Design principles for Brownian molecular machines: how to swim in molasses and walk in a hurricane

Repurposing a Catalytic Cycle for Transient Self-Assembly

Life operates out of equilibrium to enable various sophisticated behaviors. Synthetic chemists have strived to mimic biological nonequilibrium systems in such fields as autonomous molecular machines and dissipative self-assembly. Central to these efforts has been the development of new chemical reaction cycles, which drive systems out of equilibrium by conversion of chemical fuel into waste species. However, the construction of reaction cycles has been challenging due to the difficulty of finding compatible reactions that constitute a cycle. Here, we realize an alternative approach by repurposing a known catalytic cycle as a chemical reaction cycle for driving dissipative self-assembly. This approach can overcome the compatibility problem because all steps involved in a catalytic cycle are already known to proceed concurrently under the same conditions. Our repurposing approach is applicable to diverse combinations of catalytic cycles and systems to drive out of equilibrium, which will substantially broaden the scope of out-of-equilibrium systems.

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.

Excited State Dynamics in Unidirectional Photochemical Molecular Motors

Unidirectional photochemically driven molecular motors (PMMs) convert the energy of absorbed light into continuous rotational motion. As such they are key components in the design of molecular machines. The prototypical and most widely employed class of PMMs is the overcrowded alkenes, where rotational motion is driven by successive photoisomerization and thermal helix inversion steps. The efficiency of such PMMs depends upon the speed of rotation, determined by the rate of ground state thermal helix inversion, and the quantum yield of photoisomerization, which is dependent on the excited state energy landscape. The former has been optimized by synthetic modification across three generations of overcrowded alkene PMMs. These improvements have often been at the expense of photoisomerization yield, where there remains room for improvement. In this perspective we review the application of ultrafast spectroscopy to characterize the excited state dynamics in PMMs. These measurements lead to a general mechanism for all generations of PMMs, involving subpicosecond decay of a Franck-Condon excited state to populate a dark excited state which decays within picoseconds via conical intersections with the electronic ground state. The model is discussed in the context of excited state dynamics calculations. Studies of PMM photochemical dynamics as a function of solvent suggest exploitation of intramolecular charge transfer and solvent polarity as a route to controlling photoisomerization yield. A test of these ideas for a first generation motor reveals a high degree of solvent control over isomerization yield. These results suggest a pathway to fine control over the performance of future PMMs.

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.

Highly Ordered Co-Assembly of Bisurea Functionalized Molecular Switches at the Solid-Liquid Interface

Immobilization of stimulus-responsive systems on solid surfaces is beneficial for controlled signal transmission and adaptive behavior while allowing the characterization of the functional interface with high sensitivity and high spatial resolution. Positioning of the stimuli-responsive units with nanometer-scale precision across the adaptive surface remains one of the bottlenecks in the extraction of cooperative function. Nanoscale organization, cooperativity, and amplification remain key challenges in bridging the molecular and the macroscopic worlds. Here we report on the design, synthesis, and scanning tunneling microscopy (STM) characterization of overcrowded alkene photoswitches merged in self-assembled networks physisorbed at the solid-liquid interface. A detailed anchoring strategy that ensures appropriate orientation of the switches with respect to the solid surface through the use of bis-urea groups is presented. We implement a co-assembly strategy that enables the merging of the photoswitches within physisorbed monolayers of structurally similar 'spacer' molecules. The self-assembly of the individual components and the co-assemblies was examined in detail using (sub)molecular resolution STM which confirms the robust immobilization and controlled orientation of the photoswitches within the spacer monolayers. The experimental STM data is supported by detailed molecular mechanics (MM) simulations. Different designs of the switches and the spacers were investigated which allowed us to formulate guidelines that enable the precise organization of the photoswitches in crystalline physisorbed self-assembled molecular networks.

Dynamic coupling of fast channel gating with slow ATP-turnover underpins protein transport through the Sec translocon

The Sec translocon is a highly conserved membrane assembly for polypeptide transport across, or into, lipid bilayers. In bacteria, secretion through the core channel complex-SecYEG in the inner membrane-is powered by the cytosolic ATPase SecA. Here, we use single-molecule fluorescence to interrogate the conformational state of SecYEG throughout the ATP hydrolysis cycle of SecA. We show that the SecYEG channel fluctuations between open and closed states are much faster (~20-fold during translocation) than ATP turnover, and that the nucleotide status of SecA modulates the rates of opening and closure. The SecY variant PrlA4, which exhibits faster transport but unaffected ATPase rates, increases the dwell time in the open state, facilitating pre-protein diffusion through the pore and thereby enhancing translocation efficiency. Thus, rapid SecYEG channel dynamics are allosterically coupled to SecA via modulation of the energy landscape, and play an integral part in protein transport. Loose coupling of ATP-turnover by SecA to the dynamic properties of SecYEG is compatible with a Brownian-rachet mechanism of translocation, rather than strict nucleotide-dependent interconversion between different static states of a power stroke.

