The Measurement of Cellular Traction Forces

great thanks Roger so I thought what I would do is maybe dig just a little bit deeper into the methodology of how we actually measure forces and maybe talk a little bit about the different tools that have been developed and what are some of the strengths and weaknesses limitations of the various methods but I thought that would be useful for you guys along the way I also show use just a couple of examples of how we’ve used those tools to try to understand a little bit more about attraction forces in biology and I’ll obviously feel free to interrupt at any point I want this to be sort of open and interactive so so but the first thing I wanted to just mention I I know that Ray Keller gave you a nice lecture about morphogenesis and sort of development and the reason why I wanted to sort of remind you about those is that these are essentially force mediated processes right cells when they change their shape within these structures in order to to generate these kind of massive movements those require forces and one of the things that the field is very interested in is trying to understand how those forces are used in order to drive these developmental processes in the first place how you get from sort of a spherical perfectly apparently uniform egg into something that is a very complex body the other thing that is also important is to realize that these forces are not just used to change cell shape or multicellular structure but as Mike mentioned these forces also drive sort of intracellular structures such as adhesions cytoskeletal organization etc I think I pulled this off of your website now one of the things that exists within the dogma of embryogenesis is this notion that genetic programs essentially drive all of the formation of these tissues so you have certain tightly controlled gene expression programs that will turn on and those will drive say the differentiation of the various tissue types within the body during this sort of very fast and riyo genesis process and it’s thought that the gene programs can also regulate forces by simply expressing different levels of actin or myosin or other things like this rate and through that alter changes in cell shape so you can sort of conceptually think of this genetic program as sort of the master regulator that might link differentiation changes in cell shape changes and mechanics we’re not sure if this is right in fact I’m pretty sure it’s not entirely right and the reason why we we think that is that we think that there’s also another set of relationships that put forces at the top of this this sort of triangle we know that forces can feedback to regulate genetic programs so this whole area of sort of Meccano transduction how when you pull on a tissue it changes the behavior of those tissues not mechanically but biologically those cells will activate and proliferate and and adapt to those forces this is why we exercise and and strengthen our musculoskeletal system we also know that these forces can regulate differentiation of cells so stem cells cancer cells all of these are affected by forces and obviously forces can regulate cell shapes so another Dogma that is something that I want you to take away is this notion that perhaps forces are the integrating feature that links these differentiation processes during morphogenesis so that the cell that is sitting at the right place during this process differentiates into the right cell that forces might actually be the guiding principle that links them okay so all of that is to tell you that these traction forces that cells generate are really important and there have been a number of different methods that have been developed over the years to try to identify and measure those forces the first one that really put Sanger their forces on the map was this one that was

started by Albert Harris many many years ago around 1980 I think he had several papers in this area what he did was he basically took a silicon oil silicon no different than the sort of silicon lubricants that we use and by just passing that liquid through a flame the heat would polymerize a skin on the surface of that oil so you imagine sort of a solid rubber like skin on the surface of a viscous liquid and then he put cells on top and this is what he saw so I don’t know if you can see it but here’s one cell here’s one cell and here’s one cell and when you immediately notice is that the cells are sort of wrinkling thus this skin on the surface and if you pop those cells off the wrinkles sort of relax and come back down right so in some ways it’s similar to sort of use sitting on top of let’s say your your bed sheet and sort of moving around and that’s causing wrinkling except that the bed sheet is not elastic right when you walk off the that is wrinkled whereas here it smooths back out because it’s under tension so several people spent maybe about ten years using this system to simply say when do forces exist they put cells on they could sort of tell when there were forces and at some point people started wanting to know not just a digital answer is there forces or not force but is there more force than how much more force and so it turns out that this problem of sort of looking at this buckling if you will is fairly complicated right you can generate a wide range of forces that would change the degree of buckling and so now you’re sort of trying to do the inverse problem or you see buckling and you’re trying to back out how much force there is and that turns out to be a highly nonlinear process so it’s very hard to quantify so they started people started looking at other kinds of substrates that maybe would deform in in response to cell contractions and there was a seminal paper and actually 1997 by a gentleman named Julie Wang and he developed these method where he would take polyacrylamide gels which are not sticky to proteins this is why we use them in running Western blots right proteins can run through the gel without sticking to it but he found a way to couple covalent couple exercise their matrix onto the tip onto the surface of those gels and then he would plate cells down and what he saw was that cells would sit on the surface and they would sort of deform it so he collaborated with a mathematician Micah Dembo who developed a method to be able to measure the strains within that that sort of half space if you will of acrylamide gel see sort of imagine a thick gel cell sitting on the top its deforming the gel so the first thing you have to do is figure out how to measure the deformations in the gel and then what Micah did was took that input and figured out how to measure that and calculate the stresses from those tough formations so essentially what they did was they to measure the deformations remember the acrylamide gel is transparent so you can’t really see deformations is that they polymerized the gel with tiny beads embedded throughout the gel so now you just sort of imagine that as the cells are pulling on the surface then the beads would move and they could use those if they track those beads they could look at the deformations of the gel that was surrounding this bead okay does that make sense from that they they were able to calculate stresses and I’ll tell you a little bit more about how they do that in a couple of slides and I just wanted to mention that another group of any Geiger’s group soon after developed a method work instead of using acrylamide gels they went back to use silicones again except and this time they used lightly cross-linked silicones so unlike here we have sort of a hard skin on top of us very softly a viscous liquid they would have a again a half plane of gel just like in the acrylamide case and what they did was they said you know these bees are kind of hard to track that they’re randomly just organized and you can imagine that as these beads are being pulled around if you’re trying to track these in a pair of images if one bead now moves to where another bead was ready imagine all these density of beads it’s hard to know which bead was which was you know there’s so many cents so what he did was he

