Titin-mediated thick filament activation, through a mechanosensing mechanism, introduces sarcomere-length dependencies in mathematical models of rat trabecula and whole ventricle

Figures

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  Figure 1. Two-cycle model. In the model, myosin motors can follow two cycles, a non-force-generating, “resting” cycle and a force-generating, “working” cycle, connected through one motor state. In the resting cycle, motors can lie along the thick filament in the OFF or super-relaxed state, or they can rise toward the thin filament, in the ON or active state, ready to enter into the working cycle. Motors in the ON state can use energy from ATP to generate active force. Myosin motors can then strongly attach to actin filament (shown with the periodic troponin-tropomyosin units in cyan) and perform a two-step power stroke. The rate constant from the OFF to ON state, kOFF–ON, is a function of the tension, T, acting on the thick filaments, indicating a mechanosensing mechanism, while kON–OFF is a constant. Rate constants for strong attachment (kON–S) and detachment (kS–ON) are functions of the axial position of each motor, with respect its relaxed state, as in the original Huxley 1957 model35.

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  Figure 2. Simulations of isometric and isotonic twitches. Upper: Simulation of the tension generated during a physiological [Ca2+] transient in isometric conditions, at different SLs. The experimental time transient at SL = 2.2 µm (black line) is scaled to the simulated maximum tension at the same SL (red line). Simulated maximum active tensions vs. SLs are shown in the inset and compared with experimental data (simulations, filled squares; experimental data, empty triangles). Lower: A steady velocity of contraction is reached under isotonic conditions imposed near the maximum tension of a twitch. The simulated force–velocity curves (black dots, SL = 1.9 µm; black triangles, SL = 2.2 µm; and lines) quantitatively fit the experimental data, at two different SLs, without modifying the mechanokinetics properties of the motors. All experimental data are from Caremani et al.10.

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  Figure 3. Simulations of force–pCa curves at different SLs. Upper: Maximum force at different [Ca2+] values, without titin tension (at SL = 1.9 µm, red dots) and with increasing titin tensions at higher SLs. Force–pCa curves are shifted to the left at higher SLs, as was also observed experimentally. Continuous lines represent the best fits with Hill’s curves, for SL = 1.9 μm (red) and SL = 2.2 μm (black). Bottom: Relative number of motors in the OFF state at steady [Ca2+] = 0.6 µM. The higher number of active motors at higher SLs, generating higher steady values of attached motors and, thus, higher active tension values, shifting the pCa–force curve to the left.

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  Figure 4. Ventricle model simulations: Sarcomere lengths in different finite elements at the end of the diastolic phase (upper part) and active tension at peak (lower part, at 0.1 s after the beginning of the systolic phase). Two preloads are shown, at 5 and 15 mmHg (left and right, respectively). The tension is higher at 15 mmHg because of the effects of titin on the mechanosensing mechanism.

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  Figure 5. Left ventricle FE model simulations. Ejection predicted by the rotationally symmetric FE model of the rat left ventricle, against increasing preloads with the double-cycle model (red squares), compared with the experimental data (black diamonds). The ejection increases at higher preloads, showing that the model can reproduce, at least qualitatively, the Frank-Starling law. The passive tension effects of titin on the mechanosensing mechanism are eliminated from the model in two ways (blue triangles and green dots). Neither predicts an increased ejection, except for small preloads, which lead to decreased overlap of the two filaments.