Cooperative responses of multiple kinesins to variable and constant loads

Abstract

Microtubule-dependent transport is most often driven by collections of kinesins and dyneins that function in either a concerted fashion or antagonistically. Several lines of evidence suggest that cargo transport may not be influenced appreciably by the combined action of multiple kinesins. Yet, as in previous optical trapping experiments, the forces imposed on cargos will vary spatially and temporally in cells depending on a number of local environmental factors, and the influence of these conditions has been largely overlooked. Here, we characterize the dynamics of structurally defined complexes containing multiple kinesins under the controlled loads of an optical force clamp. While demonstrating that there are generic kinetic barriers that restrict the ability of multiple kinesins to cooperate productively, the spatial and temporal properties of applied loads is found to play an important role in the collective dynamics of multiple motor systems. We propose this dependence has implications for intracellular transport processes, especially for bidirectional transport.

FIGURE 1.

Bead transport by two kinesins in an optical force clamp: A, schematic diagram of the two-kinesin complex shown anchored to a 500 nm bead. The DNA scaffold is labeled in the inset. B, position-time trace for the bead (black) and trap center position (red) where the applied load was held constant at 12 pN.

FIGURE 2.

Two-kinesin force clamp traces. A and B, bead position versus time traces are shown for cases where an individual two-kinesin complex transported a bead against a constant load of 10 pN (A), and 5 pN (B). Bead positions were sampled at 30 kHz, after anti-alias filtering at 10 kHz, and then median filtered using a window size of 2 ms. Both the raw (gray) and filtered (black) data are presented.

FIGURE 3.

Two-kinesin velocity and step-size distributions against constant loads. A, velocity distribution histograms for two-kinesin complexes at applied loads ranging between 2.5 and 12 pN. The load maintained by the force clamp is indicated in each panel. Bead velocities were determined via a chi-squared minimization procedure reported in Ref. . Each plot is constructed from 7–27 trajectories (3–19 complexes). Bin counts were taken as the number of distinct trace components where beads moved with a velocity within the range of each bin for a period of 16 ms. B, distributions of bead displacement sizes found using a step-finding algorithm and their corresponding pairwise displacement distribution histograms. Bead displacement analyses are presented separately for cases where the force clamp was used to impose either low (2–5 pN; 58 traces included) or high (10–12 pN; 27 traces included) resisting loads.

FIGURE 4.

The time required for two-kinesin complexes to develop load-sharing configurations is large. Mechanical modeling of two-kinesin complexes (see Ref. 14) indicates that trailing motors will typically bind at sites positioned well behind their leading partners. When F_ap = 5 pN, this model predicts motors will be separated by 112 nm on the microtubule on average (illustration at top). The plot beneath the illustration shows a predicted dependence of the rate at which the trailing motor will bind to different sites (black line, left axis) and the corresponding load this motor will experience after a binding transition (red line, right axis). The bottom plot shows the rate that the trailing motor's portion of the 5 pN load increases assuming the separation distance between the leading and trailing motor was initially 112 nm.

FIGURE 5.

Two-kinesin velocities relax rapidly in response to abrupt changes in the applied load. Two-kinesin bead velocities were monitored in the force clamp at 5 pN constant load. Bead velocities were characterized separately in experiments where the feedback routine of the force clamp was triggered after the beads reached force thresholds (F_Trig) of either 3 pN or 7 pN (black and blue squares, respectively); transport occurs in a static trap until F_Trig is reached. Exponential fits yielded time constants of 96 and 77 ms for the 3–5 pN and 7–5 pN experiments, respectively. Single kinesin velocities are also presented (F_ap = 5 pN; F_Trig = 3 pN). Velocities are presented as mean ± S.E. Each two-kinesin plot is constructed from at least 54 trajectories generated by 6 different complexes. The blue and black lines correspond to exponential fits to the data.

FIGURE 6.

Two-kinesin force-velocity and run time analyses. A, force-velocity (F-V) relationships for two-kinesin complexes (black squares; n_events = 156, range: 4–46; n_complexes = 26, range: 2–18) and single kinesins (red circles; n_events = 125, range: 5–65, n_motor = 21, range: 3–7) measured in a force clamp. In each case, force-feedback was initiated when beads reached a threshold applied load of 2 pN. The load-dependence of two-kinesin velocities in a static trap is presented for comparison (green circles). Velocities are presented as mean ± S.E. The single-kinesin velocity data were fit to the Fisher-Kim model (25). This curve was then used to approximate a trend for two-kinesins if they are assumed to share their applied load equally (gray dashed line). B, average run lengths and run times (mean ± S.E.) measured for single kinesins and two-kinesin complexes are presented as a semi-log plots. The unloaded run lengths and times correspond to previously reported values (13).

FIGURE 7.

The impact of multistate detachment when applied loads vary spatially. When multiple motors experience spatially dependent applied loads, the partial detachment of a complex leads to rearward cargo displacements that can reduce the load on the bead. Because these displacements are accompanied by changes in the number of bound motors, this process affects the force-dependent probability that a complex will be bound via a single or both motor molecules of a complex. Measurements of reward displacement sizes in a static optical trap (κ_trap = 0.072 pN/nm) indicate that the applied load changes by 4–5 pN on average upon partial bead detachment if it exceeds kinesin's 7 pN stalling force. Such large changes in load can result in a significant reduction in the probability that a two-kinesin complex will be bound via a single motor within this force regime, and therefore result in higher cargo velocities, on average, relative to cases where the applied load remains constant or varies weakly as a function of cargo position. The lines in the plot depict exponential fits to the static trapping data.