Why doesn't muscle strength depend on its length?

Question

In case of tug of war the more people participate the more strength they represent. And in case of muscles - the longer it is, the greater the number of myosin heads bind to actin when muscles contract. So why doesn't length matter?

UPDATE:

Since I've found multiple answers that compare muscles to ropes, let me comment on why those explanations don't work for me. Ropes don't have "muscle" strength, they have tensile strength. So this analogy can only compare tensile muscle strength to tensile rope strength.

In the end I'm pretty sure I'll find out that tensile strength constraints the muscle strength. And that's probably going to be the reason why muscle strength doesn't grow with length - something does not allow it, otherwise it would get damaged.

But I'd like find out what exactly prevents further contraction. Is it mechanical receptors on the muscle cell which block deploarization? Mechanical receptors in tendons which send nervous signals (but then - do tendons get thicker in proportion with the muscle)? Something else?

Does this answer your question? Why is muscle force more dependent on cross-sectional area than on fiber length? — kmm, May 11 '21 at 12:37
@kmm, I haven't seen that question, though I tried hard to look for it. Thanks for pointing out. But no, unfortunately there are no satisfying answers there :( — Stanislav Bashkyrtsev, May 13 '21 at 08:12
@kmm, I've updated the question to explain why the rope analogy doesn't answer the question. — Stanislav Bashkyrtsev, May 13 '21 at 08:44
To those who vote for closing: this site doesn't have an answer to my question. If you close it - someone else in the future will have to ask this question again. Otherwise no one will ever answer it. — Stanislav Bashkyrtsev, May 14 '21 at 12:25
The close votes are for this question being a duplicate (which I think it is). Whether or not you find the answers here or on the other question satisfying does not change that this and the other question are basically asking about the same concept. — kmm, May 14 '21 at 13:00
@kmm, yep, I'm not arguing with that. It's just unfortunately this usually means the question won't be answered at all (unless moderators will bump it up, which they probably won't). So we'll wait for yet another duplicate.. — Stanislav Bashkyrtsev, May 14 '21 at 13:11
I think you probably just need to take the leap to understanding a muscle pulls more like a rope does than like a spring, and tensile strength is the best way to think about it. That's what the answer on both this question and the target duplicate are saying, and that's why people are considering it a dupe. Dupes are dupes because the question is effectively the same; if there is an old question you want a new answer on you could offer a bounty. — Bryan Krause, May 14 '21 at 15:00
@BryanKrause, this analogy game will bring us only so far :) A motor protein is a motor protein. It doesn't matter if goes in parallel or in a sequence - it will exert a force and therefore the muscle will become stronger. Unless there's an additional complexity hidden somewhere (which is probably the case). Bounty or not it seems like there are simply no people here who work in this field and can give a good answer. Hence we get more and more of "rope" answers.. So maybe you're right - this dupe won't help. — Stanislav Bashkyrtsev, May 14 '21 at 15:19
If you put me between two Hafþór Júlíus Björnsson and we all linked hands and pulled on each other, we would not have a pull strength of two Hafþór plus me. Each Hafþór would pull at one Hafþór, but they'd pull me apart. Think of them as two thick muscles and me as one thin muscle. You can make the chain as long as you want, we can never pull with more than my strength, you'd just stretch me until I broke. Even the chain of Hafþórs would only pull at one Hafþór, because if a Hafþór is pulled at 2X their strength they would also lengthen. — Bryan Krause, May 14 '21 at 15:41
@BryanKrause, if we assume that 3 Hafþórs don't break the weakest Hafþór then they do add up to more strength. In fact together they pull 3x as strong as 1 Hafþór. Sure, as we add more and more Hafþórs one of them will break eventually. At that point we reach the max strength. Getting back to muscles: if we add more myosin in a row - they will too pull stronger. But something doesn't let them even though now they can. So it's not that the muscle isn't getting stronger, it's that something limits it. I'd like to find out what that is and how it scales with the muscle length and width. — Stanislav Bashkyrtsev, May 14 '21 at 16:09
Myosin pulling is like a rope. It can't pull twice as hard or it breaks. If I can lift a Hafþór I can lift a Hafþór. It doesn't help me if that Hafþór can also lift another Hafþór; to pull them both I'd need to be twice as strong. If I want to double the strength I need them side by side me, not in a chain. — Bryan Krause, May 14 '21 at 16:47
I think you're missing that there is nothing in the middle to pull against. The chains are all pulling each other down the line so the total strength isn't summed. If Hafþór on one end pulls, the next Hafþór has to pull the same just to stay in the same place. — Bryan Krause, May 14 '21 at 16:48
@BryanKrause, that's because our analogies are imperfect. If we return back to the tug of war.. Hafþór is actually pulling on the rope. Not on another Hafþór. So the more Hafþórs (myosin) we have the harder they pull on the rope (actin). And in your muscles you don't have 1 myosin head per muscle cell - you have many of them in a sequence. And you have many sarcomeres in a sequence. If you remove half of them - you'll have half of Hafþórs (myosin heads) pulling on actin. — Stanislav Bashkyrtsev, May 14 '21 at 18:08
Ok then that's what you are missing: you're imaging some central rope of near infinite strength that everything acts on, like people in a tug of war. That's wrong. None of my analogies involved tug of war. Myosin pulls different actins together, like maybe the myosin is the arms and the actins are the bodies in the chain. The only ground points are the tendons at each end of the muscle, in between it's all muscle fibers pulling against each other. Bob drew the scenario reasonably below, besides the tendon/ligament confusion. — Bryan Krause, May 14 '21 at 18:32
No one in the linked duplicate referred to tug of war, either, except someone in the comments with the same confusion as you, and someone else responded to them and explained how this doesn't work. — Bryan Krause, May 14 '21 at 18:35
@BryanKrause, I now realize what was my problem, I've put it in a separate answer. Thanks! — Stanislav Bashkyrtsev, May 14 '21 at 19:38

