Title: Stall force of a cargo driven by N interacting motor proteins,
Abstract: We study a generic one-dimensional model for an intracellular cargo driven by
N motor proteins against an external applied force. The model includes
motor-cargo and motor-motor interactions. The cargo motion is described by an
over-damped Langevin equation, while motor dynamics is specified by hopping
rates which follow a local detailed balance condition with respect to change in
energy per hopping event. Based on this model, we show that the stall force,
the mean external force corresponding to zero mean cargo velocity, is
completely independent of the details of the interactions and is, therefore,
always equal to the sum of the stall forces of the individual motors. This
exact result is arrived on the basis of a simple assumption: the (macroscopic)
state of stall of the cargo is analogous to a state of thermodynamic
equilibrium, and is characterized by vanishing net probability current between
any two microstates, with the latter specified by motor positions relative to
the cargo. The corresponding probability distribution of the microstates under
stall is also determined. These predictions are in complete agreement with
numerical simulations, carried out using specific forms of interaction
potentials.