actually fabricated onto the surface of this silicon regular dots so now you don’t really have to track them because you sort of know where they came from they used to be aligned and now as they move out of out of a grid and you know what kind of deformations they’re worth so this sort of simplified the tracking problem so the key to this whole process of being able to simplify the problem of taking strains within the material backing out the stresses relies on the fact that these materials are linear elastic meaning that as you pull then you simply have a straight line in terms of the stress and strain in other words the stiffness of the material doesn’t change as you pull on it okay it turns out that all biological materials are not linear so here’s a graph of the this stress-strain done by Paul G and me many years ago where he looked at all the different types of biological polymers so I don’t know if you can read this but there’s actin collagen fibrin and in all cases what you see is that the the modulus changes with how much you strain it so that means it’s nonlinear right it strains difference so shows it’s shown for example here this is the fibrin curve and this is the collagen curve so you can see they’re highly nonlinear here’s another example there’s the shear modulus here’s the strain how much strain and as you strain this material more and more it becomes much stiffer by contrast here’s polyacrylamide right here see it has one stiffness so it’s it’s the reason that this is the reason why we can use this material for doing traction forces now the reason why that these biological polymers are not linear for the most part is because they’re filamentous sort of semi rigid materials so this is a SEM of fibrin so a cell might be sort of this big okay so you can just sort of imagine that you have all of these filaments the filaments are fairly inflexible they don’t extend very well but they Bend very easily right because they’re thin thin materials so what happens is that as you align the material as you strain it in a certain direction all of the fibers initially move very easily because they’re just bending you think of spaghetti easy to bend that the fibers but as the straining continues to increase now you know all of these aligned fibers and you reach a point at which the only additional strain that you’re getting is not from aligning fibers that is from stretching the fibers and so the stretching can become quite stiff so another example of sort of strain stiffening materials is something like a basketball net or your the fabrics in your in your t-shirt initially when you pull it’s fairly easy but as you pull more and more it becomes tougher and tougher to pull it okay so that that’s the basis for most biological materials and one of the effects of that is here shown here so here’s there’s a single cell in this image this single cell is sitting inside on on this very large gel and you won’t be able to see it but the cell is sitting inside this red square or this red circle okay so this is a very low magnification image and what what Paul did was he measured the elastic modulus locally around this cell and what you see is that this is on a fibrin gel that when you’re far away the gel appears quite soft right if in small deformation but as you get closer and closer to the cell you see the modulus increases dramatically what’s happening is that just around the cell the cell is pulling on this fiber network right so near the cell the fibers are highly aligned and the material gets stiff does that make sense so in order to solve the problem of now you’ve got these strains you can see the this is a strain map these arrows here and you want to back out the stresses it’s impossible it’s impossible because you won’t know how much this modulus has changed in this in this field so you have too many variables does that make sense okay so what do we do in these linear materials to actually generate stress maps from strains so for linear materials like acrylamide gel or these

silicone rubbers what we do is we take an image this is an image of the focal adhesions but there would be an image a similar image of all the beads that are surrounding them and from looking at the beads you would back out a strain map okay what you then do is you know that there’s a very simple equation that basically relates the strains to the stresses okay the forces that are needed to deform the gel to give you certain deformations and that the relationship is here described under this freedom integral that the transfer function if you will involves this greens function okay and for linear materials that have a half space and you’re trying to deform it on the top of the surface there’s a solution to what the greens function is and so given that that’s already known then it’s fairly easy to take a stress field apply the greens function integrate it and then give you the strain fields it’s very easy to go in this forward direction but it turns out that it’s quite difficult to go in the reverse direction give it a strain field how do you back out the stresses and the reason why is because you have to invert this integral okay so the reason why it’s hard I thought I would just give you an example is that if you apply a force at a particular point let’s just imagine that the solution to this problem was just one point force that you’re applying on the gel and now you’re looking at the strains and you want to back out hopefully rescue that point source okay so what you might normally see in a gel if you apply a force at this point right here this might be and you were tracking beads that were sort of this far away from that point force this might be the strain field that you would see in a perfect situation okay and then if you were to sort of graph that if this is the point forces right there you might see deformations that are like this right sort of a nice smooth function but the reality is that when you do these measurements there’s always noise you never perfectly find where the P it is because of optical noise and the bead doesn’t always move perfectly because nothing is a perfect material okay so what your actual strains will be is some Delta off of that position right and that’s the noise so now the data that you have looks like this right it’s not a perfectly smooth straight map if you take anything that’s noisy right and that’s on the right side of the integral and now you want to reverse it you have to do a differentiation right then these small strains these these little bits of noise get amplified right so what you would have to do to say let’s presume that these are perfect measurements we got this measure that now is this right this is the data set that I have and let’s say I’d presume that this was perfect data and now I try to solve the the force field what you’re gonna get is not this single point source right you’re gonna get something that looks like this you’ll get a point source here you have to correct for this Delta there right so then you’ll have another force that’s applied here you have to correct for this Delta here you have to put it another force here to correct for that Delta there you put another force here so now your stress field that you’ve calculated is completely different from the real solution and just because you have decided that your strain field was perfect so another way to look at it is if you put highly if you constrain the solution to be exact then your stress field has to be very complicated to account for all of those little bits of noise right so let me just go back here this is for four little beads so I don’t

