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.

An electric molecular motor.

Macroscopic electric motors continue to have a large impact on almost every aspect of modern society. Consequently, the effort towards developing molecular motors1-3 that can be driven by electricity could not be more timely. Here we describe an electric molecular motor based on a [3]catenane4,5, in which two cyclobis(paraquat-p-phenylene)6 (CBPQT4+) rings are powered by electricity in solution to circumrotate unidirectionally around a 50-membered loop. The constitution of the loop ensures that both rings undergo highly (85%) unidirectional movement under the guidance of a flashing energy ratchet7,8, whereas the interactions between the two rings give rise to a two-dimensional potential energy surface (PES) similar to that shown by FOF1 ATP synthase9. The unidirectionality is powered by an oscillating10 voltage11,12 or external modulation of the redox potential13. Initially, we focused our attention on the homologous [2]catenane, only to find that the kinetic asymmetry was insufficient to support unidirectional movement of the sole ring. Accordingly, we incorporated a second CBPQT4+ ring to provide further symmetry breaking by interactions between the two mobile rings. This demonstration of electrically driven continual circumrotatory motion of two rings around a loop in a [3]catenane is free from the production of waste products and represents an important step towards surface-bound14 electric molecular motors.

Polyrotaxanes and the pump paradigm.

The year 2022 marks the 30th anniversary of the first reports of polyrotaxanes in the scientific literature. During the past three decades, many combinations of molecular rings and polymer chains have been synthesised and characterised. Until recently, however, the permutations of polyrotaxanes available to researchers were limited by synthetic methods which typically relied on an innate affinity between the molecular rings and polymer chains. With the advent of oligorotaxane-forming molecular pumps in 2015, it has now become possible to pump multiple rings against their will onto oligomer and polymer chains which have little or no affinity for the rings. These molecular pumps, which can recruit rings actively from solution to form precise polyrotaxanes, represent a major breakthrough in the field. This Tutorial Review highlights key milestones in the synthesis and investigation of polyrotaxanes along with recent developments in the synthesis and theory relating to molecular pumps. Polyrotaxane properties, arising from their topologies, have allowed them to steal a march on traditional polymers in a wide range of applications in materials, electronic and biological science, from slide-ring gels to robust coatings on cell phones, from molecular wires to flexible binders for battery anodes, from efficient multivalent protein binders to bio-cleavable polyplexes for cellular DNA delivery. Molecular pumps have the potential to blaze a contemporary trail for the synthesis of precise mechanically interlocked materials, especially those dependent on non-equilibrium chemistry and those related to energy storage and nanomedicine.

Electron-catalysed molecular recognition.

Molecular recognition1-4 and supramolecular assembly5-8 cover a broad spectrum9-11 of non-covalently orchestrated phenomena between molecules. Catalysis12 of such processes, however, unlike that for the formation of covalent bonds, is limited to approaches13-16 that rely on sophisticated catalyst design. Here we establish a simple and versatile strategy to facilitate molecular recognition by extending electron catalysis17, which is widely applied18-21 in synthetic covalent chemistry, into the realm of supramolecular non-covalent chemistry. As a proof of principle, we show that the formation of a trisradical complex22 between a macrocyclic host and a dumbbell-shaped guest-a molecular recognition process that is kinetically forbidden under ambient conditions-can be accelerated substantially on the addition of catalytic amounts of a chemical electron source. It is, therefore, electrochemically possible to control23 the molecular recognition temporally and produce a nearly arbitrary molar ratio between the substrates and complexes ranging between zero and the equilibrium value. Such kinetically stable supramolecular systems24 are difficult to obtain precisely by other means. The use of the electron as a catalyst in molecular recognition will inspire chemists and biologists to explore strategies that can be used to fine-tune non-covalent events, control assembly at different length scales25-27 and ultimately create new forms of complex matter28-30.

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.

Active mechanisorption driven by pumping cassettes.

Over the past century, adsorption has been investigated extensively in equilibrium systems, with a focus on the van der Waals interactions associated with physisorption and electronic interactions in the case of chemisorption. In this study, we demonstrate mechanisorption, which results from nonequilibrium pumping to form mechanical bonds between the adsorbent and the adsorbate. This active mode of adsorption has been realized on surfaces of metal-organic frameworks grafted with arrays of molecular pumps. Adsorbates are transported from one well-defined compartment, the bulk, to another well-defined compartment, the interface, thereby creating large potential gradients in the form of chemical capacitors wherein energy is stored in metastable states. Mechanisorption extends, in a fundamental manner, the scope and potential of adsorption phenomena and offers a transformative approach to control chemistry at surfaces and interfaces.

