Brownian Ratchet Research Articles

A nucleotide binding rectification Brownian ratchet model for translocation of Y-family DNA polymerases

Y-family DNA polymerases are characterized by low-fidelity synthesis on undamaged DNA and ability to catalyze translesion synthesis over the damaged DNA. Their translocation along the DNA template is an important event during processive DNA synthesis. In this work we present a Brownian ratchet model for this translocation, where the directed translocation is rectified by the nucleotide binding to the polymerase. Using the model, different features of the available structures for Dpo4, Dbh and polymerase ι in binary and ternary forms can be easily explained. Other dynamic properties of the Y-family polymerases such as the fast translocation event upon dNTP binding for Dpo4 and the considerable variations of the processivity among the polymerases can also be well explained by using the model. In addition, some predicted results of the DNA synthesis rate versus the external force acting on Dpo4 and Dbh polymerases are presented. Moreover, we compare the effect of the external force on the DNA synthesis rate of the Y-family polymerase with that of the replicative DNA polymerase.

Simulations of nuclear pore transport yield mechanistic insights and quantitative predictions

To study transport through the nuclear pore complex, we developed a computational simulation that is based on known structural elements rather than a particular transport model. Results agree with a variety of experimental data including size cutoff for cargo transport with (30-nm diameter) and without (< 10 nm) nuclear localization signals (NLS), macroscopic transport rates (hundreds per second), and single cargo transit times (milliseconds). The recently observed bimodal cargo distribution is predicted, as is the relative invariance of single cargo transit times out to large size (even as macroscopic transport rate decreases). Additional predictions concern the effects of the number of NLS tags, the RanGTP gradient, and phenylalanine-glycine nucleopore protein (FG-Nup) structure, flexibility, and cross-linking. Results are consistent with and elucidate the molecular mechanisms of some existing hypotheses (selective phase, virtual gate, and selective gate models). A model emerges that is a hybrid of a number of preexisting models as well as a Brownian ratchet model, in which a cargo-karyopherin complex remains bound to the same FG-Nups for its entire trajectory through the nuclear pore complex until RanGTP severs the cargo-Nup bonds to effect release into the nucleus.

THE BROWNIAN RATCHET REVISITED: DIFFUSION FORMALISM, POLYMER-BARRIER ATTRACTIONS, AND MULTIPLE FILAMENTOUS BUNDLE GROWTH

Actin polymerization driven stochastic movement of the bacteria Listeria monocytogenes is often measured using single-particle tracking (SPT) methodology and analyzed in terms of statistics. Experimental results suggested a dynamic association between the growing actin filaments and the propelled bacteria. Based on an alternative mathematical formalism for a Brownian ratchet (BR), we introduce such an attractive interaction into the one-dimensional BR model and show that its effect is equivalent to an external resistant force on the bacterium. Such a force significantly reduces the Brownian motion of a driven bacterium, and accentuates the stepping due to polymerization. We then consider the growth, with and without a barrier, of a filamentous bundle consisting of N identical filaments. It is shown that the bundle grows with a similar rate as a single filament in the absence of a load, but can oppose N times the external force under the stalling condition. A set of relationships describing the velocity of the bacterium movement (Vz) and its apparent diffusivity (Dz) as functions of the resistant force (F) and the number of filaments in a bundle (N) are obtained. The theoretical study suggests methods for data analysis in future experiments with applied external resistant force.

Molecular motors: how to make models that can be used to convey the concept of molecular ratchets and thermal capture

A wide variety of cellular processes use molecular motors, including processive motors that move along some form of track (e.g., myosin with actin, kinesin or dynein with tubulin) and polymerases that move along a template (e.g., DNA and RNA polymerases, ribosomes). In trying to understand how these molecular motors actually move, many apply their understanding of how man-made motors work: the latter use some form of energy to exert a force or torque on its load. However, quite a different mechanism has been proposed to possibly account for the movement of molecular motors. Rather than hydrolyzing ATP to push or pull their load, they might use their own thermal vibrational energy as well as that of their load and their environment to move the load, capturing those movements that occur along a desired vector or axis and resisting others; ATP hydrolysis is required to make backward movements impossible. This intriguing thermal capture or Brownian ratchet model is relatively more difficult to convey to students. In this report, we describe several teaching aids that are very easily constructed using widely available household materials to convey the concept of a molecular ratchet.

