Trajectory and Cycle-Based Thermodynamics and Kinetics of Molecular Machines: The Importance of Microscopic Reversibility

Catalysis-driven Active Transport Across a Liquid Membrane

Biology has mastered energy transduction, converting energy between various forms, and employing it to drive its vital processes. Central to this is the ability to use chemical energy for the active transport of substances, pumping ions and molecules across hydrophobic lipid membranes between aqueous (sub)cellular compartments. Biology employs information ratchet mechanisms, where kinetic asymmetry in the fuel-to-waste (i. e., substrate-to-product) conversion results in catalysis-driven active transport. Here, we report an artificial system for catalysis-driven active transport across a hydrophobic phase, pumping a maleic acid cargo between aqueous compartments. We employ two strategies to differentiate the conditions in either compartment, showing that active transport can be driven either by adding fuel to a single compartment, or by differentiating the rates of activation and/or hydrolysis when fuel is present in both compartments. We characterize the nonequilibrium system through complete kinetic analysis. Finally, we quantify the energy transduction achieved by the catalysis-driven active transport and establish the emergence of positive and negative feedback mechanisms within the system.

Exploring the Evolution-Coupling Hypothesis: Do Enzymes' Performance Gains Correlate with Increased Dissipation?

The research literature presents divergent opinions regarding the role of dissipation in living systems, with views ranging from it being useless to it being essential for driving life. The implications of universal thermodynamic evolution are often overlooked or considered controversial. A higher rate of entropy production indicates faster thermodynamic evolution. We calculated enzyme-associated dissipation under steady-state conditions using minimalistic models of enzyme kinetics when all microscopic rate constants are known. We found that dissipation is roughly proportional to the turnover number, and a log-log power-law relationship exists between dissipation and the catalytic efficiency of enzymes. "Perfect" specialized enzymes exhibit the highest dissipation levels and represent the pinnacle of biological evolution. The examples that we analyzed suggested two key points: (a) more evolved enzymes excel in free-energy dissipation, and (b) the proposed evolutionary trajectory from generalist to specialized enzymes should involve increased dissipation for the latter. Introducing stochastic noise in the kinetics of individual enzymes may lead to optimal performance parameters that exceed the observed values. Our findings indicate that biological evolution has opened new channels for dissipation through specialized enzymes. We also discuss the implications of our results concerning scaling laws and the seamless coupling between thermodynamic and biological evolution in living systems immersed in out-of-equilibrium environments.

A Catalysis-Driven Dual Molecular Motor

We report on a head-to-tail dual molecular motor consisting of two (identical) motor units whose pyrrole-2-carboxylic rings are turned in contra-rotary (i.e., disrotatory) fashion about a common phenyl-2,5-dicarboxylic acid stator. The motors directionally rotate via information ratchet mechanisms, in which the hydration of a carbodiimide (fuel) to form urea (waste) is catalyzed through the chemomechanical cycle of a motor unit, resulting in directional rotation about a biaryl C-N bond. The head-to-tail arrangement of the motor units produces coaxial contra-rotation of the end groups while the central phenyl ring of the axis remains dynamically unbiased. The electron-rich nature of the phenyl stator contributes to rotary catalysis by the dual-motor (and therefore motor rotation itself) being ∼7× faster than the parent 1-phenylpyrrole-2,2-dicarboxylic acid single-motor when operated under identical conditions, and 90× faster than the single-motor operated using the originally reported reaction conditions. Under batch-fueled operation (i.e., all of the fuel present at the start of motor operation), the dual-motor rotates at an initial rate of 0.43 rotations per minute (rpm). Chemostating the fuel concentration by syringe pump addition produced sustained repetitive contra-rotation at a rate of 0.24 rpm for a period of 100 min. The demonstration of chemically fueled continuous contra-rotation on a time scale of 2-4 min per rotation significantly advances the chemistry and mechanics of artificial catalysis-driven molecular machinery.

Metareview: a survey of active matter reviews

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 1000 reviews on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles and books on active matter. Thereby, this article provides a useful starting point for finding literature about a specific topic.

