Abstract
Intracellular transport is performed by molecular motors that pull cargos along cytoskeletal filaments. Many cellular cargos are observed to move bidirectionally, with fast transport in both directions. This behaviour can be understood as a stochastic tug-of-war between two teams of antagonistic motors. The first theoretical model for such a tug-of-war, the Müller-Klumpp-Lipowsky (MKL) model, was based on two simplifying assumptions: (i) both motor teams move with the same velocity in the direction of the stronger team, and (ii) this velocity matching and the associated force balance arise immediately after the rebinding of an unbound motor to the filament. In this study, we extend the MKL model by including an elastic coupling between the antagonistic motors, and by allowing the motors to perform discrete motor steps. Each motor step changes the elastic interaction forces experienced by the motors. In order to elucidate the basic concepts of force balance and force fluctuations, we focus on the simplest case of two antagonistic motors, one kinesin against one dynein. We calculate the probability distribution for the spatial separation of the motors and the dependence of this distribution on the motors' unbinding rate. We also compute the probability distribution for the elastic interaction forces experienced by the motors, which determines the average elastic force 〈F〉 and the standard deviation of the force fluctuations around this average value. The average force 〈F〉 is found to decrease monotonically with increasing unbinding rate ε0. The behaviour of the MKL model is recovered in the limit of small ε0. In the opposite limit of large ε0, 〈F〉 is found to decay to zero as 1/ε0. Finally, we study the limiting case with ε0 = 0 for which we determine both the force statistics and the time needed to attain the steady state. Our theoretical predictions are accessible to experimental studies of in vitro systems consisting of two antagonistic motors attached to a synthetic scaffold or crosslinked via DNA hybridization.
Highlights
Intracellular cargos such as vesicles and organelles are transported by cytoskeletal motors.[1]
When there is no load force acting on the motor, it proceeds with all transitions to the two absorbing states being redirected with the force-free forward velocity vF
The master equations can be written in the matrix form if we define the (2J + 1)-dimensional column vector (pÀJ(t),pÀJ+1(t),. . .,pJÀ1(t),pJ(t))T |p(t)i (C.1)
Summary
Intracellular cargos such as vesicles and organelles are transported by cytoskeletal motors.[1]. In the latter case, both the force statistics and the time needed to reach the steady state are determined as a function of the elastic coupling strength
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