Particle diode: Rectification of interacting Brownian ratchets

Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth of the interaction potential at which the average velocity takes its maximum. The average velocity υ decreases monotonically with the system size N by a power law υ ∝ N(-1).

Wet granular walkers and climbers

Mechanisms of locomotion in microscopic systems are of great interest not only for technological applications but also for the sake of understanding, and potentially harnessing, processes far from thermal equilibrium. Downscaling is a particular challenge and has led to a number of interesting concepts, including thermal ratchet systems and asymmetric swimmers. Here we present a granular ratchet system employing a particularly robust mechanism that can be implemented in various settings. The system consists of wetted spheres of different sizes that adhere to each other, and are subject to a symmetric oscillating, zero average external force field. An inherent asymmetry in the mutual force network leads to force rectification and hence to locomotion. We present a simple model that accounts for the observed behaviour, underscores its robustness and suggests a potential scalability of the concept.

Force-Velocity Measurements of a Few Growing Actin Filaments

Author SummaryActin self-assembles into filaments, and this produces forces that deform cell membranes in a large number of motile processes. While physical measurements have been performed of the force produced by growth of either a single filament or a large intricate array of filaments organized in an active macroscopic gel, these measurements don't provide a clear picture of how force is produced by the assembly of each filament within a complex structure. The present study explores a situation between these two extremes by measuring the force produced by the assembly of a small number of filaments. We developed a method in which actin filaments grow from the surface of magnetic beads that are aligned by a controlled magnetic field. The distance between beads in a chain-like arrangement increases with time when the force is kept constant. We observe that the growth of actin filaments is not affected by the load, in contrast to the widely accepted “Brownian ratchet model.” Instead, our results suggest that the surface opposite growing filaments imposes restrictions on the rotational fluctuations of a filament at its free hinge anchoring point, inducing a repulsive force. The confinement of filaments increases as they grow, and this in turn increases the repulsive force developed by their growth. This entropy-based mechanism may operate during motile processes when actin networks are loosely organized.

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.

The ribosome as a molecular machine: the mechanism of tRNA–mRNA movement in translocation

Translocation of tRNA and mRNA through the ribosome is one of the most dynamic events during protein synthesis. In the cell, translocation is catalysed by EF-G (elongation factor G) and driven by GTP hydrolysis. Major unresolved questions are: how the movement is induced and what the moving parts of the ribosome are. Recent progress in time-resolved cryoelectron microscopy revealed trajectories of tRNA movement through the ribosome. Driven by thermal fluctuations, the ribosome spontaneously samples a large number of conformational states. The spontaneous movement of tRNAs through the ribosome is loosely coupled to the motions within the ribosome. EF-G stabilizes conformational states prone to translocation and promotes a conformational rearrangement of the ribosome (unlocking) that accelerates the rate-limiting step of translocation: the movement of the tRNA anticodons on the small ribosomal subunit. EF-G acts as a Brownian ratchet providing directional bias for movement at the cost of GTP hydrolysis.

Simulation of Membrane Protrusion on Cellular Scale using Coarse-Grained Brownian Ratchet Model

