Fig 1.
The mechanistic model of kinesin is schematically shown.
The kinesin molecule is composed of two heads, two neck linkers, and a neck. The neck is connected to the outer surface of the cargo via a cargo linker. The small spheres conceptually represent α and β tubulin which form the MT. Kinesins walk from the minus end to the plus end of the MT. Coordinates xc, xn, xfh and xbh are the position of the cargo, that of the neck, and the positions of the forward and backward heads. FL denotes the load acting on the cargo; its direction is along the MT. The sign of FL is plus when it is toward the minus end of the MT.
Fig 2.
The kinesin cycle is depicted.
The states in the upper box relate to the walking cycle of the kinesin. K denotes the kinesin molecule. The lower box relates to the unbound state of the kinesin. The variables denoted by k are transition rates between states, and PD0 and PD1 represent the probability of unbinding from the MT when the kinesin is in the state [K + MT] and [K.ATP + MT]1. (a) An ATP molecule binds to the leading head of the kinesin. (b) The binding of ATP to the kinesin head results in a structural changes in the head [38]. This change induces the docking of the neck linker to its head. The docking of the neck linker to the leading head generates a force to move the trailing head toward the plus end of MT. Then, the trailing head diffuses to the next binding site of MT by Brownian motion. (c) The moving head binds to the MT and releases ADP. (d) ATP in the rear head is hydrolyzed, and then this hydrolysis enables the release of phosphate (Pi) from the head. Then, the neck linker returns to the disordered state from the docked state.
Table 1.
The values of parameters regarding unbinding.
Fig 3.
The run length of single kinesins is shown.
(a) shows the run length for various loads for [ATP] = 2 mM; (b) shows the run length when [ATP] = 5 μM.
Fig 4.
The rebinding of the unbound kinesin is depicted.
The unbound kinesin has probabilities to rebind at several binding sites of the MT. PK is the probability to stay in the unbound state, while PA, j−1, PA, j, and PA, j+1 are the probabilities to rebind at the (j − 1)th, jth, and (j + 1)th binding site. kA, j is the transition rate from the unbound state to the bound state at the jth binding site. The values of kAj−1, kAj, and kAj+1 vary over the position of unbound kinesin xu, k with respect to the position of binding sites of the MT. CA is a parameter of the model which denotes the rate of rebinding to a certain binding site when the unbound kinesin is exactly above that site.
Fig 5.
The rebinding model is schematically shown.
The pdf of the position of the cargo pdf(xc) (b) is obtained from the strain energy in the structure of the bound kinesins (a). The pdf of the position of the unbound kinesin respect to the cargo pdf(xu, k − xc) (d) is obtained from the strain energy in its structure (c). The pdf of the position of the unbound kinesin pdf(xu, k) (e) is calculated as the convolution of pdf(xc) and pdf(xu, k). (f) shows the values of kA over the position of unbound kinesin. (g) The rebinding probability on each binding site during a time step is obtained by using kA, j and pdf(xu, k).
Fig 6.
Time average of the transition rate is depicted.
(a) shows the fluctuating position xu, k of unbound kinesin, and (b) shows the transition rate kA, j to rebind at the jth binding site. The rate also fluctuates over time. Circles and the bold line indicate the moving average of the rate.
Fig 7.
(a) shows the fluctuating position of unbound kinesin.
(b) shows details for xu, k between time steps t and t + T. t1…6 are the durations when xu, k exists between xℓ and xℓ + Δx.
Fig 8.
The run length distribution and mean velocity for various concentrations of kinesins are shown.
All results are obtained in the absence of loads on the cargo. Whereas the run length increases with ck, the velocity is almost constant for the shown concentrations.
Fig 9.
The unbinding probabilities for various resisting loads are presented.
The solid line denotes PD0, and the dotted line shows PD1. The unbinding probabilities for [ATP] = 2 mM (a) and 5 μm (b) are shown. Note that PD1 is much higher than PD0 in a wide range of loads for high [ATP].
Fig 10.
The transport of the cargo in the presence of obstacle is depicted.
(a) depicts transport when a static obstacle (shown as a triangle) is on the path of the cargo. (b) shows a moving obstacle (shown as a rectangle) approaching the cargo. The cargo moves backward with velocity of vobs due to the moving obstacle. Fk,1 and Fk,2 are forces (acting on the cargo) of two kinesins. The cargo overcomes the obstacle when the sum of those two forces is larger than Fobs. (c) and (d) present the probability Poc that the cargo overcomes one obstacle without unbinding from the MT. (c) shows the probabilities for static obstacles which require forces of 10, 15, and 20 pN to be overcome it. (d) shows probabilities to overcome moving obstacle when the cargo is retrograded by the obstacle with the velocity of 200 nm/s.
Fig 11.
The run length of transport by several kinesins is shown.
(a) shows the run length of one, two, and three kinesins for [ATP] = 2 mM. (b) shows an example of HLB when a resisting load of 12 pN acts on the cargo. (b1) The leading kinesin is stationary while waiting for ATP. During this long interval, another kinesin binds to the MT. (b2) It is likely that the distance between the newly bound kinesin and the cargo is less than the length of the cargo linker. Thus, the newly bound kinesin does not have a load. Consequently, the lagging kinesin walks toward the leading one (the anchor) with high velocity. (b3) The two kinesins cooperate to transport their cargo against the large load. (b4) One of the kinesins unbinds and the other kinesin acts as an anchor again.
Fig 12.
The transport velocity by teams of kinesins is depicted.
(a) is the transport velocity by one, two, and three kinesins for [ATP] = 2 mM. (b) and (c) show the effect of the binding and unbinding on the motion of the cargo when the assisting or resisting load is acted on the cargo.