The final project of PHY2018 Stochastic Processes. Thanks for Prof Anton Zilman’s valuable comments and I tried to improve this post according them. For an introduction of kinesin from a biological view, check the Chinese post 细胞生物学.

Introduction

A molecular machine, nanite, or nanomachine is a molecular component that produces quasi-mechanical movements (output) in response to specific stimuli (input) 1, whose functions are tunable under non-equilibrium conditions. Molecular machines can be divided into two broad categories; artificial and biological. 1

Artificial molecular machines

Artificial molecular machines refer to molecules that are artificially designed and synthesized 1, and these molecules machines might be promising to address several bottleneck problems. For example, people need smaller and smaller switching devices in integrated circuit design, while have come across difficulties in minimizing the existing semiconductor whose size is reaching the wavelength of radiation in use. small self-assembly molecules might be promising to play the role of nanoscale switching devices. In 1994, Bissell et al. reported a molecular shuttle consisting of a ring and an axle with two docking sites (Fig. 1). Naturally, the ring preferred to dock at the benzidine station (84%). If the benzidine site were charged positively, either by electrochemical oxidation or protonation, the ring would prefer to bind at the other site, the biphenol station 2.

Fig. 1 The structure of the molecular shuttle consists of a ring and an axle with two docking sites. Under different conditions, the ring prefer different docking sites, which makes it ‘tunable’. 2

Biological molecular machines

Biological molecular machines are commonly found in nature and have evolved into their forms after abiogenesis on Earth 1. Function in a regulated chemical reaction network, a common “force” that drives the systems away from equilibrium is ATP. Motor proteins such as myosin and kinesin can move along the cytoplasm of cells by converting the chemical energy of ATP into mechanical movement 3. These movements are complex to decode. Over decades, researchers have been working on a detailed reaction mechanism. Multiple techniques have been applied. Warshaw et al. labelled the two heads of myosin with quantum dots to visualize the hand-over-hand processivity directly 4. The research may also matter for human well-being. Using single-molecule fluorescent imaging and model simulation, Nelson et al. pinpointed the spatial point where a super relax (SRX) state of myosin happens along the filament (C-zone). Furthermore, they provided potential evidence of the misregulation of a protein at the C-zone and diseases of muscle wrong function 5.

In this report, I will focus on more than two decades of work on the mechanism of kinesin, a protein motor that moves from the negative pole to the positive pole of the microtubule (MT) filament in cells powered by ATP. The structure of kinesin consists of two heads process hand-over-hand along MT, a neck linker with two tangled threads, and a light chain which combines the load it is carrying (Fig. 2). The active movement of kinesins supports several cellular functions, including mitosis, meiosis and transport of cellular cargo 6.

Fig. 2 Kinesin moves from the negative pole to the positive pole of a microtubule filament 6.

Results

Kinesin hydrolyses one ATP per 8-nm step

Kinesin is an ATPase which hydrolyzes ATP molecules and converts the energy for its motion. In 1994, Svoboda et al. showed that the velocity of the motion and the ATP concentration has a Michaelis-Menten-like relationship 7 (See Eq. 2 in the next subsection). A core question about how many molecules of ATP are consumed per step was raised. Since direct measurements of ATPase activity were unreliable in practice, in 2000, Schnitzer et al. took advantage of statistical mechanics to analyze intervals (converted to a measurement of the Fano factor) between steps to address this problem as models of a continuous time Markov chain. The experimental data were obtained with optical tweezers 8,9.

The randomness number of time intervals is defined by

where \(n\) is the number of the states of a kinetic model, which places a limit on the complexity of potential kinetic mechanisms. This research was used to reveal the number of rate-liming transitions. They found that at limiting [ATP], where the dynamic is dominated by ATP loading time, r is slightly larger than 1. That implies only one ATP per step. However, at saturating [ATP], r dropped to about \(1/2\). That implies at least two additional states in the kinetic model (Fig. 3). That ruled out the one-to-many and many-to-one coupling of ATP and a step as a common mechanism. (Anton: Comes a bit abruptly, The reader does not know what this is or why it was a subject of a debate. Shi: haven’t got a great answer yet…)

Fig. 3 Semilogarithmic plot of the randomness parameter, r, versus ATP concentration 8.

A load-dependent Michaelis-Menten relationship

In 1999, Visscher et al. applied a molecular force clamp to obtain experimental data under different [ATP] and loads. They found that, in the Michaelis-Menten relationship of [ATP] and velocity,

where \(d\) is the length of the step (~\(8nm\)), “cat” stands for “catalysis” and “b” stands for “binding”, and \(k_{cat}\) and \(k_b\) are loads limited. They found with increasing loads, \(V_{max}\) decreases and \(k_m\) increases, which means kb must decrease faster. They predicted \(v_{max}\) and \(k_m\) should derive from two independent, mechanically sensitive rates 10.

To explain it, Schnitzer et al. in 2000 proposed a possible mechanochemical cycle (Fig. 4) which can fit the above data obtained from the force clamp experiment well (Fig. 5). They proposed the load shifts the energy landscape between the rapid conformationally composite state towards the reward substrate. The load lowers the rate constant, \(k_2\), for proceeding onwards in the cycle from the forward conformation, thereby lowering \(k_{cat}\). It also increases the reverse rate constant, \(k^{-1}\), leading to increased unbinding of ATP from the rearward conformation and thereby reducing ATP affinity. The picture proposed by the model is that the forward rates of the first ~\(4nm\) isomerization are greatly reduced by load, which becomes the rate-limiting process under a relatively large load 11.

Fig. 4 Proposed mechanochemical cycle of kinesin 11.

Fig. 5 Global fit of the Michaelis-Menten relationship between velocity, [ATP], and load.

