Collective intracellular cargo transport by multiple kinesins on multiple microtubules

The transport of intracellular organelles is accomplished by groups of molecular motors, such as kinesin, myosin, and dynein. Previous studies have demonstrated that the cooperation between kinesins on a track is beneficial for long transport. However, within crowded three-dimensional (3D) cytoskeletal networks, surplus motors could impair transport and lead to traffic jams of cargos. Comprehensive understanding of the effects of the interactions among molecular motors, cargo, and tracks on the 3D cargo transport dynamics is still lack. In this work, a 3D stochastic multiphysics model is introduced to study the synergistic and antagonistic motions of kinesin motors walking on multiple mircotubules (MTs). Based on the model, we show that kinesins attaching to a common cargo can interact mechanically through the transient forces in their cargo linkers. Under different environmental conditions, such as different MT topologies and kinesin concentrations, the transient forces in the kinesins, the stepping frequency and the binding and unbinding probabilities of kinesins are changed substantially. Therefore, the macroscopic transport properties, specifically the stall force of the cargo, the transport direction at track intersections, and the mean-square displacement (MSD) of the cargo along the MT bundles vary over the environmental conditions. In general, conditions that improve the synergistic motion of kinesins increase the stall force of the cargo and the capability of maintaining the transport. In contrast, the antagonistic motion of kinesins temporarily traps the cargo and slows down the transport. Furthermore, this study predicts an optimal number of kinesins for the cargo transport at MT intersections and along MT bundles.

Figure 1

Schematic illustration of the stochastic dynamic model. (a) A cargo is transported by two kinesins along a MT. The MT consists of 13 protofilaments in the tubular arrangement. (b) In each step, the trailing kinesin head diffuses to one of the binding sites surrounding the leading head. The probability for the trailing head to bind to one of the neighboring sites is represented by a probability vector ${\mathit{P}}_w$. (c) As cargo diffuses around, other unbound kinesins could reach the MT and bind to it. The binding probability $P_b$ is influenced by the area on the MT surfaces that is reachable to the unbound kinesin heads. (d) The simplified structure of the kinesin consists of two heads, two neck linkers, and a cargo linker.

Figure 2

The mechanochemical cycle and the stepping motion of the kinesin.

Figure 3

Schematic illustration of the binding position between a kinesin and a cargo. The binding position between kinesin $i$ and the surface of the cargo is ${\mathit{X}}_{ki}$. The cargo center is ${\mathit{X}}_{\mathrm{cg}}$. Because kinesins are uniformly distributed on the surface of the cargo, the characteristic angles are calculated as ${\alpha }_i=2\pi u$ and ${\beta }_i={\cos }^{-1}(2v-1)$, where $u$ and $v$ are random numbers uniformly distributed between 0 and 1.

Figure 4

Verification of the stochastic multiphysics model. (a) To calculated the stall force, the cargo is transported by kinesins on a single MT under an external load ${\mathit{F}}_{\mathrm{ext}}$. (b) The variation of the force $F_{\mathrm{ext}}$ applied by kinesins on the cargo along the MT direction. (c) The distribution of the stall force $F_s$. (d) Schematic illustration of the transport dynamics at a ${90}^{\circ }$ MT intersection. (e) Probabilities for the cargo to pass, pause, switch or dissociate at the intersection when it is moved on the bottom MT (MT1) to the intersection (i.e., underpass). (f) Probabilities of the cargo dynamics when it is transported on the top MT (MT2) to the intersection (i.e., overpass). The experimental data are from the previous study [18].

Figure 5

The distribution of the number of kinesins that bind to a single MT or a bundle of two parallel MTs $N_{\mathrm{bound}}$ over the different number of kinesins on the cargo $N$.

Figure 6

The distribution of the dwell time $T_d$ at the intersection. $T_d$ is calculated as $T_d=T_e-T_b$, where $T_b$ is the time when the cargo starts to move from a position located $1\mu \mathrm{m}$ away from the intersection, $T_e$ is the time when the cargo passes the intersection and moves $1\mu \mathrm{m}$ away from the intersection.

Figure 7

Transport dynamics at the intersection of two MTs is influenced by the intersection distance $H$ and the angle $\beta$. (a) The schematic illustration of the intersection distance $H$. (b) The influence of $H$ on the passing and pausing probabilities in the overpass situation when 1 or 36 kinesins are attached on the cargo. (c) The influence of $H$ on the switching and pausing probabilities in the underpass situation. Increasing the intersection distance significantly disrupts the transport in the underpass situation. Multiple kinesins on the cargo (36 kinesins in the case) reduces the impairment of $H$ on the transport. (d) A schematic illustration of the intersection angle $\beta$ when two MTs are attached to each other. [(e) and (f)] Transport dynamics influenced by the angle $\beta$ in the overpass and underpass situations.