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.

Radical-pairing-induced molecular assembly and motion.

Radical-pairing interactions between conjugated organic π-radicals are relative newcomers to the inventory of molecular recognition motifs explored in supramolecular chemistry. The unique electronic, magnetic, optical and redox-responsive properties of the conjugated π-radicals render molecules designed with radical-pairing interactions useful for applications in various areas of chemistry and materials science. In particular, the ability to control formation of radical cationic or anionic species, by redox stimulation, provides a flexible trigger for directed assembly and controlled molecular motions, as well as a convenient means of inputting energy to fuel non-equilibrium processes. In this Review, we provide an overview of different examples of radical-pairing-based recognition processes and of their emerging use in (1) supramolecular assembly, (2) templation of mechanically interlocked molecules, (3) stimuli-controlled molecular switches and, by incorporation of kinetic asymmetry in the design, (4) the creation of unidirectional molecular transporters based on pumping cassettes powered by fuelled switching of radical-pairing interactions. We conclude the discussion with an outlook on future directions for the field.

Artificial Molecular Pump Operating in Response to Electricity and Light.

The ability to control the relative motions of component parts in molecules is essential for the development of molecular nanotechnology. The advent of mechanically interlocked molecules (MIMs) has enhanced significantly the opportunities for chemists to harness such motions in artificial molecular machines (AMMs). Recently, we have developed artificial molecular pumps (AMPs) capable of producing highly energetic oligo- and polyrotaxanes with high precision. Here, we report the design, synthesis, and operation of an AMP incorporating a photocleavable stopper that allows for the use of orthogonal stimuli. Our approach employs a ratchet mechanism to pump a ring onto a collecting chain, forming an intermediate [2]rotaxane. At a subsequent time, application of light triggers the release of the ring back into the bulk solution with temporal control. This process is monitored by the quenching of the fluorescence of a naphthalene-based fluorophore. This design may find application in the fabrication of molecular transporting systems with on-demand functions.

A precise polyrotaxane synthesizer.

Mechanically interlocked molecules are likely candidates for the design and synthesis of artificial molecular machines. Although polyrotaxanes have already found niche applications in exotic materials with specialized mechanical properties, efficient synthetic protocols to produce them with precise numbers of rings encircling their polymer dumbbells are still lacking. We report the assembly line-like emergence of poly[n]rotaxanes with increasingly higher energies by harnessing artificial molecular pumps to deliver rings in pairs by cyclical redox-driven processes. This programmable strategy leads to the precise incorporation of two, four, six, eight, and 10 rings carrying 8+, 16+, 24+, 32+, and 40+ charges, respectively, onto hexacationic polymer dumbbells. This strategy depends precisely on the number of redox cycles applied chemically or electrochemically, in both stepwise and one-pot manners.

A Molecular Dual Pump.

Artificial molecular machines (AMMs) built from mechanically interlocked molecules (MIMs) can use energy ratchets to control the unidirectional motion of their component parts. These energy ratchets are operated by the alteration of kinetic barriers and thermodynamic wells, which are, in turn, determined by the switching on and off of noncovalent interactions. Previously, we have developed artificial molecular pumps (AMPs) capable of pumping rings consecutively onto a collecting chain as part of a molecular dumbbell, leading to the formation of rotaxanes. Here, we report a molecular dual pump (MDP) consisting of two individual AMPs linked in a head-to-tail fashion, wherein a single ring is pumped, in a linear manner, on and off a dumbbell involving a [2]rotaxane intermediate by exploiting the redox properties of the two pumps. This MDP, defined by the finely tuned noncovalent interactions and fueled by either chemicals or electricity, utilizes an energy ratchet mechanism to capture a ring and subsequently release it back into solution. The unidirectional motion and the resulting controlled capture and release of the ring were followed by 1D and 2D 1H NMR spectroscopy and supported by control experiments. This molecular dual pump may be considered to be a forerunner of AMMs that are capable of pumping rings across a membrane in a way similar to how bacteriorhodopsin transports protons from one side of a membrane to the other under the influence of light. Such extensive multicomponent AMMs can lead potentially to molecular transporting platforms with positional and directional control of cargo uptake and release when, and only when, instructed.

