Fig. 5: Inference of the directional preferences of the stochastic motion by MKLP1 on the microtubule lattice surface.
From: CYK4 relaxes the bias in the off-axis motion by MKLP1 kinesin-6
a Interconversion between the coordinate systems. A microtubule consists of 13 or 14 protofilaments (n = 13 or 14), linear assembly of the heterodimers of alpha/beta-tubulin with d = 8 nm spacing, aligned in parallel with a small shift in the adjacent alpha/beta-dimers (‘rise’ r = 0.82 nm)65. As the sum of the 13 rises is 12 nm = 1.5 × 8 nm, a microtubule with 13 protofilaments has a seam, a protofilament interface with a mismatch in alpha/beta subunit alignment, but the protofilaments are parallel to the axis of the tubular assembly. The sum of the 14 rises is not a half-integer multiple of 8 nm spacing. This results in a small tilt (0.73°) of the protofilaments against the microtubule axis, theta. The position along the Y-axis perpendicular to the X-axis parallel to the microtubule axis can be converted to the revolution via the length of the perimeter L. Thus, the mismatch at the seam being put aside, the trajectory data (X Y) measured by nm and revolution can be linked to the position on the lattice (z w) as (X Y) = Q R P (z w). b Workflow to infer the hopping rates and preferences. The trajectory data from the mobile segments (Fig. 4) were mapped onto the lattice via the linear transformation (Q R P)−1. The macroscopic parameters (v, D, and the coefficients for the higher-order covariances, A, B, C, E) were calculated and used to infer the microscopic parameters, i.e., the hopping rates and preferences based on the linear relationship between them. c, d The results of the Bayesian inference of the hopping rates and preferences assuming n = 13 (Similar results were obtained with n = 14, See Supplementary Fig. 6). The posterior probability distributions of the overall hopping rate (k) and preferences (p1 ~ p8, see a) (c) were presented as the density distributions of the four chains of sampling for each construct. The means and standard deviations of the hopping preferences (d) were graphically represented with a color scale shown on the right. The strong bias towards left and forward observed in M2 was lost in M2C2 and M1 (compare them on p3 (forward-right) and p7 (straight backward)). Note that the probability of hopping to the straight forward site (p2) is much higher than other probabilities and thus it appears saturated (white).
