A prototype of a rationally designed chemically powered Brownian motor

The design and development of a molecular system functioning as a prototype of a Brownian motor is presented. The road towards the molecular motor is illustrated with previous attempts preparing other mechanical devices, such as a molecular brake and a molecular ratchet. Thermal and chemical energy are used to achieve unidirectional rotation in the Brownian motor. The similarities of synthetic molecular devices with biological – microscopic – and mechanical – macroscopic – systems and the perils of extrapolating macroscopic principles to the molecular level are also discussed. Received: 15 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Experimental studies of the myosin-actin motor

The mechanical processes generated by the molecular motors, myosin and actin, were measured using single molecule imaging, manipulation, and nanometry techniques. It was shown that the mechanical events of myosin are not tightly coupled with the ATP hydrolysis reaction and that myosin molecules move stochastically. These results indicate that the movement of myosin is driven by thermal motion rather than structural changes occurring in the myosin molecules. Thermal Brownian motion must be biased using the energy released from the hydrolysis of ATP. Thus, the molecular motors can harness thermal energy to perform mechanical work efficiently. Received: 20 November 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Motor proteins transporting cargos

Processive motor proteins such as kinesin and myosin-V are enzymes that use the energy of ATP hydrolysis to travel along polar cytoskeletal filaments. One of the functions of these proteins is the transport of vesicles and protein complexes that are linked to the light chains of the motors. Modeling the light chain by a linear elastic spring, and using the two-state model for one- and two-headed molecular motors, we study the influence of thermal fluctuations of the cargo on the motion of the motor-cargo complex. We solve numerically the Fokker-Planck equations of motor motion, and find that the mean velocity of the motor-cargo complex decreases monotonously as the spring becomes softer. This effect is due to the random force of thermal fluctuations of the cargo disrupting the operation of the motor. Increasing the size (thus, the friction coefficient) of the cargo also decreases the velocity. Surprisingly, we find that for a given size of the cargo, the velocity has a maximum for a certain friction of the motor. We explain this effect by the interplay between the characteristic length of thermal fluctuations of the cargo on a spring, the motor diffusion length, and the filament period. Our results may be relevant for the interpretation of single-molecule experiments with molecular motors (bead assays), where the motor motion is observed by tracking of a bead attached to the motor.     

Introduction to the physics of Brownian motors

A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field. Received: 9 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Electron ratchet effect in semiconductor devices and artificial materials with broken centrosymmetry

Studies on nonlinear electron transport in nanometer-sized semiconductor devices with broken centrosymmetry are reviewed. In these devices, an applied alternating (rocking) electric field induces a net flow of electrons in the direction perpendicular to that of the applied field. Such an electron ratchet effect has been observed in a number of differently designed devices, fabricated from two types of semiconductor material systems. The functionality is interpreted with an extended Büttiker–Landauer formula. We show that the devices operate at both cryogenic and room temperatures and at frequencies up to at least 50 GHz. Based on a similar microscopic mechanism, we have also constructed, to the best of our knowledge, the first artificial electronic nanomaterial that operates at room temperature. The promising possibilities for practical applications, such as rectification, microwave detection, second-harmonic generation, etc., are also discussed. Received: 16 January 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Fabrication and characterization of photonic crystals with well-controlled thickness and stop-band attenuation

Photonic crystals with stop bands located in the visible region have been fabricated by crystallizing monodispersed spherical colloids (made of polystyrene or silica) into cubic-close-packed lattices within specially designed packing cells. These crystals were oriented with their (111) planes parallel to their solid supports, and the number of these planes could be conveniently controlled from 13 to 127 layers by varying the thickness of packing cells. In accordance, the stop-band attenuation of these crystals monotonically increased from 1 to 21 dB. Our transmission spectral measurements indicated that there exists a non-linear dependence between the stop-band attenuation and the total number of (111) planes, and this dependence could be quantitatively simulated using the dynamic light scattering model or the photonic analogy to KKR method. The colloidal crystals presented here should find use as components in fabricating optical devices that include sensors, mirrors, filters, switches and waveguides. Received: 17 May 2002 / Accepted: 25 July 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +1-206/685-8665, E-mail: xia@chem.washington.edu     

