Table 1.

Parameter values for WT kinesin-1 motor."

Figure 1.

Dynamics of the cooperative transport by two different kinesin motors under no external force. One corresponds to WT kinesin-1 motor having velocity v1 and rebinding rate $\mu ,$ and the other corresponds to mutant kinesin-1 motor having velocity ${v}_{1}/\alpha $ and rebinding rate $\mu .$ Lines are simulated results. Symbols are experimental data, with red circles from Rogers et al [21] and black squares from Xu et al [23]. (a) Velocity ratio v2/v1 versus $\alpha .$ The errors of the experimental data are calculated with Δ($v$2/$v$1) = $\left|\partial \left({v}_{2}/{v}_{1}\right)/\partial {v}_{1}\right|{\rm{\Delta }}{v}_{1}+\left|\partial \left({v}_{2}/{v}_{1}\right)/\partial {v}_{2}\right|{\rm{\Delta }}{v}_{2}.$ (b) Run-length ratio L2/L1 versus $\alpha .$ The errors of the experimental data are calculated with ${\rm{\Delta }}\left({L}_{2}/{L}_{1}\right)=\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{1}\right|{\rm{\Delta }}{L}_{1}$ $+\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{2}\right|{\rm{\Delta }}{L}_{2}.$ (c) Velocity distribution for asymmetric unbinding rate. Lines are Gaussian fits. Left, middle and right panels are the distribution for the cooperative transport by a WT kinesin motor and a mutant kinesin motor with its velocity slowed by 15-fold, the distribution for the single WT motor and the distribution for the single mutant motor, respectively. (d) Run-length distribution for asymmetric unbinding rate. Lines are single-exponential fits. Left, middle and right panels are the distribution for the cooperative transport by a WT kinesin motor and a mutant kinesin motor with its velocity slowed by 15-fold, the distribution for the single WT motor and the distribution for the single mutant motor, respectively."

Figure 2.

Dynamics of the cooperative transport by two different kinesin motors under the external force. One motor corresponds to WT kinesin-1 having velocity v1 and rebinding rate $\mu ,$ and the other corresponds to mutant kinesin-1 having velocity ${v}_{1}/\alpha $ ($\alpha $ = 15) and rebinding rate $\mu .$ The panel shows velocity v2 and run length L2 versus external force Fext."

Figure 3.

Dynamics of the cooperative transport by two identical kinesin motors with rebinding rate $\beta \mu .$ For kinesin-1 $\beta $ = 1, and for kinesi-2 $\beta $ = 4. Lines are simulated results. (a) Velocity ratio v2/v1 versus $\beta $ under no external force. (b) Run-length ratio L2/L1 versus $\beta $ under no external force. Symbols are experimental data from Feng et al [18], where K1–K1 represents the cooperative transport by two kinesin-1 motors and K1–K2 represents the cooperative transport by a kinesin-1 motor and a kinesin-2 motor. The errors of the experimental data are calculated with ${\rm{\Delta }}\left({L}_{2}/{L}_{1}\right)=\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{1}\right|$ ${\rm{\Delta }}{L}_{1}+\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{2}\right|{\rm{\Delta }}{L}_{2}.$ (c) Velocity v2 and run length L2 versus external force Fext for $\beta $ = 1 and $\alpha $ = 1. Inset shows stall force versus $\beta .$ (d) Velocity v2 and run length L2 versus external force Fext for $\beta $= 4 and $\alpha $ = 1."

Figure 4.

Dynamics of the cooperative transport by two different kinesin motors under no external force. One motor has velocity v1 and rebinding rate $\mu ,$ and the other has velocity ${v}_{1}/\alpha $ ($\alpha $ = 1.18) and rebinding rate $\beta \mu .$ (a) Velocity ratio v2/v1 versus $\beta .$ (b) Run-length ratio L2/L1 versus $\beta .$ (c) Velocity for transport by single kinesin-1 motor (K1), velocity for cooperative transport by two kinesin-1 motors (K1–K1) and velocity for cooperative transport by a kinesin-1 motor and a kinesin-2 motor (K1–K2). Kinesin-1 has velocity v1 and rebinding rate $\mu ,$ and kinesin-2 has velocity ${v}_{1}/\alpha $ ($\alpha $ = 1.18) and rebind rate $\beta \mu $ ($\beta $ = 4). (d) Run length for transport by single kinesin-1 motor (K1), run length for cooperative transport by two kinesin-1 motors (K1–K1) and run length for cooperative transport by a kinesin-1 motor and a kinesin-2 motor (K1–K2). For comparison, the experimental data of Feng et al [18] are also shown."

Figure 5.

Dynamics of the cooperative transport by two different kinesin motors under no external force. One motor has velocity v1 and rebinding rate $\mu ,$ and the other has velocity ${v}_{1}/\alpha $ and rebinding rate $\beta \mu .$ (a) Velocity ratio v2/v1 versus $\beta $ for different values of $\alpha .$ (b) Run-length ratio L2/L1 versus $\beta $ for different values of $\alpha .$"

Figure 6.

Dynamics of the cooperative transport by N (N > 1) identical kinesin motors under no external force. The motor has velocity v1 and rebinding rate $\mu .$ Lines are simulated results. Symbols are experimental data from Derr et al [20]. (a) Velocity ratio v2/v1 versus N. The errors of the experimental data are calculated with ${\rm{\Delta }}\left({v}_{2}/{v}_{1}\right)=\left|\partial \left({v}_{2}/{v}_{1}\right)/\partial {v}_{1}\right|{\rm{\Delta }}{v}_{1}+\left|\partial \left({v}_{2}/{v}_{1}\right)/\partial {v}_{2}\right|{\rm{\Delta }}{v}_{2}.$ (b) Run-length ratio L2/L1 versus N. The errors of the experimental data are calculated with ${\rm{\Delta }}\left({L}_{2}/{L}_{1}\right)=\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{1}\right|{\rm{\Delta }}{L}_{1}+\left|\partial \left({L}_{2}/{L}_{1}\right)/\partial {L}_{2}\right|{\rm{\Delta }}{L}_{2}.$ (c) Simulated results of velocity distribution for asymmetric unbinding rate. Lines are Gaussian fits. Left and middle panels correspond to N = 4 and 7, respectively, and right panel shows the half width of the Gaussian velocity distribution versus N. (d) Simulated results of run-length distribution for asymmetric unbinding rate. Lines are single-exponential fits. Left, middle and right panels correspond to N = 4, 5 and 7, respectively."