Modeling Predicts Non-Monotonic Dependence of Myofilament Ca2+ Sensitivity on Tropomyosin Stiffness

Abstract

The cooperative Ca2+ activation of the thin filament in cardiac muscle plays a vital role in the contraction and relaxation of the heart. Nearest-neighbor interactions between thin filament regulatory units (RUs) are widely considered the principal mechanism of cooperativity, but descriptions of these interactions vary. Previous models have assumed that interactions can be partitioned into distinct categories, such as RU-RU, RU-crossbridge (XB), and XB-XB cooperativity. Under these schemes, the strength of each type of cooperativity is described by independently adjusted parameters. While such models have produced useful insight and predictions, we sought an approach that would relate the different types of nearest-neighbor interactions, thereby constraining the model's parameters and improving its predictive power. We first assumed that cooperative interactions are transmitted along the thin filament solely through tropomyosin (Tm) and its linkages with neighboring Tm molecules. We adopted published values from structural studies for the azimuthal angle displacements of Tm as it transitions between blocked, closed, and open regulatory states. We then postulated a mechanical model by which nearest-neighbor Tms alter the activation energy of tropomyosin state transitions according to structurally motivated strain energy functions. Making simple assumptions about the functional form of the strain energy then enables kinetic rates to depend explicitly on the characteristic stiffness of the Tm chain. Our formulation naturally results in multiple forms of cooperativity that are interrelated in a compact, structurally motivated manner while reducing the number of free parameters. The model successfully fits measured steady state and dynamic Ca2+-force relations, and preliminary simulations indicate that varying Tm stiffness has complex effects on thin filament activation. This behavior suggests that Tm-Tm coupling provides both inhibiting and activating cooperation between RUs, and that these effects are non-monotonically dependent on the magnitude of Tm stiffness.