distorted.
08:16:14 Once you play with their genetic with.
08:16:19 So, a tubing a regulation system that existed diseases can also do this this is kind of funny that attack leaves when they are in the band, and then growth becomes non unregulated in some regions and they indeed distorted.
08:16:42 And sometimes growth can be such that the leaf is naturally not flat and you can form shape or structure.
08:16:50 So, I don't know, do you do you also see this black in here for that the
08:17:00 slides are okay. You see it okay so it's just me. Okay, so growth distribution leads to shape. So let's spend a short time about this connection of pink sheet static material has some growth distribution is some processing know it relaxes.
08:17:21 So we switch off the biology and on this feedback, and just asked. Okay, I have a plastic sheet is some geometry encoded by some old process inelastic process, what will be shaped.
08:17:40 So here's an example of a tall plastic sheet.
08:17:51 That was deformed planner in the plane and adopted this multi wave, a.
08:18:06 Okay, let's first understand this is a simple system.
08:18:09 out of plane, three dimensional shape. And here are examples of this is plastic sheet front inside and these are different leaves and the similarity is clear and the question.
08:18:13 And then let's hope that we can further understand the more elaborate responsive active system. So, how can we describe sheet shape that could even say sheet that undergoes some distribution of the formation in formation.
08:18:36 And so, we use the term the links between in plain informant geometry metric distances between points and shape in space.
08:18:52 And
08:18:52 it is not full and not accurate. The way I put it but it is what we need for the, for the next step. So if you think about this surface, and you induce local Fleming, or patients of elements, or you make it.
08:19:16 Build it by assembling elements with some shared some you actually specify a distribution of distances between point or equilibrium distances.
08:19:23 We can be described by a metric field.
08:19:45 rate of change of your normal if you walk a flag on a heel, your flag rotates. If you walk in.
08:19:54 If there is a fellow and then one direction it will rotate along the way you can in the other way.
08:20:15 So, there is a field, accurate way to describe these properties, it's the curvature field, it has principle.
08:20:24 Principal curvature, and the Goshen curvature is the product of these two principal curvature of the curvature of the shape. Now what God showed that this property, which we just described it as appropriately of the shape is actually completely determined
08:20:33 by the by the metric field, which I described as distances, not saying anything about the shape. So, oh, you can vote a growing belief that stocks or expand felt in different direction, actually the process of building this part.
08:20:56 Then a actually are encoding the property that will be reflected via shape. So, this is the core of, of, of,
08:21:10 what I have you I will, I will, adopting.
08:21:14 So examples of.
08:21:18 Let's make a cartoon of a growing organ let's think about the cylinder cylinder Philander mega friends have felt like I didn't greens.
08:21:31 And if I just let the system grow without any control it can grow exponentially number of films in the next week will grow faster and faster and faster but everything is symmetric known laws and the ology, the informant the biological information is is
08:21:54 identical everywhere along this funnel which is formed.
08:21:59 But then when it is fully open.
08:22:14 And there's no shape actually symmetric shape.
08:22:18 So, the structure must break the symmetry. So maybe this is the only a symmetry breaking being I will present. But again, not because anything happened, a level of the self, or the material, or even if nothing happened.
08:22:21 We see the, this is the end of the shape of the actual symmetric shape in the perimeter that we are trying to to glow to the rim is longer than two pi r.
08:22:39 It must break the symmetry and this was demonstrated both in America Lee, and in experiments that you can grow such surfaces, and boring and symmetric and present, only the length of the acceleration, let's say, But once you go beyond the threshold symmetry
08:23:02 is broken waves appear along the edge, etc etc and very natural question is whether such structure, like, if not for the Crone or the outcome of this interplay between simple biological input and non sip not simple mechanical response, and not necessarily
08:23:25 by some complicated biological network that create some blueprint of Curve, Curve down, etc etc.
08:23:36 So, this is the context.
08:23:40 In order to study the shaping of surfers know this type of the time ul Klein, and you know I want to build this system from responsive jail. Jail the trains and
08:23:56 temperature is raised above 32 centigrade.
08:24:09 The amount of shrinkage the percentage of shrink it is a function of the concentration of the gym, so if you make a disc is graduate in the concentration.
08:24:11 Once your army.
08:24:22 Then each region of it will shrink, let's call it grow in our context of a leaf a week we create a leaf. But in this leaf we know exactly what is this right hand of the loop.
08:24:29 We know what is the active string what what it wants to do locally, but it is glued together. So let's see what check it.
08:24:45 And this is a way that you can really ignore it, but this is a variation of a beast. It is they loaded here then are here so it will shrink more once we increase it them to let's increase the temperature and then decrease it so the disk is flat.
08:24:56 This this wavy here in the center is just because we hold it with one, but it is flat like this guy, but programmed to undergo and known a growth. Once activated, so let's we increase the temperature and this guy attains this panel like a duration with
08:25:17 negative gosh and curvature and once you pull it back, it goes back to it flat configuration. So here we break the symmetry, basically, everything is actually symmetric.
08:25:31 As far as the input is relevant, but selected shape is not one so it's metric up and down. And there's a game breaking of symmetry, because of mechanics and geometry is this you can make all kinds of shapes.
08:25:49 And this was the work of the RL at the time, but later on this field.
08:25:57 Normally mentioned, and spread into very different direction this is a beautiful work from Ryan hi Ward submillimeter scan surfaces from the same jail that we use.
