Molecular Mechanism of Processive Stepping of Kinesin Motors

Abstract

Kinesin-1 is a motor protein that can step processively on microtubule by hydrolyzing ATP molecules, playing an essential role in intracellular transports. To better understand the mechanochemical coupling of the motor stepping cycle, numerous structural, biochemical, single molecule, theoretical modeling and numerical simulation studies have been undertaken for the kinesin-1 motor. Recently, a novel ultraresolution optical trapping method was employed to study the mechanics of the kinesin-1 motor and new results were supplemented to its stepping dynamics. In this commentary, the new single molecule results are explained well theoretically with one of the models presented in the literature for the mechanochemical coupling of the kinesin-1 motor. With the model, various prior experimental results for dynamics of different families of N-terminal kinesin motors have also been explained quantitatively.

1. Introduction

Kinesin-1 molecular motor is the firstly discovered member of kinesin superfamily that can be classified into 14 subfamilies and an ungrouped subfamily called orphan kinesins [1,2]. Kinesin-1 has been studied thoroughly and can be regarded as the model system to study the mechanism of the mechanochemical coupling of the kinesin superfamily. Kinesin-1 can step processively on microtubules (MTs) by hydrolyzing ATP molecules, which is responsible for cargo transports in cells. To explore the molecular mechanism of the processive stepping of the kinesin-1, plenty of researches on its structure, its interaction with MT, its motor dynamics, etc., have been undertaken. For example, it was shown structurally that kinesin-1 is composed of two identical N-terminal motor domains (also called heads) connected together by a common coiled-coil stalk via the two flexible neck linkers (NLs) (with each NL having 14 residues) [3]. The dimer walks on MT in an asymmetric hand-over-hand way, with a step size of about 8 nm, the tubulin repeat period of a MT filament [4,5]. The load dependencies of the motor’s velocity, run length, ratio of forward to backward steps, dissociation rate, etc., have been well determined [6,7,8,9,10,11,12,13]. Accordingly, numerous models have been proposed to explain the available experimental results [14,15,16,17,18,19,20,21,22]. Nevertheless, the detailed mechanism of the mechanochemical coupling of the kinesin-1 is still undetermined.

Recently, Sudhakar et al. [23] developed germanium nanospheres with diameter of about 70 nm as optical trapping probes to study the stepping dynamics of truncated rat kinesin-1 motor, which enhances greatly the spatiotemporal resolution that is limited by using traditional micrometer-sized spheres. Puzzlingly, they found that each 8-nm mechanical step consists of two 4-nm substeps, with the dwell time for the second substep being much shorter than that for the first one. Instead of dissociation from MT, the slip of the motor on MT was observed under high backward loads, which occurs always during the dwell period before the second substep. In this commentary, these new single molecule results measured by Sudhakar et al. [23] are explained well by the theoretical analysis based on one of the models presented in the literature for the mechanochemical coupling of kinesin-1 motors [24]. As shown before [18,24,25,26,27,28,29,30], this model can explain quantitatively diverse experimental results about the load dependency of the stepping dynamics for various families of N-terminal kinesin motors.

