Insights from an information thermodynamics analysis of a synthetic molecular motor

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.

A Minimalistic Covalent Bond-Forming Chemical Reaction Cycle that Consumes Adenosine Diphosphate

The development of synthetic active matter requires the ability to design materials capable of harnessing energy from a source to carry out work. Nature achieves this using chemical reaction cycles in which energy released from an exergonic chemical reaction is used to drive biochemical processes. Although many chemically fuelled synthetic reaction cycles that control transient responses, such as self-assembly, have been reported, the generally high complexity of the reported systems hampers a full understanding of how the available chemical energy is actually exploited by these systems. This lack of understanding is a limiting factor in the design of chemically fuelled active matter. Here, we report a minimalistic synthetic responsive reaction cycle in which adenosine diphosphate (ADP) triggers the formation of a catalyst for its own hydrolysis. This establishes an interdependence between the concentrations of the network components resulting in the transient formation of the catalyst. The network is sufficiently simple that all kinetic and thermodynamic parameters governing its behaviour can be characterised, allowing kinetic models to be built that simulate the progress of reactions within the network. While the current network does not enable the ADP-hydrolysis reaction to populate a non-equilibrium composition, these models provide insight into the way the network dissipates energy. Furthermore, essential design principles are revealed for constructing driven systems, in which the network composition is driven away from equilibrium through the consumption of chemical energy.

Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor

Molecular motors fulfill critical functions within all living beings. Understanding their underlying working principles is therefore of great interest. Here we develop a simple model inspired by the two-component biomolecular motor F_{o}-F_{1} ATP synthase. We analyze its energetics and characterize information flows between the machine's components. At maximum output power we find that information transduction plays a minor role for free-energy transduction. However, when the two components are coupled to different environments (e.g., when in contact with heat baths at different temperatures), we show that information flow becomes a resource worth exploiting to maximize free-energy transduction. Our findings suggest that real-world powerful and efficient information engines could be found in machines whose components are subjected to fluctuations of different strength, since in this situation the benefit gained from using information for work extraction can outweigh the costs of information generation.

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.

Stepwise Operation of a Molecular Rotary Motor Driven by an Appel Reaction

To date, only a small number of chemistries and chemical fueling strategies have been successfully used to operate artificial molecular motors. Here, we report the 360° directionally biased rotation of phenyl groups about a C-C bond, driven by a stepwise Appel reaction sequence. The motor molecule consists of a biaryl-embedded phosphine oxide and phenol, in which full rotation around the biaryl bond is blocked by the P-O oxygen atom on the rotor being too bulky to pass the oxygen atom on the stator. Treatment with SOCl2 forms a cyclic oxyphosphonium salt (removing the oxygen atom of the phosphine oxide), temporarily linking the rotor with the stator. Conformational exchange via ring flipping then allows the rotor and stator to twist back and forth past the previous limit of rotation. Subsequently, the ring opening of the tethered intermediate with a chiral alcohol occurs preferentially through a nucleophilic attack on one face. Thus, the original phosphine oxide is reformed with net directional rotation about the biaryl bond over the course of the two-step reaction sequence. Each repetition of SOCl2-chiral alcohol additions generates another directionally biased rotation. Using the same reaction sequence on a derivative of the motor molecule that forms atropisomers rather than fully rotating 360° results in enantioenrichment, suggesting that, on average, the motor molecule rotates in the "wrong" direction once every three fueling cycles. The interconversion of phosphine oxides and cyclic oxyphosphonium groups to form temporary tethers that enable a rotational barrier to be overcome directionally adds to the strategies available for generating chemically fueled kinetic asymmetry in molecular systems.

Dynamic control of circumrotation of a [2]catenane by acid-base switching

Dynamic control of the motion in a catenane remains a big challenge as it requires precise design and sophisticated well-organized structures. This paper reports the design and synthesis of a donor-acceptor [2]catenane through mechanical interlocking, employing a crown ether featuring two dibenzylammonium salts on its side arms as the host and a cyclobis(paraquat-p-phenylene) (CBPQT ⋅ 4PF6 ) ring as the guest molecule. By addition of external acid or base, the catenane can form self-complexed or decomplexed compounds to alter the cavity size of the crown ether ring, consequently affecting circumrotation rate of CBPQT ⋅ 4PF6 ring of the catenane. This study offers insights for the design and exploration of artificial molecular machines with intricate cascading responsive mechanisms.