even see the dots here right but if I want a high-resolution image of what the stresses look like kind of like they shown here then there’s probably a thousand beats sitting here maybe 10,000 beads around the cell so if there’s 10,000 sources of noise can you imagine how many force errors that you’re introducing to solve this problem okay so what do we do how do we solve the problem what we do is we do something that we call regularization and this is a mathematical version of saying we’re cheating okay and what we do is we take this we try to minimize this function okay so what is this function this function is this GF is the exact solution okay and this U is the the strains that I I that I want to get okay so the this squared is just the noise term it’s how far off is my solution if I take this strain map that I have and I back out forces then I take my forces and recalculate the strain map okay so that’s if I have a perfect solution then this is zero right but for that to be zero I have to have a very complex force field remember so what I can do is I can relax that constraint I can say well I’m okay with having small errors if I have a point force here and none of the other ones and I see that when I recover my my strain field right my strain field is going to be close to the strain field that I had measured earlier but there’s going to be some error does that make sense and that error is the difference between my my the exact strain field that I measured and my calculated close strain field from my not-so-good force measurements my force calculations so I want to minimize that noise but if I came in uh my zit that I’m gonna have a very complex force field what I do is I add to this I want to not just minimize that because then I’ll just have a complex force field I’m going to add this penalty term and the penalty term is how complex is the force field so this is just lambda squared s squared right so all I’m doing is I’m putting a penalty in for having a very complex force field if this force force field gets very complicated I’m going to say that that’s not good that means that I’m sort of over complicating the solution so what have I done by doing this what I’m doing is I’m assuming that the force field is simple so what I want to do when I put in this minimization constraint is I’m saying to my student I want you to find the simplest force field that kind of approximates the strange field that you’ve measured okay so how do we do this this lambda is is a cheat term and that cheat term is there to let me play around with how much I want to penalize on this force term so if I make lambda very small I’m saying I’m okay with a fairly complex field because if I have a complex field in this this land is quite small then that penalty is not so big right but if I increased lambda then what I’m doing is I’m saying I want that force field to be very very simple right now this lambda is something that we as experimentalists impose on the system to get our solution so here is an example this is a cell that that a strain field was gathered a real dataset and then here is the force map that was arrived at based on that strain field when lambda was small that should say 0.01 when land that was small in other words we said we’re ok we’re accepting a more complicated force field because we want the force field to be more accurate that recovering the strains that we had measured but I don’t think this is real this is too complicated so what do I do as an

experimentalist I increase my lambda so I say you know I don’t like pointer one let’s try point one now I’ve tried point one and you can see now these forces smooth out so now I just have forces that are pointing this way on this end just pointing this way on this end right so now I feel pretty happy because all the forces kind of regular rise this is why it’s called regularization they look better right but what’s happening is by making them look better I’m actually making the I’m telling my solution that it’s okay not to be as accurate what happens if this lambda gets very large what happens is that ultimately you’ll end up with two point sources of force right this this will just be one force here and one force here and everything else will go away so the problem with this whole method is that as an experimentalist looking at biology as a researcher we don’t know what the forces should look like right and here we are playing around with this lambda so that we get an answer that we think feels right and that doesn’t seem like a good way to go about doing experimental science but this is how the system works it’s the only way to solve the problem yeah that’s correct so if there’s a bias and you’re in your data set let’s let’s say that your light source was not aligned and you’re looking at these speeds and in the process your your light shifts then all of your beads will show a strain in a certain direction that it that shouldn’t have been there this method won’t capture that at all so the other thing that people do to deal with systemic noise that’s Crossfield is they impose a constraint that we know should be true which is that all of the forces should sum to zero now of course that constraint cannot be perfect because if we impose it definitely to sum to zero but at the same time we say that the forces that we solve don’t have to perfectly match the strains it will never perfectly sum to zero either so what we need is something that says kind of like in this case it’s sort of close to something to zero and again we have to use one of these lambdas that lets us dial up how much we’re willing to tolerate it not something to zero versus it does some to do so what people do is I say I want it to sum to less than 10% of the total forces that are measuring then I feel okay and some people will say no I’d rather sum to one percent and you get different solutions based on that so the bottom line is that this method what you should realize is that the forces that you calculate are not determinate there are many many solutions to the same data set that you have in the beginning okay so it is still the predominant method that people use and the reason why it’s the predominant method is because polyacrylamide gels are things that are available it’s a material that all biologists already have in their labs so it’s easy to make the gel and it’s easy to put cells on it and then you can get something from it so this is an alternative approach that really it was started by Mike Sheets he said I don’t like this polyacrylamide gel method it’s sort of continuous and there’s and I might understand why it’s a little bit uncomfortable when you’re getting your data so he said why don’t we develop a device a silicon device silicon not silicon okay it’s silicon device that we fabricate so that we can put cells on top of it and then these devices these MEMS devices are designed to measure forces that people have been using cantilever-based devices that they’re sitting in all your iPhones right they measure gravity measure acceleration so when you’re shaking then you have a sensor that says oh I’m shaking that’s what those devices are designed for so you can make one of these that’s four cells so what he did was he made a pad that would sit up coplanar with the top surface of the substrate and then had this long cantilever you see that goes underneath the substrate so it’s not on

