Modeling Ca2+-Bound Troponin in Excitation Contraction Coupling

Abstract

To explain disparate decay rates of cytosolic Ca²⁺ and structural changes in the thin filaments during a twitch, we model the time course of Ca²⁺-bound troponin (Tn) resulting from the free Ca²⁺ transient of fast skeletal muscle. In fibers stretched beyond overlap, the decay of Ca²⁺ as measured by a change in fluo-3 fluorescence is significantly slower than the intensity decay of the meridional 1/38.5 nm^-1 reflection of Tn; this is not simply explained by considering only the Ca²⁺ binding properties of Tn alone (Matsuo et al., 2010). We apply a comprehensive model that includes the known Ca²⁺ binding properties of Tn in the context of the thin filament with and without cycling crossbridges. Calculations based on the model predict that the transient of Ca²⁺-bound Tn correlates with either the fluo-3 time course in muscle with overlapping thin and thick filaments or the intensity of the meridional 1/38.5 nm^-1 reflection in overstretched muscle. Hence, cycling crossbridges delay the dissociation of Ca²⁺ from Tn. Correlation with the fluo-3 fluorescence change is not causal given that the transient of Ca²⁺-bound Tn depends on sarcomere length, whereas the fluo-3 fluorescence change does not. Transient positions of tropomyosin calculated from the time course of Ca²⁺-bound Tn are in reasonable agreement with the transient of measured perturbations of the Tn repeat in overlap and non-overlap muscle preparations.

Keywords: EC-coupling; calcium; contraction; excitation; kinetics; model; muscle; troponin.

Figure 1

Summary of model. The model consists of two subsystems that partially overlap. The states of Tm (blue) include central (C), myosin-dependent (M), and blocking (B_i, i = 1–3). States of Tn (TnT, yellow; TnI, magenta; TnC, black-white) include energetically coupled (B_i) and uncoupled (T_i) states each having regulatory sites of TnC that can be Ca²⁺-free (i = 1; white), singly Ca²⁺-bound (i = 2; black), and doubly Ca²⁺-bound (i = 3; black). The diagram shows how Tn is isolated from a site of interaction with actin (gray oval) by the movement of Tm from position B to positions C and M. All constants depicted in the figure represent the ratio of component rate constants (Table 1) used to calculate the relative abundance or probability of each state as a function of a transient change in calcium concentration.

Figure 2

Standard transient of free Ca²⁺ and final steady-state conditions. Transient free Ca²⁺ data (dots) reproduced from Matsuo et al. (2010) are fit empirically by a mathematical function (green). Inset, Steady-state activation (M state) is plotted as a function of free Ca²⁺ concentration on absolute (purple) and normalized (black) scales. Adjusting steady-state constants (Table 2) shifts the curves for activation laterally (Δx_ss). Predicted Ca²⁺-bound Tn curves (gold) that simulate no crossbridges (1 pt. line), saturating rigor crossbridges (3 pt. line), and cycling crossbridges (2 pt. gold line) are calculated with $K_0^{\prime }$ set to 0, 10⁶, and 1, respectively, under the standard equilibrium/steady-state conditions of Table 1. Hill coefficients (Hill, 1910) of unity are determined for curves representing no crossbridges and rigor crossbridges.

Figure 3

Time courses of principle states of the thin filament with overlap. Plotted as a function of a pulse of free calcium (green) are calculated transients of states B (dark blue), C (red), and M (black). Total Ca²⁺-bound Tn (B₂ + B₃ + T₂ + T₃; gold) is broken down into components, i.e., fast (B₂ + B₃; blue) and slow (T₂ + T₃; gray). Plotted on the same scale are measured tension (circles) and fluo-3 fluorescence (squares) transients of muscle fibers of average sarcomere length of 2.8 μm and stimulated by a single impulse (reproduced from Matsuo et al., 2010). Adjustments in standard conditions (Table 1) alter the width (Δx_M), height (Δy_M), and center of the M peak (O) as described in Table 2.

Figure 4

Time courses of principle states of the thin filament with no overlap. Plotted as a function of a pulse of free calcium (green) are calculated transients of states B (dark blue), C (red), and M (black). Total Ca²⁺-bound Tn (B₂ + B₃ + T₂ + T₃; gold) is broken down into fast (B₂ + B₃; blue) and slow (T₂ + T₃; gray) components. For comparison, the measured fluo-3 fluorescence transient (squares) is reproduced from Figure 3.

Figure 5

Time courses of fluo-3 fluorescence and transient structural changes of troponin in nonoverlap sarcomeres. Changes in intensity of the meridional 1/38.5 nm⁻¹ reflection (triangles) and of fluo-3 fluorescence (squares) in response to a single calcium pulse are reproduced for muscle stretched beyond overlap (Matsuo et al., 2010). Plotted on the same scale in response to a simulated calcium pulse (Figure 2) are the calculated temporal change of state C (red) and calcium bound to troponin (gold) under standard conditions (Table 1) with $K_0^{\prime }$ set to null. Other adjustments in standard conditions (Table 2) alter the decay rate of Ca²⁺-bound Tn (Δx_CaB) and the relationship with the state C transient (Δdif _C).

Figure 6

Model compared with temporal responses measured in overlap sarcomeres. Intensities of the meridional 1/38.5 nm⁻¹ reflection (triangles), tension (circles), and fluo-3 fluorescence (squares) for average sarcomere length of 2.8 μm in response to a single calcium pulse are reproduced (Matsuo et al., 2010). Plotted on the same scale in response to a simulated calcium pulse (Figure 2) are the calculated temporal changes of states C (red) and M (black) and Ca²⁺-bound Tn (gold) under standard conditions (Table 1). Adjustments in standard conditions (Table 2) alter the decay rate of Ca²⁺-bound Tn (Δx_CaB).

Figure 7

Predicted time course of crossbridge-dependent Ca²⁺-bound Tn. Crossbridge-dependent Ca²⁺-bound Tn is the residual (dashed line) obtained by subtracting Ca²⁺-bound Tn calculated for the non-overlap preparation (Figure 4) from Ca²⁺-bound Tn calculated for the overlap preparation (solid gold line; Figure 3). The stimulus for both conditions (green) is taken from Figure 2.