Limits on the Precision of Catenane Molecular Motors: Insights from Thermodynamics and Molecular Dynamics Simulations

Thermodynamic uncertainty relations (TURs) relate precision to the dissipation rate, yet the inequalities can be far from saturation. Indeed, in catenane molecular motor simulations, we record precision far below the TUR limit. We further show that this inefficiency can be anticipated by four physical parameters: the thermodynamic driving force, fuel decomposition rate, coupling between fuel decomposition and motor motion, and rate of undriven motor motion. The physical insights might assist in designing molecular motors in the future.

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.

Switched "On" Transient Fluorescence Output from a Pulsed-Fuel Molecular Ratchet

We report the synthesis and operation of a molecular energy ratchet that transports a crown ether from solution onto a thread, along the axle, over a fluorophore, and off the other end of the thread back into bulk solution, all in response to a single pulse of a chemical fuel (CCl3CO2H). The fluorophore is a pyrene residue whose fluorescence is normally prevented by photoinduced electron transfer (PET) to a nearby N-methyltriazolium group. However, crown ether binding to the N-methyltriazolium site inhibits the PET, switching on pyrene fluorescence under UV irradiation. Each pulse of fuel results in a single ratchet cycle of transient fluorescence (encompassing threading, transport to the N-methyltriazolium site, and then dethreading), with the onset of the fluorescent time period determined by the amount of fuel in each pulse and the end-point determined by the concentration of the reagents for the disulfide exchange reaction. The system provides a potential alternative signaling approach for artificial molecular machines that read symbols from sequence-encoded molecular tapes.

A chemical reaction network implementation of a Maxwell demon

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest: the generated reverse chemical current, the output power, the transduction efficiency, and correlation between the number of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of partial efficiencies related to the measurement and feedback processes is examined.

Artificial Molecular Ratchets: Tools Enabling Endergonic Processes

Non-equilibrium chemical systems underpin multiple domains of contemporary interest, including supramolecular chemistry, molecular machines, systems chemistry, prebiotic chemistry, and energy transduction. Experimental chemists are now pioneering the realization of artificial systems that can harvest energy away from equilibrium. In this tutorial Review, we provide an overview of artificial molecular ratchets: the chemical mechanisms enabling energy absorption from the environment. By focusing on the mechanism type-rather than the application domain or energy source-we offer a unifying picture of seemingly disparate phenomena, which we hope will foster progress in this fascinating domain of science.

ABC transporters are billion-year-old Maxwell Demons

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

A [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.

Photoactivated Artificial Molecular Motors

Accurate control of long-range motion at the molecular scale holds great potential for the development of ground-breaking applications in energy storage and bionanotechnology. The past decade has seen tremendous development in this area, with a focus on the directional operation away from thermal equilibrium, giving rise to tailored man-made molecular motors. As light is a highly tunable, controllable, clean, and renewable source of energy, photochemical processes are appealing to activate molecular motors. Nonetheless, the successful operation of molecular motors fueled by light is a highly challenging task, which requires a judicious coupling of thermal and photoinduced reactions. In this paper, we focus on the key aspects of light-driven artificial molecular motors with the aid of recent examples. A critical assessment of the criteria for the design, operation, and technological potential of such systems is provided, along with a perspective view on future advances in this exciting research area.

Pillar[5]arene-Derived Terpyridinepalladium(II) Complex: Synthesis, Characterization, and Application in Green Catalysis

Metal nanoparticle catalysts have attracted great interest because they possess high surface-to-volume ratios and exhibit a very large number of catalytically active sites per unit area. However, high surface-to-volume ratios will induce nanoparticle aggregates during the catalytic reactions, making them lose their catalytic activity. In this work, a monoterpyridine-unit-functionalized pillar[5]arene (TP5) was synthesized successfully, which can be used as anchoring sites for the controllable preparation of well-dispersed palladium nanoparticles [TP5/Pd(0) NPs]. The as-prepared TP5/Pd(0) NPs were fully characterized by X-ray photoelectron spectroscopy, transmission electron microscopy, and powder X-ray diffraction. Importantly, the ultrafine TP5/Pd(0) NPs are found to be excellent and reusable catalysts for the reduction of nitrophenols in aqueous solution.

