Direct observation of intermediate states during the stepping motion of kinesin-1

Tension-induced suppression of allosteric conformational changes coordinates kinesin-1 stepping

Kinesin-1 walks along microtubules by alternating ATP hydrolysis and movement of its two motor domains ("head"). The detached head preferentially binds to the forward tubulin-binding site after ATP binds to the microtubule-bound head, but the mechanism preventing premature microtubule binding while the partner head awaits ATP remains unknown. Here, we examined the role of the neck linker, the segment connecting two heads, in this mechanism. Structural analyses of the nucleotide-free head revealed a bulge just ahead of the neck linker's base, creating an asymmetric constraint on its mobility. While the neck linker can stretch freely backward, it must navigate around this bulge to extend forward. We hypothesized that increased neck linker tension suppresses premature binding of the tethered head, which was supported by molecular dynamics simulations and single-molecule fluorescence assays. These findings demonstrate a tension-dependent allosteric mechanism that coordinates the movement of two heads, where neck linker tension modulates the allosteric conformational changes rather than directly affecting the nucleotide state.

Factors Determining Kinesin Motors in a Predominant One-Head-Bound or Two-Heads-Bound State During Its Stepping Cycle

At physiological or saturating ATP concentrations, some families of kinesin motors, such as kinesin-1 and kinesin-2, exhibit a predominant two-heads-bound (2HB) state during their stepping cycle on microtubules, while others, such as kinesin-3, exhibit a predominant one-head-bound (1HB) state. An interesting but unclear issue is what factors determine a kinesin motor in the predominant 1HB and 2HB states. Here, on the basis of the general chemomechanical pathway of the kinesin motors, a theory is given on fractions of 1HB and 2HB states. With the theory, the factors affecting a kinesin motor in the predominant 1HB and 2HB states are determined. The results about the effects of ATP concentration, ADP concentration and external load on the fractions of 1HB and 2HB states are presented. Furthermore, the theory is applied to kinesin-1, kinesin-2, kinesin-3, kinesin-5 and kinesin-13 motors, with the theoretical results agreeing well with published experimental data.

Kinetic regulation of kinesin's two motor domains coordinates its stepping along microtubules

The two identical motor domains (heads) of dimeric kinesin-1 move in a hand-over-hand process along a microtubule, coordinating their ATPase cycles such that each ATP hydrolysis is tightly coupled to a step and enabling the motor to take many steps without dissociating. The neck linker, a structural element that connects the two heads, has been shown to be essential for head-head coordination; however, which kinetic step(s) in the chemomechanical cycle is 'gated' by the neck linker remains unresolved. Here, we employed pre-steady-state kinetics and single-molecule assays to investigate how the neck-linker conformation affects kinesin's motility cycle. We show that the backward-pointing configuration of the neck linker in the front kinesin head confers higher affinity for microtubule, but does not change ATP binding and dissociation rates. In contrast, the forward-pointing configuration of the neck linker in the rear kinesin head decreases the ATP dissociation rate but has little effect on microtubule dissociation. In combination, these conformation-specific effects of the neck linker favor ATP hydrolysis and dissociation of the rear head prior to microtubule detachment of the front head, thereby providing a kinetic explanation for the coordinated walking mechanism of dimeric kinesin.

Sustainable Synthesis, Characterization, Cellular Effects of Gold Nanoparticles and Their Applications as Therapeutics in Cancer Therapy

In recent years, gold nanoparticles (AuNPs) have attracted much attention due to their extensive applications in fields such as biomedicine, electronics, catalysis, and environmental science. However, traditional chemical methods for AuNPs synthesis present certain challenges, such as the use of harsh chemicals and high energy consumption. These limitations have led to the development of alternative, sustainable synthesis methods that are efficient, cost-effective, and environmentally friendly. These methods focus on the principle of green chemistry, utilizing renewable biomass sources (e.g., plant tissues, bacteria, fungi, and algae) and nontoxic solvents to minimize environmental impact. Biomolecules derived from biomass, such as polyphenols, proteins, and unsaturated fatty acids, enable the synthesis of AuNPs under mild and eco-friendly conditions. This review provides a comprehensive overview of recent advancements in the sustainable synthesis and applications of AuNPs. It summarizes the specific active compounds that drive the reduction and stabilization of AuNPs. It also explores the characterization techniques and underlying mechanisms involved in synthesis. Furthermore, their cellular effects and long-term safety are discussed, along with their extensive applications in biomedical fields, including bioimaging and cancer therapies. Finally, the potential of AuNPs is summarized, highlighting future perspectives as well as emerging opportunities and challenges in biological applications.

Impact of physiological ionic strength and crowding on kinesin-1 motility

The motility of biological molecular motors has typically been analyzed by in vitro reconstitution systems using motors isolated and purified from organs or expressed in cultured cells. The behavior of biomolecular motors within cells has frequently been reported to be inconsistent with that observed in reconstituted systems in vitro. Although this discrepancy has been attributed to differences in ionic strength and intracellular crowding, understanding how such parameters affect the motility of motors remains challenging. In this report, we investigated the impact of intracellular crowding in vitro on the mechanical properties of kinesin under a high ionic strength that is comparable to the cytoplasm. Initially, we characterized viscosity in a cell by using a kinesin motor lacking the cargo-binding domain. We then used polyethylene glycol to create a viscous environment in vitro comparable to the intracellular environment. Our results showed that kinesin frequently dissociated from microtubules under high ionic strength conditions. However, under conditions of both high ionic strength and crowding with polymers, the processive movement of kinesin persisted and increased in frequency. This setting reproduces the significant variations in the mechanical properties of motors measured in the intracellular environment and suggests a mechanism whereby kinesin maintains motility under the high ionic strengths found in cells.Key words: kinesin motility, molecular crowding, ionic strength, intracellular transport, processivity of molecular motors.

