= Solution
For a head sampling phases uniformly during steady sliding, its mean <force> is $f_0$ times the phase-average bound <probability>. In the $B\ll1$ limit of <spatially gated myosin attachment>, integrating the three intervals gives
$$
\frac{\Delta\langle f\rangle}{f_0}\simeq x_1-\frac{u}{k_1}(1-A)
+(x_2-x_1)(1-A)+\frac{u}{k_2}(1-A)(1-B).
$$
The first integral is bounded by $x_1p_b$, and the last by $(u/k_2)p_b$. Relative to the plateau contribution, they are negligible when $x_1\ll x_2$ and $u/k_2\ll x_2$, respectively. Therefore
$$
\boxed{\langle f\rangle\simeq f_0\frac{x_2}{\Delta}\left(1-e^{-k_1x_1/u}\right).}
$$
This is a <constant-force spatially gated motor> approximation: complete detachment between binding windows, a narrow attachment window, a short detachment tail and essentially fixed sliding <velocity>. In particular, $k_1x_1/u$ need not be small.
Back to article page
