J an 2 00 9 Properties of tug - of - war model for cargo transport by molecular motors

Molecular motors are essential components for the biophysical functions of the cell. Our current quantitative understanding of how multiple motors move along a single track is not complete; even though models and theories for single motor chemomechanics abound. Recently, M.J.I. Müller et al. have developed a tug-of-war model to describe the bidirectional movement of the cargo (PNAS(2008) 105(12) P4609-4614). Through Monte Carlo simulations, they discovered that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we carry out a thorough analysis of the tug-of-war model. All the stable, i.e., biophysically observable, steady states are obtained. Depending on several parameters, the system exhibits either uni-, bior tristability. Based on the separating boundary of the different stable states and the initial numbers of the different motor species that are bound to the track, the steady state of the cargo movement can be predicted, and consequently the School of Mathematical Sciences, Fudan University, Shanghai 200433, China Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University Centre for Computational Systems Biology, Fudan University (E-Mail: [email protected])