Mechanical stochastic tug-of-war models cannot explain bidirectional lipid-droplet transport

Abstract

Intracellular transport via the microtubule motors kinesin and dynein plays an important role in maintaining cell structure and function. Often, multiple kinesin or dynein motors move the same cargo. Their collective function depends critically on the single motors' detachment kinetics under load, which we experimentally measure here. This experimental constraint--combined with other experimentally determined parameters--is then incorporated into theoretical stochastic and mean-field models. Comparison of modeling results and in vitro data shows good agreement for the stochastic, but not mean-field, model. Many cargos in vivo move bidirectionally, frequently reversing course. Because both kinesin and dynein are present on the cargos, one popular hypothesis explaining the frequent reversals is that the opposite-polarity motors engage in unregulated stochastic tugs-of-war. Then, the cargos' motion can be explained entirely by the outcome of these opposite-motor competitions. Here, we use fully calibrated stochastic and mean-field models to test the tug-of-war hypothesis. Neither model agrees well with our in vivo data, suggesting that, in addition to inevitable tugs-of-war between opposite motors, there is an additional level of regulation not included in the models.

Fig. 1.

Models of unidirectional (A and B) and bidirectional (C and D) transport schematic illustrations of a cargo (green) moved by N = 3 kinesin (red) or dynein (dark blue) motors, as modeled by the mean-field theory (A) or the stochastic model (B). Overall forces opposing motion (f_pos,f_neg) are distributed equally in the mean-field model (f_d per dynein, f_k per kinesin), but not in the stochastic model (f_a–f_c for dynein, f_x–f_z for kinesin). (C and D) A tug-of-war between kinesin and dynein, as modeled in the mean-field theory (C) where motors share load equally, or the stochastic model (D) where they need not.

Fig. 2.

Experimental characterization of in vitro single-molecule kinesin and dynein detachment kinetics. (A and B): Examples of experimental data traces. Beads with a single active kinesin (A) or dynein (B) (binding fraction < 0.35) were brought in contact with the microtubule at saturating ATP. Motion started (at approximately -0.2 s in these plots), causing displacement of the bead from the optical-trap center (traces start increasing). At a predefined displacement (here occurring at t = 0), the laser power was automatically increased, applying enough force to stall the moving bead (plateau immediately after t = 0). After a delay, the motor detached from the microtubule (black arrow), allowing the bead to rapidly return to the trap center. By controlling optical-trap power, we controlled the applied force. The detachment time was the interval between when trap power increased and when the bead detached; a histogram of such times is shown for one specific force for kinesin (C) and dynein (D). The characteristic detachment times were determined by fitting with decaying exponentials (red curves in C and D); the results of such fits are summarized in E and F for kinesin and dynein, respectively. G and H show the complete in vitro force-dissociation rate curves including detachment probabilities below stall (see SI Text).

Fig. 3.

Comparison of experimental measurements and theoretical predictions for detachment kinetics of two kinesin or dynein motors. Experiments were done as in Fig. 2 A and B, but a higher concentration of motors was used, so there was a small probability of having two simultaneously engaged motors. These relatively rare events were detected by force measurements: When a bead was moved further from the trap center than possible for a single motor (experimentally a threshold of 5.2 and 2.0 pN was used, for kinesin or dynein, respectively), the laser power was automatically increased to provide a superstall force. The distribution of detachment times (experimental bars, red hash marks; A and B) was compared to theory (parameter values in SI Text). The single-molecule properties (including single-motor detachment kinetics as measured in Fig. 2) constrained the model parameters. Using these constraints, the stochastic model (ST) with experimental detachment kinetics (EXPT) correctly predicted both the shape of the detachment distribution (A and B) and the correct average detachment time for both kinesin and dynein (C and D, respectively). The mean-field model with the same detachment kinetics did not, and the mean-field model with exponential detachment kinetics (EXPN) was even worse.

Fig. 4.

Examples of experimental (A) and simulated (B–F) trajectories of single bidirectionally moving lipid droplets, projected along the axis of microtubules. For experimental data (A) and stochastically simulated motion (B–D), the properties of motion (run lengths and velocities, pause durations, etc.) were determined by parsing the motion identically using a Bayesian approach (15). The blue line corresponds to run and pause segments as parsed. For the mean-field model variants (E and F), the segments were determined directly.