Cell migration is a crucial process for many physiological and pathological events, such as embryogenesis and cancer metastasis. During cell migration, a lamellipodium is formed, which is a flat and broad membrane extension filled with a dense and highly branched actin network. Protrusion of the lamellipodial leading edge, referred to as membrane protrusion, is one of the essential cellular activities for continuous cell migration and a mechanochemical process of active membrane deformation driven by actin polymerization. To explain how membrane protrusion is driven by actin polymerization, Brownian ratchet (BR) model has been suggested on the basis of the underlying molecular mechanism. However, because the BR requires a priori load that cannot be determined without information of the cell shape. Therefore, to express the membrane protrusion on the cellular scale, we propose a new mathematical model, the coarse-grained BR (CBR), which is derived on the basis of nonequilibrium thermodynamics theory. The CBR can reproduce the BR within the limit of the quasistatic process of membrane protrusion, and can estimate the protrusion velocity consistently with an effective elastic constant that represents the state of the energy of the membrane. We perform a cellular-scale simulation of migrating keratocyte in which the proposed CBR is used for the membrane protrusion model on the the cellular scale. The results show that the protrusion velocity decreases with increasing the curvature of the leading edge and the stiffness of the substrate. These trends agreed with the other experimental results. Thus, the CBR can be considered an appropriate cellular-scale model to express the membrane protrusion and explains how mechanical factors affect membrane protrusion.

Ratcheting Mechanism of T7 RNA Polymerase During Transcription Elongation

RNA polymerases (RNAPs) can act as molecular motors, moving processively along DNA and synthesizing RNA from the DNA template. The RNAP from bacteriophage T7 is a single subunit enzyme that can carry out all transcriptional functions in the absence of additional protein factors, from initiation, elongation to termination. The structure of T7 RNAP resembles some of DNA polymerases in a hand-like configuration. In this modeling study we focus on how T7 RNAP couples its translocation with nucleotide addition during transcription elongation. Based on structural information and experimental data from single molecule force measurements, we build a ‘facilitated’ Brownian ratchet model that may resolve a debate between ‘power stroke’ and ‘Brownian ratchet’ views of this RNAP. In present model, the RNAP translocation is achieved either by thermal hopping, or by a facilitated movement upon Tyr639 side chain ‘pushing’. Under this scenario, we examine as well how the RNAP efficiently selects right nucleotide starting from the nucleotide pre-insertion, a ‘ratchet’ step right after the translocation. Both O-helix and Tyr639 seem to play important roles in the nucleotide selection. The selection accounts fully for transcription fidelity of T7 RNAP due to lack of proof reading. Further, we incorporate sequence effect into the translocation model and probe intrinsic termination of T7 RNAP through a forward tracking intermediate. The termination efficiency seems to be boosted by the facilitated translocation. Our present scenario for T7 RNAP is similar to a ‘two-paw’ ratchet mechanism proposed for multi-subunit RNAP. Accordingly, functional analogies could be made between involved structural elements from the two types of RNAPs.

Thermal ratcheting of solder bonded layered plates: experiments and analysis

This paper describes experiments and analysis of the warpage of Si/solder/Cu layered plates subjected to cyclic thermal loading. As received and annealed Cu plates are used as the Cu layer, and three thickness ratios are considered for the Si and Cu layers. It is experimentally shown that the initial warpage caused by soldering either grows or recovers with an increase in the number of temperature cycles and that the cyclic growth of warpage is apparent when the Cu layer is annealed and is relatively thick. Then, by performing a three‐dimensional finite element analysis, it is demonstrated that the cyclic growth and recovery of warpage shown experimentally can be simulated well if an appropriate constitutive model is employed for kinematic hardening in the Cu layer.

An integrated thermal and mechanical investigation of molten-salt thermocline energy storage

Thermal ratcheting is a critical phenomenon associated with the cyclic operation of dual-medium thermocline tanks in solar energy applications. Although thermal ratcheting poses a serious impediment to thermocline operation, this failure mode in dual-medium thermocline tanks is not yet well understood. To study the potential for the occurrence of ratcheting, a comprehensive model of a thermocline tank that includes both the heterogeneous filler region as well as the composite tank wall is formulated. The filler region consists of a rock bed with interstitial molten salt, while the tank wall is composed of a steel shell with two layers of insulation (firebrick and ceramic). The model accounts separately for the rock and molten-salt regions in view of their different thermal properties. Various heat loss conditions are applied at the external tank surface to evaluate the effect of energy losses to the surroundings. Hoop stresses, which are governed by the magnitude of temperature fluctuations, are determined through both a detailed finite-element analysis and simple strain relations. The two methods are found to yield almost identical results. Temperature fluctuations are damped by heat losses to the surroundings, leading to a reduction in hoop stresses with increased heat losses. Failure is prevented when the peak hoop stress is less than the material yield strength of the steel shell. To avoid ratcheting without incurring excessive energy loss, insulation between the steel shell and the filler region should be maximized.