08:26:13 This is a work of Jim white with pneumatic elastomers.
08:26:18 This work is again with the same journal but printed
08:26:25 with the 3d printer.
08:26:30 This work is actually a pasta, it's from leaning your PhD in the Media Lab. And these are pastor like structures that again are in printed response once you put in the suit.
08:26:44 And this work of an alarm on your game with the magic elastomers showing that you can really program in very complicated surfaces, a flat on activated.
08:26:59 It contains the face shape. You can you can work with with
08:27:03 with
08:27:09 elastomers with high voltage activation.
08:27:17 from together with been while manage shows me call it is this bottom of it is inflated
08:27:27 This work with from
08:27:27 sheep.
08:27:28 With champion channels that expand a differentially, and you can shape it and very simply don't live in, in my love for all these structures are activated globally and externally by changing the temperature by inflating and etc.
08:27:48 And it actually made it into an auto normal animal like being by making this channel synthesizing into it the catalyst for the bottom several things key reaction.
08:28:03 And then you just put it in the dish with food to with the material of the reaction and leave it and then there's a periodic reaction that send France that lead to construction and this is a 3d measurement of the.
08:28:23 OK, so now let's go closer to plants but not yet. The leaving.
08:28:31 These are still dead materials, but there are plenty.
08:28:37 Examples of structures in plant world that actually like this seat board.
08:28:55 That used to be flat but once you drive it curls into opposite Lee twisted, a clear balance. This is how we choose to feed them this work of a chef at the time.
08:29:01 A again you can analyze it, what's going on in the small scale architecture and two layers of fibers.
08:29:10 Our Autodesk colleagues, taught us that once you dry and the hydrate and with them then they expand and shrink perpendicular to fog fiber orientation.
08:29:27 This way, that way you can solve the mechanical problem and compute these shapes.
08:29:33 You can make a gentle modem mimicking it and again he twisted.
08:29:34 You can do similar things to roads.
08:29:38 And this is a single fell from, from the owner of rhodium stock be
08:29:47 flower. And what it is wet now once, once it.
08:29:51 So these are just two examples of mechanical structures, made by plants and activated by you immediately.
08:30:10 But this is not yet what we wanted to do to to to study the closed loop. Here is a beautiful example work from the 50s, but many many structures of combining fibers and mattresses in different combination that lead to different shapes.
08:30:29 I believe that most of them would be explained by mechanics.
08:30:36 Okay, so now going beyond mechanics, so maybe this is a good time for question before we start with the real.
08:30:46 Can I ask a question, please.
08:30:49 Yes.
08:30:50 So, you show many number of examples we have a leaf, and so forth, those leaves have very prominent Venetian patterns. So, those taken into account when you think about how a leaf would curl, the, the, the architecture of the veins that supply water or
08:31:11 nutrients or whatever.
08:31:12 Okay, so this is a very good question and I will soon start showing data from Leeds, and the veins, definitely affect the, the can affect on the small scale transport might be more worrying is that you have a very significant mechanical effect.
08:31:38 And it is a question or the woody show some cases in which are the main sheet or studying it as uniform sheet, not make sense.
08:31:53 And the veins, as a mechanical structure must be taken into account. This was done by in some works of separating combining tissue and veins. As for the transport in here in what I will talk about today.
08:32:16 I'm not taking into account any effect of, you know what you need to transport.
08:32:28 Okay, so now going beyond the country. So option one is, let's play with the system that's manipulated and see if it is, if it's responsive if we can interfere with something so if the most primitive example was putting oxide growth hormone along the
08:32:48 margin of relief.
08:32:51 If there coaxing stays there. Maybe the leaf grows more along the margin, than in the interior and we might get a three dimensional shape and this isn't a demonstration with excellent leaves in a game.
08:33:09 Indeed, waving has appeared and evolved, and it became like those mechanical sheets with excess of edge, this is negative curvature, but this can be done more seriously and properly and this is work of Shaka together with Nami Ali.
08:33:24 At the time, And, in which the level of induction of access growth and on the margin could be a biological me, and the shape of the leaf, including it's out of plane way Venus measure and quantify.
08:33:43 The other thing that sort of did was okay let's, let's just measure what's going on there. How does it leave grow.
08:33:51 And this will be
08:33:54 an important part.
08:33:57 surprised us at the time.
08:34:00 So, first of all you you grow in a plant, and you want to measure its top surface of belief in three dimension and be able to also measure local expansion this growth.
08:34:30 But basically you want to measure the shape, and you want to measure the strength or the growth field.
08:34:38 And so when.
08:34:40 Yes, so the feature is on the leaf, and you can, in a way, this is p one in let's say this is a unit distance and after a while, you look at those points in space and unfair.
08:34:56 Dis element, and you can define it as the growth.
08:35:02 With this eigenvalues. And you can define the growth area growth and measure it across the leaf.
08:35:13 So, again, this is our leave it grows and expands smoothly and nicely and if we keep on playing this video we will see that it really grows. I think it's 24 hours measurement, you see that this that many many features that you easily distinguish with
08:35:32 a camera is good enough optics, you can see a lot of features, they can be used as tracers and see if you also have the three dimensional shape of, then you can really measure the strength.
08:35:47 Really the growth itself, not just keeps projection on the plane.
08:35:52 Okay, so it looks like a smooth, non uniform grows, it grows more if you if you notice it grows more here than the tea.
