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Molecular motors are essential components for the biophysical functions ofthe cell. Our current quantitative understanding of how multiple motors movealong a single track is not complete; even though models and theories forsingle motor chemomechanics abound. Recently, M.J.I. M$\ddot{\rm u}$ller {\emet al.} have developed a tug-of-war model to describe the bidirectionalmovement of the cargo (PNAS(2008) 105(12) P4609-4614). Through Monte Carlosimulations, they discovered that the tug-of-war model exhibits severalqualitative different motility regimes, which depend on the precise value ofsingle motor parameters, and they suggested the sensitivity can be used by acell to regulate its cargo traffic. In the present paper, we carry out athorough analysis of the tug-of-war model. All the stable, i.e., biophysicallyobservable, steady states are obtained. Depending on several parameters, thesystem exhibits either uni-, bi- or tristability. Based on the separatingboundary of the different stable states and the initial numbers of thedifferent motor species that are bound to the track, the steady state of thecargo movement can be predicted, and consequently the steady state velocity canbe obtained. It is found that, the velocity, even the direction, of the cargomovement change with the initial numbers of the motors which are bound to thetrack and several other parameters.

Properties of tug-of-war model for cargo transport by molecular motors