Equilibrium Blocking Model of Isometric Tension

Calcium activation of striated muscle is known to exhibit a strongly cooperative dependency on calcium. Because the calcium receptor protein, troponin (Tn) is known to bind calcium non-cooperatively and has yet to be linked to a cooperative change in the myosin-blocking protein, tropomyosin (Tm), we describe a model in which cooperativity is exclusively a myosin-dependent mechanism. The model couples the energies of three well-described reactions with actin, namely, actin-Tn, actin-Tm, and actin-Tm-myosin, to the well-documented positions of Tm, B (blocking), C (central), and M (myosin-dependent) respectively. Results of simulations with and without data are consistent with a strand of Tm composed of ~20 subunits being moved by the concerted action of 3-5 myosin heads resulting in an all-or-none activation of the entire region of the thin filament overlapped by myosin. Equations derived from the model fit both equilibrium myosin binding data and steady-state calcium-dependent tension data and simulate non-cooperative calcium binding both in the presence and absence of myosin. All parameters of the model can be determined experimentally. The mechanism is consistent with steric blocking being both necessary and sufficient for regulation of striated muscle and can be applied to any actin-based contractile system that includes Tm and filamentous myosin.

💡 Research Summary

The paper addresses a long‑standing paradox in skeletal and cardiac muscle regulation: calcium binding to troponin (Tn) is experimentally non‑cooperative, yet the force‑calcium relationship of muscle fibers displays strong cooperativity. The authors propose that cooperativity originates exclusively from the myosin‑dependent movement of tropomyosin (Tm) rather than from any intrinsic cooperative behavior of the calcium‑troponin complex.

Model Foundations
Three elementary binding reactions are coupled to the three canonical positions of Tm on the actin filament:

1. Actin‑Tn (ΔG₁) – calcium binding to Tn alters the actin‑Tn interaction energy. This step is treated as non‑cooperative (Hill coefficient ≈ 1).
2. Actin‑Tm (ΔG₂) – the Tn‑Ca²⁺ complex stabilizes Tm in the “blocking” (B) or “central” (C) positions.
3. Actin‑Tm‑Myosin (ΔG₃) – a myosin head binds to the actin‑Tm complex and provides the mechanical work required to shift Tm from B to the “myosin‑dependent” (M) position.

Tm is modeled as a continuous strand of roughly 20 subunits that moves as a single unit. The probability of each Tm state (P_B, P_C, P_M) follows a Boltzmann distribution:

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