I understand that when the muscle is relaxed tropomyosin blocks myosin binding sites on actin filaments thereby preventing muscle contraction. What I am concerned with however, is whether myosin filaments - given that ATP is found in the muscle fiber- continue trying to bind to actin, and hydrolyzing ATP...
So how are mysoin filaments stopped from trying to bind to actin when the muscle is relaxed, to stop the hydrolysis of ATP?
Relaxation of vertebrate skeletal muscle is thought to occur in the absence of ${Ca}^{2+}$ as a result of tropomyosin physically blocking the binding of myosin to actin. This steric blocking model of muscle relaxation predicts that myosin subfragment 1 (S-1) will not bind to actin under conditions where the acto-S-1 ATPase rate is inhibited.[1]
However, in a paper that questions this model, it is concluded that in the absence of ${Ca}^{2+}$, troponin-tropomyosin inhibits the ATPase activity by inhibiting a kinetic step in the cycle of ATP hydrolysis, perhaps $P_i$ release.[2]
That is the simple answer, but I think a little elaboration on the above paragraphs might help add some substance:[2]
Vertebrate skeletal muscle contraction is the result of a cyclic interaction of thick myosin filaments with the thin filaments, composed primarily of actin, troponin, and tropomyosin, causing these two sets of filaments to slide past each other. This cycling is driven by the hydrolysis of ATP by myosin in a reaction which is activated by actin.
When the sarcoplasmic reticulum lowers the free ${Ca}^{2+}$ concentration from $10^{-5}$ to $<10^{−7} m$, muscle contraction ceases and the associated actin-activated myosin ATPase activity is inhibited. The proteins troponin and tropomyosin are responsible for this effect of ${Ca}^{2+}$ on the interaction between myosin and actin.
At levels of ${Ca}^{2+}$ low enough to cause relaxation, tropomyosin is positioned away from the central groove of the F-actin filament where it appears that it might interfere with the binding of the myosin cross-bridge. This structural work formed the basis of the steric blocking hypothesis which suggests that relaxation occurs when tropomyosin, in the “relaxed” position, physically blocks the binding of the myosin cross-bridge to actin.
Three-dimensional reconstructions from electron micro-graphs have suggested that the myosin cross-bridge and the tropomyosin molecule may be in close contact with each other on the actin filament, a requirement for a steric blocking type model.
The steric blocking model predicts that in the absence of ${Ca}^{2+}$ the degree of association of S-11 should be much weaker with regulated actin than with unregulated actin. In fact, in the absence of ${Ca}^{2+}$, the binding of S-1·ADP to regulated actin is strongly inhibited in a cooperative manner.
At low levels of saturation of the actin filament with S-1·ADP, the binding of S-1·ADP to the regulated actin filament is about $10^3$ times weaker than at high levels of saturation.
However, the fact that S-1·ADP binds weakly to regulated actin does not prove the steric blocking model since, in relaxed muscle, the cross-bridges normally exist with bound ATP (or ADP · Pi) and not bound ADP. Therefore, the steric blocking model predicts that troponin-tropomyosin should inhibit the binding of S-1·ADP·Pi as well as S-1·ADP to regulated actin in the absence of ${Ca}^{2+}$.
Using stopped flow turbidity measurements, we have previously measured the effect of ${Ca}^{2+}$ on the association of S-1 · ATP and S-1 · ADP · Pi with regulated actin. Surprisingly, in the absence of ${Ca}^{2+}$, the binding constant of S-1 · ATP or S-1 · ADP · Pi to regulated actin was only decreased to 56% of the value in the presence of ${Ca}^{2+}$ although the rate of ATP hydolysis under the same conditions was decreased to 6% of the rate with ${Ca}^{2+}$ present. These data suggest, in disagreement with the steric blocking model, that inhibition of the rate of ATP hydrolysis, in the absence of ${Ca}^{2+}$, is not the result of inhibition of the binding of S-1 to regulated actin.
1- https://pubmed.ncbi.nlm.nih.gov/27065174/
2- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1266292/#FN2