Inferring Subsystem Efficiencies in Bipartite Molecular Machines

Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here, we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the F_{o} and F_{1} subunits of ATP synthase and that of kinesin pulling a diffusive cargo.

Oligo[2]catenane That Is Robust at Both the Microscopic and Macroscopic Scales

Polycatenanes are extremely attractive topological architectures on account of their high degrees of conformational freedom and multiple motion patterns of the mechanically interlocked macrocycles. However, exploitation of these peculiar structural and dynamic characteristics to develop robust catenane materials is still a challenging goal. Herein, we synthesize an oligo[2]catenane that showcases mechanically robust properties at both the microscopic and macroscopic scales. The key feature of the structural design is controlling the force-bearing points on the metal-coordinated core of the [2]catenane moiety that is able to maximize the energy dissipation of the oligo[2]catenane via dissociation of metal-coordination bonds and then activation of sequential intramolecular motions of circumrotation, translation, and elongation under an external force. As such, at the microscopic level, the single-molecule force spectroscopy measurement exhibits that the force to rupture dynamic bonds in the oligo[2]catenane reaches a record high of 588 ± 233 pN. At the macroscopic level, our oligo[2]catenane manifests itself as the toughest catenane material ever reported (15.2 vs 2.43 MJ/m³). These fundamental findings not only deepen the understanding of the structure-property relationship of poly[2]catenanes with a full set of dynamic features but also provide a guiding principle to fabricate high-performance mechanically interlocked catenane materials.

Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics - rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self-assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states' population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.

An Inbuilt Electronic Pawl Gates Orbital Information Processing and Controls the Rotation of a Double Ratchet Rotary Motor

A direct external input energy source (e.g., light, chemical reaction, redox potential, etc.) is compulsory to supply energy to rotary motors for accomplishing rotation around the axis. The stator leads the direction of rotation, and a sustainable rotation requires two mutual input energy supplies (e.g., light and heat, light and pH or metal ion, etc.); however, there are some exceptions (e.g., covalent single bond rotors and/or motors). On the contrary, our experiment suggested that double ratchet rotary motors (DRMs) can harvest power from available thermal noise, kT, for sustainable rotation around the axis. Under a scanning tunneling microscope, we have imaged live thermal noise movement as a dynamic orbital density and resolved the density diagram up to the second derivative. A second input energy can synchronize multiple rotors to afford a measurable output. Therefore, we hypothesized that rotation control in a DRM must be evolved from an orbital-level information transport channel between the two coupled rotors but was not limited to the second input energy. A DRM comprises a Brownian rotor and a power stroke rotor coupled to a -C≡C- stator, where the transport of information through coupled orbitals between the two rotors is termed the vibrational information flow chain (VIFC). We test this hypothesis by studying the DRM's density functional theory calculation and variable-temperature ¹H nuclear magnetic resonance. Additionally, we introduced inbuilt pawl-like functional moieties into a DRM to create different electronic environments by changing proton intercalation interactions, which gated information processing through the VIFC. The results show the VIFC can critically impact the motor's noise harvesting, resulting in variable rotational motions in DRMs.