score 6 · Answer 1 · answered May 11 '21 at 10:52

It's simply that the fibers are arranged end-to-end. If you simplify this down and imagine a single muscle fiber you have actin and myosin like this:

ligament-|actin-myosin-actin-myosin-actin-myosin

If you think of this as a strand of cotton pulling on a weight (ligament). Each group only pulls along the length, so the strength is not multiplied, but rather related to the strength of the individual fibre.

In reality muscles are stacked into bundles, which are much stronger as all the fibers can contract pulling with the strength of the multiple ends. Like this:

         |actin-myosin
         |actin-myosin
ligament-|actin-myosin
         |actin-myosin
         |actin-myosin

This is like the multiple strands of cotton making up a rope, the strength comes from having lots of them distributing the load.

This is something called physiological cross-sectional area, which describes the strength of a muscle by estimating the cross-section of the muscle across its thickest part.

score -1 · Answer 2 · answered May 14 '21 at 19:37

The confusion I had is that I thought that myosin pulls on actin with a force which some how isn't the maximum possible. And if we were to add another sarcomere in a series - each myosin would have to work harder and together with the new sarcomere they would exert a greater force.

But this of course isn't how it works. Myosin doesn't have a notion of a varying strength, it's binary: it either attaches to actin or not. If we were to try to pull apart actin or myosin harder by their "tails" (by a neighbouring sarcomere) - actin would've started to "slip" from myosin. Therefore putting more sarcomeres in series would not make the muscle stronger - we'd simply add more "slipping".

The other possibility in a theoretical world would be to make actin and myosin strands longer and add more myosin heads (we'd have to reinforce lots of structures though). This way we could've made the muscle stronger by making it longer. But that's not how it works: a longer muscle cell merely means more sarcomeres in series.

Thanks @Bryan Krause for nudging me into the right direction in the comments.

Why doesn't muscle strength depend on its length?

2 Answers2