Persistence length of the dynein stalk coiled-coil (CC1:2918-2977 and CC2:3106- 3165) was calculated from simulation data using the so-called “dynamic” tangent correlation method, as similarly applied to estimate bending flexibility in the tropomyosin coiled-coil [196, 197]. The coil structure was reduced to a per-residue beaded trace along its central axis by applying the TWISTER algorithm [198]. Tangent vectors were approximated over spans of 15 beads along the central axis trace (CAT, see Figures 30 and 33), leading to 46 tangent correlation measurements over the internal portion of the coil. The cosine of the angle between tangent vectors and their analogs in the average structure, cos(), was averaged for all possible arc lengths, s, over the CAT for each frame of the simulation trajectory, then over the entire trajectory ensemble of 330,000 frames. For
thermal bending fluctuations of a homogeneous rod, the ensemble average of cos([s]) decays exponentially with increasing arc length, s, along the CAT according to
〈cos(𝜃[𝑠])〉𝑠 = 𝑒(−𝑠 𝐿⁄ 𝑝), where Lp is the persistence length.
The lateral fluctuations of the distal end of the stalk were assessed by tracking the relative translation of the stalk/MTBD joint (hinge vertex, see below) in the xy-plane, where x and y represent the directions parallel and perpendicular to the dynein ring, respectively. This was accomplished by orienting a reference structure [63] with the proximal bead of the CAT at the origin, the beads corresponding to the heptad at the base of the coiled-coil region extending along the –z-axis, and the x-direction passing through the plane of the ring (Figure 31A); each frame from the simulation trajectory was aligned to the reference structure based on the heptad at the base of the coiled-coil. Fluctuations of the coil in the x- and y-directions were used to estimate stiffness parallel and perpendicular to the plane of the ring.
Figure 31: Alignments and references used in analysis of MD simulation data
A. Lateral fluctuations of the distal tip of the stalk were measured based on the translation of the stalk/MTBD hinge vertex in the xy-plane, given alignment of the heptad at the base of the coil to a reference structure. The reference structure was oriented with the proximal bead of the CAT at the origin, the CAT corresponding to the heptad at the base of the coiled-coil region extending along the –z-axis, and the x-direction passing through the plane of the AAA ring. B. Longitudinal twisting of the coiled-coil was measured based on a sum over angles between CC1-CC2 vectors along the coil, defined by connecting corresponding beads from the CAT of each α-helix. C. The angle of the stalk/MTBD hinge was measured based on theoretical attachment to a MT, estimated by alignment to an experimental reference structure containing a bound tubulin fragment. Images were rendered using VMD 1.9.2 [5].
The longitudinal twisting of the coiled-coil was measured by reducing the individual -helices of the coil to their respective CATs with the TWISTER algorithm [198], then defining vectors through paired residue beads from CC1 to CC2 along the coil (Figure 31B). The angular deviations between successive vectors over the length of the coiled-coil were summed to produce an overall angle of longitudinal twist. Longitudinal twisting of the coiled-coil was used to estimate torsional stiffness.
The hinge vertex of the stalk/MTBD junction was defined near the midpoint of the CAT beads corresponding to the conserved proline residues, adjusted slightly to align with the distal heptad of the CAT, which was designated as the coil-arm of the hinge. The angle of the stalk/MTBD hinge was measured as the angle between the coil-arm of the hinge and a vector of equivalent length representing the theoretical direction of the MT (Figure 31C). Relative orientation to a theoretically bound MT was determined by aligning the MTBD from each frame from the simulation trajectory to the MTBD of an experimental reference structure containing a bound tubulin fragment [199].
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