Dissipative Systems Driven by the Decarboxylation of Activated Carboxylic Acids

ConspectusThe achievement of artificial systems capable of being maintained in out-of-equilibrium states featuring functional properties is a main goal of current chemical research. Absorption of electromagnetic radiation or consumption of a chemical species (a "chemical fuel") are the two strategies typically employed to reach such out-of-equilibrium states, which have to persist as long as one of the above stimuli is present. For this reason such systems are often referred to as "dissipative systems". In the simplest scheme, the dissipative system is initially found in a resting, equilibrium state. The addition of a chemical fuel causes the system to shift to an out-of-equilibrium state. When the fuel is exhausted, the system reverts to the initial, equilibrium state. Thus, from a mechanistic standpoint, the dissipative system turns out to be a catalyst for the fuel consumption. It has to be noted that, although very simple, this scheme implies the chance to temporally control the dissipative system. In principle, modulating the nature and/or the amount of the chemical fuel added, one can have full control of the time spent by the system in the out-of-equilibrium state.In 2016, we found that 2-cyano-2-phenylpropanoic acid (1a), whose decarboxylation proceeds smoothly under mild basic conditions, could be used as a chemical fuel to drive the back and forth motion of a catenane-based molecular switch. The acid donates a proton to the catenane that passes from the neutral state A to the transient protonated state B. Decarboxylation of the resulting carboxylate (1acb), generates a carbanion, which, being a strong base, retakes the proton from the protonated catenane that, consequently, returns to the initial state A. The larger the amount of the added fuel, the longer the time spent by the catenane in the transient, out-of-equilibrium state. Since then, acid 1a and other activated carboxylic acids (ACAs) have been used to drive the operation of a large number of dissipative systems based on the acid-base reaction, from molecular machines to host-guest systems, from catalysts to smart materials, and so on. This Account illustrates such systems with the purpose to show the wide applicability of ACAs as chemical fuels. This generality is due to the simplicity of the idea underlying the operation principle of ACAs, which always translates into simple experimental requirements.

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.

Information flows in macroscopic Maxwell's demons

A CMOS-based implementation of an autonomous Maxwell's demon was recently proposed [Phys. Rev. Lett. 129, 120602 (2022)0031-900710.1103/PhysRevLett.129.120602] to demonstrate that a Maxwell demon can still work at macroscopic scales, provided that its power supply is scaled appropriately. Here we first provide a full analytical characterization of the nonautonomous version of that model. We then study system-demon information flows within generic autonomous bipartite setups displaying a macroscopic limit. By doing so, we can study the thermodynamic efficiency of both the measurement and the feedback process performed by the demon. We find that the information flow is an intensive quantity and that, as a consequence, any Maxwell's demon is bound to stop working above a finite scale if all parameters but the scale are fixed. However, this can be prevented by appropriately scaling the thermodynamic forces. These general results are applied to the autonomous CMOS-based demon.

Tuning the Force, Speed, and Efficiency of an Autonomous Chemically Fueled Information Ratchet

Autonomous chemically fueled molecular machines that function through information ratchet mechanisms underpin the nonequilibrium processes that sustain life. These biomolecular motors have evolved to be well-suited to the tasks they perform. Synthetic systems that function through similar mechanisms have recently been developed, and their minimalist structures enable the influence of structural changes on machine performance to be assessed. Here, we probe the effect of changes in the fuel and barrier-forming species on the nonequilibrium operation of a carbodiimide-fueled rotaxane-based information ratchet. We examine the machine’s ability to catalyze the fuel-to-waste reaction and harness energy from it to drive directional displacement of the macrocycle. These characteristics are intrinsically linked to the speed, force, power, and efficiency of the ratchet output. We find that, just as for biomolecular motors and macroscopic machinery, optimization of one feature (such as speed) can compromise other features (such as the force that can be generated by the ratchet). Balancing speed, power, efficiency, and directionality will likely prove important when developing artificial molecular motors for particular applications.

Transamidation-Driven Molecular Pumps

We report a new class of synthetic molecular pumps that use a stepwise information ratchet mechanism to achieve the kinetic gating required to sequester their macrocyclic substrates from bulk solution. Threading occurs as a result of active template reactions between the pump terminus amine and an acyl electrophile, whereby the bond-forming reaction is accelerated through the cavity of a crown ether. Carboxylation of the resulting amide results in displacement of the ring to the collection region of the thread. Conversion of the carbamate to a phenolic ester provides an intermediate rotaxane suitable for further pumping cycles. In this way rings can be ratcheted onto a thread from one or both ends of appropriately designed molecular pumps. Each pumping cycle results in one additional ring being added to the thread per terminus acyl group. The absence of pseudorotaxane states ensures that no dethreading of intermediates occurs during the pump operation. This facilitates the loading of different macrocycles in any chosen sequence, illustrated by the pump-mediated synthesis of a [4]rotaxane containing three different macrocycles as a single sequence isomer. A [5]rotaxane synthesized using a dual-opening transamidation pump was structurally characterized by single-crystal X-ray diffraction, revealing a series of stabilizing CH···O interactions between the crown ethers and the polyethylene glycol catchment region of the thread.