Brownian motors in the photoalignment of liquid crystals

Light can change the orientation of liquid-crystal molecules. Usually, the torque that causes the reorientation originates in angular-momentum transfer from the radiation field to the material. If a small amount of dichroic dye is dissolved in the liquid crystal, a light-induced torque can appear essentially without the transfer of angular momentum from light. We show that, in such cases, the dye molecules act as light-driven molecular motors which, via an orientational Brownian ratchet mechanism, transfer angular momentum, which originates at the cell walls, to the liquid crystal. Understanding the details of this mechanism is important for applications ranging from flat-panel displays to optomechanical transducers. Received: 20 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Elastically coupled molecular motors

We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays. Received: 27 November 1997 / Revised: 20 February 1998 / Accepted: 27 March 1998     

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

An introduction to the physics of the bacterial flagellar motor: a nanoscale rotary electric motor

Biological molecular motors show us how directed motion can be generated by nanometre-scale devices that work at the energy scale of the thermal bath. Direct and indirect observations of functioning single molecule motors allow us to see fundamental processes of statistical physics unfolding in microscopic detail at room temperature, something that was unimaginable only a few decades ago. In this review, we introduce molecular motors and the physics relevant to their mechanisms before focusing on our recent experiments on the bacterial flagellar motor, the rotary device responsible for bacterial locomotion.     

Force generation by polymerizing microtubules

Polymerization ratchets formed by the assembly of actin filaments and microtubules are possibly the simplest realizations of biological thermal ratchets. A variety of experimental evidence exists that significant forces are generated by these processes, but quantitative studies lag far behind similar studies for molecular motors such as kinesin and myosin. Here we present a discussion of the theory of polymerization ratchets as well as experimental techniques used in our laboratory for the study of forces generated by single growing microtubules. Data obtained with these techniques provide us with valuable information that may eventually allow us to distinguish between different models for the growth of microtubules. Received: 15 January 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Application of the ratchet effect to improve material quality (reducing vortex density in superconductors and smoothing surfaces)

Although Brownian ratchets have been conceived to describe the operation of molecular motor proteins, their basic principles are also applicable to a wide range of different physical systems. In this paper I line up two such possible applications in condensed-matter physics. The first one is the removal of vortices from superconductors. Magnetic fields frequently penetrate superconducting materials in the form of vortices, and once present, they dissipate energy and generate internal noise, limiting the operation of numerous superconducting devices. We demonstrate theoretically that the application of an alternating current to a superconductor patterned with an appropriate ratchet-like pinning potential induces an outward vortex motion. The second application is based on the fact that the Schwoebel barrier induces an asymmetry in the lattice potential of nearly flat solid surfaces. During epitaxial growth this asymmetry leads to a fast and unwanted increase in the surface roughness. We show, however, that one can take advantage of the asymmetry by applying an alternating electric field parallel to the surface, which induces a net electromigrational flow of the surface atoms from the peaks towards the wells, and thus results in a smoother surface. Received: 20 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Group-IV nanocluster formation by ion-beam synthesis

A short review of our investigations devoted to the use of ion-beam-synthesized nanoclusters for silicon-based light emission and nonvolatile memory effects is presented. Blue-violet light emission is demonstrated based on Ge-implanted silicon dioxide layers thermally grown on silicon substrates. This version of silicon-based light emission relies on Ge-related defects in the amorphous ≡Si–O–Si≡ network. The photoluminescence and electroluminescence are excited by a singlet S₀–S₁ transition of a neutral oxygen vacancy and by electron injection from the silicon substrate into the silicon dioxide layer, respectively. Whereas the photoluminescence excitation is a well-known mechanism, for the case of electroluminescence an interpretation was performed for the first time in the course of our studies. It was found that the most probable way to excite luminescence centers is the impact excitation by hot electrons. Whereas the injection is explained by trap-assisted tunneling of electrons from the substrate into the oxide, the electrons will be transported via traps or in the SiO₂ conduction band. The application of the silicon-based light-emitting devices for an integrated optocoupler arrangement is described. Another application of nanoclusters is based on the investigation of thin Si-implanted silicon dioxide layers for nonvolatile memory devices. First promising results demonstrate that the observed programming window can reach several volts and the devices exhibit excellent retention behavior. A 256 K-nv-SRAM is demonstrated showing a programming window of >1 V for write pulses of 12 V/8 ms. Received: 21 August 2002 / Accepted: 21 August 2002 / Published online: 12 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-351/260-3411, E-mail: w.skorupa@fz-rossendorf.de     

Active chiral fluids

Active processes in biological systems often exhibit chiral asymmetries. Examples are the chirality of cytoskeletal filaments which interact with motor proteins, the chirality of the beat of cilia and flagella as well as the helical trajectories of many biological microswimmers. Here, we derive constitutive material equations for active fluids which account for the effects of active chiral processes. We identify active contributions to the antisymmetric part of the stress as well as active angular momentum fluxes. We discuss four types of elementary chiral motors and their effects on a surrounding fluid. We show that large-scale chiral flows can result from the collective behavior of such motors even in cases where isolated motors do not create a hydrodynamic far field.      

