Adiabatic operation of a molecular machine

Nonequilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis

At stationary environmental conditions, a catalyst's reaction kinetics may be restricted by its available designs and thermodynamic laws. Thus, its stationary performances may experience practical or theoretical restraints (e.g., catalysts cannot invert the spontaneous direction of a chemical reaction). However, many works have reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric nonequilibrium theory to explain anomalous catalytic behaviors driven by rapidly oscillating environments where stationary-environment restraints are broken. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a single free energy landscape cannot describe catalytic kinetics at various environmental conditions, we propose a novel control-conjugate landscape to encode the reaction kinetics over a range of control parameters λ, inspired by the Arrhenius form. The control-conjugate landscape significantly simplifies the design principle applicable to large-amplitude environmental oscillations.

A [3]-catenane non-autonomous molecular motor model: Geometric phase, no-pumping theorem, and energy transduction

We study a model of a synthetic molecular motor-a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one-subjected to time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space, which corrects previous erroneous results. We also analyze the performance of the motor subjected to step-wise driving protocols in the absence and presence of an applied load. Optimization strategies for generating large currents and maximizing free energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization.

Accounts of applied molecular rotors and rotary motors: recent advances

Molecular machines are nanoscale devices capable of performing mechanical works at molecular level. These systems could be a single molecule or a collection of component molecules that interrelate with one another to produce nanomechanical movements and resulting performances. The design of the components of molecular machine with bioinspired traits results in various nanomechanical motions. Some known molecular machines are rotors, motors, nanocars, gears, elevators, and so on based on their nanomechanical motion. The conversion of these individual nanomechanical motions to collective motions via integration into suitable platforms yields impressive macroscopic output at varied sizes. Instead of limited experimental acquaintances, the researchers demonstrated several applications of molecular machines in chemical transformation, energy conversion, gas/liquid separation, biomedical use, and soft material fabrication. As a result, the development of new molecular machines and their applications has accelerated over the previous two decades. This review highlights the design principles and application scopes of several rotors and rotary motor systems because these machines are used in real applications. This review also offers a systematic and thorough overview of current advancements in rotary motors, providing in-depth knowledge and predicting future problems and goals in this area.

Energy landscape design principle for optimal energy harnessing by catalytic molecular machines

Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using an alternative geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free-energy product molecules to high free-energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energy-harvesting catalysts.

Entropy production given constraints on the energy functions

We consider the problem of driving a finite-state classical system from some initial distribution p to some final distribution p^{'} with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions E. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in {p,p^{'}} and a graph-theoretic property defined in terms of E. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation p→p^{'} can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.

Dissipation-Driven Selection under Finite Diffusion: Hints from Equilibrium and Separation of Time Scales

When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the stationary populations of all chemical states out of equilibrium. This phenomenology has been theoretically explored mainly in the infinite diffusion limit. Here, we show that the regime in which the diffusion rate is finite, and also slower than some chemical reactions, might bring about interesting features, such as the maximisation of selection or the switch of the selected state at stationarity. We introduce a framework, rooted in a time-scale separation analysis, which is able to capture leading non-equilibrium features using only equilibrium arguments under well-defined conditions. In particular, it is possible to identify fast-dissipation sub-networks of reactions whose Boltzmann equilibrium dominates the steady-state of the entire system as a whole. Finally, we also show that the dissipated heat (and so the entropy production) can be estimated, under some approximations, through the heat capacity of fast-dissipation sub-networks. This work provides a tool to develop an intuitive equilibrium-based grasp on complex non-isothermal reaction networks, which are important paradigms to understand the emergence of complex structures from basic building blocks.

Dissipation-driven selection of states in non-equilibrium chemical networks

Life has most likely originated as a consequence of processes taking place in non-equilibrium conditions (e.g. in the proximity of deep-sea thermal vents) selecting states of matter that would have been otherwise unfavorable at equilibrium. Here we present a simple chemical network in which the selection of states is driven by the thermodynamic necessity of dissipating heat as rapidly as possible in the presence of a thermal gradient: states participating to faster reactions contribute the most to the dissipation rate, and are the most populated ones in non-equilibrium steady-state conditions. Building upon these results, we show that, as the complexity of the chemical network increases, the velocity of the reaction path leading to a given state determines its selection, giving rise to non-trivial localization phenomena in state space. A byproduct of our studies is that, in the presence of a temperature gradient, thermophoresis-like behavior inevitably appears depending on the transport properties of each individual state, thus hinting at a possible microscopic explanation of this intriguing yet still not fully understood phenomenon.

Fluctuation relations for adiabatic pumping

We derive an extended fluctuation relation for an open system coupled with two reservoirs under adiabatic one-cycle modulation. We confirm that the geometrical phase caused by the Berry-Sinitsyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.

