  Non-processive molecular motors have to work together in ensembles in order
to generate appreciable levels of force or movement. In skeletal muscle, for
example, hundreds of myosin II molecules cooperate in thick filaments. In
non-muscle cells, by contrast, small groups with few tens of non-muscle myosin
II motors contribute to essential cellular processes such as transport, shape
changes or mechanosensing. Here we introduce a detailed and analytically
tractable model for this important situation. Using a three-state crossbridge
model for the myosin II motor cycle and exploiting the assumptions of fast
power stroke kinetics and equal load sharing between motors in equivalent
states, we reduce the stochastic reaction network to a one-step master equation
for the binding and unbinding dynamics (parallel cluster model) and derive the
rules for ensemble movement. We find that for constant external load, ensemble
dynamics is strongly shaped by the catch bond character of myosin II, which
leads to an increase of the fraction of bound motors under load and thus to
firm attachment even for small ensembles. This adaptation to load results in a
concave force-velocity relation described by a Hill relation. For external load
provided by a linear spring, myosin II ensembles dynamically adjust themselves
towards an isometric state with constant average position and load. The
dynamics of the ensembles is now determined mainly by the distribution of
motors over the different kinds of bound states. For increasing stiffness of
the external spring, there is a sharp transition beyond which myosin II can no
longer perform the power stroke. Slow unbinding from the pre-power-stroke state
protects the ensembles against detachment.