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

Directionality Reversal and Shift of Rotational Axis in a Hemithioindigo Macrocyclic Molecular Motor

Molecular motors are central driving units for nanomachinery, and control of their directional motions is of fundamental importance for their functions. Light-driven variants use easy to provide, easy to dose, and waste-free fuel with high energy content, making them particularly interesting for applications. Typically, light-driven molecular motors work via rotations around dedicated chemical bonds where the directionality of the rotation is dictated by the steric effects of asymmetry in close vicinity to the rotation axis. In this work, we show how unidirectional rotation around a virtual axis can be realized by reprogramming a molecular motor. To this end, a classical light-driven motor is restricted by macrocyclization, and its intrinsic directional rotation is transformed into a directional rotation of the macrocyclic chain in the opposite direction. Further, solvent polarity changes allow to toggle the function of this molecular machine between a directional motor and a nondirectional photoswitch. In this way, a new concept for the design of molecular motors is delivered together with elaborate control over their motions and functions by simple solvent changes. The possibility of sensing the environmental polarity and correspondingly adjusting the directionality of motions opens up a next level of control and responsiveness to light-driven nanoscopic motors.

Photoswitchable Imines Drive Dynamic Covalent Systems to Nonequilibrium Steady States

Coupling a photochemical reaction to a thermal exchange process can drive the latter to a nonequilibrium steady state (NESS) under photoirradiation. Typically, systems use separate motifs for photoresponse and equilibrium-related processes. Here, we show that photoswitchable imines can fulfill both roles simultaneously, autonomously driving a dynamic covalent system into a NESS under continuous light irradiation. We demonstrate this using transimination reactions, where E-to-Z photoisomerism generates a more kinetically labile species. At the NESS, energy is stored both in the metastable Z-isomer of the imine and in the system's nonequilibrium constitution; when the light is switched off, this stored energy is released as the system reverts to its equilibrium state. The system operates autonomously under continuous light irradiation and exhibits characteristics of a light-driven information ratchet. This is enabled by the dual-role of the imine linkage as both the photochromic and dynamic covalent bond. This work highlights the ability and application of these imines to drive systems to NESSs, thus offering a novel approach in the field of systems chemistry.

Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.

Molecular machines working at interfaces: physics, chemistry, evolution and nanoarchitectonics

As a post-nanotechnology concept, nanoarchitectonics combines nanotechnology with advanced materials science. Molecular machines made by assembling molecular units and their organizational bodies are also products of nanoarchitectonics. They can be regarded as the smallest functional materials. Originally, studies on molecular machines analyzed the average properties of objects dispersed in solution by spectroscopic methods. Researchers' playgrounds partially shifted to solid interfaces, because high-resolution observation of molecular machines is usually done on solid interfaces under high vacuum and cryogenic conditions. Additionally, to ensure the practical applicability of molecular machines, operation under ambient conditions is necessary. The latter conditions are met in dynamic interfacial environments such as the surface of water at room temperature. According to these backgrounds, this review summarizes the trends of molecular machines that continue to evolve under the concept of nanoarchitectonics in interfacial environments. Some recent examples of molecular machines in solution are briefly introduced first, which is followed by an overview of studies of molecular machines and similar supramolecular structures in various interfacial environments. The interfacial environments are classified into (i) solid interfaces, (ii) liquid interfaces, and (iii) various material and biological interfaces. Molecular machines are expanding their activities from the static environment of a solid interface to the more dynamic environment of a liquid interface. Molecular machines change their field of activity while maintaining their basic functions and induce the accumulation of individual molecular machines into macroscopic physical properties molecular machines through macroscopic mechanical motions can be employed to control molecular machines. Moreover, research on molecular machines is not limited to solid and liquid interfaces; interfaces with living organisms are also crucial.

