  Motor-driven cargo transport is a complex phenomenon where multiple motor
proteins attached on to a cargo engage in pulling activity, often leading to
tug-of-war, displaying bidirectional motion. However, most mathematical and
computational models ignore the details of the motor-cargo interaction. Here,
we study a generic model in which N motors are elastically coupled to a cargo,
which itself is subjected to thermal noise in the cytoplasm and to an
additional external applied force. The motor-hopping rates are chosen to
satisfy detailed balance with respect to the energy of elastic stretching. With
these assumptions, an (N+1)-variable master equation is constructed for
dynamics of the motor-cargo complex. By expanding the hopping rates to linear
order in fluctuations in motor positions, we obtain a linear Fokker-Planck
equation. The deterministic equations governing the average quantities are
separated out and explicit analytical expressions are obtained for the mean
velocity and diffusion coefficient of the cargo. We also study the statistical
features of the force experienced by an individual motor and quantitatively
characterize the load-sharing among the cargo-bound motors. The mean cargo
velocity and the effective diffusion coefficient are found to be decreasing
functions of the stiffness. While increase in the number of motors N does not
increase the velocity substantially, it decreases the effective diffusion
coefficient which falls as 1/N asymptotically. We further show that the
cargo-bound motors share the force exerted on the cargo equally only in the
limit of vanishing elastic stiffness; as stiffness is increased, deviations
from equal load sharing are observed. Numerical simulations agree with our
analytical results where expected. Interestingly, we find in simulations that
the stall force of a cargo elastically coupled to motors is independent of the
stiffness.