Energetics of Brownian motors: a review

We review the literature on the energetics of Brownian motors, distinguishing between forced ratchets, chemical motors – driven out of equilibrium by differences of chemical potential, and thermal motors – driven by temperature differences. The discussion is focused on the definition of efficiency and the compatibility between the models and the laws of thermodynamics. Received: 13 November 2001 / Accepted: 10 January 2002 / Published online: 22 April 2002     

Electrokinetic ‘ratchet’ pumps for microfluidics

The symmetry argument underlying ‘ratchet’ schemes for the motion of molecular motors and for selective transport of particles is shown to yield new means for the pumping of liquids. A practical realization consists in using surfaces bearing polar periodic arrays of electrodes addressed by an ac voltage difference. The resulting surface-induced pumping remains efficient under miniaturization and may find application in microfluidics. Received: 19 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Optically and thermally induced molecular switching processes at metal surfaces

Using light to control the switching of functional properties of surface-bound species is an attractive strategy for the development of new technologies with possible applications in molecular electronics and functional surfaces and interfaces. Molecular switches are promising systems for such a route, since they possess the ability to undergo reversible changes between different molecular states and accordingly molecular properties by excitation with light or other external stimuli. In this review, recent experiments on photo- and thermally induced molecular switching processes at noble metal surfaces utilizing two-photon photoemission and surface vibrational spectroscopies are reported. The investigated molecular switches can either undergo a trans-cis?isomerization or a ring opening-closure reaction. Two approaches concerning the connection of the switches to the surface are applied: physisorbed switches, i.e.?molecules in direct contact with the substrate, and surface-decoupled switches incorporated in self-assembled monolayers. Elementary processes in molecular switches at surfaces, such as excitation mechanisms in photoisomerization and kinetic parameters for thermally driven reactions, which are essential for a microscopic understanding of molecular switching at surfaces, are presented. This in turn is needed for designing an appropriate adsorbate-substrate system with the desired switchable functionality controlled by external stimuli.     

Ratchet patterns sort molecular shuttles

Molecular shuttles based on microtubules propelled by motor proteins can be guided on surfaces by adsorbing motors in chemical patterns or by using open guiding channels. While chemical patterns can guide microtubules based on a Brownian ratchet mechanism, the rigidity of the microtubules limits guiding to features with dimensions on the order of their persistence length (5 mm). To achieve guiding on micron-scale dimensions, physical barriers are required which can exploit the forces exerted by multiple motors to bend tubules into tight radii of curvature. Microtubule guiding is illustrated for the case of a special ratchet pattern that is capable of sorting microtubules on the basis of the direction of their motion. Received: 3 December 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Synergetic driving concepts for bundled miniature ultrasonic linear motors

Rotary ultrasonic motors have found broad industrial application in camera lens drives and other systems. Linear ultrasonic motors in contrast have only found limited applications. The main reason for the limited range of application of these very attractive devices seems to be their small force and power range. Attempts to build linear ultrasonic motors for high forces and high power applications have not been truly successful yet. To achieve larger force and higher power, multiple miniaturized motors can be combined. This approach, however, is not as simple as it appears at first glance. The electromechanical behaviour of the individual motors differs slightly due to manufacturing and assembly tolerances. The individual motor characteristics are strongly dependent on the driving parameters (frequency, voltage, temperature, pre-stress, etc.) and the driven load and the collective behaviour of the swarm of motors is not just the linear superposition of the individual drive's forces. Thus, the bundle of motors has to be synchronized and controlled appropriately in order to obtain an optimized drive that is not oversized and costly. We have investigated driving and control strategies of a set of linear ultrasonic motors. Our contribution will be divided into three main parts. In part I ultrasonic linear motors will be introduced. In part II driving strategies for a single motor as well as for a bundle of motors will be presented. These concepts will be verified by simulation results and experimental data. In part III a simplified model for the motor's electromechanical behaviour will be given.     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.