Schematic representation of the model: Turnover of myosin thick
filaments: Unbound myosin filaments bind with probability
R̄ to the center points of pairs of anti-parallel
actin filaments (A1), or, with probabilities
R± to the center points of parallel
pointed end forward (B1), respectively backward (C1) actin filaments. Myosin
forces and F-actin treadmilling have counteracting effects on the position of
myosin binding sites as by itself myosin would move towards the barbed ends,
while treadmilling moves binding sites towards the pointed ends. A2: Myosin
filaments attached to anti-parallel actin filaments shift towards the pointed
ends as treadmilling is assumed to exceed actin filament velocities through
myosin action. The value ξ represents the relative position of myosin
with respect to the centers of actin filaments in a way such that ξ =
l/2 corresponds to the pointed ends of actin filaments. A3:
Once myosin reaches the pointed ends it detaches and returns to the pool of
unbound myosin. B2: Myosin attached to a pair of pointed end-forward actin
filaments shifts towards the barbed ends as it can move with its free moving
velocity which is faster than F-actin treadmilling. The material velocity of
actin filaments moves actin and myosin simultaneously and therefore does not
affect their relative position. In the case of parallel actin filaments the
relative position ξ = l/2 corresponds to the barbed
ends of actin filaments. B3: Once myosin reaches the barbed ends, it detaches.
C2, C3: Myosin attached to a pair of pointed end-backward actin filaments moves
towards the barbed ends where it detaches. Observe that the material velocity of
pointed end backward actin filaments is now written as
−υ− as υ− by
convention is taken as negative.