Ratcheting synthesis

Synthetic chemistry has traditionally relied on reactions between reactants of high chemical potential and transformations that proceed energetically downhill to either a global or local minimum (thermodynamic or kinetic control). Catalysts can be used to manipulate kinetic control, lowering activation energies to influence reaction outcomes. However, such chemistry is still constrained by the shape of one-dimensional reaction coordinates. Coupling synthesis to an orthogonal energy input can allow ratcheting of chemical reaction outcomes, reminiscent of the ways that molecular machines ratchet random thermal motion to bias conformational dynamics. This fundamentally distinct approach to synthesis allows multi-dimensional potential energy surfaces to be navigated, enabling reaction outcomes that cannot be achieved under conventional kinetic or thermodynamic control. In this Review, we discuss how ratcheted synthesis is ubiquitous throughout biology and consider how chemists might harness ratchet mechanisms to accelerate catalysis, drive chemical reactions uphill and programme complex reaction sequences.

Interaction-induced directed transport in quantum chaotic subsystems

Quantum directed transport can be realized in noninteracting, deterministic, chaotic systems by appropriately breaking the spatiotemporal symmetries in the potential. In this work, the focus is on the class of interacting two-body quantum systems whose classical limit is chaotic. It is shown that one subsystem effectively acts as a source of "noise" to the other leading to intrinsic temporal symmetry breaking. Then, the quantum directed currents, even if prohibited by symmetries in the composite system, can be realized in the subsystems. This current is of quantum origin and does not arise from semiclassical effects. This protocol provides a minimal framework-broken spatial symmetry in the potential and presence of interactions-for realizing directed transport in interacting chaotic systems. It is also shown that the magnitude of directed current undergoes multiple current reversals upon varying the interaction strength and this allows for controlling the currents. It is explicitly demonstrated in the two-body interacting kicked rotor model. The interaction-induced mechanism for subsystem directed currents would be applicable to other interacting quantum systems as well.

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.

Functional dynamics in framework materials

Dynamic crystalline materials have emerged as a unique category of condensed phase matter that combines crystalline lattice with components that display dynamic behavior in the solid state. This has involved a range of materials incorporating dynamic functional units in the form of stimuli-responsive molecular switches and machines, among others. In particular, it has been possible by relying on framework materials, such as porous molecular frameworks and other hybrid organic-inorganic systems that demonstrated potential for serving as scaffolds for dynamic molecular functions. As functional dynamics increase the level of complexity, the associated phenomena are often overlooked and need to be explored. In this perspective, we discuss a selection of recent developments of dynamic solid-state materials across material classes, outlining opportunities and fundamental and methodological challenges for their advancement toward innovative functionality and applications.

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.

On the thermodynamics of DNA methylation process

DNA methylation is an epigenetic mechanism that plays important roles in various biological processes including transcriptional and post-transcriptional regulation, genomic imprinting, aging, and stress response to environmental changes and disease. Consistent with thermodynamic principles acting within living systems and the application of maximum entropy principle, we propose a theoretical framework to understand and decode the DNA methylation process. A central tenet of this argument is that the probability density function of DNA methylation information-divergence summarizes the statistical biophysics underlying spontaneous methylation background and implicitly bears on the channel capacity of molecular machines conforming to Shannon's capacity theorem. On this theoretical basis, contributions from the molecular machine (enzyme) logical operations to Gibb entropy (S) and Helmholtz free energy (F) are intrinsic. Application to the estimations of S on datasets from Arabidopsis thaliana suggests that, as a thermodynamic state variable, individual methylome entropy is completely determined by the current state of the system, which in biological terms translates to a correspondence between estimated entropy values and observable phenotypic state. In patients with different types of cancer, results suggest that a significant information loss occurs in the transition from differentiated (healthy) tissues to cancer cells. This type of analysis may have important implications for early-stage diagnostics. The analysis of entropy fluctuations on experimental datasets revealed existence of restrictions on the magnitude of genome-wide methylation changes originating by organismal response to environmental changes. Only dysfunctional stages observed in the Arabidopsis mutant met1 and in cancer cells do not conform to these rules.

