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Theory for strength and stability of an unusual "ligand-receptor" bond: a microtubule attached to a wall by molecular motor tethers

A microtubule (MT) is a tubular stiff filament formed by a hierarchical organization of tubulin proteins. We develop a stochastic kinetic model for studying the strength and stability of a pre-formed attachment of a MT with a rigid wall where the MT is tethered to the wall by a group of motor proteins. Such an attachment, formed by the specific interactions between the MT and the motors, is an analog of ligand-receptor bonds, the MT and the motors anchored on the wall being the counterparts of the ligand and receptors, respectively. However, unlike other ligands, the length of a MT can change with time because of its polymerization-depolymerization kinetics. The simple model developed here is motivated by the MTs linked to the cell cortex by dynein motors. We present the theory for both force-ramp and force-clamp conditions. In the force-ramp protocol we investigate the strength of the attachment by assuming imposition of a time-dependent external load tension that increases linearly with time till the attachment gets ruptured, we calculate the distribution of the rupture forces that fluctuates from one loading to another. In the force-clamp protocol, to test the stability, we compute the distribution of the lifetimes of the attachments under externally applied time-independent load tension, the results establish the MT-wall attachment to be an analog of a slip-bond.