Kinesin's biased stepping mechanism: amplification of neck linker zippering

Abstract

A physically motivated model of kinesin's motor function is developed within the framework of rectified Brownian motion. The model explains how the amplification of neck linker zippering arises naturally through well-known formulae for overdamped dynamics, thereby providing a means to understand how weakly-favorable zippering leads to strongly favorable plus-directed binding of a free kinesin head to microtubule. Additional aspects of kinesin's motion, such as head coordination and rate-limiting steps, are directly related to the force-dependent inhibition of ATP binding to a microtubule bound head. The model of rectified Brownian motion is presented as an alternative to power stroke models and provides an alternative interpretation for the significance of ATP hydrolysis in the kinesin stepping cycle.

FIGURE 1

A doubly-bound kinesin dimer oriented with the microtubule plus-end to the right. The N-terminal kinesin heads can bind to tubulin (,–43). The kinesin heads are connected by two neck linkers, ∼15 amino acids each (4), and these neck linkers end in a coiled-coil “stalk” that can connect cargo through light chains and mediate tension, indicated by F (the load force). Entropic considerations for the neck linkers suggest a thermal force, F_th, which resists neck linker extension. A microtubule-bound head in an ATP or hydrolyzed ATP (ADP.P) state will initiate immobilization (zippering) of its neck linker onto itself through a series of hydrogen bonds, schematically indicated by hatched lines. This figure outlines structures found in Protein Data Bank file: 1IA0 (43).

FIGURE 2

Key aspects of kinesin's forward (plus-end) cycle have been elucidated through a varied multitude of experiments, including cryo-EM, x-ray structural, force bead, and others (,,,–48). This process is briefly reviewed, where T labels the ATP nucleotide state, D the ADP nucleotide state, * the no-nucleotide state, and P the phosphate after ATP hydrolysis. The free head is shaded to clarify motion between frames. Frames 1,2: the free head weakly binds to the plus-end binding site, leading to strong binding once ADP is released. ATP binding to the plus-end head is inhibited by a coordinating mechanism (labeled T-gate; see subsection T-Gate) that is activated by the internal strain. Frames 3–5: hydrolysis of ATP in the minus-end head leads to an intermediate ADP-phosphate state, D.P, and phosphate release alters the binding of the minus-end head into weak binding, which allows rapid release of the minus-end head from tubulin (14). Frame 5 is to be identified with the parked state in Carter and Cross (2). Frame 6: the free head tends not to strongly bind until ATP binds to the microtubule-bound head (34). ATP binding initiates zippering of the microtubule-bound head's neck linker, coinciding with a large acceleration of the rate for the free head to bind onto microtubule. This entire forward cycle consumes one ATP and moves the center of mass of the system ∼8 nm.

FIGURE 3

Plots of zippered and unzippered stationary probability densities (in arbitrary units) versus the reduced interval [−d, d] (see Neck Linkers and the Coiled-Coil Neck and Eq. 11), for the case example in Biasing Mechanism that ignores the effects of weak state unbinding. The use of the reduced interval, which subtracts the coiled-coil extension, hides the fact that zippering is a small change (∼2 nm) compared to the distance traveled by one head (∼16 nm). Zippering probabilities, e.g., Eq. 3, are not represented in these plots. As discussed in Basic Biasing Mechanism and the Heuristic Model of Bias, the small and decreasing tails of the distribution are responsible for the generation of large biases. Apparent in these plots are the competing influences of zippering, which shifts the density toward the plus-end, and of loads, which shifts the density toward the minus-end. Stall occurs when all these effects balance one another. The inclusion of weak state unbinding in the model preserves many of the features presented here.

FIGURE 4

Much of the biasing mechanism is assumed to occur in the parked geometry of frame 5 in Fig. 2, where the external load acting on the microtubule-bound head leads to long dwell times (see Waiting Mechanism). However, the free head could have, in the time before ATP uptake, an opportunity to bind rearward during a period when forward binding is virtually excluded (due to no zippering). Thus, bias would then be [ATP] dependent due to [ATP] dependence of the waiting mechanism. In panel a, a fast step is outlined that corrects this undesired backward stepping. Since the forward head experiences strain due to the rearward-bound head, ATP uptake is greatly inhibited in the forward head, and thus, there exists a much larger probability that the rearward head detaches first (at the expense of one ATP hydrolysis). In contrast, panel b outlines how a “real” backward step may occur once the waiting mechanism has ended, i.e., once ATP has bound to the microtubule-bound head. Notice that if the rearward head binds as in panel b, the forward head is at least one chemical step ahead of the rearward head. With a few assumptions, the forward head in panel b may then be expected to release first on average. Events in panel b where instead the rearward head unbinds will alter the simple relation between binding and stepping direction, but these (potentially uncommon) events are ignored at the level of detail in this article.

FIGURE 5

Panel a illustrates a rate model to minimally describe T-gate's effect on dwell times (actually, the steady-state natural lifetime). Such a simple model would doubtfully predict detailed measurements, e.g., the randomness (49). The dashed region that contains abstract states s₁ and s₂ describes the overall ATP uptake mechanism, which includes T-gate within a Michaelis-Menten structure. The state s₃ represents the remainder of kinesin's chemical cycle. A particular form of the force-dependent rate, k(F) = 1/τ(F), is taken from Eq. 10. Panel b provides a plot of dwell times from the rate model in panel a with parameters deduced by fitting to the model of Nishiyama et al. (33), fitting with better than visual accuracy. That the agreement with Nishiyama et al. is excellent is likely a result of the choice in Eq. 10, but this is not to state that our rate model is identical with theirs (e.g., in the manner [ATP] dependence is included). Used in panel b: δ = 3.10 nm, R₀ = 193, , k₋ = 137 s⁻¹, k(0) = 857 s⁻¹, k₃ = 137 s⁻¹, and T = 300 K.

FIGURE 6

A network diagram to describe the bias of kinesin's step, providing the rates necessary for Eq. 20. The value s₀ represents the reduced interval, the state where one kinesin head remains unbound. The values s₊ and s₋ represent the plus- and minus-end weak binding states, respectively. J is the steady-state probability current entering the process (due to kinesin binding ATP to the microtubule-bound head), and J₊, J₋ are the exiting currents (due to strong binding transitions). The labels are given to the rates of weak binding from a diffusing state, to the rates of weak state unbinding (e.g., from Eq. 4), and to the rates of strong binding. As a simplification, the strong binding rates equal a constant k^S that is independent of load. The essential irreversibility of the strong binding step corresponds to a large free energy decrease for strong binding transitions (consistent with the RBM principle).