 engineering, which is a technique to treat large bone defects and it involves extraction of the stem cells followed by their isolation and 2D cultivation for cell expansion and thereafter the cells are seeded in a 3D scaffold which mainly consists of a supporting frame and the stem cells and some biochemical factors like growth factors and the medium and external stimuli. In this case that I'm going to talk about the external stimuli will be electrical stimulation to promote differentiation of these MSCs into bone cells. Now after the cells have formed a tissue, this scaffold consisting of these cells that form the bone tissue is placed back into the bone defect and the scaffold will slowly degrade and this bone defect will be gone because the bone would heal. So in this talk I will be focusing upon only the electrical stimulation on stem cell proliferation and differentiation and so in these experiments the cells were extracted from the bone cells from the bone. So these particular MSCs were taken out from adult bone and they were placed in scaffolds like I showed you which were in turn placed in cell chamber and this chamber was connected to a transformer core through which AC supply was given. So through the process eventually the cells experience external electric fields and sorry there is a little thing here. The cells were exposed each day for four hours followed by a four hour break and the total duration for which the cells were stimulated was seven days, fourteen days, twenty-one days and twenty-eight days. So to quantify the cell proliferation the total number of cells were counted at each of these days at each of these time points and to quantify the differentiation the total ALP signal of the cell which is enzyme which is produced by the cells which are just going to differentiate into the bone cells. So basically the stem cells have high ALP signal and as the cells gradually differentiate into bone cells they start to show So I just wanted to tell you if you have any questions please feel free to stop me. I'm really glad to talk about them then and there then wait till the end. So yeah so from these experiments we obtain the total number of cells and the total ALP signal in these cells and the total number of cells shows a growth with and without stimulation and the ALP signal the total ALP signal in this cell population shows initially a growth and then it falls down. So there is a decay. Sorry I have a question. So the amplitude of this field is somehow taking arbitrarily or is it connected to any real electric field that the cells are filling? Yeah so exactly so this the strength of the electric field here in these experiments is 0.36 volt per meter and this is the field strength which the cells take well. So if you go to high strengths then this is not good for cells and so this is also a field strength that is subjected to the bone defects when the implant is placed on top of the bone. So these are the field strengths which the cells can take and still happily grow and divide and differentiate. So yeah and experiments show so these experiments showed that the total number of cells over time there was no significant difference between the cells that were stimulated and the cells which were not stimulated. So if you look at the case where the cells are not stimulated the data can be fit by these two functions. So the total number of cells grows quadratically with time and as I said the ALP activity or signal goes up and then decays and it is very well captured by these two functions. So theoretically the state of the stem cell population is we describe it by this quantity Na of t where a signifies the level of the ALP of the cell at a given time t and n is the number density of cells with ALP level a at any given time t. So from this quantity we can actually get two more quantities which is capital N and phi and capital N is the total number of cells at any time t and phi is the total ALP level in all the cells at any given time t. So the general theoretical framework that we developed to describe stem cell dynamics is described by the change of Na of t with time and the different terms that contribute to this change are given by A, B, C and D where the first term A describes the process by which a cell divides and during this division the ALP level of the cell gets redistributed in the in the two cells that it divides into and thus the second term B is the process by which a cell terminally differentiates into a cell type. So in this case it would be the bone cell and because experimentally it is known that the bone cells show lower ALP levels than the stem cells. So this is basically a cell which you lose a cell in through this process B which has an ALP level of A and then there are these two processes where C is the process by which you have an ALP influx through intracellular biosynthesis and similarly you have a process D which accounts for ALP outflux through intracellular degradation. So these are all the different processes that contribute to the change in the total number density of cells with ALP level A at a given time t. A very simple model accounts for experimentally observed data and in this model we have just two processes the first one is cell division and the second one is the ALP outflux through the cell. So for cell division we have taken the choice of the cell division kernel as skd and delta A minus A prime and such a choice of cell division kernel means that the ALP redistributes equally and in the in the in the two daughter cells and it has the same amount as the cell that divided. So it's kind of a symmetric but non-conserved cell division because if you sum up the ALP level of the two daughter cells then it is basically twice of the hidden cell and the second process sorry sorry maybe this is the big question but before in the in the division you had the gain loss and a sorry a gain term and a loss term but now you only have the gain term yeah so can you explain further this yeah sure so if you take the choice of the cell division kernel which I show here in the table