Kinetic Asymmetry and Directionality of Nonequilibrium Molecular Systems

Scientists have long been fascinated by the biomolecular machines in living systems that process energy and information to sustain life. The first synthetic molecular rotor capable of performing repeated 360° rotations due to a combination of photo- and thermally activated processes was reported in 1999. The progress in designing different molecular machines in the intervening years has been remarkable, with several outstanding examples appearing in the last few years. Despite the synthetic accomplishments, there remains confusion regarding the fundamental design principles by which the motions of molecules can be controlled, with significant intellectual tension between mechanical and chemical ways of thinking about and describing molecular machines. A thermodynamically consistent analysis of the kinetics of several molecular rotors and pumps shows that while light driven rotors operate by a power-stroke mechanism, kinetic asymmetry-the relative heights of energy barriers-is the sole determinant of the directionality of catalysis driven machines. Power-strokes-the relative depths of energy wells-play no role whatsoever in determining the sign of the directionality. These results, elaborated using trajectory thermodynamics and the nonequilibrium pump equality, show that kinetic asymmetry governs the response of many non-equilibrium chemical phenomena.

ABC transporters are billion-year-old Maxwell Demons

ATP-Binding Cassette (ABC) transporters are a broad family of biological machines, found in most prokaryotic and eukaryotic cells, performing the crucial import or export of substrates through both plasma and organellar membranes, and maintaining a steady concentration gradient driven by ATP hydrolysis. Building upon the present biophysical and biochemical characterization of ABC transporters, we propose here a model whose solution reveals that these machines are an exact molecular realization of the autonomous Maxwell Demon, a century-old abstract device that uses an energy source to drive systems away from thermodynamic equilibrium. In particular, the Maxwell Demon does not perform any direct mechanical work on the system, but simply selects which spontaneous processes to allow and which ones to forbid based on information that it collects and processes. In its autonomous version, the measurement device is embedded in the system itself. In the molecular model introduced here, the different operations that characterize Maxwell Demons (measurement, feedback, resetting) are features that emerge from the biochemical and structural properties of ABC transporters, revealing the crucial role of allostery to process information. Our framework allows us to develop an explicit bridge between the molecular-level description and the higher-level language of information theory for ABC transporters.

A self-sustaining serpentinization mega-engine feeds the fougerite nanoengines implicated in the emergence of guided metabolism

The demonstration by Ivan Barnes et al. that the serpentinization of fresh Alpine-type ultramafic rocks results in the exhalation of hot alkaline fluids is foundational to the submarine alkaline vent theory (AVT) for life's emergence to its 'improbable' thermodynamic state. In AVT, such alkaline fluids ≤ 150°C, bearing H2 > CH4 > HS--generated and driven convectively by a serpentinizing exothermic mega-engine operating in the ultramafic crust-exhale into the iron-rich, CO2> > > NO3--bearing Hadean ocean to result in hydrothermal precipitate mounds comprising macromolecular ferroferric-carbonate oxyhydroxide and minor sulfide. As the nanocrystalline minerals fougerite/green rust and mackinawite (FeS), they compose the spontaneously precipitated inorganic membranes that keep the highly contrasting solutions apart, thereby maintaining redox and pH disequilibria. They do so in the form of fine chimneys and chemical gardens. The same disequilibria drive the reduction of CO2 to HCOO- or CO, and the oxidation of CH4 to a methyl group-the two products reacting to form acetate in a sequence antedating the 'energy-producing' acetyl coenzyme-A pathway. Fougerite is a 2D-layered mineral in which the hydrous interlayers themselves harbor 2D solutions, in effect constricted to ~ 1D by preferentially directed electron hopping/tunneling, and proton Gröthuss 'bucket-brigading' when subject to charge. As a redox-driven nanoengine or peristaltic pump, fougerite forces the ordered reduction of nitrate to ammonium, the amination of pyruvate and oxalate to alanine and glycine, and their condensation to short peptides. In turn, these peptides have the flexibility to sequester the founding inorganic iron oxyhydroxide, sulfide, and pyrophosphate clusters, to produce metal- and phosphate-dosed organic films and cells. As the feed to the hydrothermal mound fails, the only equivalent sustenance on offer to the first autotrophs is the still mildly serpentinizing upper crust beneath. While the conditions here are very much less bountiful, they do offer the similar feed and disequilibria the survivors are accustomed to. Sometime during this transition, a replicating non-ribosomal guidance system is discovered to provide the rules to take on the incrementally changing surroundings. The details of how these replicating apparatuses emerged are the hard problem, but by doing so the progenote archaea and bacteria could begin to colonize what would become the deep biosphere. Indeed, that the anaerobic nitrate-respiring methanotrophic archaea and the deep-branching Acetothermia presently comprise a portion of that microbiome occupying serpentinizing rocks offers circumstantial support for this notion. However, the inescapable, if jarring conclusion is drawn that, absent fougerite/green rust, there would be no structured channelway to life.

Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems

The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. The aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.

A Nitrogen Out-of-Plane (NOOP) Mechanism for Imine-Based Light-Driven Molecular Motors

Light-driven molecular motors have generated considerable interest due to their potential applications in material and biological systems. Recently, Greb and Lehn reported a new class of molecular motors, chiral N-alkyl imines, which undergo unidirectional rotation induced by light and heat. The mechanism of unidirectional motion in molecular motors containing a C═N group has been assumed to consist of photoinduced torsion about the double bond. In this work, we present a computational study of the photoisomerization dynamics of a chiral N-alkyl imine motor. We find that the location and energetics of minimal energy conical intersections (MECIs) alone are insufficient to understand the mechanism of the motor. Furthermore, a key part of the mechanism consists of out-of-plane distortions of the N atom (followed by isomerization about the double bond). Dynamic effects and out-of-plane distortions are critical to understand the observed (rather low) quantum yield for photoisomerization. Our results provide hints as to how the photoisomerization quantum yield might be increased, improving the efficiency of this class of molecular motors.

Kinetic Asymmetry versus Dissipation in the Evolution of Chemical Systems as Exemplified by Single Enzyme Chemotaxis

Single enzyme chemotaxis is a phenomenon by which a nonequilibrium spatial distribution of an enzyme is created and maintained by concentration gradients of the substrate and product of the catalyzed reaction. These gradients can arise either naturally through metabolism or experimentally, e.g., by flow of materials through microfluidic channels or by use of diffusion chambers with semipermeable membranes. Numerous hypotheses regarding the mechanism of this phenomenon have been proposed. Here, we discuss a mechanism based solely on diffusion and chemical reaction and show that kinetic asymmetry, a difference in the transition state energies for dissociation/association of substrate and product, and diffusion asymmetry, a difference in the diffusivities of the bound and free forms of the enzyme, are the determinates of the direction of chemotaxis and can result in either positive or negative chemotaxis, both of which have been demonstrated experimentally. Exploration of these fundamental symmetries that govern nonequilibrium behavior helps to distinguish between possible mechanisms for the evolution of a chemical system from initial to the steady state and whether the principle that determines the direction a system shifts when exposed to an external energy source is based on thermodynamics or on kinetics with the latter being supported by the results of the present paper. Our results show that, while dissipation ineluctably accompanies nonequilibrium phenomena, including chemotaxis, systems do not evolve to maximize or minimize dissipation but rather to attain greater kinetic stability and accumulate in regions where their effective diffusion coefficient is as small as possible. The chemotactic response to the chemical gradients formed by other enzymes participating in a catalytic cascade provides a mechanism for forming loose associations known as metabolons. Significantly, the direction of the effective force due to these gradients depends on the kinetic asymmetry of the enzyme and so can be nonreciprocal, where one enzyme is attracted to another enzyme, but the other enzyme is repelled by the one, in seeming contradiction to Newtons third law. This nonreciprocity is an important ingredient in the behavior of active matter.

Using Catalysis to Drive Chemistry Away from Equilibrium: Relating Kinetic Asymmetry, Power Strokes, and the Curtin-Hammett Principle in Brownian Ratchets