08:36:01 So, it reminds us the gels, so it can shake itself probably and this is what we had in mind, the beginning wanted to look long wavelength.
08:36:11 You have the system.
08:36:14 When shop have measured it so this is a 3d typography, this is like three hours different bit of the same area. And this is what happens to the coordinate system on this field.
08:36:27 And this is the Goldfield after 15 minutes interval 60 minutes, three hours.
08:36:34 So, this is definitely not alone, the rent ones are shrinkage, actually, is our region. These are directions in which that element got shorter.
08:36:48 But this is not what we expected and
08:36:53 apparently this is not the right way to think of growing leaf if we want to capture the governing process.
08:37:05 Actually, that also had been and our new evidence, your evidences of this heterogeneity of growth disease in Excel scale here this is a more recent work also on subtler levels of intelligence Georgian at in, in growth rate.
08:37:24 A very nearby even even neighboring cells can undergo dramatically different expansion.
08:37:32 And as we will see what we could add that.
08:37:35 Also in time.
08:37:38 First of all these different differences. Our goal for rapidly but even the same cell itself can grow and shrink and grow and shrink so it's an field which is very noisy in space, and in time.
08:37:54 So,
08:37:58 apparently, it suggests that if we want to understand the mechanism that governs this thing. We should study the statistics of.
08:38:09 It is on the one hand on the other hand, it just makes the come more and more challenging to understand how how it can grow flat. Let's see if we think about the flat leaf, whatever shape.
08:38:22 How can you grow properly. Because if everything was smooth and global okay yeah flat leaf, all the cells grow by the same factor so it's a bigger flat leaf, but no, it is so different locally, but still remains flat so this just shows that regulation
08:38:40 regulation must occur on a small scale.
08:38:45 And it's a more challenging system around. Yes, sorry this invoice do mind going back a slide, I just really want to make sure I understand the, what we were looking at.
08:38:59 So roughly what is the scale of those little sticks.
08:39:05 So how many dollars roughly per stick we're looking at density.
08:39:12 A, I will jump in slide before we work, you can work in in different scales, but typically it will be 100 micron on 100 micron so it will be bunches of several films, it's one, it's not as over here these are single cell measurements, not ours.
08:39:32 What I will present is typically bunches of.
08:39:38 And what what's the rate of cell division so we're looking Okay, so a one hour and the question is how many cells have divided. I need my little yeah I didn't say didn't mention that and I should have it.
08:39:52 When we see a leaf what we usually, and what we used a centimeter size leaf.
08:40:00 Nearly all its growth is by cell expansion no cell division only it's a basic art.
08:40:14 The bottom edges like over here and there is some division, which is the main main growth and it could be by two orders of magnitude is by cell expansion.
08:40:23 Mm hmm.
08:40:24 Okay, this is an important okay but but then. Okay no cell division, that's actually very important to know. But, No, no, it's in
08:40:37 doubles in.
08:40:40 In, we will see it in a second. Yeah, I will show you the next slide.
08:40:46 So, sorry around I have a related question, what's known about cell, cell signaling could activity of growth in one cell be down regulating the growth in neighboring cells.
08:41:04 Oh, what about communication. I must be careful when I say that things are not known, but I wouldn't think about, to me, Not much if no one, and this is the main issue, what are the relevant signals for cell
08:41:22 growth and directional cell growth. And I will mention some, some of these features. So,
08:41:34 I can't say that I know about a non signaling between a neighboring cells.
08:41:42 There are fluxes of hormones from cell to cell, and they could be directional. So in this sense, this is cell, cell interaction, because those hormones, change the, for example, that the stiffness of the of the cell wall then leading to extension, but
08:42:04 also Watson right.
08:42:05 Oh, yes, yes.
08:42:12 for example, and
08:42:18 it's not that this part is not known and it is a subject is the issue of what are the signals, what are the relevance of how can how should we think about system of many many cells that obviously interact.
08:42:27 I will try to comment about this but I think
08:42:44 And because they grow properly without some without any headquarter and but how do they interact, is it continues can we can we just
08:42:49 get it with a minimal very mechanical a model, or you should have non trivial biology signaling, etc.
08:43:00 etc. And I can see, I don't know, I think it is safe to say that it is not know.
08:43:09 Okay so, one more question. So when I say when a cell grows up after to whatever the other mechanical properties or the cells, they fixed like this stiffness or passively kind of know, and settled, even done.
08:43:27 Oh, no, and settled, even done. But first I will give partial answer, mainly because I don't know enough, but the cell matures, even if it doesn't grow it cell wall at the beginning, has some properties, but later on the outer part of the some of the
08:43:45 older part.
08:43:48 A can undergo stiffening etc so there is a maturation about. If it is, you can link mechanical properties, only to the expansion amount of expansion, I don't know, I don't think so.
08:44:06 And I think I will show some information related to this, Okay.
08:44:16 Maybe it will be a will be a proper time for discussion about about these type of questions in like 10 minutes. So, I mean, it will be nearly the end.
08:44:30 So, let's, let's see what what we measure this is the growth area growth, Instagram, and this is this other edge for bonus question about, okay, what's the rate, what's the rate of growth.
08:44:46 So, this leads in 20 minutes, would grow in one person like 4% are our in area.
08:44:58 But then he looked at the distribution of its of its pixels of itself.