2. The Model

Firstly, we describe the major elements, on the basis of which the model is established. (1) The kinesin head in empty, ATP and ADP.Pi states has a strong interaction with MT whereas in ADP state has a weak interaction, as shown by experimental data [31,32,33]. The strong interaction between the kinesin head and tubulin induces large conformational changes of the tubulin whereas the weak interaction has little effect on the conformation of the tubulin, as indicated by structural and all-atom molecular dynamics (AAMD) simulation data [34,35]. The head in ADP state has a much smaller affinity (denoted by E_w1) for the tubulin having the large conformational changes than the affinity (denoted by E_w2) for the tubulin having no large conformational changes, as shown by AAMD simulation data [35]. This, thus, implies that after Pi release from the ADP.Pi-head bound to MT a short time period t_r (of the order of 10 μs [25]) is present when the ADP-head has a much smaller affinity E_w1 for the local tubulin and in time t_r, with the changed conformation of the local tubulin returning to the normally unchanged one, the affinity of the ADP-head for the local tubulin changes to E_w2 (see Figure 1). (2) In ADP and empty states, the head has an open nucleotide-binding pocket (NBP) and a conformation, with the NL being incapable of docking onto the head, as indicated by structural and experimental results [36,37,38,39], and the head having a high binding energy to the partner ADP-head (with the relative position and orientation of the two heads being shown in Figure 2), as shown by AAMD simulation data [40]. In ATP and ADP.Pi states, NBP closing and a large conformational change of the head can take place, with the NL becoming capable of docking onto the head, as indicated by structural and experimental results [36,37,38,39], and the binding energy of the head to the partner ADP-head being reduced significantly, as shown by AAMD simulation data [40]. When NL is in the minus-end orientation, the interference of NL prohibits the closing of NBP and thus the large conformational change of the ATP-head. (3) The head with its NL in the plus-end orientation has a much higher rate of ATP hydrolysis and Pi release than the head with its NL not in the plus-end orientation. This can be explained as follows. The NL not in the plus-end orientation has little interaction with the head, while the NL in the plus-end orientation has a large interaction with the head, enhancing significantly the rate of ATP hydrolysis and Pi release. This is in line with the biochemical data showing that the head with mutation or deletion of its NL has a much smaller ATPase rate than the wild-type case while the mutation or deletion has no influence on ADP-release rate [41], because after ATP binding the NL docks rapidly in the plus-end orientation.

In the main text, we consider the case of saturating ATP and backward load on the stalk of the kinesin dimer (the case of non-saturating ATP is considered in Supplementary Materials). As at saturating ATP after ADP release from a head ATP can bind instantly, the nucleotide-free state of the head is not required to consider. As the head in both ATP and ADP.Pi states has the high binding energy to MT and has the similar conformation, for simplicity, we consider ATP hydrolysis and Pi release as one step of ATP transition to ADP. The pathway for the mechanochemical coupling of the kinesin dimer is schematically shown in Figure 3 [24].

We begin with both heads in ATP state, the trailing and leading ones binding strongly to tubulins II and III, respectively, on a MT filament (Figure 3a). First, consider ATP transition to ADP of the trailing head. Within t_r the trailing head detaches readily from tubulin II by overcoming pretty small affinity E_w1 and then diffuses forward. After the detached ADP-head diffusing to the position of the front MT-bound head, the strong interaction between them drives the detached head to move and rotate further to make its α6-helix’s N-terminus (to which the NL is connected) be biased in the plus-end position relative to that of the MT-bound head (see Figure 2b) [40]. This state with the two heads having the stable strong interaction is called intermediate (INT) state (Figure 3b, which is the same as Figure 2). Thus, the movement of the rear ADP-head from tubulin II to INT position drives the nano- or micro-sphere attached to the stalk to move forward by a substep of size d₁. In the INT state, with no NL interference, the closing of NBP and the large conformational change of the MT-bound ATP-head happen rapidly, reducing its binding energy to the partner ADP-head and inducing its NL docking (Figure 3c). Then, the ADP-head can diffuse either forward or backward. The forward diffusion makes the ADP-head bind to the front tubulin IV with affinity E_w2 (Figure 3d). The backward diffusion makes the ADP-head bind to the rear tubulin II with affinity E_w2 by overcoming the energy of the NL docking and the conformational change of the leading ATP-head (Figure 3e) (noting that the affinity of tubulin II for ADP-head has changed to E_w2 in time t_r). The transition from Figure 3c,d occurs with probability P_E and accordingly the transition from Figure 3c–e occurs with probability 1–P_E. The binding of the ADP-head to MT triggers the release of ADP, followed instantly by ATP binding (Figure 3a,f). Figure 3f is the same as Figure 3a except that the dimer took a forward step.