Chemically fueled autonomous molecular machines are catalysis-driven systems governed by Brownian information ratchet mechanisms. One fundamental principle behind their operation is kinetic asymmetry, which quantifies the directionality of molecular motors. However, it is difficult for synthetic chemists to apply this concept to molecular design because kinetic asymmetry is usually introduced in abstract mathematical terms involving experimentally inaccessible parameters. Furthermore, two seemingly contradictory mechanisms have been proposed for chemically driven autonomous molecular machines: Brownian ratchet and power stroke mechanisms. This Perspective addresses both these issues, providing accessible and experimentally useful design principles for catalysis-driven molecular machinery. We relate kinetic asymmetry to the Curtin-Hammett principle using a synthetic rotary motor and a kinesin walker as illustrative examples. Our approach describes these molecular motors in terms of the Brownian ratchet mechanism but pinpoints both chemical gating and power strokes as tunable design elements that can affect kinetic asymmetry. We explain why this approach to kinetic asymmetry is consistent with previous ones and outline conditions where power strokes can be useful design elements. Finally, we discuss the role of information, a concept used with different meanings in the literature. We hope that this Perspective will be accessible to a broad range of chemists, clarifying the parameters that can be usefully controlled in the design and synthesis of molecular machines and related systems. It may also aid a more comprehensive and interdisciplinary understanding of biomolecular machinery.

Controlling dynamics in extended molecular frameworks

Molecular machines are essential dynamic components for fuel production, cargo delivery, information storage and processing in living systems. Scientists have demonstrated that they can design and synthesize artificial molecular machines that operate efficiently in isolation - for example, at high dilution in solution - fuelled by chemicals, electricity or light. To organize the spatial arrangement and motion of these machines within close proximity to one another in solid frameworks, such that useful macroscopic work can be performed, remains a challenge in both chemical and materials science. In this Review, we summarize the progress that has been made during the past decade in organizing dynamic molecular entities in such solid frameworks. Emerging applications of these dynamic smart materials in the contexts of molecular recognition, optoelectronics, drug delivery, photodynamic therapy and water desalination are highlighted. Finally, we review recent work on a new non-equilibrium adsorption phenomenon for which we have coined the term mechanisorption. The ability to use external energy to drive directional processes in mechanized extended frameworks augurs well for the future development of artificial molecular factories.

Photogearing as a concept for translation of precise motions at the nanoscale

One of the major challenges for harnessing the true potential of functional nano-machinery is integrating and transmitting motion with great precision. Molecular gearing systems enable the integration of multiple motions in a correlated fashion to translate motions from one locality to another and to change their speed and direction. However, currently no powerful methods exist to implement active driving of gearing motions at the molecular scale. Here we present a light-fuelled molecular gearing system and demonstrate its superiority over passive thermally activated gearing. Translation of a 180° rotation into a 120° rotation is achieved while at the same time the direction of the rotation axis is shifted by 120°. Within such photogearing processes, precise motions at the nanoscale can be changed in direction and decelerated in a manner similar to macroscopic bevel-gear operations in an energy consuming way-a necessary prerequisite to employ gearing as an active component in future mechanical nano-systems.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self-propel or to break free from supramolecular structures. This catalysis-induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Molecular rotor based on an oxidized resorcinarene

Rate of rotation of substituents in a molecular single stator-double rotor based on an oxidized resorcinarene with unsaturated hemiquinonoid groups at its meso positions (i.e., a fuchsonarene) has been controlled according to solvent polarity and acidity.

A nanoscale reciprocating rotary mechanism with coordinated mobility control

Biological molecular motors transform chemical energy into mechanical work by coupling cyclic catalytic reactions to large-scale structural transitions. Mechanical deformation can be surprisingly efficient in realizing such coupling, as demonstrated by the F₁F_O ATP synthase. Here, we describe a synthetic molecular mechanism that transforms a rotary motion of an asymmetric camshaft into reciprocating large-scale transitions in a surrounding stator orchestrated by mechanical deformation. We design the mechanism using DNA origami, characterize its structure via cryo-electron microscopy, and examine its dynamic behavior using single-particle fluorescence microscopy and molecular dynamics simulations. While the camshaft can rotate inside the stator by diffusion, the stator's mechanics makes the camshaft pause at preferred orientations. By changing the stator's mechanical stiffness, we accelerate or suppress the Brownian rotation, demonstrating an allosteric coupling between the camshaft and the stator. Our mechanism provides a framework for manufacturing artificial nanomachines that function because of coordinated movements of their components.