08:45:06 Not sales but
08:45:08 area elements.
08:45:12 In, it's a very broad distribution with rates that are much much much more, much greater and much smaller than it's been, and with a lot of negative values.
08:45:28 Nearly half of the distribution is significant parties in the, in the negative. It's not just direction of shrinkage its area contraction. And this is during normal growth of belief.
08:45:42 So, This was a surprise to us and we took us like half a year to see that this is not measurement noise.
08:45:53 And this is really, really property of the growth.
08:45:57 And this is not Gaussian it's not under noise. And you can characterize several properties and I will skip it quickly because I want to get to other parts of what happens to this field when you coarse grain it in time, and in space so you can measure
08:46:15 it with longer time intervals and see what happens to its mean which is not surprised, but the ratio between the with the average.
08:46:35 It becomes eventually over a long time you hardly see shrinkage. But a short time, it's very very fluctuate thieves and field, which properly smooth out the over longer time, and over longer schemes.
08:46:51 Again, if you if you feel in coarse grained in scale the new again hardly see a shrinkage.
08:46:56 There is a difference between night and day I will skip it.
08:46:59 It's not an escaped free field. The typical link scale. If we measured the correlation function of growth.
08:47:15 Night, it is a noisy rougher field them doing day, but there is a typical scale and more interestingly, if you sit in a single point, this distribution, you can say, well, maybe the top part growth, less the middle part, or in the bottom part Martin you
08:47:26 get the eastern know if you if you fix, and you track, a single region, as it flows during growth, then it also fluctuate. In a typical time of like 45 minutes in its, you can see it with It's time for your transform.
08:47:45 So, it becomes scale of a minimum in those lives.
08:47:50 And typically, time, have, like, 45 minutes.
08:47:59 Now, a question and boys here all of the proposal.
08:48:02 years.
08:48:04 Quick question for me. How large other cells. So what's the ratio of the length scale to the same size, okay the cells can be like five micron can Nikon's a.
08:48:18 This is the typical sizing, they can grow more than they can be smaller like it depends on the age of the leaf.
08:48:27 Thanks.
08:48:30 And so, if you want to you want a simple world, then you say, Well, if something grows wrongly, then, first of all, the soul in then First of all, stress appears and the stress is a signal.
08:48:43 Then here we have a way to close the loop, and to sense it to feed it back, and to correct growth and in this is, this would be a nice way to to close the loop.
08:48:55 So, it means that, and this was also proposed in the 80s by Paul green.
08:49:02 in many many papers.
08:49:05 And so, it suggests that if we apply external stuff, we can monitor the response of this tissue of these active letters to stress, and then glued something about it responds to naturally generated stress due to a local growth.
08:49:26 So, this basically an attempt to measure the geology of a growing leaf. So, this is a leaf we can measure its growth as I described before, but now here at the bottom of the pool it with to a typist.
08:49:57 are used as.
08:49:57 Fourth, strain gauges not lonesome that score, if we can, we can measure.
08:49:57 We can measure the end.
08:50:13 This is destroying field, these are the two glowing points if the edge of the leaf. And here we see in red, the extension and in green the shrinkage color of which, and this is the other side we this is we are lucky because we have for each experiment,
08:50:17 a reference which which is not good.
08:50:22 And what do we see this is the strain rate in percent birth 10 minutes, and it is look look over here these are the relevant.
08:50:32 So in below it's the reference side. This is timing minutes.
08:50:39 This is timing minutes.
08:50:50 Direction light blue is parallel to the edge perpendicular vertical. And over here, red is parallel to the pulling direction, Brown is perpendicular. So, the material is material yields over some initial duration and actually drinks perpendicular like
08:51:02 a response to expand and if you conserve some, some area.
08:51:11 And then there's another phase and long phase of many hours, in which a growth rate, and now it is non reversible This is reversible is enhanced parallel to your pooling direction and actually suppress perpendicular below that the blue ones the brown
08:51:28 is below.
08:51:30 If you measure this plateau here is function of the applied force that you can see that it increases but that saturates.
08:51:45 Okay, which again makes sense if you need to build your material if you if you extend it too much then eventually you will usually saturated by some other effect.
08:51:50 And you can ask about directionality, so we can measure the growth here or the stream inelastic. Most of it.
08:52:00 and we can compute for this loading distress distribution that lights dress distribution and let's measure the angle between the two.
08:52:09 So, there are nearly parallel.
08:52:14 The light, stress, and that they applied stress and the measured.
08:52:20 A string in the pulling direction. Now if you go to the other side to the control and say, let's bring it to parallel and perpendicular direction, then you see that it is random this this rent curve is shows, I saw tropic a growth.
08:52:41 So it is very close to a sub topic in the, in the, non stretched region. But if you do if you persist fooling it for a long time of 10s of hours.
08:52:55 Then, this is what happened. This is what we saw before, this is the high, high correlation in orientation, which start a decay and go towards the isotopic growth, even though it is still under the same load for the tissue.
08:53:14 Correct, its growth.
08:53:16 A in a timescale of 10s of hours. It goes back to it's a rapid growth so this is after one hour or so this distribution of the alignment, which were measured locally, and after 15 hours it this distribution shifts to the ISO tropic direction.
08:53:40 Now, then you can ask okay what's going on there, a easy that some mechanical properties of the tissue or change the distress simply leads to less.
