Spatially gated myosin attachment ($p_b=1-e^{-k_{on}\Delta x/v}$)

A prescribed-velocity motor can attach only over a narrow displacement window, remain attached over a protected interval, then detach with constant rate. Converting time to displacement gives a rising attachment probability, a plateau $p_b$, and an exponential tail with spatial length $v/k_{off}$. Independent successive-site encounters require detachment before the next window, not merely a large geometric site separation. Earlier attachments can be retained in a periodic availability correction.

A prescribed-speed molecular motor model in which a head attaches only within a phase window of width $x_1$, stays bound to phase $x_2$, and then detaches at a constant rate before the next period $\Delta$. If the binding window and detachment tail are short relative to the bound plateau, the phase-average force is the plateau fraction multiplied by its attachment probability and bound-head force $f_0$.

With positive opposing load magnitude $L$ and positive viscous drag coefficient $\gamma$, steady contraction requires $L=N⟨f⟩-\gamma u$. A decreasing motor force curve and an increasing drag-magnitude line have a unique intersection for each load below the limiting stall force. Using $+\gamma u$ as the signed drag would instead make drag assist forward motion, reversing its physical role.

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.