Intracellular motor-driven transport of rodlike smooth organelles along microtubules

Molecular motors are fascinating proteins that use the energy of ATP hydrolysis to drive vesicles and organelles along cytoskeleton filaments toward their final destination within the cell. Several copies of these proteins bind to the cargo and take turns transporting the cargo attaching to and detaching from the track stochastically. Despite the relevance of molecular motors to cell physiology, key aspects of their collective functioning are still unknown. In this work we propose a one-dimensional model for the transport of extensive and smooth organelles driven by molecular motors. We ran numerical simulations to study the behavior of the cargo for different motor configurations, focusing on the transport properties observable in the experiments, e.g., average speed of the organelle and variations in length. We found that active motors drive the cargo using two different mechanisms: Either they locate in front of the cargo and pull the organelle or they situate at the cargo lagging edge and push. Variations in the organelle length is in close relation with the fraction of motors in each configuration, which depends on the resisting load. The results of this model were contrasted with experimental data obtained from the tracking of rodlike mitochondria during active transport in Xenopus laevis melanophores.

Figure 1

The model: The cargo consists of two nodes, elastically coupled. Motors can attach to these nodes and perform discrete steps along the track. When unbound from the track, motors diffuse along the cargo.

Figure 2

Schematic of the single motor states and transitions. Black arrows represent the possible transitions between states. Motors diffuse while detached from the track. They can bind to node 1 or node 2. Attached motors can either detach from the track (and node) or perform discrete steps along the MT. Motors can exert forces on the node they are attached to only when they are stretched above their natural length.

Figure 3

(a) Two-channels confocal image showing microtubules (green) and mitochondria (red) in a X. laevis melanophore cell. Scale $\mathrm{bar}=5\mu \mathrm{m}$. (b) Grayscale image of the example shown in (a) overlapping the recovered trajectories of the mitochondria indicated with the colored arrow heads. The color scale from blue to red in the trajectories indicates time evolution. (c) Recovered position along the longitudinal direction and (d) length variation for the four mitochondria shown in (b). The filled lines in (d) correspond to a smoothing of the data (dashed lines) to facilitate visualization; $\mathrm{\Delta }L=L-L_o$.

Figure 4

Experimental results. Upper panel: Mitochondria velocities during runs where the organelle length increases ($N=23$), does not change ($N=47$), or decreases ($N=48$). The mean velocities of the three sets are as follows: 75, 160, and 135 nm/s, respectively. The asterisk denotes significant differences between populations ($p$ value = 0.004). Lower panel: Mitochondria relative length variation during runs where the organelle retracts ($N=48$) or extends ($N=23$). Boxplots are presented as mean, SEM, and SD, according to Ref. [56].

Figure 5

Simulation results for identical motors teams. (a) Cargo trajectories and relative length variation (inset) for 2 (slashed line) and 10 (filled line) kinesin motor copies, $\kappa =0.003$ pN/nm. Scale bars in the inset: 500 nm and 50 s. The arrowhead indicates $\mathrm{\Delta }L=0$. (b) Organelle retraction fraction for 10 kinesin motor copies and decreasing stiffness values: $\kappa =0.03$, 0.003, and 0.0003 pN/nm. (c) Speed and (d) retraction fraction versus cargo stiffness for different motor teams: Kinesin (circles) and dynein (triangles). Open and filled symbols represent teams with 2 and 10 motor copies, respectively.

Figure 6

Simulations: (a) Motors distribution along the organelle are represented by a probability density estimate for kinesin teams with 10 (filled line), 3 (dashed line), and 2 (dotted line) motor copies. Dark dotted line is the distribution of a 10 kinesins team where motors are unable to attach to the track, so they only diffuse along the cargo. Inset: Distribution of active motors in the corresponding cases. (b) Pulling motors vs. Pushing motors relative populations as a function of the number of motors in the team for kinesin (blue circles) and dynein (red triangles).

Figure 7

Simulations: (a) Representative cargo trajectories (upper panel) and the corresponding length variation (lower panel) for two tug-of-war scenarios 10 kinesin vs. 9 (filled line) and vs. 5 (dashed line) dyneins. Scale bar in the upper panel: $20\mu \mathrm{m}$. (b) Mean cargo velocity during extension ($90\pm 72$ nm/s), retraction ($142\pm 94$ nm/s), and no length variation ($134\pm 86$ nm/s) events in the 10k-9d scenario. (c) Mean length variations for retracting and extending cargoes for the case shown in (b). Error bars computed as $\pm \mathrm{SD}$.

Figure 8

Simulations. (a) Cargo relative length variation as a function of the resisting load for different tug-of-war scenarios. Data are split for extension (filled circles) and retraction (void circles) events. The filled lines are linear regressions of the data, with slopes $2.2\pm 0.6$ and $0\pm 0.03$ %/pN. (b) Ratio between pulling and pushing motors populations as a function of the resisting load assayed for 5 (void symbols) and 10 (filled symbols) motors teams. Circles and triangles stand for kinesin and dynein, respectively. Ratios are presented as means and SD of 10 estimations using samples of 100 data points each. The filled lines are guides to the eye.