Fig 1.
Model for motor protein stepping on a microtubule track.
The track is represented as a square lattice of microtubule subunits on which the heads of the motor proteins process. Dark green sites represent subunits that are inaccessible to the motor protein. The stepping per head occurs with rate rstep. A: Kinesin heads alternate in taking steps of 8 nm in the forward direction (towards the plus end of the microtubule). B: Each dynein head has an equal chance to step, allowing one head to take multiple consecutive steps. Dynein can take forward steps (towards the minus end of the microtubule) and, with probability pbck, backward steps (toward the plus end). Dynein steps have size up to 4 × 16 nm. Both motors take sideways steps with probability pang, changing only one protofilament, but while the off-axis direction of kinesin is fixed, the direction of sideways steps of dynein is determined by the leading head, indicated by the dashed arrows. C: Sample trajectories of kinesin for different obstacle concentrations ρ. D: Sample trajectory of dynein for different ρ.
Table 1.
Summary of the parameters employed in the model.
Fig 2.
Comparison of step size distributions in simulations with experimental results from Ref. [15].
The global maximum of both distributions is at 16nm, and a significant portion (0.2) of the steps are in the backward direction. In the experiment step sizes were sampled in small bins of width 2 nm, while the simulation allows steps of size 16 nm only for dynein. We therefore re-binned the (digitized) experimental data for comparability purposes, shown in green. Inset: the distributions on a log scale. In both experiments and simulation, the tail of the distribution is experimental. For clarity, only the positive step sizes are shown, but negative steps are also exponentially distributed.
Fig 3.
Step-size distribution of dynein on decorated tracks.
While the decoration fraction ρ = 0.15 (red) shows qualitatively the same results as the clean case, ρ = 0 (blue), a decoration fraction of ρ = 0.3 (black) differs significantly in shape from the previous curves. The global maximum of the distribution shifts from 16nm to 8nm and there are approximately as many steps taken forward as backward, showing that the motor stays mainly in a single area and does not progress along its track.
Fig 4.
Average velocity of motor proteins vs decoration fraction ρ.
The velocity of kinesin decreases by an order of magnitude as ρ increases from ρ = 0 to ρ = 0.05, but the velocity of dynein decreases only slowly with the decoration fraction. Plotted here are velocities for wild-type motor proteins, with pang = 0.4. Lines are guides to the eye; errorbars are smaller than the symbol size.
Fig 5.
Velocity distributions are normal on undecorated tracks but develop a peak around v = 0 as decoration fraction ρ is increased.
A: Kinesin, whose velocity can only be positive. B: For dynein, the distribution includes also negative velocities. Lines are guides to the eye; errorbars are smaller than the symbol size.
Fig 6.
Velocity profiles for kinesin and dynein are largely unaffected by changes in the off-axis parameter pang.
For the range of pang studied, 0.02 ≤ pang ≤ 0.6, changing pang does not affect the shape of the velocity profile except in the case of dynein with pang = 0.02, where dynein is faster than kinesin only for large ρ. Lines are guides to the eye; errorbars are smaller than the symbol size.
Fig 7.
When kinesin is allowed to take backwards steps its obstacle navigational abilities increase drastically.
The effect is especially dramatic for large decoration fraction ρ. When kinesin can take backwards steps with the same probability pbck = 0.2 as wild-type dynein, for ρ > 0.15 the backwards-stepping kinesin is faster than wild-type dynein. Lines are guides to the eye; errorbars are smaller than the symbol size.