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

Movement is a fundamental characteristic of all living things. This biogenic function that is attributed to the molecular motors such as kinesin, dynein and myosin. Molecular motors generate forces by using chemical energy derived from the hydrolysis reaction of ATP molecules. Despite a large number of studies on this topic, the chemomechanical energy transduction mechanism is still unsolved. In this study, we have investigated the chemomechanical coupling of the ATPase cycle to the mechanical events of the molecular motor kinesin using single molecule detection (SMD) techniques. The SMD techniques allowed to detection of the movement of single kinesin molecules along a microtubule and showed that kinesin steps mainly in the forward direction, but occasionally in the backward. The stepping direction is determined by a certain load-dependent process, on which the stochastic behavior is well characterized by Feynman's thermal ratchet model. The driving force of the stepwise movement is essentially Brownian motion, but it is biased in the forward direction by using the free energy released from the hydrolysis of ATP.     

Protein-protein ratchets: stochastic simulation and application to processive enzymes

Interaction between a protein and a series of binding sites on a cytoskeletal substrate can create a resistance, or "protein friction," as the protein is moved along the substrate. If attachment and detachment rates are specified asymmetrically, this resistance can depend on the direction of movement, and the binding interaction acts as a ratchet. Stochastic computer simulations have been used to examine this type of protein-protein interaction. The performance of a protein-protein ratchet in the piconewton and nanometer range is significantly limited by thermal fluctuations, which in experimental measurements with single molecules are evident as Brownian motion. Simulations with a two-component model combining a conventional motor enzyme model with a protein-protein ratchet confirm previous suggestions that the processive movement of a single motor enzyme molecule against a load, as seen in experiments with inner arm dynein molecules, might be made possible by an accessory protein interaction that prevents backward slippage. When this accessory protein interaction is defined so that it acts as a ratchet, backward slippage can be prevented with minimal interference with forward progression.     

Cellular biophysics: bacterial endospore, membranes and random fluctuation

Purposeful motion of biological processes can be driven by Brownian motion of macromolecular complexes with one-sided binding biasing movement in one direction: a Brownian ratchet, now proposed to explain membrane motion during a phagocytosis-like process in bacteria.     

Analytical aspects of the Brownian motor effect in randomly flashing ratchets

The muscle contraction, operation of ATP synthase, maintaining the shape of a cell are believed to be secured by motor proteins, which can be modelled using the Brownian ratchet mechanism. We consider the randomly flashing ratchet model of a Brownian motor, where the particles can be in two states, only one of which is sensitive the applied spatially periodic potential (the mathematical setting is a pair of weakly coupled reaction-diffusion and Fokker–Planck equations). We prove that this mechanism indeed generates unidirectional transport by showing that the amount of mass in the wells of the potential decreases/increases from left to right. The direction of transport is unambiguously determined by the location of each minimum of the potential with respect to the so-called diffusive mean of its adjacent maxima. The transport can be generated not only by an asymmetric potential, but also by a symmetric potential and asymmetric transition rates, and as a consequence of the general result we derive explicit conditions when the latter happens. When the transitions are localized on narrow active sites in the protein conformation space, we find a more explicit characterization of the bulk transport direction, and infer that some common preconditions of the motor effect are redundant.     

Spontaneous reverse movement of mRNA-bound tRNA through the ribosome

During the translocation step of protein synthesis, a complex of two transfer RNAs bound to messenger RNA (tRNA-mRNA) moves through the ribosome. The reaction is promoted by an elongation factor, called EF-G in bacteria, which, powered by GTP hydrolysis, induces an open, unlocked conformation of the ribosome that allows for spontaneous tRNA-mRNA movement. Here we show that, in the absence of EF-G, there is spontaneous backward movement, or retrotranslocation, of two tRNAs bound to mRNA. Retrotranslocation is driven by the gain in affinity when a cognate E-site tRNA moves into the P site, which compensates the affinity loss accompanying the movement of peptidyl-tRNA from the P to the A site. These results lend support to the diffusion model of tRNA movement during translocation. In the cell, tRNA movement is biased in the forward direction by EF-G, which acts as a Brownian ratchet and prevents backward movement.     

The stepping motor protein as a feedback control ratchet

It is explained how going from a one headed motor protein to a stepping two headed motor protein is equivalent to going from a stochastically flashing ratchet to a feedback control ratchet. Both these ratchets have been well studied in the literature and their speeds and efficiencies are briefly reviewed. Next it is shown how a feedback control ratchet mechanism model can account for very accurate recent data obtained on kinesin. Finally, the role of internal friction in the operation of stepping motor proteins is discussed.     