and if you plug plug this end into this equation then it would simplify to just one term which has which is which is here actually okay okay so yeah so so because I have delta A minus A prime yeah if you will plug plug this in the the second term will have just n of A and it would have KD okay there's a delta function that would come that is the term which is left and the first one it's it's the it's the combination of these two that that gives you this one one term okay the first first term yeah yeah it's a bit of a calculation but but you'll find that this is basically boils boils down to this first term which is shown please yes what's the meaning of a small a small small a yeah so small a is the ELP level of a cell which I described here so this is somehow in this cartoon this this would be uh yeah so it's going from zero to one so uh a would be how much ELP is there in a cell okay thank you yeah sure um yeah so and the second term is the term that accounts for the outflux of ELP from a cell through a slow degradation and the choice of function that that we have used here is for the d0a is d0 times a so that that means that that a cell which has a high ELP level will will degrade faster so it it depends upon the ELP level of a cell so with this choice of uh uh the yeah the choice of the function for kd and d0 you can derive uh you can derive the equations the time rate of change of capital N which is a total number of cells at a given time t and this is simply uh dependent upon the cell division rate which is kd and for uh if if we use the choice for kd as 2 by t which is that means the cell division rate decreases with time you find that the solution of dn by dt is is a simple nt which is proportional to t square and this is exactly the function that that describes the time dependent behavior of the total number of cells as a function of time yeah and the second quantity phi which is the total ELP in all the cells at any given time the dynamic behavior of this quantity is is has two parts to it so there is kd phi and then there is minus d d0 phi and again keeping the keeping the same choice of function for kd time dependent form as 2 by t solving this equation we see that phi has the analytical solution which is quadratically growing and then at after a typical time of which is given by one upon d0 it exponentially decays and that's again exactly the functional form that describes the time dependent behavior of the total ELP in the cell population so i'm there sorry yeah sure i have a question please uh if a is a ELP activity in it between it is between zero and one yeah why in the answer rather is zero answer um where is uh you say that a yeah is ELP activity and it's it is between zero and one but on the integral between zero and after yeah so yeah so so this is so the first thing is that the ELP activity going from zero to one it is just for representation which i've chosen this scale but but the ELP activity per cell is actually uh is is is can is to be shown on a different scale but but just for the for the sake of showing here i put it between i've normalized it between zero and one in the integrals in the theory it is going between zero and infinity of course that's that's uh that's a situation that that has to be taken care of so so the it is it is clear that in cells you cannot have ELP activity too too high so so so you have an upper bound uh but yeah so so we are we are looking at a mean field scale where yeah where this kind of effects are very weak or the contribution because of this uh if you have an upper limit is is weaker okay thank you yes so yeah so so this so up till now we had we had looked at the case where the cells were not electrically stimulated and we can do the same analysis for the case where the cells are stimulated with external fields and the when you when you fit the same function to to the total number of cells and the total ELP activity at different time points we see that that the cell that this quantity d zero that describes the behavior of the ELP outflux from the cell and that in turn means points to the differentiation of the cell to the bone cell to the stem stem cell to the bone cell has a site difference so for the case without electrical stimulation it is around six five five five point eight days and there is a slight difference uh with electrical stimulation which this kind of a theoretical framework can capture which is six six point two uh yeah so i think this yeah so so there so the two conclusions from the first part of the talk is uh from this theoretical analysis is that the cell division rate it it is inversely proportional to the cell density so as one one can show for the choice of function for k d which is two by t that it can be written as one upon square root of a row and so that basically means that the cell division rate is decreasing as the cell density goes goes up so somehow it signifies that the cells have a signaling mechanism that can sense the cell density and can this this can in turn regulate the cell division and the second conclusion from this analysis is that the cell the the degradation rate of ALP inside the cell is inversely proportional to the external field strength and so these these are the two conclusions from the first part of my talk and if there are any questions here i'm really happy to take them before i move on i had a question so in the on the left side how do you i didn't get how do you get the second equality that two over t is one over the square root of row yeah so uh to to uh get the second equality uh we have to use the expression for n so n n goes as uh this brief prefactor times t square and if you rewrite t as square root of n i think yes you will have two two by n and then divide by v which is the volume of the scaffold in which the cells are placed and that doesn't change so it's a fixed fixed then so you divide uh so you get n by n zero n zero is the total number of cells at the start of the experiments and you divide by v zero both top and bottom numerator and denominator and you find this is which is a basic