ICONE19-43541 Conceptual Design Study for the Demonstration Reactor of JSFR : (4) Structural Design of Reactor Vessel

The concept of a compact reactor vessel has been formulated for the Japan Sodium-cooled Fast Reactor. In this concept, the reactor vessel is designed as a hot vessel to reduce the reactor vessel diameter. It is important to ensure structural integrity under both seismic and elevated-temperature conditions from the viewpoint of the structural designs for the hot reactor vessel. In this study, seismic evaluations were carried out, based on a seismic loading condition which had been revised after the Niigata-ken Chuetsu-oki Earthquake, occurred in Japan in 2007. Also, the thicknesses of the reactor vessel walls of a 750MWe-output plant and a 500MWe-output plant were determined from the viewpoint of buckling integrity, which resulted in 50mm for both plants. Buckling margins were evaluated to be more than 2.4. The difference in the plant outputs was negligible from the viewpoint of seismic design. Thermal integrity was evaluated under the condition that the reactor vessel wall is 50mm thick. Thermal ratcheting and creep-fatigue damage were evaluated under the three plant-start-up conditions of 2.2, 3.2, and 4.3 days. Thermal stress had to be lowered to avoid thermal ratcheting. As a result, the plant-start-up period needed more than 3.2 days for both plants. Thermal stress caused in both plants were nearly the same, and therefore the difference in the plant outputs was negligible from the viewpoint of thermal design. Hot vessel concept is acceptable for both plants under the conditions that the wall thickness is 50mm and the plant start-up period is 3.2 days.

Microtubule nanospool formation by active self-assembly is not initiated by thermal activation

Biotinylated microtubules partially coated with streptavidin and gliding on a surface coated with kinesin motors can cross-link with each other and assemble into nanospools with a diameter of a few micrometres. The size distribution of these nanospools is determined, and it is shown with simulations of microtubule gliding that these spools are too small to be formed by thermally activated turns in the gliding direction (a Brownian ratchet mechanism). Instead, spool formation is primarily the result of two processes: pinning of gliding microtubules to inactive motors and simultaneous cross-linking of multiple microtubules.

Hydrodynamic interactions enhance the performance of Brownian ratchets

We investigate how hydrodynamic interactions between Brownian particles influence the performance of a fluctuating ratchet. For this purpose, we perform Brownian dynamics simulations of particles that move in a toroidal trap under the influence of a sawtooth potential which fluctuates between two states (on and off). Hydrodynamic interactions are included in the Rotne-Prager approximation. We first consider spatially constant transition rates between the two ratchet states and observe that hydrodynamic interactions significantly increase the mean velocity of the particles but only when they are allowed to change their ratchet states individually. If in addition the transition rate to the off state is localized at the minimum of the ratchet potential, particles form characteristic transient clusters that travel with remarkably high velocities. The clusters form since drifting particles have the ability to push but also pull neighboring particles due to hydrodynamic interactions.

A Mathematical Model for Force Generation at the Kinetochore-Microtubule Interface

In this paper we construct and analyze a mathematical model for kinetochore (Kt) motors operating at the chromosome/microtubule interface. Motor dynamics are modeled using a jump-diffusion process that incorporates biased diffusion due to the binding of microtubules (MTs) by Kt binder elements and thermal ratchet forces that arise when the polymer grows against the Kt plate. The resulting force-velocity relationships are nonlinear and depend on the strength of MT binding at Kts, as well as the spatial distribution of binders and of MT rate-altering enzymes inside the Kt. In the case when Kt binders are weakly bound and spaced with the same period as the MT binding sites, the numerical results for the motor force-velocity relation and breaking loads are in complete agreement with our approximate analytic solutions. We show that in this limit motor velocity depends directly on the balance of polymer tip polymerization/depolymerization rates and is fairly insensitive to load variations. In the strong binding...

