 Work of a spatially gated myosin head

For attached-state elastic energy $U=\kappa (x-x_0{)}^2/2$ and a binding window much narrower than $x_0$, the expected assisting work before $x_0$ is $\kappa p_b{x}_0^2/2$. The detachment tail produces resisting work $-\kappa p_b{v}^2/k_{off}^2$. Mean force per head is $W/D$ for site spacing $D$. The detachment-time second moment, not the square of its mean, fixes the resisting term. These are idealized prescribed-velocity kinetics, not a complete muscle energy budget.