External forces influence the elastic coupling effects during cargo transport by molecular motors

Abstract

Cellular transport is achieved by the cooperative action of molecular motors which are elastically linked to a common cargo. When the motors pull on the cargo at the same time, they experience fluctuating elastic strain forces induced by the stepping of the other motors. These elastic coupling forces can influence the motors' stepping and unbinding behavior and thereby the ability to transport cargos. Based on a generic single motor description, we introduce a framework that explains the response of two identical molecular motors to a constant external force. In particular, we relate the single motor parameters, the coupling strength and the external load force to the dynamics of the motor pair. We derive four distinct transport regimes and determine how the crossover lines between the regimes depend on the load force. Our description of the overall cargo dynamics takes into account relaxational displacements of the cargo caused by the unbinding of one motor. For large forces and weak elastic coupling these back-shifts dominate the displacements. To develop an intuitive understanding about motor cooperativity during cargo transport, we introduce a time scale for load sharing. This time scale allows us to predict how the regulation of single motor parameters influences the cooperativity. As an example, we show that up-regulating the single motor processivity enhances load sharing of the motor pair.

Transport of organelles by elastically coupled motor proteins

“…However, there are two key differences between our model and that in [27]. (i) In [27], forward hopping rate of the individual motor is linearly dependent on the force (which is derived from linear force-velocity relation), while backward hopping is absent. In our model, more general, thermodynamically consistent rates (eq.18) are used.…”

“…To justify this argument, in Appendix A, we have given the Taylor coefficients (eq.11) of different orders in the presence of the stall force of the motor proteins and show that higher order terms are not negligible when κ is large. It is also pertinent to point out that force-velocity behaviour of two elastically coupled motor proteins has been studied in [27], where stall force is found to be dependent on the stiffness. However, there are two key differences between our model and that in [27].…”

“…It is also pertinent to point out that force-velocity behaviour of two elastically coupled motor proteins has been studied in [27], where stall force is found to be dependent on the stiffness. However, there are two key differences between our model and that in [27]. (i) In [27], forward hopping rate of the individual motor is linearly dependent on the force (which is derived from linear force-velocity relation), while backward hopping is absent.…”

“…Several studies have appeared in the last few years, based (mostly) on Hookean spring-like interaction between motor and the cargo [19,20,21,22,23,24,25,26,27,28,29]. In Kunwar et al [20], along with elastic interaction among the motors, non-linear force-velocity relations are assigned to different motors.…”

Molecular Motors—Self-Organization of Cytoskeletal Network

“…Second, the polar microtubules serve as tracks for the dynein and kinesin motors. These motor proteins, as we already discussed, use the energy of ATP hydrolysis to move along microtubules in a unidirectional manner, transporting spindle cargo such as chromosomes or other microtubules toward either the plus or minus end of the microtubule polymer [39]. Indeed, numerous motor proteins are involved in microtubule self-organization, including motors that cross-link antiparallel plus ends, motors that focus minus ends at the poles, and chromatid associated motors that help orient the array.…”