Enhanced Diffusion of Molecular Catalysts is Due to Convection.

Intriguing reports of enhanced diffusion in enzymes and molecular catalysts have spurred significant interest in experimental and theoretical investigations, and the mechanism of this phenomenon is the topic of lively debate. Here we use time-resolved diffusion NMR methods to measure the diffusion coefficients (D) of small molecule species involved in chemical reactions with high temporal resolution. We show the enhanced diffusion of small molecules cannot be explained by reaction velocity, and that apparent measurements of enhanced diffusion by small molecules appear to be caused by bulk fluid flow processes such as convection.

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.

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

A molecular machine is a nanoscale device that provides a mechanism for coupling energy from two (or more) processes that in the absence of the machine would be independent of one another. Examples include walking of a protein in one direction along a polymeric track (process 1, driving "force" X1 = - F⃗· l⃗) and hydrolyzing ATP (process 2, driving "force" X2 = ΔµATP); or synthesis of ATP (process 1, X1 = -ΔµATP) and transport of protons from the periplasm to the cytoplasm across a membrane (process 2, X2 = ΔµH+); or rotation of a flagellum (process 1, X1 = -torque) and transport of protons across a membrane (process 2, X2 = ΔµH+). In some ways, the function of a molecular machine is similar to that of a macroscopic machine such as a car that couples combustion of gasoline to translational motion. However, the low Reynolds number regime in which molecular machines operate is very different from that relevant for macroscopic machines. Inertia is negligible in comparison to viscous drag, and omnipresent thermal noise causes the machine to undergo continual transition among many states even at thermodynamic equilibrium. Cyclic trajectories among the states of the machine that result in a change in the environment can be broken into two classes: those in which process 1 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the environment; and those in which process 2 in either the forward or backward direction ([Formula: see text]) occurs and which thereby exchange work [Formula: see text] with the evironment. These two types of trajectories, [Formula: see text] and [Formula: see text], overlap, i.e., there are some trajectories in which both process 1 and process 2 occur, and for which the work exchanged is [Formula: see text]. The four subclasses of overlap trajectories [(+1,+2), (+1,-2), (-1,+2), (-1,-2)] are the coupled processes. The net probabilities for process 1 and process 2 are designated π+2 - π-2 and π+1 - π-1, respectively. The probabilities [Formula: see text] for any single trajectory [Formula: see text] and [Formula: see text] for its microscopic reverse [Formula: see text] are related by microscopic reversibility (MR), [Formula: see text], an equality that holds arbitrarily far from thermodynamic equilibrium, i.e., irrespective of the magnitudes of X1 and X2, and where [Formula: see text]. Using this formalism, we arrive at a remarkably simple and general expression for the rates of the processes, [Formula: see text], i = 1, 2, where the angle brackets indicate an average over the ensemble of all microscopic reverse trajectories. Stochastic description of coupling is doubtless less familiar than typical mechanical depictions of chemical coupling in terms of ATP induced violent kicks, judo throws, force generation and power-strokes. While the mechanical description of molecular machines is comforting in its familiarity, conclusions based on such a phenomenological perspective are often wrong. Specifically, a "power-stroke" model (i.e., a model based on energy driven "promotion" of a molecular machine to a high energy state followed by directional relaxation to a lower energy state) that has been the focus of mechanistic discussions of biomolecular machines for over a half century is, for catalysis driven molecular machines, incorrect. Instead, the key principle by which catalysis driven motors work is kinetic gating by a mechanism known as an information ratchet. Amazingly, this same principle is that by which catalytic molecular systems undergo adaptation to new steady states while facilitating an exergonic chemical reaction.

Stochastically pumped adaptation and directional motion of molecular machines.