Multiple kinesins speed up cargo transport in crowded environments by sharing load

Kinesin motors transport cargoes along microtubules inside of cells. Although it is well known that the cargoes are typically carried by multiple kinesins and that the more motors used, the further the cargoes travel, it has been challenging to determine the number of motors moving a cargo and any instant. Further, there is no unified statement on the relationship between cargo velocity and motor number, especially in the presence of a very crowded cytoplasmic environment. Here, we use a non-invasive method to quantify instantaneous motor number, and use it to investigate the effects of crowded environments on cargo motion when it is carried by multiple kinesins. Our experiments reveal that the velocity of the cargo depends on the number of motors on the cargo and the size of the crowders in crowded environments. Our finding suggests that kinesin tension plays a role in collective motion, which has been confirmed through stochastic kinesin simulations. Overall, our study demonstrates the broad applicability of the non-invasive method to determine engaged motor numbers and sheds light on the intriguing interplay between macromolecular crowding, kinesin tension, and kinesin-mediated cargo transport.

Mechanism and regulation of kinesin motors

Kinesins are a diverse superfamily of microtubule-based motors that perform fundamental roles in intracellular transport, cytoskeletal dynamics and cell division. These motors share a characteristic motor domain that powers unidirectional motility and force generation along microtubules, and they possess unique tail domains that recruit accessory proteins and facilitate oligomerization, regulation and cargo recognition. The location, direction and timing of kinesin-driven processes are tightly regulated by various cofactors, adaptors, microtubule tracks and microtubule-associated proteins. This Review focuses on recent structural and functional studies that reveal how members of the kinesin superfamily use the energy of ATP hydrolysis to transport cargoes, depolymerize microtubules and regulate microtubule dynamics. I also survey how accessory proteins and post-translational modifications regulate the autoinhibition, cargo binding and motility of some of the best-studied kinesins. Despite much progress, the mechanism and regulation of kinesins are still emerging, and unresolved questions can now be tackled using newly developed approaches in biophysics and structural biology.

Rational engineering of DNA-nanoparticle motor with high speed and processivity comparable to motor proteins

DNA-nanoparticle motor is a burnt-bridge Brownian ratchet moving on RNA-modified surface driven by Ribonuclease H (RNase H), and one of the fastest nanoscale artificial motors. However, its speed is still much lower than those of motor proteins. Here we resolve elementary processes of motion and reveal long pauses caused by slow RNase H binding are the bottleneck. As RNase H concentration ([RNase H]) increases, pause lengths shorten from ~70 s to ~0.2 s, while step sizes (displacements between two consecutive pauses) are constant ( ~ 20 nm). At high [RNase H], speed reaches ~100 nm s-1, however, processivity (total number of steps before detachment), run-length, and unidirectionality largely decrease. A geometry-based kinetic simulation reveals switching of bottleneck from RNase H binding to DNA/RNA hybridization at high [RNase H], and trade-off mechanism between speed and other performances. An engineered motor with 3.8-times larger DNA/RNA hybridization rate simultaneously achieves 30 nm s-1 speed, 200 processivity, and 3 μm run-length comparable to motor proteins.

Biased movement of monomeric kinesin-3 KLP-6 explained by a symmetric Brownian ratchet model

Most kinesin molecular motors dimerize to move processively and efficiently along microtubules; however, some can maintain processivity even in a monomeric state. Previous studies have suggested that asymmetric potentials between the motor domain and microtubules underlie this motility. In this study, we demonstrate that the kinesin-3 family motor protein KLP-6 can move forward along microtubules as a monomer upon release of autoinhibition. This motility can be explained by a change in length between the head and tail, rather than by asymmetric potentials. Using mass photometry and single-molecule assays, we confirmed that activated full-length KLP-6 is monomeric both in solution and on microtubules. KLP-6 possesses a microtubule-binding tail domain, and its motor domain does not exhibit biased movement, indicating that the tail domain is crucial for the processive movement of monomeric KLP-6. We developed a mathematical model to explain the biased Brownian movements of monomeric KLP-6. Our model concludes that a slight conformational change driven by neck-linker docking in the motor domain enables the monomeric kinesin to move forward if a second microtubule-binding domain exists.

Tracking Single Kinesin in Live Cells Using MINFLUX

MINFLUX is a super-resolution fluorescence microscopy technique that enables single-molecule tracking in live cells at a single-nanometer spatial and sub-millisecond temporal resolution. This chapter describes a method for tracking fluorescently labeled human kinesin-1 in live cells using MINFLUX and analyzing kinesin stepping dynamics.

Visualizing Single V-ATPase Rotation Using Janus Nanoparticles

Understanding the function of rotary molecular motors, such as rotary ATPases, relies on our ability to visualize single-molecule rotation. Traditional imaging methods often involve tagging those motors with nanoparticles (NPs) and inferring their rotation from the translational motion of NPs. Here, we report an approach using "two-faced" Janus NPs to directly image the rotation of a single V-ATPase from Enterococcus hirae, an ATP-driven rotary ion pump. By employing a 500 nm silica/gold Janus NP, we exploit its asymmetric optical contrast, a silica core with a gold cap on one hemisphere, to achieve precise imaging of the unidirectional counterclockwise rotation of single V-ATPase motors immobilized on surfaces. Despite the added viscous load from the relatively large Janus NP probe, our approach provides accurate torque measurements of a single V-ATPase. This study underscores the advantages of Janus NPs over conventional probes, establishing them as powerful tools for the single-molecule analysis of rotary molecular motors.

Uncovering kinesin dynamics in neurites with MINFLUX

Neurons grow neurites of several tens of micrometers in length, necessitating active transport from the cell body by motor proteins. By tracking fluorophores as minimally invasive labels, MINFLUX is able to quantify the motion of those proteins with nanometer/millisecond resolution. Here we study the substeps of a truncated kinesin-1 mutant in primary rat hippocampal neurons, which have so far been mainly observed on polymerized microtubules deposited onto glass coverslips. A gentle fixation protocol largely maintains the structure and surface modifications of the microtubules in the cell. By analyzing the time between the substeps, we identify the ATP-binding state of kinesin-1 and observe the associated rotation of the kinesin-1 head in neurites. We also observed kinesin-1 switching microtubules mid-walk, highlighting the potential of MINFLUX to study the details of active cellular transport.

