Force Generated by Two Kinesin Motors Depends on the Load Direction and Intermolecular Coupling

Hamid Khataee and Jonathon Howard

Phys. Rev. Lett. 122, 188101 – Published 8 May 2019

Abstract

Kinesins are molecular motors that carry cellular cargoes. While the mechanics of single kinesins are well characterized experimentally, the behavior of multiple kinesins varies considerably among experiments. The basis for this variability is unknown. Here, we resolve single-motor force measurements into a vertical component, which accelerates kinesin detachment, and a horizontal component, which decelerates the detachment when resisting the motor. This directionality, when the different experimental geometries are considered, can account for much of the variation in multiple motor dynamics.

Received 10 August 2018
Revised 16 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.188101

Physics Subject Headings (PhySH)

Biomechanics Collective behavior Intracellular transport Mathematical physics Neuroscience, neural computation & artificial intelligence

Interdisciplinary PhysicsPhysics of Living Systems

Authors & Affiliations

Hamid Khataee and Jonathon Howard^,*

Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06511, USA

^*Corresponding author. jonathon.howard@yale.edu

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Vol. 122, Iss. 18 — 10 May 2019

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Images

Figure 1
Force-detachment rate for single kinesin-1. (a) The detachment rate vs the horizontal force component applied by the optical trap [open circles: experimental data ( $mean \pm SE$ ) at 2 mM ATP 26]. The continuous curve is our two-step detachment model in Eq. (1); and see Fig. S1, Supplemental Material [31]. Inset: the plastic bead (blue) with kinesin attached by its tail (magenta) with its heads (black) moving rightwards along the microtubule (green). The drawing is approximately to scale. For a 440-nm-diameter bead and a 35-nm-long kinesin used in the experiments [26], the angle between kinesin and MT is $ϕ = 60 °$ . The vertical force component $F_{z}$ is the same irrespective of the sign of the horizontal force component $F_{x}$ , i.e., assisting (to the right, positive) or resisting (to the left, negative). (b) Decomposition of the force-detachment dependence into horizontal and vertical force dependencies. The black curve is the output of our model in (a) where the motor is subject to both horizontal and vertical forces. The green (magenta) curve is the detachment rate in the presence of only vertical (horizontal) force.
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Figure 2
Detachment rate and run length of single kinesin vs vertical and parallel force components. Lines (magenta) correspond to the force direction in experiments [26]. (a) Detachment rate is calculated using Eq. (1). (b) Mean run length is calculated as $v_{si} / k_{off}$ , where $v_{si}$ is the single-kinesin velocity (see Ref. [31]).
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Figure 3
Model of the two-kinesin complex. (a) States with zero (left), one (middle), and two (right) motors bound to a microtubule. (b) Representations of state 2 in which the vertical forces have been set to zero for clarity. The force acts at the bead (blue). Top: the strain in the spring (magenta) connecting the motors (black) is zero. Middle: the strain is $d / 2$ as the front motor takes a step to the right. Bottom: the strain is $d$ as the front motor takes another step forward. (c) Kinetic scheme for the two-motor complex. The states 0, 1, and 2 correspond to those in (a). The states $2_{j}$ correspond to those in (b) with $j = 0, 1, 2, \dots, N$ . $k_{s_{j}}$ ( $k_{r_{j}}$ ) denotes the stretching (relaxation) rate of the complex. $ω_{j_{f}}$ ( $ω_{j_{r}}$ ) denotes the detachment rates of the front (rear) motor. $k_{{on}_{j}}$ is the attachment rate of a motor to a site with strain $j d / 2$ .
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Figure 4
Force run time, force run length, force velocity, and stall force. (a)–(c) Simulations of bead assays ( $ϕ = 60 °$ ) are for single kinesin (black curve) and for two kinesins with coupling stiffness $κ = 0.4 pN / nm$ (red curve). One- and two-kinesin (1K and 2K) experimental data are from Ref. [17]. Run time, run length, and velocity are normalized to their corresponding values for single kinesin at zero force. (d) Stall force for single and two kinesins vs $κ$ at different angles $ϕ$ . The dashed line is the single-kinesin stall force ( $\sim - 5.5 pN$ for all angles).
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