In Figure 3b, before the reduction of the binding energy of the two heads, ATP transition to ADP of the MT-bound head can occur occasionally (Figure 3g). The ADP-head then has pretty small affinity E_w1 for tubulin III for the short time period t_r (termed as Period I), during which the motor can readily dissociate from MT or slip to the adjacent tubulin by overcoming E_w1. After slipping to the adjacent tubulin, the ADP-head has affinity E_w2 for the tubulin. In Figure 3d, before ADP release from the leading head, ATP transition to ADP of the trailing head can also occur. Then, the trailing head detaches readily from tubulin III by overcoming E_w1 and moves to INT position (Figure 3h). In Figure 3h, the two heads have the high binding energy and the head has weak affinity E_w2 for MT. The period in this state is termed as Period II, during which the dimer has a large probability to dissociate from MT or slip on MT. If the motor has not dissociated until ADP release from the MT-bound head, after ATP binding (Figure 3i, where no slip was shown) the system becomes the same as Figure 3b except that the dimer was moved. In Figure 3e, before ADP release from the trailing head, ATP transition to ADP of the leading head can also occur, with the leading head diffusing to INT position (Figure 3j). During Period II of Figure 3j, the motor has a large probability to dissociate from MT or slip on MT. If the motor has not dissociated until ADP release from the MT-bound head, after ATP binding (Figure 3k, where no slip was shown) the system becomes the same as Figure 3b except that dimer was moved.

Second, consider in Figure 3a ATP transition to ADP of the leading head. The leading head detaches readily from tubulin III by overcoming pretty small affinity E_w1 and then diffuses backward (Figure 3l). From Figure 3l, the detached ADP-head can either rebind to tubulin III with affinity E_w2 in time t_r (Figure 3m) or bind to tubulin I with affinity E_w2 by overcoming the energy of the NL docking and the conformational change of the ATP-head (Figure 3n). Since t_r is very short, the transition from Figure 3l–m or to Figure 3n has approximately the same probability P_E or probability 1–P_E as the transition from Figure 3c,d or to Figure 3e. The binding of the ADP-head to MT triggers the release of ADP, followed instantly by ATP binding (Figure 3a,o). Figure 3o is the same as Figure 3a except that the motor took a backward step.

In Figure 3m, before ADP release from the leading head ATP transition to ADP can also occur in the trailing head, with the trailing head diffusing to INT position and the motor being in Period II. In Figure 3n, before ADP release from the trailing head ATP transition to ADP can also occur in the leading head, with the leading head diffusing to INT position and the motor being in Period II. During Period II, the motor has a large probability to dissociate from MT or slip on MT.

3. Stepping Dynamics

As shown before [18,24,25,26,27,42], with the above model various single molecule data about velocity, run length, forward to backward stepping ratio, dissociation rate, mechanochemical coupling ratio, asymmetric or limping stepping, etc., for both wild-type kinesin-1 homodimers and the corresponding mutant ones with extension of their NLs can be explained quantitatively and consistently. In particular, the puzzling experimental results showing that under no load the wild-type human kinesin-1 consumes about one ATP per mechanical step whereas the mutant one consumes about 3.5 ATPs per mechanical step were explained well [25,26]. The puzzling single molecule data showing that the run length of Drosophila kinesin-1 is very asymmetrical under the forward and backward loads on the stalk, with the run length for a moderate forward load being much smaller than for the backward load of the similar magnitude, were explained well [18,24,27]. The puzzling single molecule results showing that the dissociation rate of Drosophila kinesin-1 from MT under the backward load exhibits the characteristic of slip-catch-slip bonds were explained well [18,24,27]. In the following, based on the model we explain the recent experimental results about substeps and/or one-head-bound (1HB) and two-heads-bound (2HB) states of kinesin-1 in the stepping cycle.