ATP Concentration-Dependent Fractions of One-Head-Bound and Two-Head-Bound States of the Kinesin Motor during Its Chemomechanical Coupling Cycle

Kinesin is a typical motor protein that can use the chemical energy of ATP hydrolysis to step processively on microtubules, alternating between one-head-bound and two-head-bound states. Some published experimental results showed that the duration of the one-head-bound state increases greatly with a decrease in ATP concentration, whereas the duration of the two-head-bound state is independent of ATP concentration, indicating that ATP binding occurs in the one-head-bound state. On the contrary, other experimental results showed that the duration of the two-head-bound state increases greatly with a decrease in ATP concentration, whereas the duration of the one-head-bound state increases slightly with a decrease in ATP concentration, indicating that ATP binding occurs mainly in the two-head-bound state. Here, we explain consistently and quantitatively these contradictory experimental results, resolving the controversy that is critical to the chemomechanical coupling mechanism of the kinesin motor.

A Model for Chemomechanical Coupling of Kinesin-3 Motor

Introduction

Kinesin-3 motor, which is in the monomeric and inactive form in solution, after cargo-induced dimerization can step on microtubules towards the plus end with a high velocity and a supperprocessivity, which is responsible for transporting the cargo in axons and dendrites. The kinesin-3 motor has a large initial landing rate to microtubules and spends the majority of its stepping cycle in a one-head-bound state. Under the load the kinesin-3 motor can dissociate more readily than the kinesin-1 motor.

Methods

To understand the physical origin of the peculiar features for the kinesin-3 motor, a model is presented here for its chemomechanical coupling. Based on the model the dynamics of the motor under no load, under the ramping load and under the constant load is studied analytically.

Results

The theoretical results explain well the available experimental data under no load and under the ramping load. For comparison, the corresponding available experimental data for the kinesin-1 motor under the ramping load are also explained. The predicted results of the velocity, dissociation rate and run length versus the constant load for the kinesin-3 motor are provided.

Conclusions

The study has strong implications for the chemomechanical coupling mechanism of the kinesin-3 dimer. The origin of the kinesin-3 dimer in the predominant one-head-bound state is due to the fact that the rate of ATP transition to ADP in the trailing head is much larger than that of ADP release from the MT-bound head. The study shows that the kinesin-3 ADP-head has an evidently longer interaction distance with microtubule than the kinesin-1 ADP-head, explaining why in the initial ADP state the kinesin-3 motor has the much larger landing rate than the kinesin-1 motor and why under the load the kinesin-3 motor can dissociate more readily than the kinesin-1 motor.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-024-00795-1.

Product inhibition slow down the moving velocity of processive chitinase and sliding-intermediate state blocks re-binding of product

Processive movement is the key reaction for crystalline polymer degradation by enzyme. Product release is an important phenomenon in resetting the moving cycle, but how it affects chitinase kinetics was unknown. Therefore, we investigated the effect of diacetyl chitobiose (C2) on the biochemical activity and movement of chitinase A from Serratia marcescens (SmChiA). The apparent inhibition constant of C2 on crystalline chitin degradation of SmChiA was 159 μM. The binding position of C2 obtained by X-ray crystallography was at subsite +1, +2 and Trp275 interact with C2 at subsite +1. This binding state is consistent with the competitive inhibition obtained by biochemical analysis. The apparent inhibition constant of C2 on the moving velocity of high-speed (HS) AFM observations was 330 μM, which is close to the biochemical results, indicating that the main factor in crystalline chitin degradation is also the decrease in degradation activity due to inhibition of processive movement. The Trp275 is a key residue for making a sliding intermediate complex. SmChiA W275A showed weaker activity and affinity than WT against crystalline chitin because it is less processive than WT. In addition, biochemical apparent inhibition constant for C2 of SmChiA W275A was 45.6 μM. W275A mutant showed stronger C2 inhibition than WT even though the C2 binding affinity is weaker than WT. This result indicated that Trp275 is important for the interaction at subsite +1, but also important for making sliding intermediate complex and physically block the rebinding of C2 on the catalytic site for crystalline chitin degradation.

Modeling the motion of disease-associated KIF1A heterodimers

KIF1A is a member of the kinesin-3 motor protein family that transports synaptic vesicle precursors in axons. Mutations in the Kif1a gene cause neuronal diseases. Most patients are heterozygous and have both mutated and intact KIF1A alleles, suggesting that heterodimers composed of wild-type KIF1A and mutant KIF1A are likely involved in pathogenesis. In this study, we propose mathematical models to describe the motility of KIF1A heterodimers composed of wild-type KIF1A and mutant KIF1A. Our models precisely describe run length, run time, and velocity of KIF1A heterodimers using a few parameters obtained from two homodimers. The first model is a simple hand-over-hand model in which stepping and detachment rates from a microtubule of each head are identical to those in the respective homodimers. Although the velocities of heterodimers expected from this model were in good agreement with the experimental results, this model underestimated the run lengths and run times of some heterodimeric motors. To address this discrepancy, we propose the tethered-head affinity model, in which we hypothesize a tethered head, in addition to a microtubule-binding head, contributes to microtubule binding in a vulnerable one-head-bound state. The run lengths and run times of the KIF1A heterodimers predicted by the tethered-head affinity model matched well with experimental results, suggesting a possibility that the tethered head affects the microtubule binding of KIF1A. Our models provide insights into how each head contributes to the processive movement of KIF1A and can be used to estimate motile parameters of KIF1A heterodimers.

Evaluating the effect of two-dimensional molecular layout on DNA origami-based transporters

Cellular transport systems are sophisticated and efficient. Hence, one of the ultimate goals of nanotechnology is to design artificial transport systems rationally. However, the design principle has been elusive, because how motor layout affects motile activity has not been established, partially owing to the difficulty in achieving a precise layout of the motile elements. Here, we employed a DNA origami platform to evaluate the two-dimensional (2D) layout effect of kinesin motor proteins on transporter motility. We succeeded in accelerating the integration speed of the protein of interest (POI) to the DNA origami transporter by up to 700 times by introducing a positively charged poly-lysine tag (Lys-tag) into the POI (kinesin motor protein). This Lys-tag approach allowed us to construct and purify a transporter with high motor density, allowing a precise evaluation on the 2D layout effect. Our single-molecule imaging showed that the densely packed layout of kinesin decreased the run length of the transporter, although its velocity was moderately affected. These results indicate that steric hindrance is a critical parameter to be considered in the design of transport systems.