hero okay thanks thank you sure okay so if there are no other questions from the first part of the talk then i'll move on i will switch gears and i will move to plant leaves so we all have looked at leaves and i think the best best time to see leaves is basically in fall season where where they fall on the ground and and we love to kick them as we as we walk through the street one really particular and very striking feature of all plant leaves is is this veins uh and one there the the the vein that goes through the center of the leaf and sort of divides the leaf into two halves is called the primary vein and then from these emerge secondary veins which are slightly thinner than the primary veins and then even more finer than the secondary veins are the tertiary veins and it goes so on and so forth uh what is known in experiments is that this whole very complex vein pattern does not emerge at once it's it's showed in experiments is that it's been seen is that they observed sequentially if if i would say so that means that the the primary veins are the veins that are formed first and then after a few days the secondary veins emerge and then the tertiary veins and and so on and so forth and also the proliferation of the vein cells is is very well defined means that the vein cells in the in the first days basically the one one day after germination which i have not shown here you cannot differentiate between a non-vein cell and a vein cell but as the days go on from third third day on you clearly see that you can differentiate between a vein cell and a non-vein cell by the by the shape of these cells and by that i mean that the vein cells are very are longer and sort of elongated and the non-vein cells have a very symmetric shape and square square like shape so you could quantify you could clearly see the difference in experiments where you can label the vein cells with some proteins and you can you can mark their shapes so in all of these theories a growth hormone oxen that plays a very important role in the plant and the leaf development experiments have shown that when you suppress the biosynthesis of oxen the leaves are smaller as as shown here in this in this picture the leaves are smaller and the veins are not formed as in the wild time you have the central vein the primary vein and then you have some sort of secondary veins but definitely not the tertiary and more final veins and then if you also experience have shown if you suppress intracellular oxen transport this can also disturb the vein patterning so here you you see in the in the in the nonperturbed case you have a vein pattern after five days as is expected but when the intracellular oxen transport is perturbed or it is I think in this case it was lower you find that there is a very thick midway and there are secondary veins that come out of the of the midway and then there are very very few tertiary veins so oxen clearly plays a very important role in in the leaf growth and the vein patterning what is also known in experiments is that oxen is not produced in all the cells but in the in the first few days following the germination it is highly localized in few cells and these these are the cells that would become the midway and the secondary veins so here as this is a biosynthetic gene Tartu it is called as Tartu which is a label for oxen biosynthetic gene and when you follow that in the in the first few days of the of the leaf following germination you see that it is highly localized to those cells that would become the midway and then the secondary vein so we developed a model to describe leaf tissue growth and study the vein patterning and the model is in this model the the the leaves are sorry the cells in the in the plant leaf tissue are described by interconnected polygons and the polygon has a certain size so it's it's a it's a it's a two-dimensional approximation because in the in the first few days the leaves are quite thin and they are they can be thought of as a lamina and so the the shape of the tissue in this model is defined by this function e which has two terms to it where a is the cell area and a naught is the preferred cell area so that's that's that's the that's the size of the cell that it would keep because of homeostatic pressure and you have a pre-factor to it which is gamma which is basically tells or defines the compressibility of a cell and then you have the second term where lig is the length of the cell wall and lig naught is the preferred cell wall length and there is a pre-factor to the second term which is defines the stiffness of the cell wall which is similar to a spring so if you have a hoax hoax spring so you have a pre-factor and the energy of such a spring would be given by k x square and so that's kind of a reminiscent of that that that kind of a term yeah and so here so so I would I would come to the cell growth rate a bit related I would I would not talk here for the cell growth rate from from this function e you can obtain the the force that acts on each vertex of the cell if you differentiate this function e with respect to the coordinates of each vertex you would get the force that acts on that vertex and from that you can also calculate the stress the total stress that acts on a given cell on any any any cell now besides the tissue growth at the scale of a single cell there is also transport of hoaxing taking place so hoaxing is being produced in cells but but it is highly localized to the cells that would be the wane wane cells so that would become the wane cells and then hoaxing can diffuse through the cell walls and be transported to the neighboring cells and that is captured by the second term here B which would be the diffusion constant and because of the cell growth the the concentration of hoaxing per cell gets diluted and so that that acts as effectively like a like a sink of hoaxing and so yeah I should have said that before C is the is the cell hoaxing concentration so it's it's a total number of hoaxing molecules divided by the cell area so now we couple the tissue growth and dynamics of hoaxing