the surface so the cell only sees this area and then that pad but all of this stuff underneath is is in a tunnel that’s that’s underneath the top surface so what happens is that now in a cell and if you can see this there’s a cell sitting here that’s just started to crawl up to the top of this cantilever and when the cell starts to crawl over it it is forming adhesions on that cantilever and you can see that as the the front of the cell is going over it you see this force that comes up and can measure the force over time as the cell is crawling over it that force measurement is direct right it’s not calculating something that you’re guessing you’re just looking at the deflection of the cantilever and that backs out the force so that was a very in my mind sort of a key breakthrough in this field the only limitation here was that I remember when Mike first debuted this technique he told us that he put cells down you can see this may be a pad here a pad here and there might be you know a few hundred of these on a surface so when you put a cell down you might get lucky when the cell is crawling around and happens to go over this pad and then you quickly record right but there’s lots of area here that that doesn’t have a sensor that’s one number two is that you can only measure the force in this direction right so if the cell is going this way and we want to measure the force in this axis we can’t measure it so in some sense this limited what we could do with the substrate just in terms of a throughput and these other things but it was far from that inspiration that we came up with this idea of building cantilevers that are not in plane but are vertical so what we did was we basically made a device or a template that had vertical cantilevers so the way that you make these sorts of things it’s very difficult to make these things in rubbers but it’s very easy to do this in lithography right so we use this plastic su8 where it’s photo photo cross-linked so what you do is you pour that material on top of a silicon again Co n silicon wafer because silicon is is flat and then you shine light through these little pinholes the the light then polymerizes a pillar and you can see these pillars turns out or not quickly vertical you notice that the kind of pointing there they’re a little bit conical and they’re conical because the light that was coming in through those those pinholes was not perfectly conical maybe not perfectly vertical okay all right and from that you can basically generate a large array of these pillars if you will then what we do is we then template those so you pour PDMS which is a silicone that you can cross-linked chemically and you pour it all over the substrate polymerize it and then you literally just peel it off peel it off and you’re left with holes right and then what we do is we pour another layer of silicone into these holes and then once that plum rises you can feel that off you’re left with basically this such right now and an elastomer something that’s linear elastic okay so with this you can generate all kinds of patterns you can make for example pillars that are not round so you can imagine if the pillars not round then the forces to pull in one direction versus the other are not the same its anisotropic and Benwell Adu has been using these kinds of substrates too now look at what happens if forces the stiffness of the surface is not isotropic and you can also vary for example the stiffness of the pillars by just varying the height of the pillars you can imagine that if the pillars are very tall then it’s very easy to bend them and by sort of simple linear beam Theory you know that as you increase the length the stiffness of that pillar decreases by length cubed okay you can also vary the diameter and the diameter also of course dramatically affects the stiffness of the pillars so these are sort of different ways in which you can sort of play with this kind of substrate so when we actually first started putting cells onto these devices the first thing you’ll notice is that the cells kind of crawl canopy over the pillars and sort of fall

down into the substrate so you can see for example the cells sort of adhering to the bottom surface here so if a cell does that you can’t really measure forces because there’s a sort of ill-defined what you really want to do is you want to put the cells on it so that the cells stay on the tips of the certain of the pillars why because again you know in a beam if you apply a load here versus if you apply a load here obviously the stiffness of the pillar will feel very different and we want to specify where it’s pulling right we want it to pull from the tip so the way that we do that is that at least we did initially it would take PDMS stamps and ink them with matrix something adhesive and then you would print the matrix down onto the pillars so now that just the pillar tips are coated right and then what we would do is we would block the rest of the surface the bottom and the side shafts of these pillars with non adhesives so that when cells attached they will only stick on the tips and you can see that here so the nice thing about this tool is that you can directly determine forces there’s nothing indeterminate about this system anytime you see a pillar Bend then you know that there’s a net force on that pillar right and so from that you can see here in this movie we were just showing cell just crawling around and generating contractile stresses and what we do is we simply look at I don’t know if you can see the grid there’s these little dots here those dots are us measuring the center of those pillars and so as those pillars move then we can simply multiply by the stiffness of the pillar to back out the force so this going from the image to the force is really really really really easy and so this this takes a few minutes to code this and then you can in real-time while you’re taking images of your cells how the force move map with you in this case this is our original pillars were quite big but these ones now are about 1 micron diameter a few microns spacings so one cell will span across between maybe a hundred and a thousand of these how much do they move so obviously that depends on the stiffness of the pillars and how much the cells are generating force we typically see deformations between I want to say 50 nanometers 2 micron and that that’s sort of the range right that’s where we want them to be below 50 nanometers is quite hard to see and above a micron then for the pillar Heights that we typically use which are several microns then the pillar starts to deflect enough that you worry about nonlinear effects okay so we usually dial the stiffness of our of our pillars to be such that they deflect a little bit so is that that was certainly a question when we started this work so far most of the things that we’ve seen the cells behave very similarly so what what changes that is if your pillars are quite far apart then obviously when a cell is trying to attach and spread then it’s harder for a hop from one’s one post to the next right but if the pillars are pretty close together like this relative to the size of the cell then it’s not really being hampered right know as Mike said all natural matrices are not continuous surfaces they’re they’re fibular structures right and so in some ways I think the cells are already naturally designed to be able to jump through space there are obviously differences there have to be differences so in some ways some of the data that that Mike showed in the last lecture actually addresses that for example when we vary the stiffness of our pillars were varying the macroscopic stiffness right how much flexibility or rigidity is there between pillars that’s what the cell would be feeling but then on a single molecule level the stiffness of the PDMS is of course the same across these different substrates whereas on a continuous