Spatial and temporal dynamics of ATP synthase from mitochondria toward the cell surface

Ectopic ATP synthase complex (eATP synthase), located on cancer cell surface, has been reported to possess catalytic activity that facilitates the generation of ATP in the extracellular environment to establish a suitable microenvironment and to be a potential target for cancer therapy. However, the mechanism of intracellular ATP synthase complex transport remains unclear. Using a combination of spatial proteomics, interaction proteomics, and transcriptomics analyses, we find ATP synthase complex is first assembled in the mitochondria and subsequently delivered to the cell surface along the microtubule via the interplay of dynamin-related protein 1 (DRP1) and kinesin family member 5B (KIF5B). We further demonstrate that the mitochondrial membrane fuses to the plasma membrane in turn to anchor ATP syntheses on the cell surface using super-resolution imaging and real-time fusion assay in live cells. Our results provide a blueprint of eATP synthase trafficking and contribute to the understanding of the dynamics of tumor progression.

Direct observation of motor protein stepping in living cells using MINFLUX

Dynamic measurements of molecular machines can provide invaluable insights into their mechanism, but these measurements have been challenging in living cells. Here, we developed live-cell tracking of single fluorophores with nanometer spatial and millisecond temporal resolution in two and three dimensions using the recently introduced super-resolution technique MINFLUX. Using this approach, we resolved the precise stepping motion of the motor protein kinesin-1 as it walked on microtubules in living cells. Nanoscopic tracking of motors walking on the microtubules of fixed cells also enabled us to resolve the architecture of the microtubule cytoskeleton with protofilament resolution.

MINFLUX dissects the unimpeded walking of kinesin-1

We introduce an interferometric MINFLUX microscope that records protein movements with up to 1.7 nanometer per millisecond spatiotemporal precision. Such precision has previously required attaching disproportionately large beads to the protein, but MINFLUX requires the detection of only about 20 photons from an approximately 1-nanometer-sized fluorophore. Therefore, we were able to study the stepping of the motor protein kinesin-1 on microtubules at up to physiological adenosine-5'-triphosphate (ATP) concentrations. We uncovered rotations of the stalk and the heads of load-free kinesin during stepping and showed that ATP is taken up with a single head bound to the microtubule and that ATP hydrolysis occurs when both heads are bound. Our results show that MINFLUX quantifies (sub)millisecond conformational changes of proteins with minimal disturbance.

Electro-detachment of kinesin motor domain from microtubule in silico

Kinesin is a motor protein essential in cellular functions, such as intracellular transport and cell-division, as well as for enabling nanoscopic transport in bio-nanotechnology. Therefore, for effective control of function for nanotechnological applications, it is important to be able to modify the function of kinesin. To circumvent the limitations of chemical modifications, here we identify another potential approach for kinesin control: the use of electric forces. Using full-atom molecular dynamics simulations (247,358 atoms, total time ∼ 4.4 μs), we demonstrate, for the first time, that the kinesin-1 motor domain can be detached from a microtubule by an intense electric field within the nanosecond timescale. We show that this effect is field-direction dependent and field-strength dependent. A detailed analysis of the electric forces and the work carried out by electric field acting on the microtubule-kinesin system shows that it is the combined action of the electric field pulling on the β-tubulin C-terminus and the electric-field-induced torque on the kinesin dipole moment that causes kinesin detachment from the microtubule. It is shown, for the first time in a mechanistic manner, that an electric field can dramatically affect molecular interactions in a heterologous functional protein assembly. Our results contribute to understanding of electromagnetic field-biomatter interactions on a molecular level, with potential biomedical and bio-nanotechnological applications for harnessing control of protein nanomotors.

Microtubules and Quantum Dots Integration Leads to Conjugates with Applications in Biosensors and Bionanodevices

This chapter describes compiled methods for the formation and manipulation of microtubule-kinesin-carbon nanodots conjugates in user-defined synthetic environments. Specifically, by using inherited self-assembly and self-recognition properties of tubulin cytoskeletal protein and by interfacing this protein with lab synthesized carbon nanodots, bio-nano hybrid interfaces were formed. Further manipulation of such biohybrids under the mechanical cycle of kinesin 1 ATP-ase molecular motor led to their integration on user-controlled engineered surfaces. Presented methods are foreseen to lead to microtubule-molecular motor-hybrid based assemblies formation with applications ranging from biosensing, to nanoelectronics and single molecule printing, just to name a few.

Estimating Entropy Production from Waiting Time Distributions

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.

Noise-Induced Acceleration of Single Molecule Kinesin-1

The movement of single kinesin molecules was observed while applying noisy external forces that mimic intracellular active fluctuations. We found kinesin accelerates under noise, especially when a large hindering load is added. The behavior quantitatively conformed to a theoretical model that describes the kinesin movement with simple two-state reactions. The universality of the kinetic theory suggests that intracellular enzymes share a similar noise-induced acceleration mechanism, i.e., active fluctuations in cells are not just noise but are utilized to promote various physiological processes.

Micromirror Total Internal Reflection Microscopy for High-Performance Single Particle Tracking at Interfaces

Single particle tracking has found broad applications in the life and physical sciences, enabling the observation and characterization of nano- and microscopic motion. Fluorescence-based approaches are ideally suited for high-background environments, such as tracking lipids or proteins in or on cells, due to superior background rejection. Scattering-based detection is preferable when localization precision and imaging speed are paramount due to the in principle infinite photon budget. Here, we show that micromirror-based total internal reflection dark field microscopy enables background suppression previously only reported for interferometric scattering microscopy, resulting in nanometer localization precision at 6 μs exposure time for 20 nm gold nanoparticles with a 25 × 25 μm² field of view. We demonstrate the capabilities of our implementation by characterizing sub-nanometer deterministic flows of 20 nm gold nanoparticles at liquid-liquid interfaces. Our results approach the optimal combination of background suppression, localization precision, and temporal resolution achievable with pure scattering-based imaging and tracking of nanoparticles at interfaces.

