Molecular Motors: Cooperative Phenomena of Multiple Molecular Motors - Multiscale Modeling in Biomechanics and Mechanobiology - page 43

Fig. 3.6 A cargo particle is transported by N motors. Each state is characterized by the number of
bound motors. In each state the cargo has velocity v n , a motor unbinds from the filament with rate
ʵ n and an additional motor binds to the filament with rate ˀ n (reprinted from Ref. [ 51 ])

medium, a larger number of motors actively pulling on the cargo can result in higher
speed [ 31 , 51 ]. Since motors unbind and rebind to the filament, the velocity of such a
cargo changes when the number of bound motors change. Therefore, a rather general
coarse-grained description for cooperative cargo transport by molecular motors can
be obtained by a discrete state-space with cargo states associated with the number
of bound motors [ 51 ]. Transitions between these states correspond to binding and
unbinding of motors, see Fig. 3.6 . Thus, the model is semistochastic, describing
the cargo movement (based on rapid steps) as a deterministic process and motor
binding/unbinding, which happens on longer timescales, as stochastic processes. In
principle, the parameters of this model, the velocities and unbinding rates can be
obtained by systematic coarse-graining as described above. However, this has so far
not been done for more than two motors. For cases with more than two motors, the
rates have been obtained by making plausible assumptions such as weak coupling
between the motors and equal sharing of load forces [ 51 , 72 ]. This approach allows
us to calculate dynamical properties of the cargo, like the run length and run time of a
cargo transported by teams of motors. Such studies have been done for unidirectional
transport by a single team of motors [ 51 ], for bidirectional transport by two teams of
motors [ 72 ], for transport by motors with different velocities [ 56 ], and for combined
directed and diffusive transport by active and inactive motors [ 10 , 75 ].
If a cargo is transported by two teams of antagonistic motors, i.e., by motors
that walk in opposite directions, the cargo is transported in a bidirectional manner,
changing direction every few seconds. A theoretical description for this transport
mode also starts by identifying discrete states associated with the numbers of bound
motors of both types, see Fig. 3.7 . Transitions between the states arise from binding
and unbinding of the motors. Since the unbinding rate depends on the external force,
motors can pull each other from the filament resulting in a tug-of-war. Such a tug-
of-war displays a rich pattern of motility depending on the single motor parameters
[ 71 - 73 ]. In particular, the analysis of this model showed that mechanical interac-
tions of the motors mediated by the two teams pulling on each other is sufficient to
generate rapid bidirectional movements [ 72 ]. No specialized coordination complex,