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.

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.

Driving a Third Generation Molecular Motor with Electrons Across a Surface

Excitation of single molecules with electrons tunneling between a sharp metallic tip of a scanning tunneling microscope and a metal surface is one way to study and control dynamics of molecules on surfaces. Electron tunneling induced dynamics may lead to hopping, rotation, molecular switching, or chemical reactions. Molecular motors that convert rotation of subgroups into lateral movement on a surface can in principle also be driven by tunneling electrons. For such surface-bound motor molecules the efficiency of motor action with respect to electron dose is still not known. Here, the response of a molecular motor containing two rotor units in the form of overcrowded alkene groups to inelastic electron tunneling has been examined on a Cu(111) surface in ultrahigh vacuum at 5 K. Upon vibrational excitation, switching between different molecular conformations is observed, including conversion of enantiomeric states of chiral conformations. Tunneling at energies in the range of electronic excitations causes activation of motor action and movement across the surface. The expected unidirectional rotation of the two rotor units causes forward movements but with a low degree of translational directionality.

Chirality-Specific Unidirectional Rotation of Molecular Motors on Cu(111)

Molecular motors have chemical properties that enable unidirectional motion, thus breaking microscopic reversibility. They are well studied in solution, but much less is known regarding their behavior on solid surfaces. Here, single motor molecules adsorbed on a Cu(111) surface are excited by voltages pulses from an STM tip, which leads to their rotation around a fixed pivot point. Comparison with calculations shows that this axis results from a chemical bond of a sulfur atom in the chemical structure and a metal atom of the surface. While statistics show approximately equal rotations in both directions, clockwise and anticlockwise, a detailed study reveals that these motions are enantiomer-specific. Hence, the rotation direction of each individual molecule depends on its chirality, which can be determined from STM images. At first glance, these dynamics could be assigned to the activation of the motor molecule, but our results show that this is unlikely as the molecule remains in the same conformation after rotation. Additionally, a control molecule, although it lacks unidirectional rotation in solution, also shows unidirectional rotation for each enantiomer. Hence, it seems that the unidirectional rotation is not specifically related to the motor property of the molecule. The calculated energy barriers for motion show that the propeller-like motor activity requires higher energy than the simple rotation of the molecule as a rigid object, which is therefore preferred.

Autonomous Non-Equilibrium Self-Assembly and Molecular Movements Powered by Electrical Energy

The ability to exploit energy autonomously is one of the hallmarks of life. Mastering such processes in artificial nanosystems can open technological opportunities. In the last decades, light- and chemically driven autonomous systems have been developed in relation to conformational motion and self-assembly, mostly in relation to molecular motors. In contrast, despite electrical energy being an attractive energy source to power nanosystems, its autonomous harnessing has received little attention. Herein we consider an operation mode that allows the autonomous exploitation of electrical energy by a self-assembling system. Threading and dethreading motions of a pseudorotaxane take place autonomously in solution, powered by the current flowing between the electrodes of a scanning electrochemical microscope. The underlying autonomous energy ratchet mechanism drives the self-assembly steps away from equilibrium with a higher energy efficiency compared to other autonomous systems. The strategy is general and might be extended to other redox-driven systems.

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.

DNA-Based Molecular Machines

Artificial molecular machines have found widespread applications ranging from fundamental studies to biomedicine. More recent advances in exploiting unique physical and chemical properties of DNA have led to the development of DNA-based artificial molecular machines. The unprecedented programmability of DNA provides a powerful means to design complex and sophisticated DNA-based molecular machines that can exert mechanical force or motion to realize complex tasks in a controllable, modular fashion. This Perspective highlights the potential and strategies to construct artificial molecular machines using double-stranded DNA, functional nucleic acids, and DNA frameworks, which enable improved control over reaction pathways and motion behaviors. We also outline the challenges and opportunities of using DNA-based molecular machines for biophysics, biosensing, and biocomputing.

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.