Nonequilibrium thermodynamics of light-induced reactions

Current formulations of nonequilibrium thermodynamics of open chemical reaction networks only consider chemostats as free-energy sources sustaining nonequilibrium behaviors. Here, we extend the theory to include incoherent light as a source of free energy. We do so by relying on a local equilibrium assumption to derive the chemical potential of photons relative to the system they interact with. This allows us to identify the thermodynamic potential and the thermodynamic forces driving light-reacting chemical systems out-of-equilibrium. We use this framework to treat two paradigmatic photochemical mechanisms describing light-induced unimolecular reactions-namely, the adiabatic and diabatic mechanisms-and highlight the different thermodynamics they lead to. Furthermore, using a thermodynamic coarse-graining procedure, we express our findings in terms of commonly measured experimental quantities, such as quantum yields.

Stereodynamics of E/Z isomerization in rotaxanes through mechanical shuttling and covalent bond rotation

The mechanical bond has opened a new world for structural and dynamic stereochemistry, which is still largely underexplored and whose significance for various applications is becoming increasingly evident. We demonstrate that designed rearrangements involving both covalent and mechanical bonds can be integrated in [2]rotaxanes, leading to interesting consequences in terms of E/Z isomerization mechanisms. Two entirely distinct and concomitant stereomutations, pertaining to the same stereogenic element but involving different kinds of linkages within the molecule, are observed and are thoroughly characterized. The rate of the two processes is affected in opposite ways upon changing solvent polarity; such a phenomenon can be used to selectively modify the rate of each motion and adjust the relative contribution of the two mechanisms to the isomerization. Although the movements are not synchronized, an analysis of the intriguing fundamental implications for transition state theory, reaction pathway bifurcation, and microscopic reversibility was triggered by our experimental observations.

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Rotaxanes that display E/Z stereoisomerism depending on the ring position

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Co-existence of two different stereomutations that yield the same product

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Mutual influence and opposite solvent dependence of the two dynamic processes

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Fundamental implications for microscopic reversibility and chemical equilibrium

The concurrence and interplay of different movements of molecular components within the same structure play a key role in providing function to naturally occurring molecular machines. Despite the progress made on artificial counterparts, the construction of molecular systems, where two (or more) motions are integrated together to produce an outcome, is still in its infancy. Molecules called rotaxanes, obtained by interlocking a ring with a dumbbell-shaped axle, are an appealing yet underexplored platform for this purpose. Here, we describe rotaxanes where two coexisting and radically different processes—rotation about a covalent bond and translation of the ring along the axle—lead to the same change in the overall molecular shape. These results are significant not only to improve our fundamental understanding of the way molecular components move but also to develop sophisticated artificial nanomachines capable of transforming or transmitting motion.

A synthetic tubular molecular transport system

Creating artificial macromolecular transport systems that can support the movement of molecules along defined routes is a key goal of nanotechnology. Here, we report the bottom-up construction of a macromolecular transport system in which molecular pistons diffusively move through micrometer-long, hollow filaments. The pistons can cover micrometer distances in fractions of seconds. We build the system using multi-layer DNA origami and analyze the structures of the components using transmission electron microscopy. We study the motion of the pistons along the tubes using single-molecule fluorescence microscopy and perform Langevin simulations to reveal details of the free energy surface that directs the motions of the pistons. The tubular transport system achieves diffusivities and displacement ranges known from natural molecular motors and realizes mobility improvements over five orders of magnitude compared to previous artificial random walker designs. Electric fields can also be employed to actively pull the pistons along the filaments, thereby realizing a nanoscale electric rail system. Our system presents a platform for artificial motors that move autonomously driven by chemical fuels and for performing nanotribology studies, and it could form a basis for future molecular transportation networks.

DNA origami can be used to control the movement of nanoscale assemblies. Here the authors construct multiple-micrometer-long hollow DNA filaments through which DNA pistons move with micrometer-per-second speeds.