Point vortex equilibria and optimal packings of circles on a sphere

We answer the question of whether optimal packings of circles on a sphere are equilibrium solutions to the logarithmic particle interaction problem for values of N =3–12 and 24, the only values of N for which the optimal packing problem (also known as the Tammes problem) has rigorously known solutions. We also address the cases N =13–23 where optimal packing solutions have been computed, but not proven analytically. As in Jamaloodeen &amp; Newton (Jamaloodeen &amp; Newton 2006 Proc. R. Soc. Lond. Ser. A 462 , 3277–3299. ( doi:10.1098/rspa.2006.1731 )), a logarithmic, or point vortex equilibrium is determined by formulating the problem as the one in linear algebra, , where A is a N ( N −1)/2× N non-normal configuration matrix obtained by requiring that all interparticle distances remain constant. If A has a kernel, the strength vector is then determined as a right-singular vector associated with the zero singular value, or a vector that lies in the nullspace of A where the kernel is multi-dimensional. First we determine if the known optimal packing solution for a given value of N has a configuration matrix A with a non-empty nullspace. The answer is yes for N =3–9, 11–14, 16 and no for N =10, 15, 17–24. We then determine a basis set for the nullspace of A associated with the optimally packed state, answer the question of whether N -equal strength particles, , form an equilibrium for this configuration, and describe what is special about the icosahedral configuration from this point of view. We also find new equilibria by implementing two versions of a random walk algorithm. First, we cluster sub-groups of particles into patterns during the packing process, and ‘grow’ a packed state using a version of the ‘yin-yang’ algorithm of Longuet-Higgins (Longuet-Higgins 2008 Proc. R. Soc. A (doi:10.1098/rspa.2008.0219)). We also implement a version of our ‘Brownian ratchet’ algorithm to find new equilibria near the optimally packed state for N =10, 15, 17–24.

Dynamics of a polymer in a Brownian ratchet

We have used Brownian dynamics simulations to study the dynamics of a bead-and-spring polymer subject to a flashing ratchet potential. To elucidate the role of hydrodynamic (HD) interactions, simulations were carried out for the cases where HD interactions are present and when they are absent. The average speed of the polymer and its conformational properties were examined upon variation in the polymer length, N, and the ratchet spatial period, L. Two distinct dynamical regimes were evident. In the low-N/high-L regime, the velocity decreases with increasing N, and center-of-mass diffusion is a key part of the motional mechanism. By contrast, in the high-N /low-L regime, the velocity is insensitive to variation in N, and motion is achieved via the coupling of internal modes to the cycling of the ratchet potential. The location of the regimes is correlated with the average conformational state of the polymer. Incorporating HD interactions increases the average polymer velocity for all polymer lengths and ratchet spatial periods considered. The dynamical behavior of polymers in the low-N/high-L regime can be understood using simple a theoretical model that yields quantitatively reasonable predictions of the polymer velocity.

Direct observation of stepped proteolipid ring rotation in E. coli FoF1-ATP synthase

Although single-molecule experiments have provided mechanistic insight for several molecular motors, these approaches have proved difficult for membrane bound molecular motors like the F₀F₁-ATP synthase, in which proton transport across a membrane is used to synthesize ATP. Resolution of smaller steps in F₀ has been particularly hampered by signal-to-noise and time resolution. Here, we show the presence of a transient dwell between F₀ subunits a and c by improving the time resolution to 10 μs at unprecedented S/N, and by using Escherichia coli F₀F₁ embedded in lipid bilayer nanodiscs. The transient dwell interaction requires 163 μs to form and 175 μs to dissociate, is independent of proton transport residues aR210 and cD61, and behaves as a leash that allows rotary motion of the c-ring to a limit of ∼36° while engaged. This leash behaviour satisfies a requirement of a Brownian ratchet mechanism for the F₀ motor where c-ring rotational diffusion is limited to 36°.