Virial-like thermodynamic uncertainty relation in the tight-binding regime

We presented a methodology to approximate the entropy production for Brownian motion in a tilted periodic potential. The approximation stems from the well known thermodynamic uncertainty relation. By applying a virial-like expansion, we provided a tighter lower limit solely in terms of the drift velocity and diffusion. The approach presented is systematically analyzed in the tight-binding regime. We also provide a relative simple rule to validate using the tight-binding approach based on drift and diffusion relations rather than energy barriers and forces. We also discuss the implications of our results outside the tight-binding regime.

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.

Information thermodynamics for deterministic chemical reaction networks

Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved.

Insights into Chemically Fueled Supramolecular Polymers

Supramolecular polymerization can be controlled in space and time by chemical fuels. A nonassembled monomer is activated by the fuel and subsequently self-assembles into a polymer. Deactivation of the molecule either in solution or inside the polymer leads to disassembly. Whereas biology has already mastered this approach, fully artificial examples have only appeared in the past decade. Here, we map the available literature examples into four distinct regimes depending on their activation/deactivation rates and the equivalents of deactivating fuel. We present increasingly complex mathematical models, first considering only the chemical activation/deactivation rates (i.e., transient activation) and later including the full details of the isodesmic or cooperative supramolecular processes (i.e., transient self-assembly). We finish by showing that sustained oscillations are possible in chemically fueled cooperative supramolecular polymerization and provide mechanistic insights. We hope our models encourage the quantification of activation, deactivation, assembly, and disassembly kinetics in future studies.

Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics

Most computer simulations of molecular dynamics take place under equilibrium conditions-in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.

F1-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory

In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F1-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F1-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium "controlled rotation" experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5-6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.

Phototriggered Complex Motion by Programmable Construction of Light-Driven Molecular Motors in Liquid Crystal Networks

Recent developments in artificial molecular machines have enabled precisely controlled molecular motion, which allows several distinct mechanical operations at the nanoscale. However, harnessing and amplifying molecular motion along multiple length scales to induce macroscopic motion are still major challenges and comprise an important next step toward future actuators and soft robotics. The key to addressing this challenge relies on effective integration of synthetic molecular machines in a hierarchically aligned structure so numerous individual molecular motions can be collected in a cooperative way and amplified to higher length scales and eventually lead to macroscopic motion. Here, we report the complex motion of liquid crystal networks embedded with molecular motors triggered by single-wavelength illumination. By design, both racemic and enantiomerically pure molecular motors are programmably integrated into liquid crystal networks with a defined orientation. The motors have multiple functions acting as cross-linkers, actuators, and chiral dopants inside the network. The collective rotary motion of motors resulted in multiple types of motion of the polymeric film, including bending, wavy motion, fast unidirectional movement on surfaces, and synchronized helical motion with different handedness, paving the way for the future design of responsive materials with enhanced complex functions.

Insights from an information thermodynamics analysis of a synthetic molecular motor

Information is physical, a realization that has transformed the physics of measurement and communication. However, the flow between information, energy and mechanics in chemical systems remains largely unexplored. Here we analyse a minimalist autonomous chemically driven molecular motor in terms of information thermodynamics, a framework that quantitatively relates information to other thermodynamic parameters. The treatment reveals how directional motion is generated by free energy transfer from chemical to mechanical (conformational and/or co-conformational) processes by 'energy flow' and 'information flow'. It provides a thermodynamic level of understanding of molecular motors that is general, complements previous analyses based on kinetics and has practical implications for machine design. In line with kinetic analysis, we find that power strokes do not affect the directionality of chemically driven machines. However, we find that power strokes can modulate motor velocity, the efficiency of free energy transfer and the number of fuel molecules consumed per cycle. This may help explain the role of such (co-)conformational changes in biomachines and illustrates the interplay between energy and information in chemical systems.

Progressive Local Accumulation of Self-Assembled Nanoreactors in a Hydrogel Matrix through Repetitive Injections of ATP

Cellular functions are regulated with high spatial control through the local activation of chemical processes in a complex inhomogeneous matrix. The development of synthetic macroscopic systems with a similar capacity allows fundamental studies aimed at understanding the relationship between local molecular events and the emergence of functional properties at the macroscopic level. Here, we show that a kinetically stable inhomogeneous hydrogel matrix is spontaneously formed upon the local injection of ATP. Locally, ATP templates the self-assembly of amphiphiles into large nanoreactors with a much lower diffusion rate compared to unassembled amphiphiles. The local depletion of unassembled amphiphiles near the injection point installs a concentration gradient along which unassembled amphiphiles diffuse from the surroundings to the center. This allows for a progressive local accumulation of self-assembled nanoreactors in the matrix upon repetitive cycles of ATP injection separated by time intervals during which diffusion of unassembled amphiphiles takes place. Contrary to the homogeneous matrix containing the same components, in the inhomogeneous matrix the local upregulation of a chemical reaction occurs. Depending on the way the same amount of injected ATP is administered to the hydrogel matrix different macroscopic distributions of nanoreactors are obtained, which affect the location in the matrix where the chemical reaction is upregulated.