08:53:53 Always train, or maybe some signals were turned on and the attempted active growth was erected in a way, to, to, not wanting to grow it too much or too to pull back.
08:54:10 So, we can monitor the mechanical properties of the leaf as a material as engineers do. So we launched it now in a short time cycle of owning and operating a load.
08:54:28 strength and strength, and the loss models that are related to their shift in faith.
08:54:46 And if you plot them one versus the other. you can get it in blue.
08:54:58 open its area with related to the loss to the viscose models.
08:55:07 And this is what you get from you can get very nice measurements and very high accuracy with this material.
08:55:16 And let's see what happens after we load.
08:55:19 So, we know we go and measure mechanical properties of region, then loaded for 24 hours and then we're going again and see what happened to this material, and you can get measurements and this is basically what you see this is before.
08:55:39 After that we hear BC, how you're slow, meaning larger strain for given forth.
08:55:46 your slow, meaning larger strain for given force. And after the slope is lower, it got stiffer.
08:55:55 The same the same force induces less strain. This is in the wrong direction power level to the constant low.
08:56:01 And so this can be measured. And you can see that, again, the material, this active material.
08:56:10 Have indications of remodeling, it became stiffer powerless to you're pulling extended pulling direction and software.
08:56:21 And this is frequency dependent right it depends.
08:56:25 Yes.
08:56:26 We didn't scan the frequency. Yes, this, this, this is something that could have been done but this frequency is very shortly here, an entire loop is completed within less than five minutes, and all that fast.
08:56:41 yes yes yes so.
08:56:45 So, can I just go back, I've been puzzled by this time ago, so did I understand correctly, that in some auto correlation function that you flashed at some point, there was a peek at 45 minutes.
08:57:03 So it's a cycle going on there you know other cells moralists taking what the in and out.
08:57:09 Yes, I think this will be. Yes, I believe, yes and we will get to it. Okay. But right now, what you can say that yes if you, if you look at this.
08:57:23 at this surface, you will see it breeze, or vibrates locally locally at every place in this typical a timescale of 45 minutes. Now on top of this we load it, and then measure it.
08:57:43 And then, country continuum in a way.
08:57:49 Now, the last part of the talk is about something we found a surprise to find him at a school, better understanding again, if we want to discover what's going on inside and so we are feared.
08:58:11 We first characterize and then we load, and now we see something that happens naturally.
08:58:17 And this is a measurement of the blue side decided, and see that it is a long time, and here this is a daytime and then night is off and then we see huge peak in the strain.
08:58:33 Right.
08:58:34 and then nights goes and then light is on, and we see the very dramatic population in strain rate and this is global, this is not measured locally,
08:58:49 meaning it's not a big some wise.
08:58:53 This this type of flow of blood, it's in a small region of the leaf but it is reflecting the entire life. Now if we look at what happens to the stretched side, this is what happened so this is our initial polling steady state during day, then lights off
08:59:10 there is a bump in both direction of the pooling and the perpendicular. And then when light on, we see this up, let's let's let's say, zoom, a bit here.
08:59:28 So the non stretch shrinks negative string rate overshoot and stabilizes back on the growth rate, the perpendicular one we see that when the direction that we pull in this time.
08:59:45 Once this shrinks actually This yields.
08:59:49 And does the opposite. A
08:59:54 calculations of the pulling in the perpendicular direction.
08:59:59 I will talk about this switch night light darkness to light, but just mentioned that in the opposite, switch, there is a different mechanism, both together.
09:00:12 Expand, there is a expansion and then shut down, new steady state but if I pulled. I don't see this opposite. So, again, both direction, perpendicular parallel expand and go back to normal.
09:00:28 So let's see what what what this thing is this is part of the life cycle of a normal leaf. All these dramatic affiliations.
09:00:38 And what we did at the time she measured these a, so. So, if this is the affiliation, this is when the light turns on. And now she measured the Young's modules modules of the leaf.
09:00:55 Using this technique and the last modules of the of the of the leave a with this technique.
09:01:04 And you can see the least get stuff done.
09:01:08 And then stiffens again and go back to steady state. Now, what is the mechanism.
09:01:16 So, first of all, these are, look at this is the one, this leads have.
09:01:29 I don't remember exactly their age, things very stem, but these are young leaf. And this is a month, same leaves the same region for a month. And we see that this change in mechanical properties which is very obvious, very dramatic in the young lady.
09:01:42 Gradually disappears over time so leaves, as they mature they become less and less responsive to whatever it is.
09:01:51 The first thing we wanted to see if it was your guardian, it is not your card. So here we see.
09:02:09 With change of light day to light is on all the time, the effect beers. And then, day three, again, illumination variation and the effect recovers. So, what we believe and I think it's related voice to what you just asked about it is related to a water
09:02:20 balance to the drawings.
09:02:23 This is work from 20 years ago, and the effect of belonging, the wind on the surface of locally of surface of the leaf and this is a measurement of the toolbar pressure, and this is the duration.
09:02:40 When turns on here and off here, and you see a drop in the pressure, and then recovery over timescale of like 30 minutes.
09:02:50 When we repeat this experiment and we don't measure the pressure but we measure these young models of the tissue. Then we see the same effect, it doesn't it's not a fact of life, it's.
09:03:03 Then you can use an inhibitory of stomata activity.
09:03:10 Different inhibitors one is sensitive to light one is just affecting the stomata but in both, you see that the effect disappears after this treatment.