material if we vary the stiffness the way we’re doing is we’re changing the molecular cross-linking density so that affects the nanometer scale flexibility of the material as well as the kind of macroscopic so that they’re a little bit different but for us the biology the cells seem to treat them fairly similarly so some of the advantages are also that you can pattern the matrix so for example this right we can print down regions to be adhesive and not adhesive and that’s very useful for my group because we’re interested in studying somebody’s effects of cell shape and I’ll show you an example of that for acrylamide gels or other sort of soft gels if you try to print on them you damage the gel that the physical contact can fracture the gel the other thing is that obviously discreet sensors is a positive and a negative right and as you said it’s a discontinuous surface and that can be a positive or a negative depending on what you’re trying to look at so it sort of depends on the situation whether you would reach out to use this tool versus reach out to use another one so I thought what I would do is just tell you a very very short story about some of the tool use that we’ve had with this one of the areas that my group is studying is how saw shape regulate cell function and the reason why were interested in this is in the context of development the Sir Joseph lay embryo there’s lots of changes in cell shape as cells are kind of squishing and stretching and moving in order to get to where they want to go in order to change tissue structure and we also know from work that was done by Judah Folkman many many years ago that as cells attach on surfaces as they change their shape they change their behavior so we were sort of interested in this link between shape and behavior so we were studying this cell called the musical stem cell it’s a human this is a human cell that it’s derived from bone marrow now people have found these stem cells all over your body and that they basically are stromal cells I can differentiate into bone or cartilage or fat and we were interested in sort of understanding whether changes in cell shape again thinking about this development of context would change how they behave what we found was that we we were using patterns to control cell shape what we do is we would print extracellular matrix onto flat surfaces and you could plate cells down on top of it and if we could change the the size of the spot as you would that the cell attaches on then you would change its shape so if a cell was sitting on a very small spot it would remain largely spherical if the cell was sitting a lot on a large spot that it would sort of flatten out like a pancake and what we found was that when we did that the cells that were round would differentiate into fat cells and the dipa sites and when the cells were very well spread they would differentiate into bone cells or osteoblasts and you can see here as we change the island sizes this sort of switch and that’s commitment of the cells to different lineages so we thought that was pretty interesting it turned out that what we had found was that as the cells were able to spread out they would turn on this protein called Rho a and this Rho a is very important for driving change in cytoskeletal organization and activating myosin and so we had postulated that this activation of myosin would generate tension and that tension was somehow important for this sensing of switch to switch between these two different cell types but even though we had implicated Rho for us to then leap forward and say it was definitely a force mediated response we have to build a measure of the tension in these cells okay and then related to that one of my colleagues at at Penn Dennis Disher had shown that if you take these same cells and you put them on two substrates with different stiffnesses then as the cells were sitting on it’s difference to four substrates they would again switch to different lineages that become bone as they are on stiff surfaces and they would become other cell types as they were in softer surfaces and of course that was very interesting because we know in our own bodies that all of our tissues are different stiffnesses cells that live in fat tissue are in a very soft environment cells in the brain are in a very soft environment cells and muscle and a little stiffer environment cells and bone obviously are in a very stiff environment so perhaps these

changes in the mechanics of the local environment are something that cells can sense in a way that allows these stem cells to differentiate into the right lineages of course for us we had this question of whether these two findings were really linked whether these changes in cell shape and what we thought was contractility was related to this effect of substrate stiffness on differentiation so what we did was we took our pillars and we varied the height of the pillars to change the stiffness so you can imagine that if you have short pillars again cells were sitting on a stiffer substrate than if they’re on a soft on a tall pillar and what we found was indeed when they’re sitting on the short pillars they would differentiate in the bone when they were in soft pillars they were differentiate into fact so now here’s the interesting thing when we look at the cells they change shape so when the cells are sitting on the soft surfaces they remain basically spherical and when they are on the stiff surfaces they spread and flatten very nicely okay and here are SVM’s you’ll notice that the scale bars are different but basically you can see that the cells are quite different in their their structure yeah ah so yes if we but to do that we have to detach the cell right which means putting it into suspension and then putting it out of this surface and then it doesn’t spread that’s right we don’t have a way of making this substrate while the cell is still sitting on it make it soft and see what happens but if we move it yes in fact I’ll tell you this this this is maybe an interesting piece of data but these cells become bone and these cells become fat right it takes about a week for them to turn into these cell types so one thing that we did was that we would take these cells and culture them on these surfaces and then after a day two days three days or four days we would lift them off the surface and switch them because we wanted to know when was the decision to differentiate versus when did they actually execute the differentiation program what we found was that at around day three day four they made the decision so in other words if we took the cell here and we put it over here on day two they would become fat but if we did the same experiment where we moved them at day four they would still become both so they’re sensing these stiffness of for a period of time then they make a decision now when we took that data set and recall that these are all on pillars so we can measure the forces on all of these situations and we find is that when the cells are sitting on the stiffer substrates then the cells would spread out and you can sort of see the mean spreading us here in this case about 6000 microns squared and when the cells are seen on a soft surface so you can see that the mean is quite small right but if we crashed the amount of focal adhesions that they made for every cell we found is that regardless of whether the rigid media were soft what predicted how much focal adhesions that they formed was how well spread they were so as the cells were more spread then they would generate more focal adhesions and the reason why I say that the stiffness wasn’t really the driver here is that in terms of affecting focal adhesions was that you would have some cells sitting on this sort surface that were less spread right and some cells over here that were more spread and those that were more spread had more adhesions than those that were here there were less print had less adhesions yeah yes that prevents this sound oh yeah sorry it’s right that that’s a great question so these cells when you culture them there’s a special media that you use to propagate them that prevents them from differentiating so then when we put them on these substrates we change the media to allow them to differentiate so it’s the what’s in the soluble mix that triggers this beginning to differentiate and so then we add that when the cells are already on the substrate that we want sorry that that wasn’t clear and then if we look at the traction forces you see the same thing the amount of

force they generate is predicted by how well spread they were now here you can see that the the datasets are spread out a little bit when the cells are sitting on the stiff surfaces they’re on a slightly higher absolute values and when they’re on the softer surfaces which are over here so what this tells you is that traction force how much force they generate is mostly determined by cell spread area if you think of it as a principal component and also a little bit even when they’re spread to the same area then there’s a little bit of an effect from the stiffness so this is starting to tell us a little bit about how cells are using these different kinds of environmental cues to decide what to do so we had this model that when cells bind to a surface they’re sort of sensing the stiffness as Mike alluded to initially and that stiffness that affects how well spread they are and as they decide to spread out in flat on the surface that ultimately drives how much force they generate that force generation then impacts adhesion assembly okay and in our system there’s music normal stem cells we think that the adhesion assembly in fact of impacts how these cells sense growth factors within the media to then signal and drive different kinds of differentiation program so this is how the mechanical environment is sort of links to the biochemical environment in the cell so you can see here’s an example where we add these differentiation factors when the cells are sitting on a surface that they’re well spread as soon as I see that they start to increase there contractility okay I’m gonna skip over a slide here and show you that if we look at the differentiation as the cells are starting to differentiate over days and we track the amount of force that they generate we find is that the cells that become bone increase their contractility within the first day and the cells that don’t differentiate don’t increase their contractility so in fact remember I told you that it took them about three days to decide which lineage to become but by the first day they already changed their mechanics so we think that the mechanical response in some ways predicts what they’re gonna do later oops sorry skip this life so interestingly if you now drive contractility you can drive the differentiation of the cells so if we increase contractility by turning on that row protein to turn on myosin in a cell that is just sitting on a substrate it starts them to contract they immediately turn on the genetic program to become both if we block the contractility so the cells relaxed they now become fat so this shows you how this whole system of adhesion spreading contractility is all related to a differentiation program and as I told you at the beginning of the talk we think that those forces are not just used for mechanical purposes but are used for chemistry as well so all of these tools that that we have now to measure traction forces whether these are cool amide gels or micro posts in my view where we’re really enabling for the field that now start to link mechanical forces to stop function but one of the big questions is that all of this was based on using planar substrates and as I’ve shown you in examples in morphogenesis cells aren’t always on a surface sometimes they’re embedded within a material and they’re sort of pulling and by changing the dimensionality of the situation the boundary conditions may be the mechanics change right so we’d really like to do is also measure those forces when cells are sort of within a 3d environment and see what happens so there have been some attempts to do this and recall that when cells are plated into biological polymers that you can’t solve this problem because the cells you can’t back out the stresses from the strains but you can still

