Dynamics of kinesin motor proteins under longitudinal and sideways loads
Introduction
Kinesins constitute a superfamily of motor proteins, which can move on microtubule (MT) powered by the hydrolysis of ATP molecules, performing functions of transporting cargo, regulating MT dynamics, segregating chromosome during mitosis, etc., in cells (Vale, 2003, Miki et al., 2005, Hirokawa et al., 2009). The superfamily can be divided into 15 families, including kineins-1 through kinesin-14 families and an ungrouped family called orphan kinesins (Lawrence et al., 2004). For members of kinesin-1 through kinesin-12 families and orphan kinesin PAKRP2 their motor domains (also called heads) are located in the N-terminus of the polypeptide, for members of kinesin-14 family their heads are located in the C-terminus of the polypeptide, while for members of kinesin-13 family their heads are located in the middle of the polypeptide. In this work, we focus on the N-terminal kinesin dimers, with the two heads being connected together by a coiled-coil stalk via their two flexible neck linkers (NLs). Except for some members of kinesin-5 family which can move processively towards both the minus and plus ends of MT (Singh et al., 2018), most of the N-terminal kinesin dimers can move processively towards the plus end.
To explore the chemomechanical coupling mechanism of the N-terminal kinesin dimers that move processively on MT by hydrolyzing ATP, here we take six species of the N-terminal kinesin dimers, including Loligo pealei kinesin-1, Drosophila kinesin-1, truncated kinesin-5/Eg5, truncated kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB dimers, as examples to study the motor dynamics. It was determined that these motors advance stepwise over the MT surface lattice in about 8.2 nm increments, the tubulin hetrodimer repeat distance, and moves towards the plus end of MT in a hand-over-hand manner (Asbury et al., 2003, Yildiz et al., 2004). By using single-molecule optical trapping methods, the dynamics of these motors under longitudinal load (i.e., the load in the direction opposite to or along the moving direction) has been studied in details (Nishiyama et al., 2002, Carter and Cross, 2005, Milic et al., 2014, Milic et al., 2017, Milic et al., 2018, Andreasson et al., 2015a, Valentine et al., 2006, Valentine and Block, 2009). The single-molecule data showed that different kinesin dimers have very different features on the dependences of run length and dissociation rate upon the longitudinal load (Milic et al., 2017, 2018). The dynamics of Loligo pealei kinesin-1 under sideways load has also been studied using single-molecule optical trapping methods (Block et al., 2003). In contrast to the case under the longitudinal load, where a backward load (i.e., a load in the direction opposite to the moving direction) affects sensitively the velocity and a backward load of about 6 pN can lead to stall of the motor, a sideways load of as much as 8 pN has only a weak effect on the velocity (Block et al., 2003). For example, a rightward load of 8 pN caused the velocity to decrease by only about 15% relative to the unloaded velocity (Block et al., 2003). Here, ‘rightward’ is defined as the direction of loading as seen by an observer facing in the direction of kinesin motion along the MT filament. However, even a small sideways load can cause a large reduction in the run length (Block et al., 2003), which is similar to the case under the forward load but is contrast to the case under the backward load where a small backward load causes only a small decrease of the run length (Milic et al., 2014, Andreasson et al., 2015a).