and the way we do it is that the cell area growth rate is a function of the cellular hoaxing so the concentration of the cells hoaxing and so this dA by dT for a given cell is given the growth rate is given by G which is a function of C and the way C changes is that when the concentration hoaxing concentration of a cell is below a threshold then the cell grows at a growth rate G0 but when it would be above that threshold then the cells would start to grow at a rate G1 and the ways the rules for the cell division is such that when the area of the cell becomes doubled the cell would divide along the short axis as shown here in this cartoon yeah with these few ingredients in our model we initialize the leaf at the start of the experiment that would correspond to a leaf bud at at the two two day after germination and we describe the cells such that you have few cells which produce hoaxing which are shorter in dark green and light light greens are the cells that do not produce hoaxing and the gray cells are the cells that represent the cells which are stiff stiff base that are connected to the plant plant so these these cells do not divide and yeah they have very high stiffness so with these ingredients and the values for the model taken from experiments literature when we run the simulation you see that the cells grow divide and wane cells which are shown in dark green they get constricted to fewer cells and they get they finally get this kind of a shape which is quite similar to us observing experiments so maybe I should point this out that this growth rule of cell area that depends upon hoaxing concentration this is only applying to the cells which are non-wane cells the wane cells at all times grow at the same rate g zero and if you look at the concentration of hoaxing in the whole leaf tissue you see that there is the wane cells have high concentration of hoaxing and then it has this kind of a characteristic diffusion diffusive profile through the tissue we could we could calculate the forces that acts on each vertex of a cell and we see that the forces that act on the wane cell from the non-wane cells are are are quite high and these are the forces that constrict the wane cells from dividing in sideways and and they sort of like squeeze them so that they become elongated yeah and you can also calculate the total cellular force map which which would be basically the sum of all the force vectors for a given cell and then shown by this color code and we see that the forces in immediate neighboring of the of the wane cells it is it's it's quite high and so what what this what this tells is that the wild type wane wane pattern of the mid wane is mainly because of the immediately neighboring cells and and not not not too far far away from the midway so it is a cells which are immediately next to the wane cells how they grow defines the shape of the midway so there was also experiments that were done where hoaxing transport was inhibited and clearly in these experiments the wanes were quite different from in the in the control case we we saw quite broad midway here in this case the experiments are looking at just the first two to three three days after germination and it can be also seen here the hoaxing bio biosynthetic cells are no more highly localized but they are quite diffuse and dispersed so in the simulation we take the diffusion the the the diffusion term which accounts for hoaxing transport across the cells and if i decrease the value of d by some fold then what we see is yeah i think the simulation is running what what we see is the cells grow and divide but in this case because hoaxing transport is much lower to to cause the neighboring cells to reach the threshold so that they can grow faster the midway cells do not experience sufficient force that would cause them to be constricted and and and squeeze them from the sides to get that that shape that is elongated so here we see also in simulations that the hoaxing bio synthetic cells have a very dispersed pattern and this is also yeah shown here that the diffusion profile the the hoaxing concentration profile in in these experiments is quite different from the wild wild type and the forces that act on the weight cells are are much weaker as compared to to the wild wild type so there was a experiment a double inhibition experiment and in this experiment you have the control case where where the where the cells were not inhibited or treated with anything they were they were just grown and when when these cells were treated were treated with hoaxing transport inhibitor we lose the big weight patterning as as we expected but then when the same leaves were treated with hoaxing synthesis inhibitor interestingly the the weight pattern was recovered as was seen in the wild type so the theory explains this observed behavior and so the explanation is is that if you if you think of the the the case where the cell divisions are the the cell division rate is much slower as compared to the hoaxing transport then you can basically sorry there is a typo here so so so c is not a function of d you can consider this to be a steady state and you can can solve this and the solution for this turns out to be a simple prefactor which is dependent upon the hoaxing bio biosynthesis which is s zero divided by the square root of the cell hoaxing transport rate which is given by d and the cell growth growth rate now if the if the as an experiment the cell hoaxing hoaxing synthesis rate has been decreased and the cell hoaxing transport rate has been decreased then to recover the hoaxing profile across the tissue uh one has to also decrease the cell growth rate uh so if you if you uh divide for instance s zero by a factor uh and also divide d by a factor as was done in the experiment and also here to get the same profile you would have to divide it by the g by a factor two so that this would cancel out here in the exponential term and also in the prefactor and that is what was also confirmed in the simulation so you have the wild type case where you get the midway impact and as observed