Kinesin’s Network of Chemomechanical Motor Cycles

A general network theory for the molecular motor kinesin is developed that is based on the distinct chemical states of the motor and on recent observations about its mechanical steps. For small concentrations of adenosine diphosphate (ADP), the motor’s behavior is governed by the competition of two chemomechanical motor cycles which determine the motor’s stall force. A third cycle becomes important for large ADP concentrations. The theory provides a quantitative description for the functional dependencies of different motor properties as observed in single molecule experiments.

Figure 1

(a) Chemical cycle for a single motor head and its reduction to 3 states; (b) Kinesin state space consisting of $3^2=9$ chemical states and 18 chemical transitions (full lines) between these states; and (c) 6-state model obtained from (b) by omitting the three states $EE$, $DD$ and $TT$. The six states $i=1,2,\dots 6$ form a single chemical cycle, $⟨1234561⟩$. The mechanical stepping transition $⟨25⟩$ (broken line) divides this chemical cycle up into two chemomechanical cycles, $\mathcal{F}$ and $\mathcal{B}$, see text. Every line between two states $i$ and $j$ represents both the forward transition, $|ij⟩$, from $i$ to $j$ and the backward transition, $|ji⟩$, from $j$ to $i$. As indicated by the vertical head displacements, the $E$ and $T$ states are strongly bound whereas the $D$ state is weakly bound to the microtubule [6, 16].

Figure 2

(a) Motor velocity $v$ and (b) ratio $q$ of the number of forward to backward steps as a function of external load force $F$ (data from 15). The ratio $q$ has been calculated via $q=P_2{\omega }_{25}/(P_5{\omega }_{52})$. The vertical dotted line corresponds to the stall force $F_s$; (c) Motor velocity and (d) randomness parameter $2D_b/(\ell v)$ as a function of force $F$ (data from 9). The randomness is proportional to the bound state diffusion constant $D_b$. The solid and broken lines correspond to the 6- and 7-state model, respectively. In (a)–(c), the broken lines are (partially) masked by the solid lines.

Figure 3

(a,b) Motor velocity $v$ as a function of (a) P and (b) ADP concentration (data from 12). The solid and broken lines are for the 6- and 7-state model, respectively; (c,d) Mean run length $\Delta x$ as a function of (c) load force $F$ and (d) ATP concentration (data from 10). The broken and dotted lines correspond to the 7-state model with $[\mathrm{P}]=[\mathrm{ADP}]=0.5\mu M$ and $[\mathrm{P}]=[\mathrm{ADP}]=0\mu M$, respectively.