Tropomyosin flexural rigidity and single ca(2+) regulatory unit dynamics: implications for cooperative regulation of cardiac muscle contraction and cardiomyocyte hypertrophy

Abstract

Striated muscle contraction is regulated by dynamic and cooperative interactions among Ca(2+), troponin, and tropomyosin on the thin filament. While Ca(2+) regulation has been extensively studied, little is known about the dynamics of individual regulatory units and structural changes of individual tropomyosin molecules in relation to their mechanical properties, and how these factors are altered by cardiomyopathy mutations in the Ca(2+) regulatory proteins. In this hypothesis paper, we explore how various experimental and analytical approaches could broaden our understanding of the cooperative regulation of cardiac contraction in health and disease.

Keywords: calcium activation; cardiomyopathy; cooperativity; heart; persistence length; sarcomere; thin filament; tropomyosin.

Figure 1

Schematic diagram of four-state model. On the left hand side are states where myosin forms weak, non-force-producing crossbridges. On the right hand side are force generating states where myosin binds strongly to actin. The upper states represent Ca²⁺ free states whereas the lower states represent Ca²⁺ bound. Ca²⁺ binds to TnC and activates regulatory units with rate constants k_on (left) and $k_{\text{on}}^{\prime }$ (right), while k_off (left) and $k_{\text{off}}^{\prime }$ (right) reflect the kinetics of processes associated with regulatory units returning to the blocked state. Strong crossbridge formation and dissociation from thin filaments are governed by rate constants f and g, respectively. g′ Describes the rate of crossbridge detachment from regulatory units without Ca²⁺, as may occur during relaxation of skeletal muscle; the rate of strong crossbridge formation (f′) is practically non-existent in this condition. State 4 (upper right) is needed to model P–k_TR relationships in skeletal muscle, but can be omitted when modeling cardiac muscle (Hancock et al., 1997).

Figure 2

Overlay of signals (traces in black and gray) from two reporter probes corresponding to two regulatory subunits on a single thin filament. (A) Correlated signals from two reporter probes separated by a short distance demonstrate predicted result for cooperative interactions along a thin filament. (B) Uncorrelated signals from two reporter probes separated by a longer distance. The insets depict single thin filaments where the dots correspond to reporter probes on individual regulatory subunits; arrows represent distances between the reporter probes.

Figure 3

Tropomyosin rigidity is an important factor in the propagation of activation signal along the thin filament. (A) In the absence of Ca²⁺, tropomyosin sterically blocks myosin binding sites on actin (top). In the presence of Ca²⁺, a rigid (L_p ≫ L_c) tropomyosin strand (middle left) moves azimuthally nearly as a single unit, uncovering most of the myosin binding sites on actin along multiple SRUs (two SRUs, denoted by shading, are shown from each thin filament). In contrast, for semi-flexible (L_p ∼ L_c) tropomyosin (middle right), only a portion of the strand moves azimuthally and just 1–2 SRUs are activated. (B) Reduction in rigidity of an initially rigid tropomyosin has little impact on thin filament activation (bottom left), as activation signal still propagates along multiple SRUs. In contrast, a reduction in rigidity of a semi-flexible tropomyosin (bottom right) will significantly reduce the effective propagation length of activation signal, but also increases the likelihood of activation at lower Ca²⁺.

Figure 4

Correction due to intrinsic curvature of tropomyosin is less significant when apparent L_p approaches the contour length. According to Eq. 1, the percentage correction to apparent L_p due to intrinsic L_p (dashed line, right axis) is non-linear and is much smaller at values of apparent L_p ≤ L_c than at longer values. Dynamic L_p (solid line, left axis), measurement of the true mechanical flexibility obtained after the correction, is also close to apparent L_p when apparent L_p ≤ L_c. For reference, the linear relation obtained for molecules with no intrinsic bend is also shown (dot-dashed line, left axis). Also for reference, L_c (=40 nm) for Tm molecules is highlighted by the vertical, gray dashed line.

Figure 5

Variation of structural perturbation signal transmitted from (A) the ends to the middle of a tropomyosin molecule, or (B) from the Ca²⁺ bound end to the Ca²⁺ free end of a tropomyosin molecule as a function of the flexural rigidity of tropomyosin. (A) When the two ends of a Tm molecule are either both Ca²⁺ free, or both have Ca²⁺ bound, the structural change in the middle of the molecule, relative to that at either end, is greater for a rigid Tm (L_p > L_c, dotted-dash line) than for a semi-flexible Tm (L_p ∼ L_c, solid line) as expected. The effect of a reduction in flexural rigidity as is hypothesized to be found in some cases of FHC (compare left side of graph with initial value at right) is substantially more significant for the initially semi-flexible Tm (L_p ∼ L_c, solid line) than the rigid Tm (L_p > L_c, dotted-dash line); for the case of semi-flexible Tm (L_p ∼ L_c, solid line), an additional ∼25% drop is predicted when the initial rigidity is halved. (B) Thin filaments are not fully saturated by Ca²⁺ during systolic activation of cardiac muscle. When only one end of a Tm molecule has Ca²⁺ bound, the structural change at the Ca²⁺ free end relative to that at the end with Ca²⁺ bound is greater for a rigid Tm (L_p > L_c, dotted-dash line) than for a semi-flexible Tm (L_p ∼ L_c, solid line) as expected. As in panel A, the effect of a reduction in flexural rigidity as is hypothesized to be found in some cases of FHC (compare left side of graph with initial value at right) is much more significant for the initially semi-flexible Tm (L_p ∼ L_c, solid line) than the rigid Tm (L_p > L_c, dotted-dash line). For the case of a rigid Tm (L_p > L_c, dotted-dash line), 63% of the signal is transmitted when the initial rigidity is halved. In comparison, only 29% of the signal is transmitted in the case of a semi-flexible Tm (L_p ∼ L_c, solid line).