measure the strains so what what then Fabri did was he put cells inside collagen or fiber and gels with beads in them and from that you can track the beads and you can get a strain map so what he’s done is he said you know what we can get strain maps and we can’t measure the stresses but we might feel that at least estimate the strain energy within the system how much is the cell doing work into the substrates we’re not sure you know if ty does we’re not sure if those estimates are accurate because let’s remember that the material strain hardens I’m sorry strains difference and and so as you stiff as you pull and deform the material then incrementally as you pull a little bit harder the amount of work to go from here to here is quite a bit higher than going from here to here and so he hasn’t really figured out yet how to incorporate the non-linearity into these calculations so the key to be able to get stresses from strains if you recall is linearity within the material linear deformations so what we did at least eyewall acrylamide gels as much as i find them difficult at least they’re linear elastic materials and so we could find a way to develop a linear elastic material that’s like acrylamide gels but instead of putting cells on top of it you could put cells inside you can’t do that with acrylamide because they’re krill amides toxic so what we did we used it’s probably ethylene glycol as a monomer and polyethylene glycol is not toxic and we simply cross-linked the that gel with cells around inside it if you do that what happens is that the cells kind of stay inside the gel but the cells stay spherical why because probably acrylamide gels and polyethylene glycol gels are non adhesive remember so if the cell can’t stick to it then it’s not going to generate any forces so we have to do is you have to put adhesive materials onto the polyethylene glycol backbone the way that they do this now with probably put on my gels is they form the gel then on the surface they coat it with a cross linker and then capture matrix onto it well because we’re now putting cells inside the gel we can’t cross-linked it after we put the cells there because that would be toxic so we have to somehow put the adhesive material directly into the monomer and then polymerize it so the way we do that is we take small short peptides that are fragments of extracellular matrix molecules that we know bind to cells and we couple them covalently into the gel so now what we do is we have that adhesive moiety we put the cells in we mix that everything as monomer as we polymerize it and now this house can grab onto the gel and what we found is that the cells still didn’t generate much force and they stayed spherical and what you realize is that cells even they can adhere to the gel they can’t spread in the gel because the gel remember the pore sizes of gels are on the order of nanometers to maybe a micron and so the South Canyon would extend processes into the jaw because it can’t sneak through the holes the pores it has to actually build a cut into the gel to then spread through it so we have to find a way to make our polyethylene glycol in a form that cells can dig through it so what we did was we took the polyethylene glycol background which is shown here at backbone and we embedded inside the backbone another peptide and this peptide comes from collagen it’s a peptide that call it in collagen that cells cut as they dig through things so they use these metalloproteases in order to dig through matrices so we simply put that into the material so now when cells are attached they spread into the material and they cut through it and now they can generate force and so this is how we do that just to show you that sort of mechanical characterization you can see that the modulus that the stiffness of the material doesn’t change with the strain of the material right so it’s not strain hardening it’s just like polyacrylamide gels it’s well behaved so shown here is a data set we have lots of beads now in 3d with a cell sitting inside that’s spreading into the gel right so we have to track those beads and of course this is a little bit more challenging because now we have to do confocal stacks throughout this structure this volume to find where all the beads are and if we want high resolution we need more beads and we have to do finer stacks once we have all the beads you can imagine in a stressed state you have beads in a