Unsupervised selection of optimal single-molecule time series idealization criterion

Single-molecule (SM) approaches have provided valuable mechanistic information on many biophysical systems. As technological advances lead to ever-larger data sets, tools for rapid analysis and identification of molecules exhibiting the behavior of interest are increasingly important. In many cases the underlying mechanism is unknown, making unsupervised techniques desirable. The divisive segmentation and clustering (DISC) algorithm is one such unsupervised method that idealizes noisy SM time series much faster than computationally intensive approaches without sacrificing accuracy. However, DISC relies on a user-selected objective criterion (OC) to guide its estimation of the ideal time series. Here, we explore how different OCs affect DISC’s performance for data typical of SM fluorescence imaging experiments. We find that OCs differing in their penalty for model complexity each optimize DISC’s performance for time series with different properties such as signal/noise and number of sample points. Using a machine learning approach, we generate a decision boundary that allows unsupervised selection of OCs based on the input time series to maximize performance for different types of data. This is particularly relevant for SM fluorescence data sets, which often have signal/noise near the derived decision boundary and include time series of nonuniform length because of stochastic bleaching. Our approach, AutoDISC, allows unsupervised per-molecule optimization of DISC, which will substantially assist in the rapid analysis of high-throughput SM data sets with noisy samples and nonuniform time windows.

Scattering-based Light Microscopy: From Metal Nanoparticles to Single Proteins

Our ability to detect, image, and quantify nanoscopic objects and molecules with visible light has undergone dramatic improvements over the past few decades. While fluorescence has historically been the go-to contrast mechanism for ultrasensitive light microscopy due to its superior background suppression and specificity, recent developments based on light scattering have reached single-molecule sensitivity. They also have the advantages of universal applicability and the ability to obtain information about the species of interest beyond its presence and location. Many of the recent advances are driven by novel approaches to illumination, detection, and background suppression, all aimed at isolating and maximizing the signal of interest. Here, we review these developments grouped according to the basic principles used, namely darkfield imaging, interferometric detection, and surface plasmon resonance microscopy.

Fast Leaps between Millisecond Confinements Govern Ase1 Diffusion along Microtubules

Diffusion is the most fundamental mode of protein translocation within cells. Confined diffusion of proteins along the electrostatic potential constituted by the surface of microtubules, although modeled meticulously in molecular dynamics simulations, has not been experimentally observed in real-time. Here, interferometric scattering microscopy is used to directly visualize the movement of the microtubule-associated protein Ase1 along the microtubule surface at nanometer and microsecond resolution. Millisecond confinements of Ase1 and fast leaps between these positions of dwelling preferentially occurring along the microtubule protofilaments are resolved, revealing Ase1's mode of diffusive translocation along the microtubule's periodic surface. The derived interaction potential closely matches the tubulin-dimer periodicity and the distribution of the electrostatic potential on the microtubule lattice. It is anticipated that mapping the interaction landscapes for different proteins on microtubules, finding plausible energetic barriers of different positioning and heights, can provide valuable insights into regulating the dynamics of essential cytoskeletal processes, such as intracellular cargo trafficking, cell division, and morphogenesis, all of which rely on diffusive translocation of proteins along microtubules.

Molecular Mechanism of Processive Stepping of Kinesin Motors

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.

Effects of Gold Nanoparticles on the Stepping Trajectories of Kinesin

A substantial increase in the temporal resolution of the stepping of dimeric molecular motors is possible by tracking the position of a large gold nanoparticle (GNP) attached to a labeled site on one of the heads. This technique was employed to measure the stepping trajectories of conventional kinesin (Kin1) using the time-dependent position of the GNP as a proxy. The trajectories revealed that the detached head always passes to the right of the head that is tightly bound to the microtubule (MT) during a step. In interpreting the results of such experiments, it is assumed that the GNP does not significantly alter the diffusive motion of the detached head. We used coarse-grained simulations of a system consisting of the MT-Kin1 complex with and without attached GNP to investigate how the stepping trajectories are affected. The two significant findings are: (1) The GNP does not faithfully track the position of the stepping head, and (2) the rightward bias is typically exaggerated by the GNP. Both these findings depend on the precise residue position to which the GNP is attached. Surprisingly, the stepping trajectories of kinesin are not significantly affected if, in addition to the GNP, a 1 μm diameter cargo is attached to the coiled coil. Our simulations suggest the effects of the large probe have to be considered when inferring the stepping mechanisms using GNP tracking experiments.

Fluid Jet Stimulation of Auditory Hair Bundles Reveal Spatial Non-uniformities and Two Viscoelastic-Like Mechanisms

Hair cell mechanosensitivity resides in the sensory hair bundle, an apical protrusion of actin-filled stereocilia arranged in a staircase pattern. Hair bundle deflection activates mechano-electric transduction (MET) ion channels located near the tops of the shorter rows of stereocilia. The elicited macroscopic current is shaped by the hair bundle motion so that the mode of stimulation greatly influences the cell’s output. We present data quantifying the displacement of the whole outer hair cell bundle using high-speed imaging when stimulated with a fluid jet. We find a spatially non-uniform stimulation that results in splaying, where the hair bundle expands apart. Based on modeling, the splaying is predominantly due to fluid dynamics with a small contribution from hair bundle architecture. Additionally, in response to stimulation, the hair bundle exhibited a rapid motion followed by a slower motion in the same direction (creep) that is described by a double exponential process. The creep is consistent with originating from a linear passive system that can be modeled using two viscoelastic processes. These viscoelastic mechanisms are integral to describing the mechanics of the mammalian hair bundle.

Multiscale Coarse-Grained Model for the Stepping of Molecular Motors with Application to Kinesin

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps toward the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin, there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multiscale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with a focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted, allowing the step to be completed in tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full three-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

AutoStepfinder: A fast and automated step detection method for single-molecule analysis

Single-molecule techniques allow the visualization of the molecular dynamics of nucleic acids and proteins with high spatiotemporal resolution. Valuable kinetic information of biomolecules can be obtained when the discrete states within single-molecule time trajectories are determined. Here, we present a fast, automated, and bias-free step detection method, AutoStepfinder, that determines steps in large datasets without requiring prior knowledge on the noise contributions and location of steps. The analysis is based on a series of partition events that minimize the difference between the data and the fit. A dual-pass strategy determines the optimal fit and allows AutoStepfinder to detect steps of a wide variety of sizes. We demonstrate step detection for a broad variety of experimental traces. The user-friendly interface and the automated detection of AutoStepfinder provides a robust analysis procedure that enables anyone without programming knowledge to generate step fits and informative plots in less than an hour.

