Sarcomere length-tension relationship

So I'm going to draw up the length-tension relationship. This will be the key idea we're going to talk about in this video. And it's very related to some stuff we've already talked about. So we've talked about, for example, the Frank-Starling curve. And that was talking about how if you stretch out heart cells, and all of the things within heart cells-- all the proteins-- that it actually changes the force of contraction. And actually, force of contraction is very much related to this length-tension relationship as well. So I'm going to put that up here. Force of contraction. And instead of using that terminology, though, we're going to use the term tension. I mean, you can essentially think of them the same way. But classically, the word tension is what everyone uses. So we're going to use that same word. And then, as far as length, specifically the length that we're talking about is the length of a sarcomere. So I'm going to write sarcomere here. And the sarcomere, just keep in mind, is really going from one z-disc to another z-disc. So to draw this out, to actually write it out maybe, we can start with myosin. And so maybe this is our myosin, right here. And I'll draw some myosin heads here. And maybe some myosin heads on this side, as well. And, of course, you know it's going to be symmetric looking, roughly symmetric. So this is our myosin. And actually, I'm going to make some copies of it now, just to make sure that I don't have to keep drawing it out for you. But something like that. And we'll move it to be just below so that you can actually see, when I draw a few of them, how they differ from one another. So I'm going to put them, as best I can, right below one another. And we'll do a total of, let's say, five. And I think, by the time we get to the fifth one, you'll get an idea of what this overall graph will look like. So these are our five myosins. And to start out at the top, I'm going to show a very crowded situation. So this will be what happens when really nothing is spread out. It's very, very crowded. And you recall that you have actin, this box, or this half box that I'm drawing, is our actin. And then you have two of them, right? And they have their own polarity, we said. And they kind of go like that. And so, in this first scenario, this very, very first one that I'm drawing, this is our scenario one. We have a lot of crowding issues. That's kind of the major issue, right? Because you can see that our titin, which is in green, is really not allowing any space. Or there is no space, really. And so, these ends, remember these are our z-discs right here. This is Z and this is Z over here. Our z-discs are right up against our myosin. In fact, there's almost no space in here. This is all crowded on both sides. There's no space for the myosins to actually pull the z-disc any closer. So because there's no space for them to work, they really can't work. And really, if you give them ATP and say, go to work. They're going to turn around and say, well, we've got no work to do, because the z-disc is already here. So in terms of force of contraction for this scenario one, I would say, you're going to get almost no contraction. So when the length is very low, so let's say this is low. Maybe low is not a good word for length. Let's say this is, I'll use the word short. The sarcomere is short. And here the sarcomere is long. So when it's short, meaning this distance is actually very short, then we would say the amount of tension is going to be actually zero. Because you really can't get any tension started unless you have a little bit of space between the z-disc and the myosin. So now in scenario two, let's say this is scenario two. And this is my one circle over here. In scenario two, what happens? Well, here you have a little bit more space, right? So let's draw that. Let's draw a little bit more space. Let's say you've got something like that. And I'm going to draw the other actin on this side, kind of equally long, of course. I didn't draw that correctly. Because if it's sliding out, you're going to have an extra bit of actin, right? Something like that. And it comes up and over like that. So this is kind of what the actin would look like. And, of course, I want to make sure I draw my titin. Titin is kind of helpful, because it helps demonstrate that there's now a little bit of space there where there wasn't any before. And so now there is some space between the z-disc and this myosin right here. So there is some space between these myosins and the z-discs. In fact, I can draw arrows all the way around. And so there is a little bit of work to be done. But I still wouldn't say that it's maximal force. Because look, you still have some overlap issues. Remember, these myosins, right here, they're not able to work. And neither are these, because of this blockage that's happening here. This blockage. Because of the fact that, of course, actin has a certain polarity. So they're getting blocked. They can't do their work. And so even though you get some force of contraction, it wouldn't be maximal. So I'll put something like this. This will be our second spot. This will be number two. Now in number three, things are going to get much better. So you'll see very quickly now you have a much more spread out situation. Where now these are actually-- these actins are really not going to be in the way of each other. You can see they're not bumping into each other, they're not in the way of each other at all. And so all of the myosins can get to work. So the z-discs are now out here. My overall sarcomere, of course, as I said, was from z-disc to z-disc. So my sarcomere is getting longer. And you can also see that because now there's more titin, right? And there isn't actually more titin. I shouldn't use that phrase. But the titin is stretched out. So here, more work is going to get done. And now my force, I would say, is maximal. So I've got lots, and lots of force finally. And so it would be something like this. And so based on my curve, I've also demonstrated another point, which is that, the first issue, getting us from point one to point two, really helped a lot. Really. I mean, that was the big, big deal. Because you needed some space here. Again, this space really was necessary to do work at all. And now that we've gotten rid of the overlap issue, now that we've gotten these last few myosins working, we have even more gain. But the gain was really-- the biggest advantage was in that first step. Now as we go on, let's go to step four. So this is step four now. As we go here, you're going to basically see that this is going to continue to work really well. Because you have your actin, like that, and all of your myosins are still involved in making sure that they can squeeze. So all the myosins are working. And our titin is just a little bit more stretched out than it was before. And our force of contraction is going to be maximal. And you're going to have-- and so here, I'm drawing the z-discs again. They're very spread out. Our sarcomere is getting longer and longer. And our force of contraction is the same. Now let's just take a pause there and say, why is it the same? Why did it not go up? Well, it's because here, in stage three, you had 20 myosin heads working. 20 out of 20. Up here, you had something like 16 out of 20 working. Here, we said maybe zero out of 20 right? And here, you again have 20 out of 20. So you still have an advantage in terms of all of the myosins working. But there's no difference between 0.3 and 0.4. Because again, all the myosins are working. You can't do better than 100%, right? So now in stage five, we kind of take this a little too far, right? So let me actually just make a little bit of space here. We take this a little bit too far in the sense that our actin is going to slip out all the way over here. And it's going to be out all the way over here. So we've got a huge, huge gap now. And, of course, our titin is completely stretched out. It's about as stretched out as our titin is going to get. This green titin protein. And now the question is, of course, would you get any force? And the answer's probably no. Because the myosins aren't even touching the actins anymore. So really, again, you have zero out of 20 myosins at work. And of course, that means that then the amount of force would be zero. So we go back down to zero. So this is part five. So you can see now, as we've gotten longer and longer, things were good for a while, but then they drifted all the way back down. And this curve that I'm showing you, this tension-length curve, is now based on exactly what you see on the right. It's based completely on the idea that as you stretch things out, the amount of force changes depending on the length of the sarcomere.