Before revision:  For constant binding and unbinding rates, we find that introducing confinement effectively enhances the unbinding rate and thereby reduces the motor processivity, leading to smaller effective diffusivity and average velocity . For spatially varying binding rates that depend on confinement, the average velocity is further reduced when the average binding rate is equal to the constant binding rate without confinement. However, confinement may lead to an enhancement in the average velocity if it results in a greater average binding rate than in the absence of confinement .
After revision:  For constant binding and unbinding rates, we find that introducing confinement effectively enhances the unbinding rate and thereby reduces the motor processivity, leading to smaller effective diffusivity and average velocity , except when it results in a greater average binding rate than in the absence of confinement .