Modeling Studies of the Mechanism of Context-Dependent Bidirectional Movements of Kinesin-14 Motors

Abstract

Kinesin-14s, a subfamily of the large superfamily of kinesin motor proteins, function mainly in spindle assembly and maintenance during mitosis and meiosis. KlpA from Aspergillus nidulans and GiKIN14a from Giardia intestinalis are two types of kinesin-14s. Available experimental results puzzlingly showed that while KlpA moves preferentially toward the minus end in microtubule-gliding setups and inside parallel microtubule overlaps, it moves preferentially toward the plus end on single microtubules. More puzzlingly, the insertion of an extra polypeptide linker in the central region of the neck stalk switches the motility direction of KlpA on single microtubules to the minus end. Prior experimental results showed that GiKIN14a moves preferentially toward the minus end on single microtubules in either tailless or full-length forms. The tail not only greatly enhances the processivity but also accelerates the ATPase rate and velocity of GiKIN14a. The insertion of an extra polypeptide linker in the central region of the neck stalk reduces the ATPase rate of GiKIN14a. However, the underlying mechanism of these puzzling dynamical features for KlpA and GiKIN14a is unclear. Here, to understand this mechanism, the dynamics of KlpA and GiKIN14a were studied theoretically on the basis of the proposed model, incorporating potential changes between the kinesin head and microtubule, as well as the potential between the tail and microtubule. The theoretical results quantitatively explain the available experimental results and provide predicted results. It was found that the elasticity of the neck stalk determines the directionality of KlpA on single microtubules and affects the ATPase rate and velocity of GiKIN14a on single microtubules.

Keywords: chemo–mechanical coupling mechanism; kinesin; molecular motor; movement direction.

Figure 1

The model for the interaction of the head with MTs and the orientation of the neck stalk for the kinesin-14 motor. The head and tail domain of the motor are drawn in red and green, respectively. (a) Interaction potential of the head in the ADP state with a tubulin (upper panel) and with an MT filament (lower panel) for the non-processive motor. (b) Interaction potential of the head in the ADP state with a tubulin (upper panel) and with an MT filament (lower panel) for the processive motor. (c) Interaction potential of the tail domain with an MT filament. (d) Two orientations of the neck stalk relative to the head bound to the MT, with the upper panel corresponding to the orientation of the ADP or nucleotide-free state and the lower panel corresponding to the orientation of the ATP or ADP.Pi state.

Figure 2

Schematic illustrations of the chemo–mechanical coupling pathway of the KlpA motor. (a–e) The single KlpA-Δtail motor moving on a single MT (see Section 2.1.1 for detailed descriptions). (a′–f′) MT gliding by KlpA or the KlpA-3 $\times$ GS motor (see Section 2.1.2 for detailed descriptions). (a″–e″) The single full-length KlpA or KlpA-3 $\times$ GS motor moving on a single MT (see Section 2.1.3 for detailed descriptions). In (d″,e″), the position of the head drawn in red represents the one where the head has a larger probability to locate and that in yellow represents the one where the head has a smaller probability to locate for the case of full-length KlpA.

Figure 3

Relationship between the ATPase rate k of the KlpA motor and the asymmetric parameter $\alpha$ for the interaction potential of its head with MTs, under which the computed MT gliding velocity v₁ = 298 nm/s.

Figure 4

Dynamics of the KlpA motor. Lines represent the theoretical results. Symbols represent experimental data from Popchock et al. [15] and Wang et al. [16], with the black triangles and blue circles for ‘MT gliding’ representing the MT gliding velocity by the KlpA and KlpA-Δtail motors, respectively, and the other two black triangles representing the velocity of the single KlpA-3 $\times$ GS and KlpA motors moving on a single MT. Positive velocity represents the plus end movement of the MT in MT gliding or the minus-end-directed movement of the motor on the single MT. (a) Velocity of the single KlpA motor moving on a single MT versus $\kappa \Delta$. (b) Velocity of the single KlpA motor moving on a single MT versus $\kappa$ for $\Delta$ = 2 nm.

Figure 5

Dynamics of the KlpA motor inside two parallel MTs. (Upper panel) illustrates the motor with its head (red) in its ATP state bound to one tubulin on one MT and its tail domain (green) bound to one binding site on the other MT. (Lower panel) shows the theoretical results for the velocity of the motor moving inside the MT overlap versus $\kappa$ (solid blue line), with unfilled squares corresponding to the predicted results for KlpA and KlpA-3 $\times$ GS. For comparison, the theoretical results for the velocity of the motor moving on the single MT versus $\kappa$ are also shown (dashed red line), with filled triangles representing the prior experimental results for KlpA and KlpA-3 $\times$ GS [15,16]. A positive velocity represents the motor moving toward the minus end.

Figure 6

Schematic illustrations of the chemo–mechanical coupling pathway of the GiKIN14a motor. The head of the motor is drawn in red or yellow, while the tail domain is drawn in green. (a–e) The single GiKIN14a-Δtail motor moving on a single MT (see Section 2.2.1 for detailed descriptions). In (c–e), the position of the head drawn in red represents the one where the head has a larger probability to locate and that in yellow represents the one where the head has a smaller probability to locate. (a′–d′) The single full-length GiKIN14a or GiKIN14a-3 $\times$ GS motor moving on a single MT (see Section 2.2.1 for detailed descriptions). In (c′,d′), the position of the head drawn in red represents the one where the head has a larger probability to locate and that in yellow represents the one where the head has a smaller probability to locate.

Figure 7

Dynamics of the GiKIN14a motor. Lines represent the theoretical results. (a) Chemo–mechanical coupling efficiency versus $\kappa$. (b) Normalized ATPase rate versus $\kappa$. Filled circles represent the experimental data from Tseng et al. [17]. Errors of the experimental data for the full-length GiKIN14a or GiKIN14a-3 $\times$ GS motors were computed with $\Delta \overline{k}$ = $\Delta \left(k/k_0\right)$ = $\left|\partial \left(k/k_0\right)/\partial k\right|\Delta k+\left|\partial \left(k/k_0\right)/\partial k_0\right|\Delta k_0$, where k and $\Delta k$ represent, respectively, the ATPase rate and the corresponding error for the full-length GiKIN14a or GiKIN14a-3 $\times$ GS motors, while k₀ and $\Delta k_0$ represent, respectively, the ATPase rate and the corresponding error for GiKIN14a-Δtail motor. Error of the experimental data for the GiKIN14a-Δtail motor was computed with $\Delta k_0/k_0$. (c) Velocity versus $\kappa$. Filled circles represent the experimental data from Tseng et al. [17]. The unfilled square represents the predicted result. The positive velocity represents the motor moving toward the minus end.