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.

Kinetic and energetic insights into the dissipative non-equilibrium operation of an autonomous light-powered supramolecular pump

Natural and artificial autonomous molecular machines operate by constantly dissipating energy coming from an external source to maintain a non-equilibrium state. Quantitative thermodynamic characterization of these dissipative states is highly challenging as they exist only as long as energy is provided. Here we report on the detailed physicochemical characterization of the dissipative operation of a supramolecular pump. The pump transduces light energy into chemical energy by bringing self-assembly reactions to non-equilibrium steady states. The composition of the system under light irradiation was followed in real time by ¹H NMR for four different irradiation intensities. The experimental composition and photon flow were then fed into a theoretical model describing the non-equilibrium dissipation and the energy storage at the steady state. We quantitatively probed the relationship between the light energy input and the deviation of the dissipative state from thermodynamic equilibrium in this artificial system. Our results provide a testing ground for newly developed theoretical models for photoactivated artificial molecular machines operating away from thermodynamic equilibrium.

Chemical fuels for molecular machinery

Chemical reaction networks that transform out-of-equilibrium 'fuel' to 'waste' are the engines that power the biomolecular machinery of the cell. Inspired by such systems, autonomous artificial molecular machinery is being developed that functions by catalysing the decomposition of chemical fuels, exploiting kinetic asymmetry to harness energy released from the fuel-to-waste reaction to drive non-equilibrium structures and dynamics. Different aspects of chemical fuels profoundly influence their ability to power molecular machines. Here we consider the structure and properties of the fuels that biology has evolved and compare their features with those of the rudimentary synthetic chemical fuels that have so far been used to drive autonomous non-equilibrium molecular-level dynamics. We identify desirable, but context-specific, traits for chemical fuels together with challenges and opportunities for the design and invention of new chemical fuels to power synthetic molecular machinery and other dissipative nanoscale processes.

Free-Energy Transduction in Chemical Reaction Networks: from Enzymes to Metabolism

We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary---linear or nonlinear---open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the stoichiometric matrix and of the chemostatted species (i.e. the species maintained at constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force) thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they are able to transduce free energy.

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.

Autonomous fuelled directional rotation about a covalent single bond

Biology operates through autonomous chemically fuelled molecular machinery¹, including rotary motors such as adenosine triphosphate synthase² and the bacterial flagellar motor³. Chemists have long sought to create analogous molecular structures with chemically powered, directionally rotating, components^4-17. However, synthetic motor molecules capable of autonomous 360° directional rotation about a single bond have proved elusive, with previous designs lacking either autonomous fuelling^7,10,12 or directionality⁶. Here we show that 1-phenylpyrrole 2,2'-dicarboxylic acid^18,19 (1a) is a catalysis-driven^20,21 motor that can continuously transduce energy from a chemical fuel^9,20-27 to induce repetitive 360° directional rotation of the two aromatic rings around the covalent N-C bond that connects them. On treatment of 1a with a carbodiimide^21,25-27, intramolecular anhydride formation between the rings and the anhydride's hydrolysis both occur incessantly. Both reactions are kinetically gated^28-30 causing directional bias. Accordingly, catalysis of carbodiimide hydration by the motor molecule continuously drives net directional rotation around the N-C bond. The directionality is determined by the handedness of both an additive that accelerates anhydride hydrolysis and that of the fuel, and is easily reversed additive³¹. More than 97% of fuel molecules are consumed through the chemical engine cycle²⁴ with a directional bias of up to 71:29 with a chirality-matched fuel and additive. In other words, the motor makes a 'mistake' in direction every three to four turns. The 26-atom motor molecule's simplicity augurs well for its structural optimization and the development of derivatives that can be interfaced with other components for the performance of work and tasks^32-36.

Polyrotaxanes and the pump paradigm

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