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Fast, automated, and bias-free detection of steps within single-molecule trajectories

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Robust step detection without any prior knowledge on the data

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A dual-pass strategy for the detection of steps over a wide variety of scales

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A user-friendly interface for a simplified step fitting procedure

Single-molecule techniques have made it possible to track individual protein complexes in real time with a nanometer spatial resolution and a millisecond timescale. Accurate determination of the dynamic states within single-molecule time traces provides valuable kinetic information that underlie the function of biological macromolecules. Here, we present a new automated step detection method called AutoStepfinder, a versatile, robust, and easy-to-use algorithm that allows researchers to determine the kinetic states within single-molecule time trajectories without any bias.

Nanoscopic Structural Fluctuations of Disassembling Microtubules Revealed by Label-Free Super-Resolution Microscopy

Microtubules are cytoskeletal polymers of tubulin dimers assembled into protofilaments that constitute nanotubes undergoing periods of assembly and disassembly. Static electron micrographs suggest a structural transition of straight protofilaments into curved ones occurring at the tips of disassembling microtubules. However, these structural transitions have never been observed and the process of microtubule disassembly thus remains unclear. Here, label-free optical microscopy capable of selective imaging of the transient structural changes of protofilaments at the tip of a disassembling microtubule is introduced. Upon induced disassembly, the transition of ordered protofilaments into a disordered conformation is resolved at the tip of the microtubule. Imaging the unbinding of individual tubulin oligomers from the microtubule tip reveals transient pauses and relapses in the disassembly, concurrent with increased organization of protofilament segments at the microtubule tip. These findings show that microtubule disassembly is a discrete process and suggest a stochastic mechanism of switching from the disassembly to the assembly phase.

Cutting-Edge Single-Molecule Technologies Unveil New Mechanics in Cellular Biochemistry

Single-molecule technologies have expanded our ability to detect biological events individually, in contrast to ensemble biophysical technologies, where the result provides averaged information. Recent developments in atomic force microscopy have not only enabled us to distinguish the heterogeneous phenomena of individual molecules, but also allowed us to view up to the resolution of a single covalent bond. Similarly, optical tweezers, due to their versatility and precision, have emerged as a potent technique to dissect a diverse range of complex biological processes, from the nanomechanics of ClpXP protease-dependent degradation to force-dependent processivity of motor proteins. Despite the advantages of optical tweezers, the time scales used in this technology were inconsistent with physiological scenarios, which led to the development of magnetic tweezers, where proteins are covalently linked with the glass surface, which in turn increases the observation window of a single biomolecule from minutes to weeks. Unlike optical tweezers, magnetic tweezers use magnetic fields to impose torque, which makes them convenient for studying DNA topology and topoisomerase functioning. Using modified magnetic tweezers, researchers were able to discover the mechanical role of chaperones, which support their substrate proteinsby pulling them during translocation and assist their native folding as a mechanical foldase. In this article, we provide a focused review of many of these new roles of single-molecule technologies, ranging from single bond breaking to complex chaperone machinery, along with the potential to design mechanomedicine, which would be a breakthrough in pharmacological interventions against many diseases.

Structural snapshots of the kinesin-2 OSM-3 along its nucleotide cycle: implications for the ATP hydrolysis mechanism

Motile kinesins are motor proteins that translocate along microtubules as they hydrolyze ATP. They share a conserved motor domain which harbors both ATPase and microtubule-binding activities. An ATP hydrolysis mechanism involving two water molecules has been proposed based on the structure of the kinesin-5 Eg5 bound to an ATP analog. Whether this mechanism is general in the kinesin superfamily remains uncertain. Here, we present structural snapshots of the motor domain of OSM-3 along its nucleotide cycle. OSM-3 belongs to the homodimeric kinesin-2 subfamily and is the Caenorhabditis elegans homologue of human KIF17. OSM-3 bound to ADP or devoid of a nucleotide shows features of ADP-kinesins with a docked neck linker. When bound to an ATP analog, OSM-3 adopts a conformation similar to those of several ATP-like kinesins, either isolated or bound to tubulin. Moreover, the OSM-3 nucleotide-binding site is virtually identical to that of ATP-like Eg5, demonstrating a shared ATPase mechanism. Therefore, our data extend to kinesin-2 the two-water ATP hydrolysis mechanism and further suggest that it is universal within the kinesin superfamily. PROTEIN DATABASE ENTRIES: 7A3Z, 7A40, 7A5E.

Germanium nanospheres for ultraresolution picotensiometry of kinesin motors

Kinesin motors are essential for the transport of cellular cargo along microtubules. How the motors step, detach, and cooperate with each other is still unclear. To dissect the molecular motion of kinesin-1, we developed germanium nanospheres as ultraresolution optical trapping probes. We found that single motors took 4-nanometer center-of-mass steps. Furthermore, kinesin-1 never detached from microtubules under hindering load conditions. Instead, it slipped on microtubules in microsecond-long, 8-nanometer steps and remained in this slip state before detaching or reengaging in directed motion. Unexpectedly, reengagement and thus rescue of directed motion was more frequent. Our observations broaden our knowledge on the mechanochemical cycle and slip state of kinesin. This state and rescue need to be accounted for to understand long-range transport by teams of motors.