Shortcuts to Adiabatic Pumping in Classical Stochastic Systems

Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be nonzero even in the absence of a bias. However, as the driving speed is increased, nonadiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.

Nonadiabatic Control of Geometric Pumping

We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting field, we illustrate that it enhances the current.

Mastering the non-equilibrium assembly and operation of molecular machines

In mechanically interlocked compounds, such as rotaxanes and catenanes, the molecules are held together by mechanical rather than chemical bonds. These compounds can be engineered to have several well-defined mechanical states by incorporating recognition sites between the different components. The rates of the transitions between the recognition sites can be controlled by introducing steric "speed bumps" or electrostatically switchable gates. A mechanism for the absorption of energy can also be included by adding photoactive, catalytically active, or redox-active recognition sites, or even charges and dipoles. At equilibrium, these Mechanically Interlocked Molecules (MIMs) undergo thermally activated transitions continuously between their different mechanical states where every transition is as likely as its microscopic reverse. External energy, for example, light, external modulation of the chemical and/or physical environment or catalysis of an exergonic reaction, drives the system away from equilibrium. The absorption of energy from these processes can be used to favour some, and suppress other, transitions so that completion of a mechanical cycle in a direction in which work is done on the environment - the requisite of a molecular machine - is more likely than completion in a direction in which work is absorbed from the environment. In this Tutorial Review, we discuss the different design principles by which molecular machines can be engineered to use different sources of energy to carry out self-organization and the performance of work in their environments.

Geometric fluctuation theorem for a spin-boson system

We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.

Validity of the no-pumping theorem in systems with finite-range interactions between particles

The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle systems with zero-range interactions. Interestingly, it is known that the theorem is violated by systems with exclusion interactions. These two paradigmatic interactions differ by two qualitative aspects: the range of interactions and the dependence of branching fractions on the state of the system. In this work two different models are studied in order to identify the qualitative property of the interaction that leads to breakdown of no pumping. A model with finite-range interaction is shown analytically to satisfy no pumping. In contrast, a model in which the interaction affects the probabilities of reaching different sites, given that a particle is making a transition, is shown numerically to violate the no-pumping theorem. The results suggest that systems with interactions that lead to state-dependent branching fractions do not satisfy the no-pumping theorem.

The Physics and Physical Chemistry of Molecular Machines

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Directional Molecular Transportation Based on a Catalytic Stopper-Leaving Rotaxane System

Ratchet mechanism has proved to be a key principle in designing molecular motors and machines that exploit random thermal fluctuations for directional motion with energy input. To integrate ratchet mechanism into artificial systems, precise molecular design is a prerequisite to control the pathway of relative motion between their subcomponents, which is still a formidable challenge. Herein, we report a straightforward method to control the transportation barrier of a macrocycle by selectively detaching one of the two stoppers using a novel DBU-catalyzed stopper-leaving reaction in a rotaxane system. The macrocycle was first allowed to thread onto a semidumbbell axle from the open end and subsequently thermodynamically captured into a nonsymmetrical rotaxane. Then, it was driven energetically uphill until it reached a kinetically trapped state by destroying its interaction with ammonium site, and was finally quantitatively released from the other end when the corresponding stopper barrier was removed. Although the directional transportation at the present system was achieved by discrete chemical reactions for the sake of higher transportation efficiency, it represents a new molecular transportation model by the strategy of using stopper-leavable rotaxane.

Molecular machines operating on the nanoscale: from classical to quantum

The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

Stochastic thermodynamics of hidden pumps

We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed.

Universal expression for adiabatic pumping in terms of nonequilibrium steady states

We develop a unified treatment of pumping and nonequilibrium thermodynamics. We show that the pumping current generated through an adiabatic mechanical operation in equilibrium can be expressed in terms of the stationary distribution of the corresponding driven nonequilibrium system. We also show that the total transfer in pumping can be evaluated from the work imported to the driven counterpart. These findings lead us to a unified viewpoint for pumping and nonequilibrium thermodynamics.

No-pumping theorem for many particle stochastic pumps

Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.

Method to describe stochastic dynamics using an optimal coordinate

A general method to describe the stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems: the determination of an optimal coordinate for the description of stochastic dynamics; the reconstruction of time from an ensemble of stochastic trajectories; and the decomposition of stationary stochastic dynamics into eigenmodes which do not decay exponentially with time. The problems are solved by introducing additive eigenvectors which are transformed by a stochastic matrix in a simple way - every component is translated by a constant distance. Such solutions have peculiar properties. For example, an optimal coordinate for stochastic dynamics with detailed balance is a multivalued function. An optimal coordinate for a random walk on a line corresponds to the conventional eigenvector of the one-dimensional Dirac equation. The equation for the optimal coordinate in a slowly varying potential reduces to the Hamilton-Jacobi equation for the action function.