We firstly present the expression for effective probability P_E (see Figure 3) as the function of the load. Due to the flexibility, NL cannot support the compressive force on the two ends and can solely support the stretching force. Consequently, the backward load on the stalk can only act on the NL of the head in the leading position. Hence, during diffusion of the detached head from the rear tubulin to the front MT-bound head, the backward load on the stalk acts mainly on the NL of the leading MT-bound head. The load thus would nearly have no effect on this diffusion. Then, during the further movement and rotation of the detached head to the finally stable INT state, the load on the stalk acts mainly on the NL of the detached head. Due to the strong interaction between the two heads, after the detached head reaching the front MT-bound head the detached head would have nearly 100% probability to transit to INT state even under a large backward load. Thus, under any load after the trailing head detaching from the rear tubulin it would have a nearly 100% probability to transit to INT state. From the INT state, the rate for the detached head to diffuse forward and then bind to the front tubulin can be approximately expressed as $k_{\mathrm{F}}=\left(1/t_0\right)\exp \left(-\beta F{d}^{(+)}\right)$, where 1/t₀ is the rate under no load, F is the backward load, d⁽⁺⁾ is the characteristic distance and ${\beta }^{-1}=k_{\mathrm{B}}T$ is Boltzmann constant times the absolute temperature. From the INT state, the rate for the detached head to diffuse backward and then bind to the rear tubulin can be approximately expressed as $k_{\mathrm{R}}=\left(1/t_0\right)\exp \left(\beta E_{\mathrm{D}}\right)$, where E_D is the free energy change of the NL docking and large conformational change of the head in ATP state. The above expression for k_R is under the following consideration. After the reduction of the binding energy of the two heads, firstly the backward load drives the rapid clockwise rotation of the detached head (see Figure 2) and then the detached head diffuses backward. During the latter diffusion, the load acts mainly on NL of the MT-bound head. P_E can be calculated by $P_{\mathrm{E}}=k_{\mathrm{F}}/\left(k_{\mathrm{F}}+k_{\mathrm{R}}\right)$. Substituting above expressions for k_F and k_R into above expression for P_E, we have:

$$P_{\mathrm{E}}=\frac{\exp \left(\beta E_{\mathrm{D}}\right)\exp \left(-\beta F{d}^{(+)}\right)}{\exp \left(\beta E_{\mathrm{D}}\right)\exp \left(-\beta F{d}^{(+)}\right)+1}.$$

(1)

Let k⁽⁺⁾ stand for the rate of ATP transition to ADP in the head (e.g., the trailing head) with its NL in the forward orientation and k^(–) stand for the rate of ATP transition to ADP in the head (e.g., the leading head) with its NL not in the forward orientation. As stated before [18,24,25,26,27], to be in line with the available experimental results [43,44,45,46], k⁽⁺⁾ and k^(–) are independent of the force on the two NLs. The available biochemical results indicated that ADP release is a non-rate-limiting step of the ATPase activity of the kinesin-1 head bound to MT [43]. Moreover, the dwell time in INT state is much smaller than the total dwell time between two steps [23]. Thus, from the pathway of Figure 3 the velocity of the motor can be approximately written as:

$$v=\left[P_{\mathrm{E}}{k}^{(+)}-\left(1-P_{\mathrm{E}}\right)k^{(-)}\right]d,$$

(2)

where d = 8 nm is the step size equal to the tubulin repeat period in a MT filament. From Equation (2) it is seen that if $P_{\mathrm{E}}{k}^{(+)}$ > $\left(1-P_{\mathrm{E}}\right)k^{(-)}$ the motor moves forward (toward the plus end) and if $P_{\mathrm{E}}{k}^{(+)}$ < $\left(1-P_{\mathrm{E}}\right)k^{(-)}$ the motor moves backward (toward the minus end). Thus, the moving direction of the dimer is determined by two factors. One factor is the relative magnitude between k⁽⁺⁾ and k^(–), depending on the NL orientation. The other one is P_E that is dictated by energy E_D (see Equation (1)), with NL docking increasing P_E.

From Equations (1) and (2) it is noted that to calculate the load dependency of velocity, values of four parameters k⁽⁺⁾, k^(–), E_D and d⁽⁺⁾ are required. As mentioned above, k^(–) << k⁽⁺⁾. Here, we fix k^(–) = 1 s⁻¹ (

Table 1. Values of parameters for truncated rat kinesin-1 under the experimental condition of Sudhakar et al. [23].

