Network Complexity and Parametric Simplicity for Cargo Transport by Two Molecular Motors

Abstract

Cargo transport by two molecular motors is studied by constructing a chemomechanical network for the whole transport system and analyzing the cargo and motor trajectories generated by this network. The theoretical description starts from the different nucleotide states of a single motor supplemented by chemical and mechanical transitions between these states. As an instructive example, we focus on kinesin-1, for which a detailed single-motor network has been developed previously. This network incorporates the chemical transitions arising from ATP hydrolysis on both motor heads. In addition, both the chemical and the mechanical transition rates of a single kinesin motor were found to depend on the load force experienced by the motor. When two such motors are attached via their stalks to a cargo particle, they become elastically coupled. This coupling can be effectively described by an elastic spring between the two motors. The spring extension, which is given by the deviation of the actual spring length from its rest length, determines the mutual interaction force between the motors and, thus, affects all chemical and mechanical transition rates of both motors. As a result, cargo transport by two motors leads to a combined chemomechanical network, which is quite complex and contains a large number of motor cycles. However, apart from the single motor parameters, this complex network involves only two additional parameters: (i) the spring constant of the elastic coupling between the motors and (ii) the rebinding rate for an unbound motor. We show that these two parameters can be determined directly from cargo trajectories and/or trajectories of individual motors. Both types of trajectories are accessible to experiment and, thus, can be used to obtain a complete set of parameters for cargo transport by two motors.

Elastic Coupling Effects in Cooperative Transport by a Pair of Molecular Motors

“…These approaches typically take one of two roads: They either start by splitting the state with two bound motors, C 2 into several substates, 7,14,19,20,37,57,61 in which case some results can still be obtained analytically, or use detailed computational models that particularly emphasize on the geometry of the motor-complex or the arrangement of motors on a bead. 13,39,41 In reference, 37 a detailed chemomechanical network for two-motor complexes is used to generate trajectories and to show that the parameters 2 and v 2 can be deduced in a unique manner from the statistical properties of the trajectories. As mentioned already in the introduction, there exist considerable differences between the predictions obtained from different models with respect to interference effects.…”

“…Below we will follow the first type of approach using the general model described in Berger et al 7 to obtain specific results for coupled kinesin-1 motors and to discuss effects of different types and strengths of coupling (we note that we have also pursued a complementary approach to coupled motors, 37 which starts from a detailed description of the chemomechanical dynamics of a single motor). We will specifically be interested in the build-up dynamics of force between the motors to study the conditions under which elastic coupling between the motors leads to interference effects such as enhanced unbinding ( 2 >2 1 ), as observed for kinesin pairs, 53 or a reduced velocity (v 2 < v 1 ), as observed for pairs of myosin V motors.…”

“…They can be measured directly if trajectories can reliably be partitioned into sequences of 1-motor runs and 2-motor runs, i.e. into segments where the cargo is bound to the filament through one or two motors, respectively, see also Keller et al 37 The overall motility of such cargoes are characterized by the average velocity and the overall run length, which may also be determined without the need to resolve such partitioning of the trajectories. Within the model, these quantities can be calculated via Eqs.…”

“…The dependence of the dynamic parameters on the ATP concentration is, however, complex, as a variation of the ATP concentration modulates the chemomechanical cycle of a motor 37 and may also affect other parameters in addition to the velocity. In particular, the ATP concentration may affect the (single motor) unbinding rate.…”

“…This confusing (theoretical) situation has led us to re-examine the case of two coupled motors. 7,37 In a recent study 7 we have shown that such systems can exhibit four distinct transport regimes that depend on both the parameters of the motor molecule itself and on the elastic coupling between the motors. We have proposed simple time scale arguments that lead to an intuitive picture of the effects of elastic coupling between two motors.…”