in experiments and to this if you decrease the hoaxing transport rate uh by a factors here it was 20 divided by by 20 you lose the midway pattern and then to the same so so similar experiment when you add also decreasing the growth rate and the hoaxing bio synthesis uh by a factor then you again recover the vein pattern as was seen in the wild type so uh clearly uh in the in the early stages of the midway development uh is is is clearly uh regulated by interplay of mechanics due to the cell growth and hoaxing distribution because of intercellular transport and so with that I would like to thank you for your attention and very happy to take questions thank you thanks a lot and give you a virtual clap uh name of everyone and so we um this is open to questions any other question or speaker students anyone okay all the birth rate yes please there was a question okay maybe I had a question about the the model in the tissue of the plant cells so you showed some qualitative behaviors in which um you you change the growth rate and then it changes the pattern in the in the plant which is very interesting and I wanted I wonder if you can take experimental data from the microscope and images and and fit any in a way uh many parameter of your model is it possible or is it too complicated because it is very complicated to assimilation no yes so so one one thing which which we are actually now looking at is is one way to quantify because here it is at still at the qualitative level so we want to quantify one one way to do that is is to obtain so here in experiments so here in the simulations what we can get is um uh the the cell height and width and this is also similarly uh a quantity that can be extracted in experiments so here like I showed you in these pictures uh yeah so in this way so we can we can basically quantify the shape of the cell and uh fit it or or compare it with the with the ones obtained from the model so that would be one way to compare and that's that's an ongoing work so we have to yeah we have to segment this these leaves and and yeah get these shapes also can you discriminate between different uh free energy functions because you you assume there is one free energy you know in your model so this would be more complicated you know if you want to compare models with different interaction terms yeah okay so so this is um so so in so this these of course there could be more they're sure I mean it's it's far more complex than than what what this function captures but but these could be uh uh thought of as the as the main contributing factors uh for that define the shape shape of the cell so you have a tug of pressure so the plant cells are mostly filled with water uh and so that that that is what defines this first term and the second term is basically the bond tension so so that's that's basically keeps keeps the length of the cell wall because the plant cells are different in the in the sense that they have very long cell walls and they have really uh you you cannot squeeze them infinitely to a to a point where you see some kind of rearrangements as have been seen in zebra fish uh like t1 and t2 uh so that that is uh that is uh no no go here in in plant plant cells so um yeah so what yeah so this this this kind of a framework has been very popular in explaining shape shape changes include fly of course the functional form of these these terms is not the same same there um but yeah so it it could have uh additional terms uh that could describe additional biological processes uh but at this level we we've kept it also simple because we want to learn as much about what's what's happening and not get lost in several terms and yeah thank you um so any other questions from the audience uh what plant species you use the for the experiment data because you often just mentioned that it is the uh the the plant system blah blah blah I think that probably the the proper this plant if the plant lift development maybe already be uh specific to the certain range of the plant species rather than it is working for all plants right yeah so just I wonder primarily which plant species actually do this experiment religion regarding the option or the kind of things obtained was it is it aridosis or yeah yeah yeah so so the plant that was used was uh aridopsis uh here yeah so these are these are the leaves from from that plant and I think you're you yeah you're correct in in in uh pointing this this out that that the leaf leaf patterns of of is dependent upon the species yeah so you you have different leaf patterns you have the maple leaves which are which are having yeah like this kind of shape which is quite different from from this leaf um yeah so so so here it is uh aridopsis thaliana but do you believe that that at least some the some uh some general on the kind of the but do you believe that at least your your model your framework to be able to work for the other plant the leaf of other the development of leaf of other species that they're just probably their parameters to maybe different but do you think that that kind of patterns will be universally observed for other plants so one one thing which is uh which we focused at here in in this uh species of plant is is we we were looking at just the formation of the midway so this this leaf has uh vein vein pattern where you have a midway and then your secondary veins so if we want to study a different species of plant I I think uh we have to still have this kind of uh uh structure of of vein pattern where you have a midway that is formed first and from that emerges the secondary veins and so on and so forth um so it's it's um interesting thing to look at uh but this mod model and this is a kind of a uh description which I showed here uh uh is is um for such leaves where you have a midway that forms first during the uh developmental course and from from there on forms the secondary and tertiary veins yeah thank you thank you're welcome all right all the questions so I don't see any other uh so then uh let's uh thank again Jonathan for his uh nice talk and thank you very much