Polyrotaxanes and the pump paradigm

The year 2022 marks the 30th anniversary of the first reports of polyrotaxanes in the scientific literature.

Photochemical Energy Conversion with Artificial Molecular Machines

The exploitation of sunlight as a clean, renewable, and distributed energy source is key to facing the energetic demand of modern society in a sustainable and affordable fashion. In the past few decades, chemists have learned to make molecular machines, that is, synthetic chemical systems in which energy inputs cause controlled movements of molecular components that could be used to perform a task. A variety of artificial molecular machines operated by light have been constructed by implementing photochemical processes within appropriately designed (supra)molecular assemblies. These studies could open up new routes for the realization of nanostructured devices and materials capable to harness, convert, and store light energy.

Designing light-driven rotary molecular motors

The ability to induce and amplify motion at the molecular scale has seen tremendous progress ranging from simple molecular rotors to responsive materials. In the two decades since the discovery of light-driven rotary molecular motors, the development of these molecules has been extensive; moving from the realm of molecular chemistry to integration into dynamic molecular systems. They have been identified as actuators holding great potential to precisely control the dynamics of nanoscale devices, but integrating molecular motors effectively into evermore complex artificial molecular machinery is not trivial. Maximising efficiency without compromising function requires conscious and judicious selection of the structures used. In this perspective, we focus on the key aspects of motor design and discuss how to manipulate these properties without impeding motor integrity. Herein, we describe these principles in the context of molecular rotary motors featuring a central double bond axle and emphasise the strengths and weaknesses of each design, providing a comprehensive evaluation of all artificial light-driven rotary motor scaffolds currently present in the literature. Based on this discussion, we will explore the trajectory of research into the field of molecular motors in the coming years, including challenges to be addressed, potential applications, and future prospects.

Chemically Fueled Self-Assembly in Biology and Chemistry

Life is a non-equilibrium state of matter maintained at the expense of energy. Nature uses predominantly chemical energy stored in thermodynamically activated, but kinetically stable, molecules. These high-energy molecules are exploited for the synthesis of other biomolecules, for the activation of biological machinery such as pumps and motors, and for the maintenance of structural order. Knowledge of how chemical energy is transferred to biochemical processes is essential for the development of artificial systems with life-like processes. Here, we discuss how chemical energy can be used to control the structural organization of organic molecules. Four different strategies have been identified according to a distinguishable physical-organic basis. For each class, one example from biology and one from chemistry are discussed in detail to illustrate the practical implementation of each concept and the distinct opportunities they offer. Specific attention is paid to the discussion of chemically fueled non-equilibrium self-assembly. We discuss the meaning of non-equilibrium self-assembly, its kinetic origin, and strategies to develop synthetic non-equilibrium systems.

A catalysis-driven artificial molecular pump

All biological pumps are autonomous catalysts; they maintain the out-of-equilibrium conditions of the cell by harnessing the energy released from their catalytic decomposition of a chemical fuel^1-3. A number of artificial molecular pumps have been reported to date⁴, but they are all either fuelled by light^5-10 or require repetitive sequential additions of reagents or varying of an electric potential during each cycle to operate^11-16. Here we describe an autonomous chemically fuelled information ratchet^17-20 that in the presence of fuel continuously pumps crown ether macrocycles from bulk solution onto a molecular axle without the need for further intervention. The mechanism uses the position of a crown ether on an axle both to promote barrier attachment behind it upon threading and to suppress subsequent barrier removal until the ring has migrated to a catchment region. Tuning the dynamics of both processes^20,21 enables the molecular machine^22-25 to pump macrocycles continuously from their lowest energy state in bulk solution to a higher energy state on the axle. The ratchet action is experimentally demonstrated by the progressive pumping of up to three macrocycles onto the axle from bulk solution under conditions where barrier formation and removal occur continuously. The out-of-equilibrium [n]rotaxanes (characterized with n up to 4) are maintained for as long as unreacted fuel is present, after which the rings slowly de-thread. The use of catalysis to drive artificial molecular pumps opens up new opportunities, insights and research directions at the interface of catalysis and molecular machinery.

