Proposed mechanism for the length dependence of the force developed in maximally activated muscles

Figure 1. Relative tension and fraction of active motors along the thick filament at SL = 1.9 μm. The tension, normalized respect the maximum tension generated at the SL of 1.9 μm (T1.9max), at different [Ca2+] (upper panel) shows a non-linear increment along the thick filament, even at high [Ca2+], when the thin filament is fully activated. The non-linearity is due to a non-uniform activation of the motors along the thick filament (lower panel). At pCa = 4.5, there is a region of the thick filament, close to the M-line, which is fully activated, thanks to the high active tension generated by the motors upstream toward the Z-line. The low tension near the Z-line, instead, generates a region of slight more than constitutively activated motors, which survives even at this high level of [Ca2+]. The effect is more pronounced the less the thin filament is activated.

Figure 2. Relative tension and fraction of active motors along the thick filament at different SLs. The non-linear part of the tension along the thick filament is reduced at longer SLs (upper panel). This is due to the higher extension of fully activated region of the thick filament (lower panel) at longer SLs. At SL = 2.3 µm, the motors are almost fully activated, except for the very end of the thick filament. The small decrease in the activation close to the M-line at SL = 2.3 µm, is due to a partial loose of overlapping of the thin and thick filaments due the imposed geometry.

Figure 3. Normalized tension-[Ca2+] curves at different SLs. The simulated tensions at different [Ca2+] and SLs reproduce the experimental data showing that the proposed mechanism is able to explain the increment in Tmax at longer SLs.

Figure 4. Influence of the constitutively ON motors on the increase in Tmax. At the given parameters for the MS mechanism, the increment in the SL, and consequently in the passive tension, affects more the increase in Tmax at low SLs than at high SLs (1.9 and 2.3 µm in figure, upper panel). The effect is more pronounced at lower percentages of constitutively ON motors (lower panel), and tends to decrease at values higher than 5%. A value of 3% is predicted by the model to account for the 40% increment observed experimentally.

Figure 5. Tension during a twitch and tension-velocity curves for the single trabecula model at different SLs. Attachment-detachment rates and power-stroke energetic landscape for myosin motors are fitted to experimental data for the tension-time curves during a twitch (upper panel) and for the isotonic velocity of contraction (lower panel). The different behaviours at different SLs are matched. Dashed line in the upper figure is obtained by extrapolation of experimental data from Caremani et al.4 and adapted to the experimental maximum tension at SL = 2.2 µm.

Figure 6. Tension and fraction of active motors along the thick filament averaged among all the left ventricle elements at different preloads. The average tension (upper panel) increases from the thick filament free end toward the M-line in a non-linear manner. As in the half-sarcomere model, this is due to the non-uniform activation of the myosin motors (lower panel). Increasing the preload, increases the active motors and consequently the tension generated. Data is taken 96 ms after the beginning of the systolic phase.

Figure 7. Ventricle model and a portion of a representative sarcomere at two different preloads. The FE model of the left ventricle (upper part of the figure), shows a higher tension in the elements when preload increases from 5 to 15 kPa (left and right part of the figure respectively), especially in the central region of the ventricle wall. The higher tension is due to a longer SL, which activate a higher number of myosin motors through the higher passive tension generated by the titin (lower part of the figure). Myosin motors in figure are shown in their simulated state during a beat: OFF detached state (clear blue), ON detached state (blue), and attached (violet). Data is taken 96 ms after the beginning of the systolic phase.

Figure 8. Simulated ejection volume at different preloads (grey circles) and comparison with experimental data40 for rat myocardium (filled dots) and old model (grey boxes). The new model is able to predict an increase in the ejection volume at higher preloads, due to the higher tension generated at longer SLs. However, the increase is not as much as observed experimentally, indicating that other mechanisms are involved in the Frank-Starling law of the heart. More interestingly, the increase in the EV is very similar to the one predicted from our previous model which generates the same Tmax for all SLs (the two simulated data are not superimposed for the intrinsic differences between the models, in the new model the ejection volume at 5 kPa has been chosen for the initial fitting of the FE parameters). This result opens the question about the relative importance of the second component of the LDA in physiological situations.

Figure 9. Proposed mechanism. Myosin motors are in a detached OFF state (clear blue, folded on the thick filament), a ON detached state (blue), or an attached state which generates force (violet) At the onset of the contraction the motors have the same probability to be active (upper panel). However, when an active motor strongly attaches to the thin filament, it generates tension only on the portion of the thick filament toward the M-line (intermediate panel). The higher tension generates a higher probability of the downstream motors to be activated (lower panel) and then to produce force, generating the reservoir toward the Z-line.