The enhancement of the energetic efficiency by the cooperation of low-efficient flashing ratchets

The energetic efficiency of the classical flashing ratchet model is much lower (around 1%) than the experimental results (around 50%). Jülicher and Prost have provided a prototype of the cooperative ratchet model [Jülicher, F., Prost, J., 1995. Cooperative molecular motors. Phys. Rev. Lett. 75, 2618-2621], whose energetic efficiency is of the order of 50%. However, it remains an unsettled question how the low-efficient flashing ratchets cooperate with each other and achieve higher energetic efficiency. In this paper, we investigate two energy dissipation rates as well as the energetic efficiency for the single and the cooperative flashing ratchet model, close to and far from the equilibrium, based on the stochastic energetics. By comparing these quantities between the single and the cooperative ratchet, we provide an interpretation of the efficiency enhancement by the cooperation of low-efficient flashing ratchets.     

Evolution of conditional dispersal: a reaction–diffusion–advection model

To study evolution of conditional dispersal, a Lotka-Volterra reaction-diffusion-advection model for two competing species in a heterogeneous environment is proposed and investigated. The two species are assumed to be identical except their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but one species has stronger biased movement (i.e., advection along the environmental gradients) than the other one. It is shown that at least two scenarios can occur: if only one species has a strong tendency to move upward the environmental gradients, the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat; if both species have such strong biased movements, it can lead to overcrowding of the whole population at places of locally most favorable environments, which causes the extinction of the species with stronger biased movement. These results provide a new mechanism for the coexistence of competing species, and they also imply that selection is against excessive advection along environmental gradients, and an intermediate biased movement rate may evolve.     

RNA polymerase pushing

Molecular motors can exhibit Brownian ratchet or power stroke mechanisms. These mechanistic categories are related to transition state position: An early transition state suggests that chemical energy is stored and then released during the step (stroke) while a late transition state suggests that the release of chemical energy rectifies thermally activated motion that has already occurred (ratchet). Cellular RNA polymerases are thought to be ratchets that can push each other forward to reduce pausing during elongation. Here, by constructing a two-dimensional energy landscape from the individual landscapes of active and backtracked enzymes, we identify a new pushing mechanism which is the result of a saddle trajectory that arises in the two-dimensional energy landscape of interacting enzymes. We show that this mechanism is more effective with an early transition state suggesting that interacting RNAPs might translocate via a power stroke.     

Are histones, tubulin, and actin derived from a common ancestral protein?

Histones and the cytoskeletal components tubulin and actin all act as thermal ratchets, using the energy present in Brownian motion to do work. All three also bind to nucleotides. Here we suggest that histones, tubulin, and actin derive from a common ancestral protein. There is some sequence similarity between histone 2A and the bacterial tubulin homologue FtsZ. Histones and actin also share some sequence similarity in the nucleotides and at phosphate-binding sites. Thus, actin and tubulin may also be related, although this is not obvious from sequence analysis. Indeed, actin and tubulin are closely functionally related and cooperate in many cellular processes. Interestingly, recent advances in nanotechnology suggest that thermal ratchets may be able to impart lifelike properties; thus, the evolution of the ancestral histone, tubulin, and actin thermal ratchet may have been crucial in the development of complexity in living organisms.     

Chemomechanical coupling of the forward and backward steps of single kinesin molecules

The molecular motor kinesin travels processively along a microtubule in a stepwise manner. Here we have studied the chemomechanical coupling of the hydrolysis of ATP to the mechanical work of kinesin by analysing the individual stepwise movements according to the directionality of the movements. Kinesin molecules move primarily in the forward direction and only occasionally in the backward direction. The hydrolysis of a single ATP molecule is coupled to either the forward or the backward movement. This bidirectional movement is well described by a model of Brownian motion assuming an asymmetric potential of activation energy. Thus, the stepwise movement along the microtubule is most probably due to Brownian motion that is biased towards the forward direction by chemical energy stored in ATP molecules.     

Mesoscopic Model of Actin-Based Propulsion

Two theoretical models dominate current understanding of actin-based propulsion: microscopic polymerization ratchet model predicts that growing and writhing actin filaments generate forces and movements, while macroscopic elastic propulsion model suggests that deformation and stress of growing actin gel are responsible for the propulsion. We examine both experimentally and computationally the 2D movement of ellipsoidal beads propelled by actin tails and show that neither of the two models can explain the observed bistability of the orientation of the beads. To explain the data, we develop a 2D hybrid mesoscopic model by reconciling these two models such that individual actin filaments undergoing nucleation, elongation, attachment, detachment and capping are embedded into the boundary of a node-spring viscoelastic network representing the macroscopic actin gel. Stochastic simulations of this ‘in silico’ actin network show that the combined effects of the macroscopic elastic deformation and microscopic ratchets can explain the observed bistable orientation of the actin-propelled ellipsoidal beads. To test the theory further, we analyze observed distribution of the curvatures of the trajectories and show that the hybrid model''s predictions fit the data. Finally, we demonstrate that the model can explain both concave-up and concave-down force-velocity relations for growing actin networks depending on the characteristic time scale and network recoil. To summarize, we propose that both microscopic polymerization ratchets and macroscopic stresses of the deformable actin network are responsible for the force and movement generation.     

