Single molecule processes on the stepwise movement of ATP-driven molecular motors

Flagella-Driven Motility of Bacteria

The bacterial flagellum is a helical filamentous organelle responsible for motility. In bacterial species possessing flagella at the cell exterior, the long helical flagellar filament acts as a molecular screw to generate thrust. Meanwhile, the flagella of spirochetes reside within the periplasmic space and not only act as a cytoskeleton to determine the helicity of the cell body, but also rotate or undulate the helical cell body for propulsion. Despite structural diversity of the flagella among bacterial species, flagellated bacteria share a common rotary nanomachine, namely the flagellar motor, which is located at the base of the filament. The flagellar motor is composed of a rotor ring complex and multiple transmembrane stator units and converts the ion flux through an ion channel of each stator unit into the mechanical work required for motor rotation. Intracellular chemotactic signaling pathways regulate the direction of flagella-driven motility in response to changes in the environments, allowing bacteria to migrate towards more desirable environments for their survival. Recent experimental and theoretical studies have been deepening our understanding of the molecular mechanisms of the flagellar motor. In this review article, we describe the current understanding of the structure and dynamics of the bacterial flagellum.

Translation initiation in eukaryotes: versatility of the scanning model

It is generally accepted that the initiation of translation in eukaryotes involves the binding of the 40S ribosomal subunit to the capped 5' end of an mRNA and subsequent scanning of 5' UTR in search of an initiation codon. However, until recently this has remained a mere hypothesis. This review describes the novel experimental evidence in support of this classical model. Data on the participation of various factors in the eukaryotic initiation process are summarized. The sequence of initiation events is described in light of the latest experimental data. The existing physical models of scanning are presented. Special attention is paid to discussion of alternative models of eukaryotic initiation of translation. It is demonstrated that the canonical mechanism of initiation is more versatile than previously thought.

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the "Driven by Detachment (DbD)" mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.

Unidirectional constant rate motion of the ribosomal scanning particle during eukaryotic translation initiation

According to the model of translation initiation in eukaryotes, the 40S ribosomal subunit binds to capped 5'-end of mRNA and subsequently migrates along 5'-UTR in searching for initiation codon. However, it remains unclear whether the migration is the result of a random one-dimensional diffusion, or it is an energy-driven unidirectional movement. To address this issue, the method of continuous monitoring of protein synthesis in situ was used for high precision measurements of the times required for translation of mRNA with 5'-UTRs of different lengths and structures in mammalian and plant cell-free systems. For the first time, the relationship between the scanning time and the 5'-UTR length was determined and their linear correlation was experimentally demonstrated. The conclusion is made that the ribosome migration is an unidirectional motion with the rate being virtually independent of a particular mRNA sequence and secondary structure.

One-dimensional Brownian motion of charged nanoparticles along microtubules: a model system for weak binding interactions

Various proteins are known to exhibit one-dimensional Brownian motion along charged rodlike polymers, such as microtubules (MTs), actin, and DNA. The electrostatic interaction between the proteins and the rodlike polymers appears to be crucial for one-dimensional Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with MTs. These hydrophilic nanoparticles bound to MTs and displayed one-dimensional Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for one-dimensional Brownian motion. The diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBT per charge), whereas the duration of the interaction increased exponentially (exponent of 0.22 kBT per charge). These results can be explained semiquantitatively if one assumes that a particle repeats a cycle of binding to and movement along an MT until it finally dissociates from the MT. During the movement, a particle is still electrostatically constrained in the potential valley surrounding the MT. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which the two parameters of the equilibrium constant between binding and movement, and the rate of dissociation from the MT, are derived as a function of the particle charge density. This study highlights the possibility that the weak binding interactions between proteins and rodlike polymers, e.g., MTs, are mediated by a similar, nonspecific charge-dependent mechanism.