Chemically-powered swimming and diffusion in the microscopic world

The past decade has seen intriguing reports and heated debates concerning the chemically-driven enhanced motion of objects ranging from small molecules to millimetre-size synthetic robots. These objects, in solutions in which chemical reactions were occurring, were observed to diffuse (spread non-directionally) or swim (move directionally) at rates exceeding those expected from Brownian motion alone. The debates have focused on whether observed enhancement is an experimental artefact or a real phenomenon. If the latter were true, then we would also need to explain how the chemical energy is converted into mechanical work. In this Perspective, we summarize and discuss recent observations and theories of active diffusion and swimming. Notably, the chemomechanical coupling and magnitude of diffusion enhancement are strongly size-dependent and should vanish as the size of the swimmers approaches the molecular scale. We evaluate the reliability of common techniques to measure diffusion coefficients and finish by considering the potential applications and chemical to mechanical energy conversion efficiencies of typical nanoswimmers and microswimmers.

Reversible catalysis

We describe as 'reversible' a bidirectional catalyst that allows a reaction to proceed at a significant rate in response to even a small departure from equilibrium, resulting in fast and energy-efficient chemical transformation. Examining the relation between reaction rate and thermodynamic driving force is the basis of electrochemical investigations of redox reactions, which can be catalysed by metallic surfaces and biological or synthetic molecular catalysts. This relation has also been discussed in the context of biological energy transduction, regarding the function of biological molecular machines that harness chemical reactions to do mechanical work. This Perspective describes mean-field kinetic modelling of these three types of systems - surface catalysts, molecular catalysts of redox reactions and molecular machines - with the goal of unifying concepts in these different fields. We emphasize that reversibility should be distinguished from other figures of merit, such as rate or directionality, before its design principles can be identified and used to engineer synthetic catalysts.

Molecular Pumps and Motors

Pumps and motors are essential components of the world as we know it. From the complex proteins that sustain our cells, to the mechanical marvels that power industries, much we take for granted is only possible because of pumps and motors. Although molecular pumps and motors have supported life for eons, it is only recently that chemists have made progress toward designing and building artificial forms of the microscopic machinery present in nature. The advent of artificial molecular machines has granted scientists an unprecedented level of control over the relative motion of components of molecules through the development of kinetically controlled, away-from-thermodynamic equilibrium chemistry. We outline the history of pumps and motors, focusing specifically on the innovations that enable the design and synthesis of the artificial molecular machines central to this Perspective. A key insight connecting biomolecular and artificial molecular machines is that the physical motions by which these machines carry out their function are unambiguously in mechanical equilibrium at every instant. The operation of molecular motors and pumps can be described by trajectory thermodynamics, a theory based on the work of Onsager, which is grounded on the firm foundation of the principle of microscopic reversibility. Free energy derived from thermodynamically non-equilibrium reactions kinetically favors some reaction pathways over others. By designing molecules with kinetic asymmetry, one can engineer potential landscapes to harness external energy to drive the formation and maintenance of geometries of component parts of molecules away-from-equilibrium, that would be impossible to achieve by standard synthetic approaches.

Active and Unidirectional Acceleration of Biaryl Rotation by a Molecular Motor

Light-driven molecular motors possess immense potential as central driving units for future nanotechnology. Integration into larger molecular setups and transduction of their mechanical motions represents the current frontier of research. Herein we report on an integrated molecular machine setup allowing the transmission of potential energy from a motor unit onto a remote receiving entity. The setup consists of a motor unit connected covalently to a distant and sterically encumbered biaryl receiver. By action of the motor unit, single-bond rotation of the receiver is strongly accelerated and forced to proceed unidirectionally. The transmitted potential energy is directly measured as the extent to which energy degeneration is lifted in the thermal atropisomerization of this biaryl. Energy degeneracy is reduced by more than 1.5 kcal mol-1 , and rate accelerations of several orders of magnitude in terms of the rate constants are achieved.

Simplicity in the Design, Operation, and Applications of Mechanically Interlocked Molecular Machines

Mechanically interlocked molecules are perhaps best known as components of molecular machines, a view further reinforced by the Nobel Prize in 2016 to Stoddart and Sauvage. Despite amazing progress since these pioneers of the field reported the first examples of molecular shuttles, genuine applications of interlocked molecular machines remain elusive, and many barriers remain to be overcome before such molecular devices make the transition from impressive prototypes on the laboratory bench to useful products. Here, we discuss simplicity as a design principle that could be applied in the development of the next generation of molecular machines with a view to moving toward real-world applications of these intriguing systems in the longer term.