Kinesin processivity is gated by phosphate release

How the energy consumed from ATP is used in the process is still unclear. One of the predictions of the above model is that the ‘trapping’ of the mobile neck linker concomitant with ATP binding by one head may enable ongoing conformational fluctuations in the partner head to become mechanically productive, thereby triggering ADP release and forward movement. The energy of ATP hydrolysis is used to prevent the next ATP hydrolysis before a mutual step rather than driving the conformational change. However, this remained a hypothesis to be tested. In 2014, Milic et al.’s experiment proposed another mechanism.

From optical trapping experiments, increasing the steady-state population of the post-hydrolysis ADP·Pi state (by adding free Pi in solution) nearly doubled the kinesin run length, reducing either the ATP binding rate or hydrolysis rate had no effects 12. Thus, the sequence should be ATP binding, rear head forward, ATP hydrolysis, rear head binds at the front, and former front head unbind (Fig. 6).

Fig. 6 Comparison of the proposed model for the kinesin mechanochemical cycle and the prevailing model 12.

Inter-head tension and gating mechanism

Gating means the state of one head influences its partner to ensure that the mechanochemical cycles of the heads are maintained out of phase so that the hand-over-hand processivity of kinesin will not be failed by disassociation or futile ATP hydrolysis. Former work supposes how the neck linker and the tension within the neck linker may accomplish the two heads’ communication.

To examine this, Andreasson et al. release the tension within the neck linker by inserting extra amino acid into it to make it longer, test their performance, and then summarized their conclusions in a minimal 3-state model (Fig. 7). The model was built above Milic et al.’s scheme. It consists of a load-dependent force-producing mechanical step ([1] -> [2]), which is the rate-limiting process under moderate load, the ATP hydrolysis event ([2] -> [3]), which is a sole biochemical process independent of mechanical force, and the rear head release ([3] -> [1]) process, which depend on both external load and inter-head tension. Coordinating the data and the model, they proposed that the gating mechanism responsible for processivity in the 2-HB state does not require inter-head tension, but rather occurs through modulation of the rates of biochemical processes occurring at the front head, including ATP hydrolysis and possibly productive ATP binding (mainly front-head gating) 13.

Fig. 7 The minimal 3-state model 12.

Discussion

Definitely, we never “see” the animation like (Fig. 2) or the mechanochemical cycle like (Fig. 4) or (Fig. 6), since our ability to “see” is too weak to detect a mechanism of all range of spatial and temporal resolution. We can only penetrate the problem step by step by inferring and guessing.

First, researchers proposed the 1:1 coupling of ATP consuming and an 8nm step by statistical mechanics. Then, researchers proposed how the isomerization change depends on the load by fitting the experimental data within a model involving a view of the energy landscape. However, researchers overturn some aspects of the model by experimental data supporting their points, in particular, the stage of the ATP hydrolysis within the cycle. This discrepancy led to different inferences about how energy is used in mechanical motion. Researchers tried to decode the external load force and internal inter-head tension by experiments on mutant kinesin with a longer neck linker (lower inter-head tension) and then proposed a front-gating mechanism.

As discussed in “the introduction”, investigating the complete description of the mechanism is a significant core goal. We may figure out some clues about human diseases caused by the misregulation of these mechanisms. From an evolutional point of view, we may also find how the selected structure optimizes the function. For example, the regulation of load and [ATP] dependent disassociation enable reliable transport of reasonable load but facilitate necessary disassociation when stuck by other intracellular macromolecules, such as actin filament 11. Also, neck linker length is optimized for processivity under hindering loads or unloaded conditions 12. These might be “design principles” if we want to improve our artificial molecular machines.

However, as discussed before, limited by our poor “resolution”, these interpretations of mechanisms come from inference. From the related papers, we often find “there are three candidate explanations, we favor one of them by ruling out the other two”. The authenticity of this reasoning depends on how rigorous the “ruling out” argument is, and the imagination of considering all candidates. We can reach a logically plausible conclusion, but always be aware that it might be turned over in the future.

References

[1] Molecular machine. (2022, June 10). In Wikipedia. online

[2] Bissell, Richard A., et al. “A chemically and electrochemically switchable molecular shuttle.” Nature 369.6476 (1994): 133-137. online

[3] Motor protein. (2022, December 14). In Wikipedia. online

[4] Warshaw, David M., et al. “Differential labeling of myosin V heads with quantum dots allows direct visualization of hand-over-hand processivity.” Biophysical journal 88.5 (2005): L30-L32. online

[5] Nelson, Shane R., et al. “Imaging ATP consumption in resting skeletal muscle: one molecule at a time.” Biophysical Journal 119.6 (2020): 1050-1055. online

[6] Kinesin. (2022, December 3). In Wikipedia. online

[7] Svoboda, K. & Block, S. M (1994). Force and velocity measured for single kinesin molecules. Cell 77, 773–784. online

[8] Schnitzer MJ & Block SM (1997). Kinesin hydrolyses one ATP per 8-nm step. Nature 388, 386–390. online

[9] Moffitt, J. R., & Bustamante, C. (2014). Extracting signal from noise: kinetic mechanisms from a Michaelis-Menten-like expression for enzymatic fluctuations. The FEBS journal, 281(2), 498–517. online

[10] Visscher K, Schnitzer MJ & Block SM (1999) Single kinesin molecules studied with a molecular force clamp. Nature 400, 184–189. online

[11] Force production by single kinesin motors. MJ Schnitzer, K Visscher, SM Block (2000) Nature cell biology 2 (10), 718-723. online

[12] Milic B, Andreasson JOL, Hancock WO, Block SM. 2014. Kinesin processivity is gated by phosphate release. Proceedings of the National Academy of Sciences of USA 111:14136–14140. online