The "Water Problem"(sic), the Illusory Pond and Life's Submarine Emergence-A Review

The assumption that there was a "water problem" at the emergence of life-that the Hadean Ocean was simply too wet and salty for life to have emerged in it-is here subjected to geological and experimental reality checks. The "warm little pond" that would take the place of the submarine alkaline vent theory (AVT), as recently extolled in the journal Nature, flies in the face of decades of geological, microbiological and evolutionary research and reasoning. To the present author, the evidence refuting the warm little pond scheme is overwhelming given the facts that (i) the early Earth was a water world, (ii) its all-enveloping ocean was never less than 4 km deep, (iii) there were no figurative "Icelands" or "Hawaiis", nor even an "Ontong Java" then because (iv) the solidifying magma ocean beneath was still too mushy to support such salient loadings on the oceanic crust. In place of the supposed warm little pond, we offer a well-protected mineral mound precipitated at a submarine alkaline vent as life's womb: in place of lipid membranes, we suggest peptides; we replace poisonous cyanide with ammonium and hydrazine; instead of deleterious radiation we have the appropriate life-giving redox and pH disequilibria; and in place of messy chemistry we offer the potential for life's emergence from the simplest of geochemically available molecules and ions focused at a submarine alkaline vent in the Hadean-specifically within the nano-confined flexible and redox active interlayer walls of the mixed-valent double layer oxyhydroxide mineral, fougerite/green rust comprising much of that mound.

An Asymmetric Mechanism in a Symmetric Molecular Machine

The design of molecular architectures exhibiting functional motions is a promising area for disruptive technological development. Toward this goal, rotaxanes and catenanes, which undergo relative motions of their subunits in response to external stimuli, are prime candidates. Here, we report on the computational analysis of the contraction/extension of a bistable [c2]daisy chain rotaxane. Using free-energy calculations and transition path optimizations, we explore the free-energy landscape governing the functional motions of a prototypical molecular machine with atomic resolution. The calculations reveal a sequential mechanism in which the asynchronous gliding of each ring is preferred over the concerted movement. Analysis of the underlying free-energy surface indicates that the formation of partially rearranged intermediates entails crossing of much smaller barriers. Our findings illustrate an important design principle for molecular machines, namely that efficient exploitation of thermal fluctuations may be realized by breaking down the large-scale functional motions into smaller steps.

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.

The PLB measurement for the connector in Phi29 bacteriophage reveals the function of its channel loop

The connector protein, also known as the portal protein, located at the portal vertex in the Phi29 bacteriophage has been found to play a key role in the genome DNA packaging motor. There is a disordered region, composed of 12 sets of 18-residue loops N229-N246, that has been assumed to serve as a "clamp" to retain the DNA within the pressurized capsid when DNA is fully packaged. However, the process remains undefined about how the clamping of DNA occurs and what signal is used to engage the channel loops to clamp the DNA near the end of DNA packaging. In this study, we use the planar lipid bilayer (PLB) membrane technique to study the connector with its loops cleaved. The channel properties are compared with those of the connector with corresponding wild-type loops at different membrane potentials. On the basis of the hypothesis of the Donnan effects in the flashing Brownian ratchet model, we associate the PLB experimental results with the outcomes from the relevant biochemical experiments on the proheads containing the connectors without the loops, which enables us to provide a clear picture about how the DNA clamping occurs. A mathematical relationship between the Donnan potential and the DNA packaging density is established, demonstrating that they are both in essence the same signal that is received and transmitted by the connector to dictate DNA clamping and the termination of DNA packaging. At the end of the study, the PLB technique is proposed as a viral research tool, and its potential use to study the functions of specific domains in a portal protein of the tailed bacteriophages is highlighted.

Repurposing Existing Molecular Machines through Accurate Regulation of Cooperative Motions

To understand how different external stimuli affect the cooperative motions in a molecular machine consisting of multiple components, we have investigated at the atomic level the effects of pH, solvent, and ionic strength on the mechanism underlying the ring-through-ring movement in a saturated [3]rotaxane. Our results indicate that different external stimuli regulate the stable states, the shuttling rate, and the mechanism that governs the ring-through-ring motion by controlling the cooperative movement of the components and triggering a gamut of responses, thereby opening to a vast number of potential applications, such as quaternary logical calculations. The present work cogently demonstrates that with existing nanomachines possessing a simple topology, but using different external stimuli-an approach coined multidimensional regulation-challenging tasks requiring precise control of the molecular motions at play can be achieved, and our methodology is particularly germane for de novo design of intelligent molecular machines.

