Fig 1.
Overview of modeled kinetic transitions.
Our computational model combines two three-state cycles to simulate activation of thin-filament regulatory units (rt,ij) and the cycling of cross-bridges (rx,ij). Thin-filament activation is described by an initial state where calcium is unbound from the troponin complex and tropomyosin blocks the actin-target zone (TF1), a second state where calcium is bound to troponin but tropomyosin remains in a blocking conformation (TF2), and a final state where the calcium activation of troponin shifts tropomyosin and reveals the actin-target zone (TF3). Following TF3, cross-bridge binding occurs in three states: an initial unbound state (XB1), a low-force bearing, pre-power stroke state (XB2), and a high-force bearing, post-power stroke state (XB3).
Fig 2.
Protocol for simulating length transients.
A) Following activation, the half-sarcomere was shortened by 100 nm (~10% half-sarcomere length) at a velocity between 0.1 and 4.5 muscle lengths per second (ML/s). Sarcomeres were held at this new length for 250 ms and then returned to the initial length at the same velocity they were shortened. B) Force traces over this period show decreased force during shortening and increased force during lengthening, with a dependence on the velocity of shortening and lengthening. Example traces from 0.5 and 1.5 ML/s are shown here, superimposed.
Fig 3.
Velocity-dependent measurements with XB stiffness fixed at 3 pN nm-1.
A) Active force increased during lengthening and decreased during shortening, reaching maximal unloaded shortening around 3 ML/s. B) Power was calculated during the shortening transient as the product of force and velocity, producing a hyperbolic curve with peak power around 1 ML/s. C) The fraction of cross-bridges bound to the thin-filament was greatest during relatively slow length transients in either direction. D) The ratio of total force distributed amongst the bound cross-bridges increased during lengthening and decreased during shortening. E) The amount of ATP consumed for the total number of myosin heads in the system decreased slightly during the lengthening transients and increased with shortening velocity. F) The ratio of force to ATPase activity was greatest during lengthening and lowest during unloaded shortening.
Table 1.
Summary of force and power data with varying cross-bridge stiffness.
Fig 4.
Velocity-dependent measurements as a function of XB stiffness.
A) Decreased XB stiffness resulted in the maintenance of more force during sarcomere shortening and a faster unloaded shortening velocity, while the converse occurred with increased stiffness. B) Decreased XB stiffness resulted in greater power generation, with the peak power shifted towards a faster shortening velocity. C) Decreased XB stiffness resulted in a greater fraction of bound XBs, particularly during slow shortening transients. D) Decreased XB stiffness resulted in less force per bound XB, though force was maintained at faster velocities in sarcomeres with more stiff XBs. E) Decreasing XB stiffness significantly increased the total ATPase activity during isometric and non-isometric contractions. F) Decreasing XB stiffness lowered the economy of force production during both lengthening and shortening transients compared to sarcomeres with greater XB stiffness (up to their respective unloaded shortening velocities).
Fig 5.
Velocity-dependent force measurements as a function of thin-filament stiffness.
Decreasing thin-filament compliance by an order of magnitude resulted in lower tension during isometric contractions. However, increasing or decreasing the compliance of the thin-filament had minimal effects on the force-velocity relationship during sarcomere shortening.