A lot of works have been presented to study theoretically and numerically the dynamics of the N-terminal kinesin motor such as kinesin-1 (Fisher and Kolomeisky, 2001, Liepelt and Lipowsky, 2007, Khataee and Wee-Chung Liew, 2014, Sumi, 2017, Wang et al., 2017, Sasaki et al., 2018, Mugnai et al., 2020). These prior studies were generally based on the kinetic models with the chemomechanical coupling cycle being reduced to a network of intermediate chemical states connected by load-dependent transition rates. Although the studies can explain the experimental data on the dependences of velocity, stepping ratio, etc., upon longitudinal load, they generally predicted that the dissociation rate increases monotonically with the increase in the magnitude of the external load. This cannot explain the experimental data showing that, for example, with the increase in the magnitude of the backward load, the dissociation rate increases firstly and then decreases for kinesin-2/Kif17 (Milic et al., 2017), the dissociation rate changes only slightly for kinesin-5/Eg5 (Milic et al., 2018) while the dissociation rate decreases monotonically for kinesin-12/Kif15 (Milic et al., 2018) (see Section 5). Thus, a general theory that can give a consistent and quantitative explanation of the available experimental data on the dependences of velocity, run length, dissociation rate, etc., upon the longitudinal load for different kinesin species is lacking. The physical mechanism of different species having very different features on the curve of dissociation rate and/or run length versus the longitudinal load is unclear. In addition, theoretical studies on the dynamics of the kinesin motors under sideways loads have not been paid much attention (Fisher and Kim, 2005). In particular, even a qualitative explanation of the dramatic effect of the sideways load on the run length is unavailable. The origin of the sideways load affecting weakly the velocity but affecting strongly the run length is unclear. Clarifying the above issues has strong implications for the molecular mechanism of the processive motion of the kinesin motors.
To address these unclear issues, here we modify the model presented before (Xie et al., 2019, Xie, 2020). With the previous model, the dependences of the velocity, stepping ratio, etc., upon the longitudinal load for kinesin-1 have been studied analytically whereas the effect of the sideways load as well as the dissociation rate and run length have not been considered (Xie et al., 2019, Xie, 2020). Here, based on the modified model we provide a consistent, analytical study of the dynamics, such as velocity, stepping ratio or backstepping probability, run length, dissociation rate, chemomechanical coupling efficiency, etc., of the six species of kinesin dimers under both the longitudinal and sideways loads, explaining consistently and quantitatively the available experimental data and moreover providing predicted results.
Section snippets
Model
It is proposed here that the N-terminal Loligo pealei kinesin-1, Drosophila kinesin-1, kinesin-5/Eg5, kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB motors share the same chemomechanical coupling mechanism. The model for the mechanism can be illustrated schematically in Fig. 1, which is modified from that presented previously (Xie et al., 2019, Xie, 2020). There are three main elements, on the basis of which the model is built up.
(i) A kinesin head in nucleotide-free, ATP or ADP.Pi
Under longitudinal load
In this section, on the basis of the model (Fig. 1) we derive equations for the dynamics of a kinesin dimer under the longitudinal load on the stalk. Considering the collision of the bead with MT in the experimental setup, both the x-component (Fx) and y-component (Fy) of the load are present and no z-component (Fz) is present (i.e., Fz = 0), with , where and , with RB being the radius of the bead and lK = 35 nm being the kinesin stalk length. Throughout,
Parameter values
In this work, we consider six species of kinesin: Loligo pealei kinesin-1, Drosophila kinesin-1, kinesin-5/Eg5, kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB. We firstly present a detailed discussion of the choice of the parameter values for Loligo pealei kinesin-1. Then, we briefly discuss the choice of the parameter values for other species.
The first species is Loligo pealei kinesin-1, with a bead of radius RB = 250 nm attached to the stalk, as used in the experiments of Block et al.
Dynamics of Loligo pealei kinesin-1
As shown before (Guo et al., 2017, Guo et al., 2018), for kinesin-1, due to the large internally elastic force, upon Pi release the ADP-head can easily escape from the potential well of depth Ew1 and then diffuse to INT position. Thus we take P0(0) = 1. In Fig. 2a – c we show the dependences of velocity v, run length L and dissociation rate upon longitudinal load for Loligo pealei kinesin-1. It is seen that the theoretical results are in agreement with the prior single-molecule data (Block et
Concluding remarks
In this work, with our proposed model (Fig. 1) we study theoretically the dynamics of six N-terminal kinesin dimers including Loligo pealei kinesin-1, Drosophila kinesin-1, truncated kinesin-5/Eg5, truncated kinesin-12/Kif15, kinesin-2/Kif17 and kinesin-2/Kif3AB under longitudinal and sideways loads acting on the stalk of the dimers. The theoretical results about the load dependences of velocity, run length, dissociation rate, backstepping probability, etc., reproduce quantitatively the
Author contributions
P.X. proposed the model, made analysis, and wrote the manuscript.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 11775301).
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