Figure 8

The influence of intersection angle $\beta$ on the transport dynamics in the underpass situation. (a) The distribution of the number of kinesins on MT1 and MT2 at the intersection when $N$ is 36. (b) The distribution of the association time on the two MTs as well as the diffusion time. The association time on a MT is defined as the time interval when at least one kinesin binds to that MT.

Figure 9

The collective transport dynamics influenced by the number of kinesins $N$ at a ${90}^{\circ }$ MT intersection. (a) The schematic view of a cargo being transported along the bottom MT and switching to the top MT at the intersection. The intersection distance is 0 nm. [(b) and (c)] The influence of the number of kinesins $N$ on the transport dynamics when the cargo is transported along the bottom MT (b) or the top MT (c) toward the intersection. (d) In the underpass situation, the distribution of the association time on MT1 and MT2 as well as the diffusion time when $N$ is 4, 25, and 64. (e) In the underpass situations, the distribution of the number of associated kinesins on MT1 and MT2 over different $N$. (f) The schematic illustration of the influence of kinesin number $N$ on the transport dynamics.

Figure 10

The collective transport dynamics influenced by the number of kinesins $N$ in the overpass situation. (a) The distribution of the association time on MT1 and MT2 as well as the diffusion time when $N$ is 4, 25, and 64. (b) The distribution of the number of associated kinesins on MT1 and MT2 over different $N$. The intersection distance is 0 nm and the intersection angle is ${90}^{\circ }$.

Figure 11

Schematic illustration of the influence of cargo levitation and torque diffusion on the proportion distribution of motors on different MTs. (a) Kinesins transport the cargo from MT1 toward the intersection. (b) Cargo levitation increases the proportion of kinesins on MT2 by changing the distances between the cargo and MTs. (c) A counterclockwise torque changes forces inside the kinesins and increases the proportion of kinesins on MT2.

Figure 12

The collective transport dynamics influenced by kinesin number $N$ along a parallel MT bundle. (a) The schematic illustration of the kinesins binding between the cargo and the MTs. Kinesins are classified as trailing kinesins and leading kinesins based on whether the positions of their heads locate behind the center of the cargo. (b) The MSDs of the cargo over different number of kinesins $N$. The motion of the cargo is superdiffusive because of the active forces applied by kinesins. In addition, the gray line represents the MSD of the cargo transported by 16 impaired kinesins. The impairment of the kinesin is defined as decreasing the binding rate $k_{b0}$ to half of its original value and increasing the unbinding rate $P_{u0}$ and $k_{u0}$ to twice of the original values. (c) The distribution of the number of trailing kinesins when $N$ is 16, 36, and 64. (d) The distribution of the duration of a chemical reaction cycle for the leading kinesins over $N$. (e) The distribution of the association time of the trailing and leading kinesins on the MTs and the diffusion time over $N$.

Figure 13

The realization of 100 simulation results of the MSDs along a parallel MT bundle over different kinesin number $N$. The gray lines are the MSDs over time calculated in each of the 100 simulations. Red lines are the ensemble average of the 100 MSD curves.

Figure 14

Three types of collective kinesin dynamics (of two kinesins) along a single MT. (a) Independent dynamics happens when two identical kinesins walk with similar stepping rate and pull the cargo. (b) Antagonistic dynamics is caused by the two kinesins pull the cargo toward different directions. The leading kinesin experiences a resisting force and the chemical reaction on its heads is likely to be slowed down. (c) Synergistic dynamics helps two kinesins transport the cargo under an external load. The leading kinesin shares a larger load and its chemical reaction happens slower than the trailing kinesins. The first column of the plots contains the schematic representations of the cargo (black circle), MT (green line), and two kinesins. The leading kinesin (kinesin 1) is represented as blue. The trailing kinesin (kinesin 2) is represented as red. The second column of plots represent the distribution of forces inside the two kinesins. Positive values represent the direction of the force is the same as the walking direction. The third column of plots are the distributions of the time a kinesin takes to complete a chemical reaction cycle and walk one step forward.

Figure 15

The interruption of a neighboring MT on the transport for various number of kinesins $N$. (a) An illustration of the situation when a cargo is transported by kinesins along two parallel MTs. Extra kinsesins on the cargo can bind to the neighboring track and disrupt the transport. The neighboring track is placed perpendicularly to the two parallel MTs. The shortest distance between the surfaces of the neighboring MT and the two parallel MTs is 850 nm. (b) The probability of passing the neighboring MT without being disrupted over different value of $N$.