Recent developments in synthetic molecular motors and pumps have sprung from a remarkable confluence of experiment and theory. Synthetic accomplishments have facilitated the ability to design and create molecules, many of them featuring mechanically bonded components, to carry out specific functions in their environment-walking along a polymeric track, unidirectional circling of one ring about another, synthesizing stereoisomers according to an external protocol, or pumping rings onto a long rod-like molecule to form and maintain high-energy, complex, nonequilibrium structures from simpler antecedents. Progress in the theory of nanoscale stochastic thermodynamics, specifically the generalization and extension of the principle of microscopic reversibility to the single-molecule regime, has enhanced the understanding of the design requirements for achieving strong unidirectional motion and high efficiency of these synthetic molecular machines for harnessing energy from external fluctuations to carry out mechanical and/or chemical functions in their environment. A key insight is that the interaction between the fluctuations and the transition state energies plays a central role in determining the steady-state concentrations. Kinetic asymmetry, a requirement for stochastic adaptation, occurs when there is an imbalance in the effect of the fluctuations on the forward and reverse rate constants. Because of strong viscosity, the motions of the machine can be viewed as mechanical equilibrium processes where mechanical resonances are simply impossible but where the probability distributions for the state occupancies and trajectories are very different from those that would be expected at thermodynamic equilibrium.

Mastering the non-equilibrium assembly and operation of molecular machines.

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

The Physics and Physical Chemistry of Molecular Machines.

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

Design and Synthesis of Nonequilibrium Systems.

The active transport of ions and molecules across cell membranes is essential to creating the concentration gradients that sustain life in all living organisms, be they bacteria, fungi, plants, animals or Homo sapiens. Nature uses active transport everywhere for everything. Molecular biologists have long been attracted to the study of active transport and continue to this day to investigate and elucidate the tertiary structures of the complex motor proteins that sustain it, while physicists, interested in nonequilibrium statistical mechanics, have developed theoretical models to describe the driven ratcheting motions that are crucial to its function. The increasingly detailed understanding that contemporary science has acquired relating to active transport, however, has yet to lead to the design and construction of artificial molecular motors capable of employing ratchet-driven motions that can also perform work against concentration gradients. Mechanically interlocked molecules (MIMs) in the form of pseudo- and semirotaxanes are showing some encouraging signs in meeting these goals. This review summarizes recent progress in making artificial molecular motors that can perform work by "pumping" tetracationic rings into high-energy states. The launching pad is a bistable [2]rotaxane whose dumbbell component contains two electron-donating recognition sites, one, a tetrathiafulvalene (TTF) unit, which interacts more strongly with the ring component, cyclobis(paraquat-p-phenylene) (CBPQT(4+)), containing two electron-accepting bipyridinium units, than does the other 1,5-dioxynaphthalene (DNP) unit. Switching can be induced electrochemically by oxidizing the TTF unit to a TTF(•+) radical cation, whereupon Coulombic repulsion takes care of moving the ring to the DNP unit. Reduction of the radical cation resets the switch. Molecular switches operate at, or close to, equilibrium. Any work done during one switching event is undone during the reset. Molecular motors, on the other hand, rely on a flux of energy, and a ratchet mechanism to make periodic changes to the potential energy surface of a system in order to move molecules uphill to higher energy states. Forging a path from molecular switches to motors involved designing a molecular pump prototype. An asymmetric dumbbell with a 2-isopropylphenyl (neutral) end and a 3,5-dimethylpyridinium (charged) end with a DNP recognition site to entice CBPQT(4+) rings out of solution exhibits relative unidirectional movement of the rings with respect to the dumbbell. Redox chemistry does the trick. During the oxidative cycle, the rings enter the dumbbell by passing over the neutral end onto the recognition site; in the reduction cycle, much of the recognition is lost and the rings find their way back into solution by leaving the dumbbell from the charged end. This on-one-end, off-the-other process can be repeated over and over again using light as the energy source in the presence of a photosensitizer and a compound that shuttles electrons back and forth. Although this prototype demonstrates ratchet-driven translational motion, no work is done. A ring enters the dumbbell from one end and leaves from the other end. Another deficiency of the prototype is the fact that, although the recognition site is muted on reduction, it retains some attraction for the ring. What if the recognition site was attractive initially and then became repulsive? This question was answered by turning to radical chemistry and employing the known stabilization behavior of a bipyridinium radical cation and the bisradical dication, generated on reduction of the CBPQT(4+) ring, to pluck rings out of solution and thread them over the charged end of the pump portion of a semidumbbell. On subsequent oxidation, the pump is primed and the rings pass through a one-way door, given a little thermal energy, onto a collecting-chain where they find themselves accumulating where they would rather not be present. In this manner, an artificial molecular pump mimics the pumping machinery commonplace in biological systems. Looking beyond this state-of-the-art artificial molecular pump, we discuss, from a theoretical standpoint, the measures that would need to be taken in order to render its operation autonomous.