Parameter	k(+)	k(−)	ED	d(+)	kNL	t0
	(s−1)	(s−1)	(kBT)	(nm)	(s−1)	(ms)
value	117 ± 4	1	1 ± 0.1	3.1 ± 0.2	1500	0.24 ± 0.03

). By adjusting values of the other three parameters, with k⁽⁺⁾ = 117 ± 4 s⁻¹, E_D = (1 ± 0.1) k_BT and d⁽⁺⁾ = 3.1 ± 0.2 nm (Table 1), the single molecule data about the load dependency of velocity for the truncated rat kinesin-1 measured by Sudhakar et al. [23] can be reproduced quantitatively (Figure 4a). Notice that the ATPase rate of the motor, k⁽⁺⁾ + k^(–) = 118 s⁻¹, is in line with the biochemical results [43,47]. The small value of E_D = 1 k_BT is consistent with the experimental results indicating that the free energy change of the NL docking is smaller than 1 k_BT [48] and the AAMD simulations showing that the energy change of the large conformational change of the head induced by the binding of ATP is only about 1 k_BT [49]. In addition, from the structural data determined from the AAMD simulations (Figure 2b), it is noted that the movement of the detached ADP-head from the rear tubulin to INT position would drive the optically-trapped nanosphere attached to the stalk to move a distance of about 4 nm, giving the size of the first substep d₁ ≈ 4 nm. Thus, the second substep also has a size of d₂ = d − d₁ ≈ 4 nm. These agree with the single molecule results of Sudhakar et al. [23].

Since in the INT state, the large conformational change of the MT-bound ATP-head induces both the reduction of its binding energy to the partner ADP-head and its NL docking, it is expected that the rate of the reduction of the binding energy is nearly the same as that of the NL docking, with both rates being denoted by k_NL. Thus, the dwell time for the backward Substep 2 can be written as ${\tau }_2=1/k_{\mathrm{NL}}+t_0\exp \left(\beta E_{\mathrm{D}}\right)$. The dwell time for the forward Substep 2 can be written as:

$${\tau }_2=\frac{1}{k_{\mathrm{NL}}}+t_0\exp \left(\beta F{d}^{(+)}\right).$$

(3)

As conducted in the previous work [24], we take k_NL = 1500 s⁻¹ (see Table 1), which is in line with the biochemical results indicating that the rate constant of NL docking is larger than 800 s⁻¹ [50]. Using Equation (3) and adjusting value of t₀ = 0.24 ± 0.03 ms (Table 1), the single molecule results about the load dependency of dwell time for the forward Substep 2 of the truncated rat kinesin-1 measured by Sudhakar et al. [23] can be reproduced quantitatively (Figure 4b). The value of t₀ = 240 µs is reasonable by considering that the diffusion of the detached head requires overcoming both the large drag force on the 70-nm sphere [23] and the large elastic force arising from NL stretching [25].

In the single molecule assays of Sudhakar et al. [23], due to the rapid and large fluctuations the short dwells of the motor in INT state under the backward load F < 2 pN are unable to distinguish. As shown above, we have E_D = 1 k_BT and d⁽⁺⁾ = 3.1 nm (Table 1) for the truncated rat kinesin-1 under the experimental conditions of Sudhakar et al. [23]. Thus, the dwell time for the backward Substep 2 under any backward load is equal to the dwell time for the forward Substep 2 under the backward load $F=E_{\mathrm{D}}/d^{(+)}$ = 1.33 pN, which is smaller than 2 pN. Hence, the short dwells of the motor in INT state for the backward Substep 2 under any backward load are unable to distinguish in the experiments [23]. Accordingly, under any backward load, the measured dwell time ${\tau }_1$ for the forward Substep 1 can be calculated by:

$${\tau }_1=\frac{1}{k^{(+)}{P}_E}.$$

(4)

Using Equation (4) and parameter values presented in Table 1, the calculated results about the load dependency of dwell time for the forward Substep 1 are also consistent with the single molecule results of Sudhakar et al. [23] (Figure 4c).