09:03:22 So, all these large expansion shrinkage change in models of material of the measure of the global measurement of mature are probably driven by activity of stomata it changing releasing water closing increasing pressure pressurizing the tissue.
09:03:48 Now, this might. First thing is we said, well, we hope to find signals and stuff, and find that it is an artifact of breathing.
09:04:01 But I don't think this is the way to look at it, I think, in fact, it shows that the leaf is a structure in incredible interest incredibly interesting mechanical structure that very suitable for businesses to deal with.
09:04:22 Because the tomatoes are actually a way to manipulate this pressure term in Lockhart equations locally.
09:04:33 And, in fact, when you read more of the literature, you find a, for example, the effect of the phenomenon of touchiness of stomata activity and collective behavior of stomata i, this is something I'm not an expert of.
09:04:50 But again, it seems stomata opening is actually also controlled by pressure of the epidermis of the guard cells.
09:04:59 So what happens actually when all these over shoots are done by okay light is on its tomatoes are open water evaporates, but then stomata is open more because the loss of pressure.
09:05:15 So it's a not only in our element, built in, in, in the in the tissue and obviously stomata expansion and closure of stomata can affect neighboring cells.
09:05:27 So all the hydraulic within this structure is extremely interesting and non truth.
09:05:34 I think with this I would like to summarize, and mention, and just flash things that I present and thank you.
09:05:46 And if there are questions.
09:05:48 I will try to answer.
09:05:50 Thank you so much, that was great. I actually have.
09:05:54 So if you have questions, feel free to just jump in, or raise your hand if there are going to be a bunch, you can use the raise hand button, and we'll address those and turn, I don't see any right now.
09:06:06 Can I can I jump in. Yeah, go for it. Mm hmm.
09:06:09 Can you please take us back to the slide where you show the growth response and growth in response to stretching.
09:06:20 Right, you had these two regimes first.
09:06:23 This is a tropic allegation with pause on ratio, and then more or less isotopic.
09:06:33 Yes, I know what you mean.
09:06:38 We are here.
09:06:41 So there was some crossover one. Yeah, and I think maybe the one before you had some crossover time from one to the other.
09:06:49 This one
09:06:52 for me before before before before two slides before.
09:06:59 Yeah.
09:07:03 So, time off the stretch. So, this is a minutes.
09:07:06 So the first fancy and is within 40 minutes I'm just wondering if.
09:07:13 Right, so, correct me if I'm wrong but what I'm taking home right now. Well I guess I am hope
09:07:23 is that there are two time skills and there is this breathing time scale, where the water comes in and out.
09:07:30 And so the correlation time of that.
09:07:36 Or at least characteristic time is a water of 40 minutes.
09:07:40 So the first thing that happens is when you pull your sort of squeeze the water in or out or or between. Yes, yes. And the growth kicks in later but this first tree MC and reversible response is sort of pumping water.
09:08:01 I think this is a passive spongy material in a way. Yes Go elastic material.
09:08:08 But then starts growth.
09:08:12 Yes, yes.
09:08:14 And then there is another time school, in which the material.
09:08:20 Probably revealed itself, we tried I didn't mention it.
09:08:24 David is here. And so it is related to the main load carrying element at the cell wall of plant are defined cellulose fibers.
09:08:38 And they're very, we try to monitor with the optical activity, they're very active.
09:08:47 Active politically, in terms of polarization we tried to measure global changes in a build up of global orientation, you to load of of a syllable fibers we didn't succeed, it doesn't mean it's not exist.
09:09:05 The works of Olivia mount, together with that let's keep the load on Mary stems suggest that the monitor correlations between directions of stresses.
09:09:19 To orientation of micro troubles in the cell membrane, which are known to be to dictate the position the orientation of the position of syllables fibers, which could be a signal, how, how stress or strain is converted into an actual topic mechanical productive,
09:09:43 but there's also cell division at that stage right and the cell is, I guess, along the micro two balls right so they're sort of direct coupling to your cell division and, but here there there is no cell division.
09:10:00 He does not sound division.
09:10:03 This isn't much cruder monitoring of this material.
09:10:11 And, as David mentioned before the veins he, etc. But I don't think in this in this young leaves the veins are also very, very soft. A, and I don't think these type of effects can would change much of this time scales and dominant effect.
09:10:37 We don't have a do believe that that that water, and he drank is apparently important.
09:10:46 We don't know if it is dead dominant effect. And what is the downstream effect of all this stuff.
09:10:57 By no means I claim that this is the only process, I definitely believe that this is part of the game.
09:11:04 And that other biological cycles must be linked to this
09:11:14 physical into Alec.
09:11:21 The Shadow, you have a question.
09:11:24 Okay, thank you, a lead from my camera around.
09:11:29 My question is, is it possible in some way to measure the pre stress, the stress inside the cell you to grow, because it could be that growth is compatible, so use you, there is a change of shape, but not a change of stress to use the metric is embed
09:11:51 the boat so. So it would be very interesting to measure the received was threats inside the leaf, for example, cutting the leaf and measuring a change of shape you to the cat so measure how much elastic elastic energies in the belief.
09:12:09 Okay, so this is a good idea. In general, I don't know about our leave.
09:12:27 But it is known and very dramatic examples of of leads and soft and Greenie organs of brands that carry a lot of residual stuff.