How does a scanning ribosomal particle move along the 5'-untranslated region of eukaryotic mRNA? Brownian Ratchet model

A model of the ATP-dependent unidirectional movement of the 43S ribosomal initiation complex (=40S ribosomal subunit + eIF1 + eIF1A + eIF2.GTP.Met-tRNA(i) + eIF3) during scanning of the 5'-untranslated region of eukaryotic mRNA is proposed. The model is based on the principles of molecular Brownian ratchet machines and explains several enigmatic data concerning the scanning complex. In this model, the one-dimensional diffusion of the ribosomal initiation complex along the mRNA chain is rectified into the net-unidirectional 5'-to-3' movement by the Feynman ratchet-and-pawl mechanism. The proposed mechanism is organized by the heterotrimeric protein eIF4F (=eIF4A + eIF4E + eIF4G), attached to the scanning ribosomal particle via eIF3, and the RNA-binding protein eIF4B that is postulated to play the role of the pawl. The energy for the useful work of the ratchet-and-pawl mechanism is supplied from ATP hydrolysis induced by the eIF4A subunit: ATP binding and its hydrolysis alternately change the affinities of eIF4A for eIF4B and for mRNA, resulting in the restriction of backward diffusional sliding of the 43S ribosomal complex along the mRNA chain, while stochastic movements ahead are allowed.

The Tumbleweed: towards a synthetic proteinmotor

Biomolecular motors have inspired the design and construction of artificial nanoscale motors and machines based on nucleic acids, small molecules, and inorganic nanostructures. However, the high degree of sophistication and efficiency of biomolecular motors, as well as their specific biological function, derives from the complexity afforded by protein building blocks. Here, we discuss a novel bottom-up approach to understanding biological motors by considering the construction of synthetic protein motors. Specifically, we present a design for a synthetic protein motor that moves along a linear track, dubbed the "Tumbleweed." This concept uses three discrete ligand-dependent DNA-binding domains to perform cyclically ligand-gated, rectified diffusion along a synthesized DNA molecule. Here we describe how de novo peptide design and molecular biology could be used to produce the Tumbleweed, and we explore the fundamental motor operation of such a design using numerical simulations. The construction of this and more sophisticated protein motors is an exciting challenge that is likely to enhance our understanding of the structure-function relationship in biological motors.

A possible mechanism for determining the directionality of myosin molecular motors

There is a large superfamily of myosins, which play various fundamental roles in cellular motility. In this superfamily, most of myosins, including myosins II and V, move to the barbed end of an actin filament, whereas myosin VI was found to move in the opposite direction to the pointed end. Although myosin VI has structural differences compared with the other myosins, the mechanism for the reversal of the directionality has not been satisfactorily explained by conventional theories for myosin motility, including the widely accepted lever-arm hypothesis. In this paper, a simple mechanism for determining the directionality is proposed. The mechanism assumes that the driving force for the power stroke is caused by elastic energy stored within a myosin molecule at the joint between the head and the neck. The elastic energy originates from the attractive force between myosin and actin, and accumulates during the docking process. The energy of ATP is used to reduce the attractive force between myosin and actin and to facilitate the dissociation of these molecules. Therefore, it is not directly engaged in the power stroke. With this mechanism, the directionality of the myosin motility is simply determined by the direction of the neck with respect to the head in the dissociated configuration. This structural difference is actually observed in myosin VI. The same mechanism also explains the behavior of a backward moving engineered myosin. Computer simulations demonstrated the feasibility of this working mechanism.

Back-stepping, hidden substeps, and conditional dwell times in molecular motors

Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one knows biochemically that one or more mechanochemical substeps remain hidden in each enzymatic cycle. In order to properly interpret experimental data for back-to-forward step ratios, mean conditional step-to-step dwell times, etc., a first-passage analysis has been developed that takes account of hidden substeps in N -state sequential models. The explicit, general results differ significantly from previous treatments that identify the observed steps with complete mechanochemical cycles; e.g., the mean dwell times tau(+) and tau(-) prior to forward and back steps, respectively, are normally unequal although the dwell times tau(++) and tau(--) between successive forward and back steps are equal. Illustrative (N=2) -state examples display a wide range of behavior. The formulation extends to the case of two or more detectable transitions in a multistate cycle with hidden substeps.

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.

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

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.