Hypothetical Efficiency of Electrical to Mechanical Energy Transfer during Individual Stochastic Molecular Switching Events

There are now many examples of single molecule rotors, motors, and switches in the literature that, when driven by photons, electrons, or chemical reactions, exhibit well-defined motions. As a step toward using these single molecule devices to perform useful functions, one must understand how they interact with their environment and quantify their ability to perform work on it. Using a single molecule rotary switch, we examine the transfer of electrical energy, delivered via electron tunneling, to mechanical motion and measure the forces the switch experiences with a noncontact q-plus atomic force microscope. Action spectra reveal that the molecular switch has two stable states and can be excited resonantly between them at a bias of 100 mV via a one-electron inelastic tunneling process which corresponds to an energy input of 16 zJ. While the electrically induced switching events are stochastic and no net work is done on the cantilever, by measuring the forces between the molecular switch and the AFM cantilever, we can derive the maximum hypothetical work the switch could perform during a single switching event, which is ∼55 meV, equal to 8.9 zJ, which translates to a hypothetical efficiency of ∼55% per individual inelastic tunneling electron-induced switching event. When considering the total electrical energy input, this drops to 1 × 10^-7% due to elastic tunneling events that dominate the tunneling current. However, this approach constitutes a general method for quantifying and comparing the energy input and output of molecular-mechanical devices.

Enhanced catalytic activity under non-equilibrium conditions

The development of non-equilibrium synthetic systems provides access to innovative materials with life-like properties. Non-equilibrium systems require a continuous input of energy to retain their functional state, which makes for a fundamental difference to systems that operate at thermodynamic equilibrium. Kinetic asymmetry in the energy consumption pathway is required to drive systems out of equilibrium. This understanding has permitted chemists to design dissipative synthetic molecular machines and high-energy materials. Here we show that kinetic asymmetry also emerges at the macroscopic level by demonstrating that local energy delivery in the form of light to a hydrogel containing gold nanoparticles installs a non-equilibrium steady state. The instalment and maintenance of the macroscopic non-equilibrium state is facilitated by the gel matrix in which motion is governed by diffusion rather than convection. The non-equilibrium state is characterized by a persistent gradient in the surface composition of the nanoparticles embedded in the gel, which affects the fluorescent and catalytic properties of the system. We show that the overall catalytic performance of the system is enhanced under these non-equilibrium conditions. In perspective it will be possible to develop out-of-equilibrium matrices in which functional properties emerge as a result of spatially controlled energy delivery and spatially controlled chemistries.

Precision Molecular Threading/Dethreading

The general principles guiding the design of molecular machines based on interlocked structures are well known. Nonetheless, the identification of suitable molecular components for a precise tuning of the energetic parameters that determine the mechanical link is still challenging. Indeed, what are the reasons of the "all-or-nothing" effect, which turns a molecular "speed-bump" into a stopper in pseudorotaxane-based architectures? Here we investigate the threading and dethreading processes for a representative class of molecular components, based on symmetric dibenzylammonium axles and dibenzo[24]crown-8 ether, with a joint experimental-computational strategy. From the analysis of quantitative data and an atomistic insight, we derive simple rules correlating the kinetic behaviour with the substitution pattern, and provide rational guidelines for the design of modules to be integrated in molecular switches and motors with sophisticated dynamic features.

Cycle Completion Times Probe Interactions with Environment

Recent measurements of the durations of nonequilibrium processes provide valuable information on microscopic mechanisms and energetics. Theory for corresponding experiments to date is well-developed for single-particle systems only. Little is known for interacting systems in nonequilibrium environments. Here we introduce and study a basic model for cycle processes interacting with an environment that can exhibit a net particle flow. We find a surprising richness of cycle time variations with environmental conditions. This manifests itself in unequal cycle times τ⁺ and τ^- in forward and backward cycle directions with both asymmetries τ^- < τ⁺ and τ^- > τ⁺, speeding up of backward cycles by interactions, and dynamical phase transitions, where cycle times become multimodal functions of the bias. The model allows us to relate these effects to specific microscopic mechanisms, which can be helpful for interpreting experiments.