certain position and to de-stress them to find out where the zero stress state is on a 2d gel the way you do that is you detach the gels you detach the cells so the cells are sitting on a surface there have certain beaten positions you detach the cell the beads all move and now you know the zero stress state right but the way we do this in 3d is you can’t detach so you have to kill the cell what we do is we just add detergent so when you had to charge it the cell blows up I mean that literally but the membranes dissolve and the proteins all leach out and you get the zero stress State now the hardest part of this was having this array of beads before the motion and this array of beads after two pictures and then you got to figure out which bead was which so you can get the strains and so the way that you do that is you basically take each bead and you ask where are the positions of all of its neighbors and so you generate sort of a 3d kind of like a file at finite element mesh of where everything is and then you do the same after this train has been removed and what you find is that the shapes of all of these different structures right that are due to that just random position all the beads every shape is unique and so from that you can sort of find out how to register the two images and find the strings once you have the strains then you can start to calculate the stresses so the first thing you have to do in in our case is that you have to generate a finite element model of the material itself and the reason why you have to do that is because the cell has a unique shape inside this structure all right think of it as a void it’s just a hole in there and you’re pulling on the surface of that void well that means that you have to generate kind of this model of what the the jail looks like with that hole inside for that particular situation for the 2d situation it’s always a half space so you just have to do it once but here for every time the set you get an image you have to then redraw what the cell looks like and regenerate a new finite element model of that gel once you have it then if you have the deformations of all the beads and where they are then you generate the strain maps right and then from that strain map so here’s a strain map you can see the positions of all the beats and sort of how they moved in response to this this cell then we generate that finite element model of the surrounding hydrogel we can build the greens function for that particular hydrogel yeah we do because our bead density within the gel is very high so we know where the void is because there’s no beads in there yeah yeah that’s right and and we do that on every section so then you build a 3d space and that’s so then you generate your greens function for that particular geometry right and then from that you do your inversion to get to the stresses so it’s essentially the same mathematics as we did for the 2d and it’s just that you have to add a couple of extra things one is you have to customize your greens function for every particular geometry and then the rest of it is basically the same so what you find is that when cells are sitting inside these gels is that you see similar kinds of forces the forces tend to be high near the tips of the cells which is the way we see it in 2d and the forces tend to be pointing back towards the center of the cell they never push into the gel they always pull again just like you would expect in in 2d what are they really interesting findings that we had was that when the cells are sitting inside the the gel has single cells they always pull inwards but occasionally for example here in this this was a very large tumor mass when we grow cells into little clusters they could apply pressures they could push out into the gel and you can see here they’re sort of pushing out so you can sort of change the mechanical stress environment when the cells are single cells versus multiple cells and we don’t understand how that happens so we’re trying to figure out how what makes it work Ruth this is not just cell growth

so for example if we look at MDC KS they form a sinner structures you they’ll form them in the absence of growth but you’ll still get pressures in that case we think that the pressures are driven by the osmotic pumps so they’re pumping fluid into the center of this structure and that pushes outwards in the case of the cancer cells if we stop the proliferation the stresses are stable they’re still there but if we stop it early then they don’t grow to form that pressure so in that case of course the elevation is driving it so an example of how we’re using this sort of 3d methods again I wanted to show that to use is sort of my goal is for you to sort of understand how the methods work and not feel intimidated by them and understand how you could incorporate those I just want to show you briefly one last thing I know we’ve got a little bit over but I’ve been answering questions all along is that you know forces drive massive reorganizations right within these developmental context what I showed you right now are sort of single style motions where there’s just a little bit of deformations and those are very easy to measure with these gels and these other types of substrates that I’ve shown you because they all behave linearly when you have small deformations but when you have very large deformations then as far as we know right now it’s impossible to get these high resolution stress maps because there’s just too much motion so again just to show you sort of an example of this is a neurogenesis just the formations or these structures are very large changes in the organization so one model that people have used to sort of study this is actually have very simple models looking at collagen and how it contracts into different types of shapes so if you take a college in gel and you put cells in it cells will contract the gels and they normally contract it to about ten percent of the original volume and they’ll contract it into a little sphere sort of a tight ball and what you can do is you can pin the you can see here there’s four pins here you can pin these gels so that as our contracting they get anchored to these to these anchor points and what happens then is then the collagen starts to contract and it starts to sort of a line and form these sort of web-like patterns and we were sort of interested this had been described again actually by Albert Harris and and snowpack early in the 80s but they hadn’t been able to quantify these these sorts of motions and we wanted to measure the forces so what we did was we used our fabrication tools to again build elastomeric pillars and kate in this case they’re quite large these are instead of one micron diameter they’re sort of like 50 micron diameter right and this dimension is more on the order of several hundred microns so that what would happen is that you could fit inside here a collagen gel with maybe 50 hundred 500 cells into that into that gel and what happens is as you can see when you first seed the cells they’re distributed inside the collagen jail and then they start to contract the gel and you can see that gel gets pinned by these anchors and they start to align the collagen fibers and you can start to see that the pillars start to bend inwards right and as they bend inwards you can back out the forces that are being generated so we’ve been using this to just sort of make what I would call sort of like a little micro tissue and studying the forces of that process and you can see here if we add LPA which is an agent that will increase contractility you see this very rapid increase in contractility if we add a boost and then sort of dissipates one of the reasons why we liked to use this kind of miniaturization was that we don’t have to do with diffusion limitations of small molecules that we’re adding into the media we want it to penetrate into the tissue very quickly so we can sort of see what happens so one of the applications that we’ve been using is forced to make cardiac tissues so we do is we take cardiac cells and put them into these structures and they contract again into these sort of dog bone shaped structures the cells align and because they compact the collagen they get very close to each other and as I get close to each other in the case of cardiac cells they’ll form tight cell cell junctions what those tight cells on

