A simplified tether model for molecular motor transporting cargo

Molecular motors are proteins or protein complexes whichfunction as transporting engines in biological cells. This papermodels the tether between motor and its cargo as a symmetric linearpotential. Different from Elston and Peskin's work for whichperformance of the system was discussed only in some limiting cases,this study produces analytic solutions of the problem for generalcases by simplifying the transport system into two physical states,which makes it possible to discuss the dynamics of the motor--cargosystem in detail. It turns out that the tether strength betweenmotor and cargo should be greater than a threshold or the motor willfail to transport the cargo, which was not discussed by formerresearchers yet. Value of the threshold depends on the diffusioncoefficients of cargo and motor and also on the strength of theBrownian ratchets dragging the system. The threshold approaches afinite constant when the strength of the ratchet tends to infinity.