09:12:40 and other examples in which you make a cottage.
09:12:45 And I know I remember demonstrations of an NGO really about rhubarb
09:12:45 Match anymore.
09:12:47 I doubt also examples in Bowling Green actually which were mentioned was you did this work, and decreased column I did work by when laser ablation of familiar in the marriage Thurman you see an opening of this card.
09:13:09 Reflecting the stresses that are there so I think in general.
09:13:17 I can't say how big they are in these leads in this age.
09:13:21 He, there are stressing.
09:13:24 And I just say that having this noisy map of growth, highly variable and fluctuating and heavy
09:13:39 perfectly stress free is, then it is even more fascinating to to understand how it created, I believe that the simpler view is that yes there are stresses, but they are never accumulated over large scales and large values.
09:14:00 And then the question is, okay what, how, how it happens over which time scales and obviously if you are to the system, then you do get quicker than crumpled leaves.
09:14:13 This is the system. It has the potential has the potential of building up stresses and deforming itself and distorting, it just does not happen in the, in the normal growth.
09:14:25 Thank you,
09:14:29 David the landscape.
09:14:31 Question.
09:14:32 Aaron.
09:14:33 Yeah, I was wondering if you could return to your punch line about the stigmata and hope you'll excuse my ignorance about plants, but so I think you said that there's a positive feedback, where this tomato let out some water vapor this lowers the target
09:14:51 pressure and this opens this tomato more, is that correct, yes, maybe, maybe I will switch, I think I had
09:15:05 open my.
09:15:08 it.
09:15:12 Okay, so I will not attempt it. Okay, the tomatoes are, are basically to the two guards.
09:15:25 Like,
09:15:25 Foster jersey No way.
09:15:28 And, and when they they open. They buckle, you to pressure, and then there's, then it opens up.
09:15:41 Now, what sets if they are buckled or not by code are also mechanical stress is in the epidermis.
09:15:49 So, what is not. It is known by botanist as the wrong way, response of systematized, you would expect that stabilizing element.
09:16:01 If you open and now you lose too much water you would like to close.
09:16:07 But what happens there is that they are open.
09:16:11 And then the pressure around in their surroundings drops, and then they open further, and only on a larger time scan which is typically this 3040 minutes.
09:16:29 There is a recovery of pressure which closes. So this leads to this overshoot. Now if I can share some thoughts of mine.
09:16:39 Then I can say that thinking of the big question of how a leaf grows properly. So we say okay, don't be stressed relaxation but then how will it, maintain its proper shape while relaxing stresses.
09:16:52 Then, looking at this stomata element is overshoot, and you might add all these monitoring of softness What is this softness that sorry I didn't I didn't.
09:17:09 Remember that if I, if I pull it stretches along the pulling in shrinks perpendicular. Basically, you take your, your friends and you reduce the world, who
09:17:15 This softness that we see here.
09:17:25 you lost to water. Now there are no more regions. They can be easily deformed, it becomes soft, a little bit like in this model of the, of the vertical model of the Federal feature but with modification.
09:17:45 So I think if you locally, reduce a water content. Let your system become more fluidic locally.
09:18:09 re adapt to the, and then inflated again back to the new boundaries of this area, and then do it in a different way, different touch in a different direction and different but then maybe it's a way of locally release, relaxing stressors, but still keeping
09:18:16 one right 90% of the leaf is still in its proper shape, so I don't know if it is possible.
09:18:24 Okay, thanks.
09:18:28 Sir, button and again,
09:18:30 I guess.
09:18:35 I'm so still puzzled by a little confused by this 45 minutes.
09:18:40 I'm still waiting for you to say that the bloody thing is just oscillating.
09:18:44 So this business of, you know, wrong sign of feedback. It's only wrong, if you're trying to stabilize the thing around this steady state, your evidence is that it's not a steady state that it's, It's an oscillator albeit spatially disordered.
09:19:05 Yes.
09:19:06 So.
09:19:13 So, what do we know is that, is this a disorder oscillator. I mean is this enough. spatial temporal oscillator.
09:19:23 I mean, is it really is this the right model and oscillator or what type of an oscillator. I do think that a proper natural growth of a leaf involves local populations of elements on the scale of a millimeter in the leads that we started the oscillate
09:19:42 in a typical scale of 10s of minutes.
09:19:46 Okay, in a, in a non correlated, necessarily, we look for ways we looked for space time correlations and to see if they're propagating France.
09:19:58 It's not clear I don't think necessarily the stuff. Now, this patch Enos of stomata that I mentioned that, that a mod is really an expert in this monitoring the exchange of the temperature of the leaf, which marks Corporation.
09:20:18 You also see patching as they work, you see regions, all the leaf, all the time, oscillates in terms of what they measured as evaporation, but what shall have measured is expansion.
09:20:31 So I do think that normal growth of release in must involve a lot of stretching relaxing stretching relaxing and large strange as we so much much larger than the average that you would measure on a large and long time scale.
09:20:45 And this is obviously what how it works. Why is it necessary, is it doesn't give a hint of how we regulate itself, I don't know but this is how the system works.
09:21:00 So around I have a couple of questions. The first is a very simple one, you measure you make measurements with the light off.
09:21:09 What color of light Do you use tomorrow Good night okay okay okay, I don't have it here, and I must say that I don't remember the details but we can use different, a different kind of light, especially for this.