A kinetic dissection of the fast and superprocessive kinesin-3 KIF1A reveals a predominant one-head-bound state during its chemomechanical cycle

The kinesin-3 family contains the fastest and most processive motors of the three neuronal transport kinesin families, yet the sequence of states and rates of kinetic transitions that comprise the chemomechanical cycle and give rise to their unique properties are poorly understood. We used stopped-flow fluorescence spectroscopy and single-molecule motility assays to delineate the chemomechanical cycle of the kinesin-3, KIF1A. Our bacterially expressed KIF1A construct, dimerized via a kinesin-1 coiled-coil, exhibits fast velocity and superprocessivity behavior similar to WT KIF1A. We established that the KIF1A forward step is triggered by hydrolysis of ATP and not by ATP binding, meaning that KIF1A follows the same chemomechanical cycle as established for kinesin-1 and -2. The ATP-triggered half-site release rate of KIF1A was similar to the stepping rate, indicating that during stepping, rear-head detachment is an order of magnitude faster than in kinesin-1 and kinesin-2. Thus, KIF1A spends the majority of its hydrolysis cycle in a one-head-bound state. Both the ADP off-rate and the ATP on-rate at physiological ATP concentration were fast, eliminating these steps as possible rate-limiting transitions. Based on the measured run length and the relatively slow off-rate in ADP, we conclude that attachment of the tethered head is the rate-limiting transition in the KIF1A stepping cycle. Thus, KIF1A's activity can be explained by a fast rear-head detachment rate, a rate-limiting step of tethered-head attachment that follows ATP hydrolysis, and a relatively strong electrostatic interaction with the microtubule in the weakly bound post-hydrolysis state.

Elementary processes of DNA surface hybridization resolved by single-molecule kinetics: implication for macroscopic device performance

Direct monitoring of single-molecule reactions has recently become a promising means of mechanistic investigation. However, the resolution of reaction pathways from single-molecule experiments remains elusive, primarily because of interference from extraneous processes such as bulk diffusion. Herein, we report a single-molecule kinetic investigation of DNA hybridization on a metal surface, as an example of a bimolecular association reaction. The tip of the scanning tunneling microscope (STM) was functionalized with single-stranded DNA (ssDNA), and hybridization with its complementary strand on an Au(111) surface was detected by the increase in the electrical conductance associated with the electron transport through the resulting DNA duplex. Kinetic analyses of the conductance changes successfully resolved the elementary processes, which involve not only the ssDNA strands and their duplex but also partially hybridized intermediate strands, and we found an increase in the hybridization efficiency with increasing the concentration of DNA in contrast to the knowledge obtained previously by conventional ensemble measurements. The rate constants derived from our single-molecule studies provide a rational explanation of these findings, such as the suppression of DNA melting on surfaces with higher DNA coverage. The present methodology, which relies on intermolecular conductance measurements, can be extended to a range of single-molecule reactions and to the exploration of novel chemical syntheses.

Hybridization of a single DNA molecule on a surface was investigated by electrical conductance measurements. The hybridization efficiency increases with increasing the DNA concentration, in contrast to preceding studies with ensemble studies.

Backstepping Mechanism of Kinesin-1

Kinesin-1 is an ATP-driven molecular motor that transports cellular cargo along microtubules. At low loads, kinesin-1 almost always steps forward, toward microtubule plus ends, but at higher loads, it can also step backward. Backsteps are usually 8 nm but can be larger. These larger backward events of 16 nm, 24 nm, or more are thought to be slips rather than steps because they are too fast to consist of multiple, tightly coupled 8-nm steps. Here, we propose that not only these larger backsteps, but all kinesin-1 backsteps, are slips. We show first that kinesin waits before forward steps for less time than before backsteps and detachments; second, we show that kinesin waits for the same amount of time before backsteps and detachments; and third, we show that by varying the microtubule type, we can change the ratio of backsteps to detachments without affecting forward stepping. Our findings indicate that backsteps and detachments originate from the same state and that this state arises later in the mechanochemical cycle than the state that gives rise to forward steps. To explain our data, we propose that, in each cycle of ATP turnover, forward kinesin steps can only occur before Pi release, whereas backslips and detachments can only occur after Pi release. In the scheme we propose, Pi release gates access to a weak binding K⋅ADP-K⋅ADP state that can slip back along the microtubule, re-engage, release ADP, and try again to take an ATP-driven forward step. We predict that this rescued detachment pathway is key to maintaining kinesin processivity under load.

Polycationic gold nanorods as multipurpose in vitro microtubule markers

Gold nanoparticles are intriguing because of their unique size- and shape-dependent chemical, electronic and optical properties. Gold nanorods (AuNRs) are particularly promising for various sensor applications due to their tip-enhanced plasmonic fields. For biomolecule attachment, AuNRs are often functionalized with proteins. However, by their intrinsic size such molecules block the most sensitive near-field region of the AuNRs. Here, we used short cationic thiols to functionalize AuNRs. We show that the functionalization layer is thin and that these polycationic AuNRs bind in vitro to negatively charged microtubules. Furthermore, we can plasmonically stimulate light emission from single AuNRs in the absence of any fluorophores and, therefore, use them as bleach- and blinkfree microtubule markers. We expect that polycationic AuNRs may be applicable to in vivo systems and other negatively charged molecules like DNA. In the long-term, microtubule-bound AuNRs can be used as ultrasensitive single-molecule sensors for molecular machines that interact with microtubules.

A common chemomechanical coupling model for orphan and conventional kinesin molecular motors

Orphan and conventional kinesin dimers represent two families of the kinesin superfamily molecular motors. Conventional kinesin, having a 14-residue neck linker (NL) in each head, can step processively on microtubule (MT), with an ATP hydrolysis being coupled with a mechanical stepping under no load. Orphan kinesin phragmoplast-associated kinesin-related protein 2 (PAKRP2) dimer, despite having a NL of 32 residues in each head, can also step processively on MT and exhibits tight chemomechanical coupling under no load. However, the dynamic properties of the wild type PAKRP2 and the mutant one with each NL truncated to 14 residues are very different from those of the wild type conventional kinesin and the mutant one with each NL being replaced by the 32-residue NL from PAKRP2. Here, based on a common chemomechanical coupling model we study computationally the dynamics of the two families of the kinesin dimers, with the simulated results explaining quantitatively the available experimental data. The large differences in the dynamics between the two families of kinesin dimers arise mainly from different rate constants of NL docking and ATPase activity and different weak affinities of the head in ADP state for MT. The studies indicate that both the orphan kinesin PAKRP2 and conventional kinesin use the same mechanism for processive motility.

