The length-tension relationship
For muscles to contract, the muscle proteins called actin and myosin must interact with each other. This occurs when they are optimally aligned opposite each other. If they are too far away from each other, they can't interact optimally, and the same thing happens if they are too close.
Think of two trapeze artists. One of them will be caught by the other - but only if they jump at the right moment. If they jump when they are too far apart, then that artist will fall. If the artist jumps when they are too close, they are likely to collide.
You're going to explore this effect of overlap between actin and myosin in the muscle on the amount of useful force (active force) that the muscle can produce.
Video transcript
One way in which we can change the amount of force that a muscle generates is by changing its length. Now, as soon as I said that you would've realised immediately that's a theoretical issue only, because after all you can't rip your muscle off, stretch it out, stick it back on in the same place and expect it to work.
However, the data that you will get while you do this experiment requires you to understand the physiology very well to interpret. So although this is purely a theoretical mechanism, it has great educational value in making you think about the underlying physiology.
And so one of the experiments you will be doing is what's known as the length-tension curve. In essence what you will do is stretch the muscle, apply an electrical stimulus to it, and record the response; the muscle force or muscle tension generated when the electrical stimulus makes the muscle contract.
You'll find that in fact, that force consists of two components:
One component is what is known as active tension. Active tension is the tension or force that's useful in doing work. It's the force or tension generated by the interaction of actin and myosin.
You will recall from the lectures that actin and myosin are found as thick and thin filaments in the sarcomere. When you stretch or compress a muscle, what you're doing is changing the amount of overlap between the thick and thin filaments.
You may pull the muscle apart so much that the thick and thin filaments do not overlap. In which case, when you apply electrical stimulus, they can't interact, and therefore no tension will be generated.
At the other extreme, you can cause the muscle to compress so much, that the thick and thin filaments interfere with each other, and now when you stimulate the muscle you will get very little tension. In other words, there's going to be some optimal position where the overlap between the thick and thin filaments allows for the best interaction between the actin and myosin, and then you get the greatest amount of tension that will be produced.
So that active tension will vary in a very systematic order. I'm going to draw a diagram of it, and this is the sort of data you should expect to see with the active tension.
So you have a plot of muscle length in millimetres, versus tension.
Now for active tension, as I've just indicated, you would expect to see that if the muscle is very highly compressed, there's very little active tension that's generated. In contrast, equally if the muscle has been stretched too much, there's very little tension that's generated.
So you should expect to see something like this bell-shaped curve, where there is some particular optimal muscle length, where you get the greatest amount of active tension.
And this is the tension that is useful for carrying out work, because it's the tension that can be used to move things.
However, it's not the only form of tension that a muscle can generate. Muscle doesn't just consist of the contractile elements of thick and thin filaments. Muscle also contains a number of tissues that hold these elements in place.
These include connective tissues, they include proteins such as Titin, which act very much like rubber bands. And you know the rubber band, when you stretch it, and stretch it and stretch it, each time you stretch it you're developing more tension in the rubber band. That tension is known as passive tension.
This is the sort of effect that you would expect to see for passive tension. When the muscle is highly compressed obviously there's going to be no stretching of those passive elements, the connective tissue elements, the titin, so there will be no passive tension generated.
If you keep stretching the muscle, that process will still continue, until finally when you start reaching the optimal muscle length is where you will start to see increases in the passive tension as you keep stretching the muscle.
This is the sort of curve that you would expect to see for passive tension. Very little passive tension at short muscle lengths. When you start reaching the optimal muscle length where active tension is highest, thereafter you will start developing greater passive tension.
Unfortunately, passive tension itself is not useful for doing work. Think of the rubber band. If you keep stretching the rubber band, eventually you're going to get to a point where the rubber band is going to stretch and snap. That's what will happen if you're going to carry on stretching the muscle.
In effect, this is the sort of data that you would be generating. An active tension curve, which is a bell shaped curve. A passive tension curve, which is an exponentially increasing curve. And finally of course, you can sum up the two to generate a total muscle tension curve, which will look exactly like this. To join up with the passive tension curve.
These are the three sorts of tensions that you will be measuring. In your virtual component, the practical class itself separates out the three tensions. So when you setup the experiment to do the virtual component, when you apply stimulus the data that will be shown on the data graph will be data from the active tension, passive tension, and finally the total tension.
We want you to collect all three sets of data, enter it into the table each time you apply a stimulus, and subsequently print out that table or extract that table in a way which allows you to generate a graph like this.
To understand this, you're going to need to understand the physiology that I've given you a very brief sketch for, and that's why this sort of experiment is very useful. It's pedagogically quite a valuable experiment.
So this first screen grab that you can see is a contraction of the muscle obtained with the muscle at its optimal length. In this part of the experiment we're going to vary the length of the muscle going down to much shorter muscle lengths, non-optimal lengths, as well as going up beyond the optimal length to longer, non-optimal lengths, to look at what happens when we interfere with the overlap between thick and thin filaments.
So this screen grab that you've got here shows you seven muscle contractions done from different muscle lengths. The one right at the bottom was obtained with a very short muscle length of about 53mm on our scale here, and then progressively increasing it by about 2mm steps.
You can see two different things. First and foremost, you can see that the size of the contraction, the active tension in other words, increases initially, until you look at the very last two where you'll see that the last one appears to be smaller than the one preceding it.
So you've got to the optimal length, and you've gone beyond it. So you've produced the maximum amount of active tension, and then it's decreased. The second thing you can see is if you look at the left, right at the start of the recording, you will notice that the baseline prior to muscle contraction itself is changing.
We're going to do a zoom of that, so that we can see this in greater detail where we will simply expand the baseline to show you the shift in this baseline. And that is the passive tension I was talking about. Each time we stretch the muscle, we stretch the elastic elements of it, and thereby increase the passive tension.
