Kinesins with extended neck linkers: a chemomechanical model for variable-length stepping

Abstract

We develop a stochastic model for variable-length stepping of kinesins engineered with extended neck linkers. This requires that we consider the separation in microtubule binding sites between the heads of the motor at the beginning of a step. We show that this separation is stationary and can be included in the calculation of standard experimental quantities. We also develop a corresponding matrix computational framework for conducting computer experiments. Our matrix approach is more efficient computationally than large-scale Monte Carlo simulation. This efficiency greatly eases sensitivity analysis, an important feature when there is considerable uncertainty in the physical parameters of the system. We demonstrate the application and effectiveness of our approach by showing that the worm-like chain model for the neck linker can explain recently published experimental data. While we have focused on a particular scenario for kinesins, these methods could also be applied to myosin and other processive motors.

Fig. 1

The gross anatomy of a kinesin motor protein

Fig. 2

An illustration of uniform-length stepping

Fig. 3

An illustration of variable-length stepping for a motor with neck linkers long enough to permit a separation of two binding sites. S* is the initial separation of the heads, S is the final separation, and Z is the step size

Fig. 4

A chemical model for variable-length stepping. For this model, the maximum separation of the heads is two binding sites, and so this chemical model corresponds to the stepping diagrammed in Fig. 3. Note that k_on corresponds to the binding of one molecule of ATP

Fig. 5

The grid of numbered binding sites used to devise the second version of the B matrix

Fig. 6

The WLC drift function for four values of L_p—0.8 nm (solid), 2 nm (dashed), 4 nm (dotted), and 6 nm (dash-dot)

Fig. 7

Experimental results from Yildiz et al. (2008). At left, run length and speed from single molecule assays of kinesins engineered with extended neck linker domains. At right, step size distributions, measured by monitoring the position of a quantum dot attached to one head domain. With this geometry, a normal 8-nm step taken by the motor corresponds to a 16-nm displacement of the labeled head domain (steps in which the unlabeled head takes a step correspond to zero displacement and are not recorded). 6P to 26P correspond to the number of proline residues inserted into the neck linker domain (in addition to two lysines and one glycine), and 14GS denotes a 14 amino acid insert containing glycine and serine residues. Permission for figure pending from Cell Press (Dec, 2010)

Fig. 8

Comparison of WLC and FENE for the no tension scenario. Each plot shows asymptotic velocity, effective diffusion, or expected run length for various neck linker lengths—WT, 6P, 13P, 19P, and 26P. Each WLC plot shows curves for four values of L_p—0.8 nm (solid), 2 nm (dashed), 4 nm (dotted), and 6 nm (dash-dot). The spring constant for the FENE model was set at κ = 0.1

Fig. 9

Comparison of WLC and FENE for the scenario of strain-dependent detachment. Each WLC plot shows curves for various combinations of d_b and L_p—(2, 2) (solid); (2, 4) (short dash); (2, 6) (dot); (4, 4) (dash-dot); and (4, 6) (long dash). Each FENE plot shows curves for d_b equal to 2 (solid) and 4 (long dash) (with κ = 0.1)

Fig. 10

Step-size distributions for the strain-dependent detachment scenario, assuming that only one head has been tagged. For the WLC plots, d_b = 2 and L_p = 4, and for the FENE plots, d_b = 2

Fig. 10

Step-size distributions for the strain-dependent detachment scenario, assuming that only one head has been tagged. For the WLC plots, d_b = 2 and L_p = 4, and for the FENE plots, d_b = 2

Fig. 11

Plots of V_∞, D, and $\mathbb{E}$R that correspond to the distributions shown in Fig. 10

Fig. 12

Plots of V_∞, μ_Z, and μ_τ versus neck linker length for the WLC model in the strain-dependent detachment (dashed) and no strain-dependent detachment (solid) scenarios. L_p = 4 for both scenarios, and d_b = 2 for the strain-dependent detachment scenario