The kinesin cycle is depicted.

<p>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 <i>P</i>_<i>D</i>0 and <i>P</i>_<i>D</i>1 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 [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003981#pcbi.1003981.ref038" target="_blank">38</a>]. 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.</p

The values of parameters regarding unbinding.

<p>The values of parameters regarding unbinding.</p

The rebinding model is schematically shown.

<p>The pdf of the position of the cargo pdf(<i>x</i>_<i>c</i>) (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(<i>x</i>_{<i>u</i>, <i>k</i>} − <i>x</i>_<i>c</i>) (d) is obtained from the strain energy in its structure (c). The pdf of the position of the unbound kinesin pdf(<i>x</i>_{<i>u</i>, <i>k</i>}) (e) is calculated as the convolution of pdf(<i>x</i>_<i>c</i>) and pdf(<i>x</i>_{<i>u</i>, <i>k</i>}). (f) shows the values of <i>k</i>_<i>A</i> over the position of unbound kinesin. (g) The rebinding probability on each binding site during a time step is obtained by using <i>k</i>_{<i>A</i>, <i>j</i>} and pdf(<i>x</i>_{<i>u</i>, <i>k</i>}).</p

The velocity and run length of kinesins over the density of motors.

<p>(a) depicts the motions of the kinesin in (K + M^Φ), (K + M⁺), and (K + M⁻) situations. Motors with an arrow directed to the right are moving kinesins. Motors with an arrow directed to the left are minus-end directed motors. Immobile kinesins are presented as motors without an arrow. <i>ρ</i> represents the molar ratio of immobile kinesins and tubulins for (K + M^Φ), the molar ratio of walking kinesins and tubulins for (K + M⁺), or the molar ratio of minus-end directed motors and tubulins for (K + M⁻). Note that the MT is saturated with kinesins when <i>ρ</i> is about 0.43. The line denotes the velocity and run length for (K + M^Φ) obtained from Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147676#pone.0147676.e008" target="_blank">5</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147676#pone.0147676.e009" target="_blank">6</a>. The results shown as circles, stars and diamonds are calculated from our stochastic model.</p

Spring model of kinesin NLs.

<p>(a) shows a kinesin molecule and the binding sites around it. Note that the directions of <i>x</i>, <i>y</i>, and <i>z</i> axis are the same with those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0147676#pone.0147676.g001" target="_blank">Fig 1</a>, and the view direction is along the <i>z</i> axis. NLs are depicted with springs, and gray circles represent the neighboring binding sites. (b) is a schematic cross section through the coiled-coil structure of the neck. The coils are bonded to each other by using the interactions of their AA residues. The neck is connected to two springs corresponding to the docked NL and undocked NL. (c) shows the changes of the force (<i>F</i>_UDNL) over the length (<i>ℓ</i>_UDNL) of undocked NL. (d1) depicts the calculated <i>F</i>_<i>x</i>(<i>x</i>, <i>y</i>), where (<i>x</i>, <i>y</i>) denotes the <i>x</i> and <i>y</i> positions of the free head. (d2) shows the calculated <i>F</i>_<i>y</i>(<i>x</i>, <i>y</i>).</p

The transport velocity by teams of kinesins is depicted.

<p>(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.</p

Walking motion of a kinesin molecule on the MT.

<p>(a) depicts one kinesin molecule transporting a cargo by walking on the MT. The dotted box indicates the domain where the motion of the kinesin head is realized. (b) shows the components of the kinesin structure and the procedure for its walking motion. The kinesin has one pair of identical heads and NLs. <i>x</i> represents the direction of MT-axis, and <i>y</i> is the tangential direction of the MT. <i>xy</i>-plane represents the outer surface of the MT. The cylinder with bold outlines denotes the fixed head on the MT, and the cylinder with thin outlines is the free head. The neighboring binding sites of the kinesin are shown as gray ellipses. The plus and minus signs denote the polarity of the MT.</p

The mechanistic model of kinesin is schematically shown.

<p>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 <i>α</i> and <i>β</i> tubulin which form the MT. Kinesins walk from the minus end to the plus end of the MT. Coordinates <i>x</i>_<i>c</i>, <i>x</i>_<i>n</i>, <i>x</i>_<i>fh</i> and <i>x</i>_<i>bh</i> are the position of the cargo, that of the neck, and the positions of the forward and backward heads. <i>F</i>_<i>L</i> denotes the load acting on the cargo; its direction is along the MT. The sign of <i>F</i>_<i>L</i> is plus when it is toward the minus end of the MT.</p

Time average of the transition rate is depicted.

<p>(a) shows the fluctuating position <i>x</i>_{<i>u</i>, <i>k</i>} of unbound kinesin, and (b) shows the transition rate <i>k</i>_{<i>A</i>, <i>j</i>} to rebind at the <i>j</i>^th binding site. The rate also fluctuates over time. Circles and the bold line indicate the moving average of the rate.</p

The run length of transport by several kinesins is shown.

<p>(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.</p