09:21:26 This guy this ups are it, which is activated by a blue light I think, and not by the red light and you would not see the effect with that light and, and you would see the effect of the suppression.
09:21:45 I don't remember exactly the details, there are details about life I don't remember I cannot tell you.
09:21:53 Right. All the most of the measurements were done with blue light always combination of of red, blue and green.
09:22:02 That's why, light, and there are issues about this which I'm not, I don't know and I'm not an expert in the wants to to light a huge amount of data, but it is important.
09:22:19 Now an important thing, maybe this is the next question.
09:22:23 In all what I showed here, the change from dark to light was sharp.
09:22:30 Shocking away.
09:22:33 And we did some experiments with moderate growth and then there is still on. It is not as sharp.
09:22:41 Okay, and.
09:22:44 But again, if you think about a leaf that goes, and if you see that in only some, some wind. The wind north winds, not very erupted like here, and leads to this effect then you see that and leave that is in the shed and in the light and the wind and we're
09:23:13 the time. Expect exposes undergoes this very large strains, as a normal
09:23:21 girl.
09:23:21 That's
09:23:21 cool. I also have in the dark.
09:23:26 Is there an oscillation in the dark.
09:23:29 Yes, Yes, so in a way you would you would, I would say well if the stomata closed in the dark.
09:23:39 And we're still measure affiliations.
09:23:43 And then, it means that it is not just stomata. Yes, but we do measure relations in fact, even even sometimes more severe. And in, during the daylight.
09:24:06 Right.
09:24:07 Sorry, shouldn't be here.
09:24:09 But then, how does the growth vary between light and dark so the in the dark i think i think it's here.
09:24:13 A mistake. Just a second.
09:24:27 I lost this part, let me just get you off death was the next.
09:24:27 This is an old measurement of.
09:24:33 Don't do.
09:24:33 we don't see your screen yet.
09:24:37 Okay, so this is a global measurement of the global area of the leaf, these are the dark light, dark light, etc etc. And this is the area of the leaf.
09:24:57 And there are similar measurements of this, not ours but by other groups and you see these oscillations 24 hours in the global growth rate, but it's not exactly that.
09:25:03 You can say when it is other edges larger correct to say that it grows more Here it is.
09:25:12 And this is a measure of effect and many people measured.
09:25:20 So I had one other question around I think I just missed something on the slide where you showed that after it was the reality slide. So you showed that after you applied some tension to one side of leaf, then that side of the leaf had an N and isotopic
09:25:38 young specialist response.
09:25:40 And then I'm on the right side of that slide, there was a phase change plot.
09:25:49 And I think I missed. I think I just missed the how the details there. Can you return to that slide and perhaps others might have also
09:26:03 missed the punch line as I did. So, so it's it's showing really that the ratio of the elastic to Los Angeles is also changing is that right.
09:26:23 I think it, this, this, this thing. Yes. Yeah. I didn't spend time on this, let's let let's look at this. So this is the elastic modules.
09:26:30 It got stiffer parallel pulling direction, and it gets softer perpendicular me.
09:26:37 Now this is about the last one of those things were lost when this is the face to face, only.
09:26:48 And yet it.
09:26:50 And you can see it actually here that the loop shrunk after it became less viscous here. I don't know if there's a punch line here. I must say, especially about.
09:27:22 What if anyone has an idea emerging from from from this.
09:27:27 I have, I can say something, or can
09:27:27 believe this is an important feature. But this guy here about the last, I don't know exactly what to say and a.
09:27:30 Be very, very nice like, I don't have any, any anything to say about that either.
09:27:42 So, these are observations.
09:27:45 Be didn't succeed.
09:27:47 We didn't really work hard to but simple, quick test to see if we can monitor let's say fiber orientation build up on this we did and I believe it is possible to do this work.
09:28:04 These are very easy to measure very accessible
09:28:11 cooperates very well.
09:28:14 But we didn't
09:28:18 conclude this part of the story.
09:28:21 So when you say phase ratio, it's the, the phase delay between.
09:28:27 Yes, the strain applied for. All right.
09:28:34 Yes.
09:28:38 Okay, so, and yes, this delta here. Yeah, between the stress and the strain.
09:28:56 It's also yes just need to bear in mind what we measure is not the proper or logical measurement, first of all, even though in this in this cloth here.
09:28:57 Yes, so it's not as though Delta changes sign, it's just that it grows or shrinks yes i a different amount and the two different directions. Yes.
09:29:08 The.
09:29:10 There is negative value.
09:29:12 We don't compress them, right, it would back up so we have a DC. And then these oscillations can go to zero but, and.
09:29:23 And in addition the leaf growth. So for example over here.
09:29:28 Here, the first this is the first measurement you see that it doesn't go back to the snow look right this is this is 40 minutes this yield. And only then it starts making something which is close to a new.
09:29:43 If we're doing short enough time.
09:29:46 So, this is not a
09:29:53 exact a measurement, but I think it does reflect reflect those properties that beast.
09:30:05 Thank you.
09:30:09 Okay, maybe now it's time to stop.
09:30:13 Um, thank you very much for the talk. Thank you. Thank you.
09:30:17 And thanks everybody for participating. Next month we will host Nippon Patel, and Madison in June, so stay tuned for more messages and do that.
09:30:31 Thank you for joining.
09:30:32 By.
09:30:33 All right, thank you.
09:30:35 Thanks again for presenting around was great.