Crystalline chitin hydrolase is a burnt-bridge Brownian motor

Motor proteins are essential units of life and are well-designed nanomachines working under thermal fluctuations. These proteins control moving direction by consuming chemical energy or by dissipating electrochemical potentials. Chitinase A from bacterium Serratia marcescens (SmChiA) processively moves along crystalline chitin by hydrolysis of a single polymer chain to soluble chitobiose. Recently, we directly observed the stepping motions of SmChiA labeled with a gold nanoparticle by dark-field scattering imaging to investigate the moving mechanism. Time constants analysis revealed that SmChiA moves back and forth along the chain freely, because forward and backward states have a similar free energy level. The similar probabilities of forward-step events (83.5%=69.3%+14.2%) from distributions of step sizes and chain-hydrolysis (86.3%=(1/2.9)/(1/2.9+1/18.3)×100) calculated from the ratios of time constants of hydrolysis and the backward step indicated that SmChiA moves forward as a result of shortening of the chain by a chitobiose unit, which stabilizes the backward state. Furthermore, X-ray crystal structures of sliding intermediate and molecular dynamics simulations showed that SmChiA slides forward and backward under thermal fluctuation without large conformational changes of the protein. Our results demonstrate that SmChiA is a burnt-bridge Brownian ratchet motor.

DNA-Modulated Plasmon Resonance: Methods and Optical Applications

The near-field effects in the vicinity of metallic nanoparticle surfaces, as induced by electromagnetic radiation with specific wavelength, give rise to a variety of novel optical properties and attractive applications because of surface plasmons, which are the coherent oscillations of conduction electrons on a metal surface. The interdisciplinary field of plasmonics has witnessed vigorous growth, promoting research on the modulation of plasmon resonance by constructing advanced plasmonic nanoarchitectures with controllable size, morphology, or interparticle coupling. Among diversified tools, deoxyribonucleic nucleic acid (DNA) possesses prominent superiority as a result of its designability, programmability, addressability, and ease of nanomaterial modification. In this review, we focus on the methods and optical applications of plasmon resonance modulation accomplished by DNA nanotechnology. Recent developments in the construction of DNA-mediated plasmonic nanoarchitecture and key ongoing research directions utilizing unique optical features are highlighted. Obstacles and challenges in this field are pointed out, followed by preliminary suggestions on some areas of opportunity that deserve attention.

Experimental and theoretical energetics of walking molecular motors under fluctuating environments

Molecular motors are nonequilibrium open systems that convert chemical energy to mechanical work. Their energetics are essential for various dynamic processes in cells, but largely remain unknown because fluctuations typically arising in small systems prevent investigation of the nonequilibrium behavior of the motors in terms of thermodynamics. Recently, Harada and Sasa proposed a novel equality to measure the dissipation of nonequilibrium small systems. By utilizing this equality, we have investigated the nonequilibrium energetics of the single-molecule walking motor kinesin-1. The dissipation from kinesin movement was measured through the motion of an attached probe particle and its response to external forces, indicating that large hidden dissipation exists. In this short review, aiming to readers who are not familiar with nonequilibrium physics, we briefly introduce the theoretical basis of the dissipation measurement as well as our recent experimental results and mathematical model analysis and discuss the physiological implications of the hidden dissipation in kinesin. In addition, further perspectives on the efficiency of motors are added by considering their actual working environment: living cells.

Small stepping motion of processive dynein revealed by load-free high-speed single-particle tracking

Cytoplasmic dynein is a dimeric motor protein which processively moves along microtubule. Its motor domain (head) hydrolyzes ATP and induces conformational changes of linker, stalk, and microtubule binding domain (MTBD) to trigger stepping motion. Here we applied scattering imaging of gold nanoparticle (AuNP) to visualize load-free stepping motion of processive dynein. We observed artificially-dimerized chimeric dynein, which has the head, linker, and stalk from Dictyostelium discoideum cytoplasmic dynein and the MTBD from human axonemal dynein, whose structure has been well-studied by cryo-electron microscopy. One head of a dimer was labeled with 30 nm AuNP, and stepping motions were observed with 100 μs time resolution and sub-nanometer localization precision at physiologically-relevant 1 mM ATP. We found 8 nm forward and backward steps and 5 nm side steps, consistent with on- and off-axes pitches of binding cleft between αβ-tubulin dimers on the microtubule. Probability of the forward step was 1.8 times higher than that of the backward step, and similar to those of the side steps. One-head bound states were not clearly observed, and the steps were limited by a single rate constant. Our results indicate dynein mainly moves with biased small stepping motion in which only backward steps are slightly suppressed.

The Impact of Rate Formulations on Stochastic Molecular Motor Dynamics

Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active transport is necessary to organize large structures on the short timescales necessary for biological function. The main mechanism of this transport is by cargo attachment to motors which walk in a directed fashion along intracellular filaments. There are a number of models which seek to describe the motion of motors with attached cargo, from detailed microscopic to coarse phenomenological descriptions. We focus on the intermediate-detailed discrete stochastic hopping models, and explore how cargo transport changes depending on the number of motors, motor interaction, system constraints and rate formulations, which are derived from common thermodynamic assumptions. We find that, despite obeying the same detailed balance constraint, the choice of rate formulation considerably affects the characteristics of the overall motion of the system, with one rate formulation exhibiting novel behavior of loaded motor groups moving faster than a single unloaded motor.

How kinesin waits for ATP affects the nucleotide and load dependence of the stepping kinetics

Conventional kinesin, responsible for directional transport of cellular vesicles, takes multiple nearly uniform 8.2-nm steps by consuming one ATP molecule per step as it walks toward the plus end of the microtubule (MT). Despite decades of intensive experimental and theoretical studies, there are gaps in the elucidation of key steps in the catalytic cycle of kinesin. How the motor waits for ATP to bind to the leading head is controversial. Two experiments using a similar protocol have arrived at different conclusions. One asserts that kinesin waits for ATP in a state with both the heads bound to the MT, whereas the other shows that ATP binds to the leading head after the trailing head detaches. To discriminate between the 2 scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observable quantities (the distribution of run length, the distribution of velocity [[Formula: see text]], and the randomness parameter) as a function of an external resistive force (F) and ATP concentration ([T]). The differences in the predicted bimodality in [Formula: see text] as a function of F between the 2 models may be amenable to experimental testing. Most importantly, we predict that the F and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of F and [T] can be quantitatively measured from stepping trajectories with very little prejudice in data analysis. Therefore, an accurate measurement of the randomness parameter and the velocity distribution as a function of load and nucleotide concentration could resolve the apparent controversy.