In addition, it is seen from the pathway (Figure 3) that only in INT state can the motor has a weak affinity to MT and thus has a large probability to dissociate from MT or slip on MT. This implies that the dissociation or slip of the motor can occur mainly during the dwell period for Substep 2, which is also in line with the single molecule results of Sudhakar et al. [23]. Moreover, from the interaction potential of ADP-head with a MT filament (Figure 1c), it is seen evidently that the motor would slip in discrete steps of size d = 8 nm, also in line with the single molecule results of Sudhakar et al. [23]. The origin that the slip was usually observed in the optical trapping experiments of Sudhakar et al. [23] whereas the dissociation was usually observed in the traditional optical trapping experiments [12,13] can be explained as follows. In the former experiments, a 70-nm sphere was used whereas in the latter experiments a micrometer-sized sphere was used. Thus, the magnitude of the vertical component of the load relative to that of the horizontal component for the former case is much smaller than that for the latter case [42]. Hence, under the large backward load, for the former case the motor would have a larger probability to move along the MT filament (leading to slip) than that to move in the vertical direction (leading to dissociation), whereas for the latter case the motor would have a smaller probability to move along the MT filament (leading to slip) than that to move in the vertical direction (leading to dissociation).

To further verify the model, we provide predicted results about the load dependency of the mechanochemical coupling efficiency, which is defined as the reciprocal of the mean number of ATPs consumed per step (including both forward and backward steps). The number can be written as:

$$N=\frac{k^{(+)}+k^{(-)}}{P_{\mathrm{E}}{k}^{(+)}+\left(1-P_{\mathrm{E}}\right)k^{(-)}}.$$

(5)

Using Equation (5) and parameter values presented in Table 1, the predicted results are shown in Figure 5. It is seen that N ≈ 1.37 under near zero load, which is close to the prior experimental results [51,52,53]. The number of ATP molecules hydrolyzed per step rises significantly with the increase in the backward load.

Up to now, we have only focused on saturating ATP. The studies at non-saturating ATP are given in Supplementary Materials. With the pathway of kinesin stepping at non-saturating ATP (Figure S1), the contradictory single molecule results about the dependency of lifetime of 1HB state and that of 2HB state in the stepping cycle on ATP concentration observed by different research groups can be explained quantitatively (Figures S2 and S3). For example, the single molecule results measured by Isojima et al. [54] for cysteine-light human kinesin-1 showed that the lifetime of 1HB state increases significantly with the decrease of ATP concentration whereas the lifetime of 2HB state changes insensitively with the change of ATP concentration (Figure S2). By contrast, the single molecule results measured by Mickolajczyk et al. [55] for truncated Drosophila kinesin-1 showed that the lifetime of 2HB state increases greatly with the decrease of ATP concentration whereas the lifetime of 1HB state has a small increase with the decrease of ATP concentration (Figure S3). The contradictory results for the ATP-concentration dependency of the lifetime of 1HB and that of 2HB are due to different values of the high binding energy between the MT-bound nucleotide-free head and the partner ADP-head, which are in turn due to different kinesin-1 species and different buffer conditions used in different assays. Moreover, the single molecule results of Sudhakar et al. [23] about the dependencies of velocity, dwell time for the forward Substep 1 and dwell time for the forward Substep 2 on the backward load at low ATP concentration (10 μM) for the truncated rat kinesin-1 motor can also be reproduced well (Figure S4).

4. Concluding Remarks

The recent single molecule results of Sudhakar et al. about stepping mechanics [23] and the single molecule results about lifetimes of 1HB and 2HB states in the stepping cycle [23,54,55] for kinesin-1 motors are explained well with the model shown schematically in Figure 3. In prior studies, with the model various experimental results for both wild-type kinesin-1 motors and the mutant ones with extension of their NLs were explained quantitatively and consistently [18,24,25,26,27,42]. Moreover, with the model, the single molecule results for other families of N-terminal kinesin motors such as kinesin-2, kinesin-3, kinesin-5, kinesin-8, kinesin-12, orphan kinesin PAKRP2, etc., were also explained well and consistently [27,28,29,30]. All of these support strongly the model, deepening greatly our understanding of the mechanism of mechanochemical coupling of the N-terminal kinesin motors. To further verify the model it is hoped to test the predicted results (Figure 5) by future experiments.