junctions do is it allows the cardiac cells to now electrically couple so you can see here that initially when these things form you see these this is a calcium imaging you can see these little sparks right that are turning on but in general that the cells are kind of decoupled from each other but over time you can see that once they get connected when these got when any one of these activates it causes a calcium wave throughout the structure and the whole thing contracts as a single unit and when they contract as a unit you can see here we have these things moving and from that you can back out again a trace of the forces that are generated so the reason why we’re using a system is now we can model sort of the static tension how much there is there when the cells are relaxed they’re not really fully relaxed it’s just a diastolic tension and then as they beat then they generate this kind of pulse and we want to study that wave so so one of the nice things about this model is that when the cells form this 3d band right there now in kind of a three-dimensional aligned tissue structure and you can see here that that alignment what it does to the cardiac cells is it allows them to form these cell-cell contacts and really elongate and when they do then you can see these sarcomeres that Mike was talking about in cardiac cells those sarcomeres are highly regular and organized right and in in non muscle cells that’s not the case but you can see that here you see this banding pattern you actually measure the distance from one spot to another and that tells you the length of the sarcomeres that are being formed so why are we studying this what we’re really interested in the mechanical responses of cardiac cells to to external environmental changes so what I want to show you here is that when we increase the matrix stiffness and all of our 2d surfaces what happens you increase the stiffness and the cells become more contractile right when we increase the stiffness here you see that the cells become less contractile so what’s happening is it just that there’s something about 3d Ness that makes them sense stiffness differently it turns out that we don’t think that that’s the case I think it’s happening is that when we increase the tissue stiffness that stiffness of the material at the cells sitting in now the cell may try to contract harder but is more difficult to contract the tissue so if you will the cell is now doing more work to just deform the tissue which means less work is being applied to the external pillars which is what we’re measuring right so another way of thinking about this is if you have a cardiac tissue and it infarct if it can if you had a heart attack that wall region that is not getting oxygen starts to fibrosis and become stiffer and what ultimately happens is that even though you have cells in there that are kind of trying to contract that part of the wall stops moving because the tissue has gotten stiff and in in the cardiac world we call that sort of concretization so that it’s like it’s becoming more concrete instead of something soft so that’s bad now our goal is trying to study the mechanics in a way that we would find what are the positive effects or what are the negative effects so here’s another interesting piece of data if we increase the stiffness of the pillars then we see this really nice increase in contractility of the the tissue so here what we’re doing is we’re just changing the stiffness of the external device right the constraints that the cells is sitting in now the cells respond to that they sense that there’s something stiffer on the outside and they start contracting more against that surface so what is that in some ways that’s like increasing your blood pressure you’re not changing the mechanics of your heart itself the tissue what you’re doing is changing this external boundary of a pressure that the heart now has to pump against and it turns out that is very well described that one of the unique properties of heart tissue is that when it gets stretched or when it gets expanded due to blood pressure it contracts harder and that feedback loop is actually critical when you first stand up and they start running the heart has to immediately be able to react by pumping harder otherwise it’s going to blow up okay are you changing

major stiffness we changed the college intensity now you can also do it by changes of the collagen cross-linking so that locally changes the stiffness and the matrix but it doesn’t do anything to the external boundary or stresses so the stiffnesses that we’ve measured our I mean the forces it urgent oh how much force can they generate right now these tissues are generating them not bad maybe a quarter to a third of what we measure in adults heart so it’s within reason the reason why we think that it’s not reached the same level is that in cardiac tissue in the heart the measurements have been made in adults and people that have had 20 years of exercise induced improvements and so if we look at these guys this is after a week and I imagine that if we waited a year that they would get stronger yeah yeah it’s a great question we haven’t done it so LPA is a really nice manipulation because it will increase the basal contractility that black bars and it shouldn’t affect this this external pump but if it does then that means that the cell is sensing this sort of non muscle myosin tension and the effect of that on the cardiac muscle tension so yeah it’s a really interesting question I think there’s a lot of interesting stuff to do that we haven’t gotten to yet so one of the other cool things that you can do with this kind of system is that you can put in different numbers of pillars and you can sort of change the structure so for example here if we have four pillars instead of having a really aligned tissue now you have something that looks like a planar tissue it has sort of biaxial stress and what you find is that if you look at the stresses here versus here the stresses here are going to be much higher because it’s very close to this this post right that the cells are contracting against and what was interesting is that when we started to stain for different kinds of matrix proteins and we were doing that just to look at the matrix itself what we found is that fibronectin is concentrated in these areas of high stress we found in fact a lot more remodeling by the cells in these areas of high stress so we realized and we didn’t do this upfront but after the fact we realized that this model is a really nice model to look at gradients of stress within a tissue and seeing how cells respond to local gradients and so now we’re we’re starting to use this to try to study whether cells can sense those things locally I guess I should also mention sorry that this is work that we’re now doing with Viola Vogel at ETH so she has and I bring this up because yet another approach she has this fret sensor where she’s made a fibronectin molecule that has fluorophores in it so that when it’s in a closed conformation when the permit is not stretched you have very high fret but then as the molecule gets stretched then the fluorophores get pulled away from each other and fret decreases so she’s been using this to look at how fibronectin is stretched by cells and so we talked to her because we measure forces but we can’t do this at a molecular level and we put her frets enter into these constructs and what we found is that as these constructs develop they do increase their forces and we can see that the fret ratio on the fibronectin decreases meaning that there’s more and more stress on the fibronectin as the stuff is developing and so I bring that up to again show you how a lot of these sort of I’ll call them mechanical devices and tools can give you some direct measures of force but it’s really coupling them to these sort of molecular approaches of looking at how specific molecules are being stretched or not stretched and and Mike showed some of that in his talk I think that’s gonna be a very interesting mix of research that’s coming out on these are presumably fibronectin fibers that is our symbol on yes yes that’s right so they’re assembled on the college in Java but interestingly they’re also replacing the college in gel that we put in there in the first place so as a seller contracting the gel they’re templating new fibronectin on the

collagen getting rid of the old collagen and then templating new collagen on top of the fibronectin so there’s this big feedback loop between the matrix production and the sensing of what’s already there and it’s stress mediated and so it’s really complicated unfortunately which means it’s gonna take us a long time to figure out how it all happens yeah so just to end I hope I’ve given you sort of some insights and system of the different types of tools that we currently have available to sort of measure these kinds of forces all the way from kind of basic materials to these sort of molecular sensors and in all of those cases what we really want to get at is trying to understand how forces are driving functional responses in cells and now forces drive changes in cell structure multicellular organization so on the one hand they’re sort of the principles that we’re learning about how there are these links between cell structure and forces and adhesions and multicellular Architecture they’re all sort of linked to each other and those links we feel are really important in connecting how cell tissue mechanics and structure are related to cell and tissue organization and function so that’s sort of a sort of quiet logical inside if you would but I would also like to point out that the tools that we have to study these processes are really just starting to kind of come online and I feel like there’s a lot of opportunity amongst the engineers to develop even better tools to try to get at these things because you can see we’re still a little bit distant between the sort of basic biological systems and our force measurement school sort of trying to figure out how to get those things closer together do you have any questions