You can see this increases well beyond the optimal muscle length. It would continue increasing, because as we said in the rubber band analogy, you can do this until eventually the rubber band (muscle) will snap.
The purpose of this experiment is to examine how Passive and Active forces developed by the muscle change with muscle length. The video above explains some of the physiology involved in this process, and discusses expected results in the simulation and if you were doing a wet practical on this aspect of muscle function.
Video instructions
For this simulation, the voltage has been pre-set to achieve the peak muscle contraction response. This simulation looks at the effect of muscle length on contraction strength.
Video transcript
As you saw in the background video explanation, when the muscle length is too short, when you cause compression of the muscle, you can actually cause active interference between the actin and the myosin, reducing the number of cross-bridges that they can form, and thereby reducing the amount of tension that the muscle could optimally perform.
As you then progressively stretch the muscle, you take the muscle to the position where there is optimal overlap between the actin and myosin, allowing for the best possible number of cross-bridges to be formed, and muscle tension to be at its optimal.
As you then progressively increase the muscle beyond this length, what you should expect to see is that in fact there will be an increase in one form of tension, and a decrease in the other form.
The one form of tension where you will get an increase, is the form known as passive tension. As you saw in the preceding video, this is like when you were stretching a rubber band, you're stretching the elastic elements of the muscle, and you will see an increase in the resting muscle tension.
However, because now you've stretched the muscle to the point where there is non-optimal overlap between the actin and myosin, the active tension (the tension formed by the cross-bridge interaction) will actually start to decrease, because now there's less overlap.
Let's demonstrate this with a few test lengths. Let's start off with the baseline length of 42 millimetres. Press simulate.
And you can see that there's no muscle tension generated. Increase it in 0.5 millimeter lengths, but I'm only going to try a couple.
Let's go to 43.5 for the sake of this demonstration. Notice now that you've got muscle contraction, but you'll notice also there's a small shift in the baseline. That's the shift of the passive tension that I was talking about.
The difference between that baseline, and the peak, represents the active tension of the tension that's produced by the muscle contraction.
Let's go up a little bit more to 47 millimetres. Simulate. And here you can see very clearly the increase in passive tension, as well as the increase in active tension between baseline and peak, compared to the active tension here. So we're getting a more optimal overlap between the actin and myosin.
Let's go a bit further to 49.5, again an increase in the passive tension, clearly here the active tension appears to be greater than the previous length.
Let's try something like 51 millimetres. Notice now, there's a massive increase in the passive tension, but this time the active tension (between baseline and peak) is now clearly significantly smaller than previously, indicating you've stretched the muscle beyond its optimal length.
And if we go to 52 millimetres and press, we will see an even further increase in passive tension, and a further decrease in the active tension. These data are plotted below in the graph, where you can see here the active tension (shown in blue) increases, reaches a peak and then declines.
Passive tension on the other hand, more slowly begins to increase but then increases exponentially, and so the total tension (which is simply a sum of these two), shows in increase, probably a small inflection around here when you collect the data in finer detail, and then a further increase.
Once you've finished this part of the experiment and collected the data, press "Clear Data" to go to the next experiment.
Please note that although this video demonstrates an older version of the simulation, it should function the same.
Instructions:
- Begin by setting the muscle at its shortest length. (42.0mm)
- Apply a single electrical stimulus and observe the passive (baseline) force, and the active tension (the difference between the peak force and the baseline).
- Increase the muscle length by 0.5mm to 42.5mm. Stimulate the nerve supplying the muscle, observing the changes to both passive and active tensions.
- Continue this until you get three successive recordings where you have increased voltage with no increase in muscle twitch size.
- Systematically increase the muscle length by 0.5mm for the remaining values presented in the scroll box. Press stimulate, then observe the results.
Once you have finished, look at the second graph which plots the active, passive and total tensions for each muscle length. What trends do you observe? How does this relate to the physiology?
Simulating the length-tension relationship
Full instructions can be found on the previous tab. In short:
- Muscle length can be selected from the scroll box on the left.
- First, stimulate the muscle's nerve with the muscle set at 42.0mm.
- Systematically increase the length of the muscle by 0.5mm at a time. Stimulate the nerve at each length.
- Observe the changes in active and passive tension.
Muscle Length:
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Actin Myosin Visualisation:
Once you've completed the data collection, you can use the visualisation below to understand the processes underlying the active tension curve in the length-tension graph.
Interact with the slider or select buttons A through E to see how different lengths correspond to points on the tension graph.
Explanation in next tab
Explanation of the Actin Myosin Visualisation
The active tension produced by muscle is the force that can be used to do useful work. It is produced by the cross bridge interaction between the muscle contractile proteins, myosin and actin. During this cross-bridge cycle, actin combines with myosin and ATP to produce force, resulting in the ATP being broken down into adenosine diphosphate and inorganic phosphate.
In each muscle fibre (myofibril), these proteins are organized into repeating segments, called sarcomeres (one of which is shown in the visualization above). Each sarcomere consists of overlapping thick filaments (myosin; dark blue in the illustration above) and thin filaments (actin; red in the illustration).
Muscles contract by the thick and thin filaments interacting and sliding along each other. This interaction occurs when certain actin-binding-sites (the spiky "twigs" on the blue myosin filaments) bind to sites on the actin. Notice that these actin-binding heads are not found along the full length of the myosin filaments, but only at the ends. That means that there will a certain sarcomere length where these actin-binding heads will overlap optimally with the actin filaments - at longer lengths the overlap will be less, and at shorter sarcomere lengths the actin filaments will overlap with each other, so that there will less than optimal actin sites for the myosin actin-binding heads to bind to, to produce the cross bridge cycle.
This will become clearer when you play with the visualization in the previous tab.