Myosin motors: missing structures and hidden springs

High-resolution structures of the motor domain of myosin II and lower resolution actin-myosin structures have led to the "swinging lever arm" model for myosin force generation. The available kinetic data are not all easily reconciled with this model and understanding the final details of the myosin motor mechanism must await actin-myosin co-crystals. The observation that myosin can populate multiple states in the absence of actin has nonetheless led to significant insights. The currently known myosin structures correspond to defined kinetic states that bind weakly (K(d)>microM) to actin. It is possible that the myosin lever arm could complete its swing before strong binding to actin and force generation--a process that would correspond, in the absence of load, to a Brownian ratchet. We further suggest that, under load, internal springs within the myosin head could decouple force generation and lever arm movement.     

Bacterial Translocation Ratchets: Shared Physical Principles with Different Molecular Implementations

Secretion systems enable bacteria to import and secrete large macromolecules including DNA and proteins. While most components of these systems have been identified, the molecular mechanisms of macromolecular transport remain poorly understood. Recent findings suggest that various bacterial secretion systems make use of the translocation ratchet mechanism for transporting polymers across the cell envelope. Translocation ratchets are powered by chemical potential differences generated by concentration gradients of ions or molecules that are specific to the respective secretion systems. Bacteria employ these potential differences for biasing Brownian motion of the macromolecules within the conduits of the secretion systems. Candidates for this mechanism include DNA import by the type II secretion/type IV pilus system, DNA export by the type IV secretion system, and protein export by the type I secretion system. Here, we propose that these three secretion systems employ different molecular implementations of the translocation ratchet mechanism.     

Cells as Active Particles in Asymmetric Potentials: Motility under External Gradients

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion.     

Cells as Active Particles in Asymmetric Potentials: Motility under External Gradients

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion.     

驱动蛋白定向运动的动力学分析

将布朗粒子的定向运动,看作是系统受到外部非平衡涨落作用的结果,并建立相应的扩散模型。通过蒙特卡罗模拟方法,得到布郎粒子定向梯跳运动曲线。结果表明：非对称锯齿势,外部含时闪烁力及加性色噪声协调与联合作用,可使布朗粒子做梯跳或锯齿运动。作为一种可能的解释,将驱动蛋白Ｋｉｎｅｓｉｎｓ沿微管定向梯跳运动看作是上述协调作用的结果。     

The mechanics of translocation: a molecular "spring-and-ratchet" system

The translation of genetic information into proteins is a fundamental process of life. Stepwise addition of amino acids to the growing polypeptide chain requires the coordinated movement of mRNA and tRNAs through the ribosome, a process known as translocation. Here, we review current understanding of the kinetics and mechanics of translocation, with particular emphasis on the structure of a functional mammalian ribosome stalled during translocation by an mRNA pseudoknot. In the context of a pseudoknot-stalled complex, the translocase EF-2 is seen to compress a hybrid-state tRNA into a strained conformation. We propose that this strain energy helps overcome the kinetic barrier to translocation and drives tRNA into the P-site, with EF-2 biasing this relaxation in one direction. The tRNA can thus be considered a molecular spring and EF-2 a Brownian ratchet in a "spring-and-ratchet" system within the translocation process.     

Diffusion of MMPs on the surface of collagen fibrils: the mobile cell surface-collagen substratum interface

Remodeling of the extracellular matrix catalyzed by MMPs is central to morphogenetic phenomena during development and wound healing as well as in numerous pathologic conditions such as fibrosis and cancer. We have previously demonstrated that secreted MMP-2 is tethered to the cell surface and activated by MT1-MMP/TIMP-2-dependent mechanism. The resulting cell-surface collagenolytic complex (MT1-MMP)₂/TIMP-2/MMP-2 can initiate (MT1-MMP) and complete (MMP-2) degradation of an underlying collagen fibril. The following question remained: What is the mechanism of substrate recognition involving the two structures of relatively restricted mobility, the cell surface enzymatic complex and a collagen fibril embedded in the ECM? Here we demonstrate that all the components of the complex are capable of processive movement on a surface of the collagen fibril. The mechanism of MT1-MMP movement is a biased diffusion with the bias component dependent on the proteolysis of its substrate, not adenosine triphosphate (ATP) hydrolysis. It is similar to that of the MMP-1 Brownian ratchet we described earlier. In addition, both MMP-2 and MMP-9 as well as their respective complexes with TIMP-1 and -2 are capable of Brownian diffusion on the surface of native collagen fibrils without noticeable dissociation while the dimerization of MMP-9 renders the enzyme immobile. Most instructive is the finding that the inactivation of the enzymatic activity of MT1-MMP has a detectable negative effect on the cell force developed in miniaturized 3D tissue constructs. We propose that the collagenolytic complex (MT1-MMP)₂/TIMP-2/MMP-2 represents a Mobile Cell Surface – Collagen Substratum Interface. The biological implications of MT1-MMP acting as a molecular ratchet tethered to the cell surface in complex with MMP-2 suggest a new mechanism for the role of spatially regulated peri-cellular proteolysis in cell-matrix interactions.