Factors Determining Kinesin Motors in a Predominant One-Head-Bound or Two-Heads-Bound State During Its Stepping Cycle

Abstract

At physiological or saturating ATP concentrations, some families of kinesin motors, such as kinesin-1 and kinesin-2, exhibit a predominant two-heads-bound (2HB) state during their stepping cycle on microtubules, while others, such as kinesin-3, exhibit a predominant one-head-bound (1HB) state. An interesting but unclear issue is what factors determine a kinesin motor in the predominant 1HB and 2HB states. Here, on the basis of the general chemomechanical pathway of the kinesin motors, a theory is given on fractions of 1HB and 2HB states. With the theory, the factors affecting a kinesin motor in the predominant 1HB and 2HB states are determined. The results about the effects of ATP concentration, ADP concentration and external load on the fractions of 1HB and 2HB states are presented. Furthermore, the theory is applied to kinesin-1, kinesin-2, kinesin-3, kinesin-5 and kinesin-13 motors, with the theoretical results agreeing well with published experimental data.

Keywords: kinesin; one-head-bound state; stepping manner; two-heads-bound state.

Figure 1

General chemomechanical pathway of the kinesin motor. T represents ATP and ADP. Pi, D represents ADP, and ϕ represents nucleotide-free. The inset shows schematically the normal tubulin with no large conformational changes, the tubulin with the large conformational changes induced by the strong binding of the kinesin head in the ϕ or T state to the tubulin, and the structural components of the kinesin dimer. For clarity, only in the inset is the motor’s stalk shown. Stages (a–m) state transitions (see Section 2 for detailed descriptions). After the dimer in the ADP state binds to MT (a), ADP is released from the MT-bound head (b), followed by ATP binding (c). Then, the transitions from stage (c) through stage (k), which include the futile coupling transitions from stage (d) to (m) and returning to stage (c), correspond to a stepping cycle of the motor. The mechanical steps include the diffusion of the ADP-head from the local tubulin to the intermediate (INT) position, i.e., the transition from stage (e) to (g), from stage (h) to (i), from stage (j) to (k), or from stage (m) to (c), which occurs after ATP transition to ADP in the TH, and the diffusion of the detached ADP-head from the INT position to the nearest tubulin, i.e., the transition from stage (d) to either stage (e) or (f), which occurs after the decrease in the binding energy of the MT-bound ATP-head to the detached ADP-head. The other transitions correspond to the ATPase activity and the large conformational change associated with the NL docking of the head. Since the rates of the mechanical steps (on the order of 1 μs⁻¹) are much larger than the rate constants of the ATPase activity and the large conformational change in the ATP head (on the order of 1~10 ms⁻¹), the rates of the mechanical steps are not indicated.

Figure 2

Ratio of the fraction of 2HB state to that of 1HB state, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$, under saturating ATP concentrations, no load and no free ADP. Under this condition, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ is determined mainly by $\alpha =k^{(+)}/k_{\mathrm{D}}$ and mildly by $\beta =k_{\mathrm{NL}}/k_{\mathrm{D}}$. Thin dotted lines correspond to $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ = 1, at which the 1HB and 2HB states have the same fraction. When $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ > 1, the motor is in the predominant 2HB state, and when $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ < 1, the motor is in the predominant 1HB state. (a) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. $\alpha$ for various values of $\beta$. (b) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. $\beta$ for various values of $\alpha$.

Figure 3

Effect of ATP concentration, [ATP], on the ratio of the fraction of the 2HB state to that of the 1HB state, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$, under no free ADP and no load. Thin dotted lines correspond to $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ = 1, at which the 1HB and 2HB states have the same fraction. When $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ > 1, the motor is in the predominant 2HB state, and when $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ < 1, the motor is in the predominant 1HB state. (a) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. [ATP] for various values of $\alpha$ at small $\beta$ = 2. (b) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. [ATP] for various values of $\alpha$ at large $\beta$ = 100.

Figure 4

Effect of backward load, F, on the ratio of the fraction of 2HB state to that of 1HB state, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ at saturating ATP concentrations and no free ADP. Thin dotted lines correspond to $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ = 1, at which the 1HB and 2HB states have the same fraction. When $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ > 1, the motor is in the predominant 2HB state, and when $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ < 1, the motor is in the predominant 1HB state. (a) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. F for various values of $\alpha$ at small $\beta$ = 2. (b) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. F for various values of $\alpha$ at large $\beta$ = 100.

Figure 5

Effect of ADP concentration on velocity and ratio of the fraction of 2HB state to that of 1HB state, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$, under no load for kinesin-1 from bovine brain. Lines are theoretical results, and symbols are experimental data from Schief et al. [40]. (a) Velocity vs. ATP concentration for [ADP] = 0 mM, 1 mM and 5 mM. (b) Velocity vs. ADP concentration for [ATP] = 300 μM, 1 mM, 3 mM, 10 mM and 20 mM. (c) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. ATP concentration for [ADP] = 0 mM, 1 mM and 5 mM. (d) $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ vs. ADP concentration for [ATP] = 300 μM, 1 mM, 3 mM, 10 mM and 20 mM. Thin dotted lines in (c,d) correspond to $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ = 1, at which the 1HB and 2HB states have the same fraction. When $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ > 1, the motor is in the predominant 2HB state, and when $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ < 1, the motor is in the predominant 1HB state.

Figure 6

Effect of the ATP concentration, [ATP], on 1HB and 2HB states of human kinesin-1 under no load. (a) Ratio of the fraction of 2HB state to that of 1HB state, $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$, versus [ATP]. The thin dotted line corresponds to $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ = 1, at which the 1HB and 2HB states have the same fraction. When $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ > 1, the motor is in the predominant 2HB state, and when $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ < 1, the motor is in the predominant 1HB state. (b) Duration of 1HB state, ${\tau }_{1\mathrm{HB}}$, versus [ATP]. (c) Duration of 2HB state, ${\tau }_{2\mathrm{HB}}$, versus [ATP]. In (a–c), lines are theoretical results calculated with the parameter values being indicated, and red dots are experimental data from Isojima et al. [13], with the experimental data for $F_{2\mathrm{HB}}/F_{1\mathrm{HB}}$ being calculated from those for ${\tau }_{1\mathrm{HB}}$ and ${\tau }_{2\mathrm{HB}}$.