Geometric heat flux for classical thermal transport in interacting open systems

We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system, we identify the geometric-phase-like effect and examine its impact on the classical heat transport. We find that the nonlinear interaction as well as the closely related temperature dependence of system parameters are crucial in manifesting the geometric-phase contribution of heat flux. Finally, we propose an electronic experiment based on RC circuits to verify our theoretical predictions.

Great expectations: can artificial molecular machines deliver on their promise?

The development and fabrication of mechanical devices powered by artificial molecular machines is one of the contemporary goals of nanoscience. Before this goal can be realized, however, we must learn how to control the coupling/uncoupling to the environment of individual switchable molecules, and also how to integrate these bistable molecules into organized, hierarchical assemblies that can perform significant work on their immediate environment at nano-, micro- and macroscopic levels. In this tutorial review, we seek to draw an all-important distinction between artificial molecular switches which are now ten a penny-or a dime a dozen-in the chemical literature and artificial molecular machines which are few and far between despite the ubiquitous presence of their naturally occurring counterparts in living systems. At the single molecule level, a prevailing perspective as to how machine-like characteristics may be achieved focuses on harnessing, rather than competing with, the ineluctable effects of thermal noise. At the macroscopic level, one of the major challenges inherent to the construction of machine-like assemblies lies in our ability to control the spatial ordering of switchable molecules-e.g., into linear chains and then into muscle-like bundles-and to influence the cross-talk between their switching kinetics. In this regard, situations where all the bistable molecules switch synchronously appear desirable for maximizing mechanical power generated. On the other hand, when the bistable molecules switch "out of phase," the assemblies could develop intricate spatial or spatiotemporal patterns. Assembling and controlling synergistically artificial molecular machines housed in highly interactive and robust architectural domains heralds a game-changer for chemical synthesis and a defining moment for nanofabrication.

Time-resolved vibrational spectroscopy of a molecular shuttle

Time-resolved vibrational spectroscopy is used to investigate the inter-component motion of an ultraviolet-triggered two-station molecular shuttle. The operation cycle of this molecular shuttle involves several intermediate species, which are observable in the amide I and amide II regions of the mid-IR spectrum. Using ab initio calculations on specific parts of the rotaxane, and by comparing the transient spectra of the normal rotaxane with that of the N-deuterated version, we can assign the observed vibrational modes of each species occurring during the shuttling cycle in an unambiguous way. The complete time- and frequency-dependent data set is analyzed using singular value decomposition (SVD). Using a kinetic model to describe the time-dependent concentrations of the transient species, we derive the absorption spectra associated with each stage in the operation cycle of the molecular shuttle, including the recombination of the charged species.

Periodic one-dimensional hopping model with transitions between nonadjacent states

A one-dimensional hopping model is useful for describing the motion of microscopic particles in a thermal noise environment. Recent experiments on the new generation of light-driven rotary molecular motors found that a motor in state i can jump forward to state i+1 or i+2 or backward to state i-1 or i-2 directly. In this paper, inspired by these experiments, such a modified periodic one-dimensional hopping model with arbitrary period N is studied theoretically. The mean velocity, effective diffusion constant, and mean dwell time in one single mechanochemical cycle are obtained. The corresponding results are illustrated and verified by being applied to the synthetic rotary molecular motors.

Supersymmetry and fluctuation relations for currents in closed networks

We demonstrate supersymmetry in the counting statistics of stochastic particle currents and use it to derive exact nonperturbative relations for the statistics of currents induced by arbitrarily fast time-dependent protocols.

Efficiency of autonomous soft nanomachines at maximum power

We consider nanosized artificial or biological machines working in steady state enforced by imposing nonequilibrium concentrations of solutes or by applying external forces, torques, or electric fields. For unicyclic and strongly coupled multicyclic machines, efficiency at maximum power is not bounded by the linear response value 1/2. For strong driving, it can even approach the thermodynamic limit 1. Quite generally, such machines fall into three different classes characterized, respectively, as "strong and efficient," "strong and inefficient," and "balanced." For weakly coupled multicyclic machines, efficiency at maximum power has lost any universality even in the linear response regime.

Flow density of a reversible ratchet

By defining "flow density" in a reversible ratchet, a kind of Brownian motor that runs four processes in a two-dimensional parameter space to complete a cycle, we analytically investigate the behavior of the motor's integrated flow in terms of the magnitude and location of the density maximum. It turns out that flow density gives information that can serve as a guide for obtaining the most suitable integrated flow important in the design of reversible ratchets.