Electric dipole theory and thermodynamics of actomyosin molecular motor in muscle contraction

Movements in muscles are generated by the myosins which interact with the actin filaments. In this paper we present an electric theory to describe how the chemical energy is first stored in electrostatic form in the myosin system and how it is then released and transformed into work. Due to the longitudinal polarized molecular structure with the negative phosphate group tail, the ATP molecule possesses a large electric dipole moment (p(0)), which makes it an ideal energy source for the electric dipole motor of the actomyosin system. The myosin head contains a large number of strongly restrained water molecules, which makes the ATP-driven electric dipole motor possible. The strongly restrained water molecules can store the chemical energy released by ATP binding and hydrolysis processes in the electric form due to their myosin structure fixed electric dipole moments (p(i)). The decrease in the electric energy is transformed into mechanical work by the rotational movement of the myosin head, which follows from the interaction of the dipoles p(i) with the potential field V(0) of ATP and with the potential field Psi of the actin. The electrical meaning of the hydrolysis reaction is to reduce the dipole moment p(0)-the remaining dipole moment of the adenosine diphosphate (ADP) is appropriately smaller to return the low negative value of the electric energy nearly back to its initial value, enabling the removal of ADP from the myosin head so that the cycling process can be repeated. We derive for the electric energy of the myosin system a general equation, which contains the potential field V(0) with the dipole moment p(0), the dipole moments p(i) and the potential field psi. Using the previously published experimental data for the electric dipole of ATP (p(0) congruent with 230 debye) and for the amount of strongly restrained water molecules (N congruent with 720) in the myosin subfragment (S1), we show that the Gibbs free energy changes of the ATP binding and hydrolysis reaction steps can be converted into the form of electric energy. The mechanical action between myosin and actin is investigated by the principle of virtual work. An electric torque always appears, i.e. a moment of electric forces between dipoles p(0) and p(i)(/M/ > or = 16 pN nm) that causes the myosin head to function like a scissors-shaped electric dipole motor. The theory as a whole is illustrated by several numerical examples and the results are compared with experimental results.

Entropy rectifies the Brownian steps of kinesin

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. The physical mechanism underlying the unidirectional bias of the kinesin steps is not fully understood. Here we explored the mechanical kinetics and thermodynamics of forward and backward kinesin steps by analyzing their temperature and load dependence. Results show that the frequency asymmetry between forward and backward steps is produced by entropy. Furthermore, the magnitude of the entropic asymmetry is 6 k(B)T, more than three times greater than expected from a current model, in which a mechanical conformational change within the kinesin molecular structure directly biases the kinesin steps forward. We propose that the stepping direction of kinesin is preferably caused by an entropy asymmetry resulting from the compatibility between the kinesin and microtubule interaction based on their polar structures.

Mechanics of the kinesin step

Kinesin is a molecular walking machine that organizes cells by hauling packets of components directionally along microtubules. The physical mechanism that impels directional stepping is uncertain. We show here that, under very high backward loads, the intrinsic directional bias in kinesin stepping can be reversed such that the motor walks sustainedly backwards in a previously undescribed mode of ATP-dependent backward processivity. We find that both forward and backward 8-nm steps occur on the microsecond timescale and that both occur without mechanical substeps on this timescale. The data suggest an underlying mechanism in which, once ATP has bound to the microtubule-attached head, the other head undergoes a diffusional search for its next site, the outcome of which can be biased by an applied load.

The elongation and contraction of actin bundles are induced by double-headed myosins in a motor concentration-dependent manner

Many types of myosin have been found and characterized to date, and already nearly 20 classes have been identified. However, these myosin motors can be classified more simply into two groups according to their head-structure, i.e. double- or single-headed myosins. Why do some myosin motors possess a double-headed structure? One obvious possible reason would be that the two heads improve the motor's processivity and sliding performance. Previously, to investigate the possibility that the double-headed myosins simultaneously interact with parallel arrayed two actin filaments in the presence of Mg-ATP, we developed an in vitro assay system using actin bundles formed by inert polymers. Using that system, we show here that skeletal muscle heavy meromyosin (HMM), a double-headed myosin derivative, but not subfragment-1 (S-1), a single-headed one, was able to contract or elongate actin bundles in a concentration-dependent manner. Similar elongation or contraction of actin bundles can also be induced by other double-headed myosin species isolated in the native state from Dictyostelium, from green algae Chara or from chicken brain. The results of this study confirm that double-headed myosin motors can induce sliding movements among neighboring actin filaments. The double-headed structure of myosins may also be important for generating tension or elongation in actin bundles or gels, and for organizing polarity-sorted actin networks, not just for improving their motor processivity or activity.