On the conditions for mimicking natural selection in chemical systems

The emergence of natural selection, requiring that reproducing entities present variations that may be inherited and passed on, was arguably the most important breakthrough in the self-organization of life. In this Perspective, the assumptions governing biological reproduction are confronted with physico-chemical principles that control the evolution of material systems. In biology, the reproduction of living organisms is never considered to be reversible, whereas microscopic reversibility is an essential principle in the physical description of matter. Here, we show that this discrepancy places constraints on the possibility of finding kinetic processes in the chemical world that are equivalent to natural selection in the biological one. Chemical replicators can behave in a similar fashion to living entities, provided that the reproduction cycle proceeds in a unidirectional way. For this to be the case, kinetic barriers must hinder the reverse process. The system must, thus, be held far from equilibrium and fed with a non-degraded (low-entropy) form of energy. The ensuing constraints must be factored in when proposing scenarios that account for the origin of life at the molecular level.

On the beneficent thickness of water

In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.

Building machines with DNA molecules

In nature, DNA molecules carry the hereditary information. But DNA has physical and chemical properties that make it attractive for uses beyond heredity. In this Review, we discuss the potential of DNA for creating machines that are both encoded by and built from DNA molecules. We review the main methods of DNA nanostructure assembly, describe recent advances in building increasingly complex molecular structures and discuss strategies for creating machine-like nanostructures that can be actuated and move. We highlight opportunities for applications of custom DNA nanostructures as scientific tools to address challenges across biology, chemistry and engineering.

Kinetic asymmetry allows macromolecular catalysts to drive an information ratchet

Molecular machines carry out their function by equilibrium mechanical motions in environments that are far from thermodynamic equilibrium. The mechanically equilibrated character of the trajectories of the macromolecule has allowed development of a powerful theoretical description, reminiscent of Onsager’s trajectory thermodynamics, that is based on the principle of microscopic reversibility. Unlike the situation at thermodynamic equilibrium, kinetic parameters play a dominant role in determining steady-state concentrations away from thermodynamic equilibrium, and kinetic asymmetry provides a mechanism by which chemical free-energy released by catalysis can drive directed motion, molecular adaptation, and self-assembly. Several examples drawn from the recent literature, including a catenane-based chemically driven molecular rotor and a synthetic molecular assembler or pump, are discussed.

The mechanism by which macromolecular catalysts use energy from exergonic reactions to move, adapt, and assemble has been unclear. In this Perspective article, R. Dean Astumian shows that in addition to disequilibrium of the catalyzed reaction, kinetic asymmetry is the essential feature required to drive non-equilibrium response by an information ratchet mechanism.

How Defects Control the Out-of-Equilibrium Dissipative Evolution of a Supramolecular Tubule

Supramolecular architectures that work out-of-equilibrium or that can change in specific ways when absorbing external energy are ubiquitous in nature. Gaining the ability to create via self-assembly artificial materials possessing such fascinating behaviors would have a major impact in many fields. However, the rational design of similar dynamic structures requires to understand and, even more challenging, to learn how to master the molecular mechanisms governing how the assembled systems evolve far from the equilibrium. Typically, this represents a daunting challenge due to the limited molecular insight that can be obtained by the experiments or by classical modeling approaches. Here we combine coarse-grained molecular models and advanced simulation approaches to study at submolecular (<5 Å) resolution a supramolecular tubule, which breaks and disassembles upon absorption of light energy triggering isomerization of its azobenzene-containing monomers. Our approach allows us to investigate the molecular mechanism of monomer transition in the assembly and to elucidate the kinetic process for the accumulation of the transitions in the system. Despite the stochastic nature of the excitation process, we demonstrate how these tubules preferentially dissipate the absorbed energy locally via the amplification of defects in their supramolecular structure. We find that this constitutes the best kinetic pathway for accumulating monomer transitions in the system, which determines the dynamic evolution out-of-equilibrium and the brittle behavior of the assembly under perturbed conditions. Thanks to the flexibility of our models, we finally come out with a general principle, where defects explain and control the brittle/soft behavior of such light-responsive assemblies.