Thermodynamics and kinetics of molecular motors

Molecular motors are first and foremost molecules, governed by the laws of chemistry rather than of mechanics. The dynamical behavior of motors based on chemical principles can be described as a random walk on a network of states. A key insight is that any molecular motor in solution explores all possible motions and configurations at thermodynamic equilibrium. By using input energy and chemical design to prevent motion that is not wanted, what is left behind is the motion that is desired. This review is focused on two-headed motors such as kinesin and Myosin V that move on a polymeric track. By use of microscopic reversibility, it is shown that the ratio between the number of forward steps and the number of backward steps in any sufficiently long time period does not directly depend on the mechanical properties of the linker between the two heads. Instead, this ratio is governed by the relative chemical specificity of the heads in the front-versus-rear position for the fuel, adenosine triphosphate and its products, adenosine diphosphate and inorganic phosphate. These insights have been key factors in the design of biologically inspired synthetic molecular walkers constructed out of DNA or out of small organic molecules.

Dynamical fluctuations in biochemical reactions and cycles

We develop theory for the dynamics and fluctuations in some cyclic and linear biochemical reactions. We use the approach of maximum caliber, which computes the ensemble of paths taken by the system, given a few experimental observables. This approach may be useful for interpreting single-molecule or few-particle experiments on molecular motors, enzyme reactions, ion-channels, and phosphorylation-driven biological clocks. We consider cycles where all biochemical states are observable. Our method shows how: (1) the noise in cycles increases with cycle size and decreases with the driving force that spins the cycle and (2) provides a recipe for estimating small-number features, such as probability of backward spin in small cycles, from experimental data. The back-spin probability diminishes exponentially with the deviation from equilibrium. We believe this method may also be useful for other few-particle nonequilibrium biochemical reaction systems.

Thermodynamic large fluctuations from uniformized dynamics

Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we report that, using the technique of uniformization, the thermodynamic large deviation functions of continuous-time Markov processes can be obtained from Markov chains evolving in discrete time. This formulation offers theoretical and numerical approaches to explore large deviation properties. In particular, the time evolution of autonomous and nonautonomous processes can be expressed in terms of a single Poisson rate. In this way the uniformization procedure leads to a simple and efficient way to simulate stochastic trajectories that reproduce the exact fluxes statistics. We illustrate the formalism for the current fluctuations in a stochastic pump model.

Bilability is defined when one electron is used to switch between concerted and stepwise pathways in Cu(I)-based bistable [2/3]pseudorotaxanes

Supramolecular switches operate as simple machines by using a stimulus to turn stations off and on, generating thermodynamic differences that define bistability and enable motion. What has not been previously investigated, yet is required to gain further control over molecular movements for complex operations, is an understanding of how the same stimulus can also switch pathways off and on, thus, defining the kinetic property of bilability. To address this challenge, the mechanisms of the forward and return reactions of redox-switchable Cu(I)-based [2/3]pseudorotaxanes have been quantitatively characterized utilizing mechanistic cyclic voltammetry and employing a series of isosteric bis-bidentate ligands. First, the bistability of the switch is retained across the series of ligands: Reduction of the ligand drives the reaction forward where a [2]pseudorotaxane switches into a reduced [3]pseudorotaxane and reoxidation drives the switching cycle back to the beginning. Second, the switch is bilabile with the forward reaction following an association-activated interchange pathway (concerted), whereas the reverse reaction follows a different dissociation-based dethreading pathway (stepwise). The forward reaction is more sensitive to denticity (bidentate tetrazinyl ligand, k(2) = 12,000 M(-1) s(-1), versus the monodentate pyrazinyl ligand, k(2) = 1500 M(-1) s(-1)) than to electronics (k(2) = 12,000 M(-1) s(-1) for methyl and trifluoromethyl substituents). The rate of return with the pyrazinyl ligand is k(1) = 50 s(-1). Consequently, both the mechanism and the thermodynamics of switching are stimuli dependent; they change with the oxidation state of the ligand. These findings have implications for the future design of molecular motors, which can be built from systems displaying allosterically coupled bistability and bilability.

Interactions of dithiolated tetraazamacrocyclic copper(II) and nickel(II) complexes self-assembled on gold electrodes with pi-electron deficient molecules in solution

Self-assembled monolayers of dithiolated neutral monotetraazamacrocyclic complexes of copper(II) and nickel(II) can provide molecularly defined platforms for the formation of a pseudorotaxane-like nanostructures on the gold electrode surface. We propose these complexes as pi-donor building blocks for the construction of new molecular devices. We show that these perpendicularly oriented macrocyclic complexes anchored to the electrode surface act as pi-electron rich species interacting with pi-electron deficient compounds dissolved in solution, such as fluorine derivatives of tetracyanoquinodimethane (F(4)TCNQ) or a charged bismacrocyclic tetraaza complex of copper(II). The interactions of the surface immobilized macrocyclic complexes with F(4)TCNQ and with ring-shaped acceptor molecules are monitored and characterized by linear scan voltammetry. The interactions with the bismacrocyclic compound lead to a new pseudorotaxane array supported on the electrode surface and switched on and off by the application of appropriate potentials.

Model studies of the dynamics of bacterial flagellar motors

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.