Thermodynamic efficiency in dissipative chemistry

Progressive Endergonic Synthesis of Diels-Alder Adducts Driven by Chemical Energy

The overwhelming majority of artificial chemical reaction networks respond to stimuli by relaxing towards an equilibrium state. The opposite response-moving away from equilibrium-can afford the endergonic synthesis of molecules, of which only rare examples have been reported. Here, we report six examples of Diels-Alder adducts formed in an endergonic process and use this strategy to realize their stepwise accumulation. Indeed, systems respond to repeated occurrences of the same stimulus by increasing the amount of adduct formed, with the final network distribution depending on the number of stimuli received. Our findings indicate how endergonic processes can contribute to the transition from responsive to adaptive systems.

Dissipative Self-Assembly of Patchy Particles under Nonequilibrium Drive: A Computational Study

Inspired by biology and implemented using nanotechnology, the self-assembly of patchy particles has emerged as a pivotal mechanism for constructing complex structures that mimic natural systems with diverse functionalities. Here, we explore the dissipative self-assembly of patchy particles under nonequilibrium conditions, with the aim of overcoming the constraints imposed by equilibrium assembly. Utilizing extensive Monte Carlo (MC) and Molecular Dynamics (MD) simulations, we provide insight into the effects of external forces that mirror natural and chemical processes on the assembly rates and the stability of the resulting assemblies comprising 8, 10, and 13 patchy particles. Implemented by a favorable bond-promoting drive in MC or a pulsed square wave potential in MD, our simulations reveal the role these external drives play in accelerating assembly kinetics and enhancing structural stability, evidenced by a decrease in the time to first assembly and an increase in the duration the system remains in an assembled state. Through the analysis of an order parameter, entropy production, bond dynamics, and interparticle forces, we unravel the underlying mechanisms driving these advancements. We also validated our key findings by simulating a larger system of 100 patchy particles. Our comprehensive results not only shed light on the impact of external stimuli on self-assembly processes but also open a promising pathway for expanding the application by leveraging patchy particles for novel nanostructures.

Non-equilibrium self-assembly for living matter-like properties

The soft and wet machines of life emerged as the spatially enclosed ensemble of biomolecules with replicating capabilities integrated with metabolic reaction cycles that operate at far-from-equilibrium. A thorough step-by-step synthetic integration of these elements, namely metabolic and replicative properties all confined and operating far-from-equilibrium, can set the stage from which we can ask questions related to the construction of chemical-based evolving systems with living matter-like properties - a monumental endeavour of systems chemistry. The overarching concept of this Review maps the discoveries on this possible integration of reaction networks, self-reproduction and compartmentalization under non-equilibrium conditions. We deconvolute the events of reaction networks and transient compartmentalization and extend the discussion towards self-reproducing systems that can be sustained under non-equilibrium conditions. Although enormous challenges lie ahead in terms of molecular diversity, information transfer, adaptation and selection that are required for open-ended evolution, emerging strategies to generate minimal metabolic cycles can extend our growing understanding of the chemical emergence of the biosphere of Earth.

Thermodynamics of Growth in Open Chemical Reaction Networks

We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by considering the fraction of the chemical work supplied from the surroundings that is converted into CRN free energy. We find that indefinite growth cannot arise in CRNs chemostatted by fixing the concentration of some species at constant values, or in continuous-flow stirred tank reactors. Indefinite growth requires a constant net influx from the surroundings of at least one species. In this case, unimolecular CRNs always generate equilibrium linear growth, i.e., a continuous linear accumulation of species with equilibrium concentrations and efficiency one. Multimolecular CRNs are necessary to generate nonequilibrium growth, i.e., the continuous accumulation of species with nonequilibrium concentrations. Pseudounimolecular CRNs-a subclass of multimolecular CRNs-always generate asymptotic linear growth with zero efficiency. Our findings demonstrate the importance of the CRN topology and the chemostatting procedure in determining the dynamics and thermodynamics of growth.

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.

Characterizing the conditions for indefinite growth in open chemical reaction networks

The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics are presented in Srinivas et al. [Phys. Rev. Lett. 132, 268001 (2024)10.1103/PhysRevLett.132.268001]. Unimolecular CRNs can accumulate only equilibrium concentrations of species while multimolecular CRNs are needed to produce indefinite growth with nonequilibrium concentrations. Within multimolecular CRNs, pseudo-unimolecular CRNs produce nonequilibrium concentrations with zero efficiencies. Nonequilibrium growth with efficiencies greater than zero requires dynamically nonlinear CRNs. In this paper, we provide a detailed analysis supporting these results. Mathematical proofs are provided for growth in unimolecular and pseudo-unimolecular CRNs. For multimolecular CRNs, four models displaying very distinctive topological properties are extensively studied, both numerically and partly analytically.

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.

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.

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.

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.

Stochastic paths controlling speed and dissipation

Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.

Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates

We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including nonideal and open systems. For this purpose, we explicitly construct dual affine coordinate systems, which completely designate an information-geometric structure, using the extent of reactions and the affinities of reactions as coordinates on a linearly constrained space of amounts of substances. The resulting structure induces a metric and a divergence (a function of two distributions of amounts), both expressed with chemical potentials. These quantities have been partially known for ideal-dilute solutions, but their extensions for nonideal solutions and the complete underlying structure are novel. The constructed geometry is a generalization of dual affine coordinates for stochastic thermodynamics. For example, the metric and the divergence are generalizations of the Fisher information and the Kullback-Leibler divergence. As an application, we identify the chemical-thermodynamic analog of the Hatano-Sasa excess entropy production using our divergence.

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.

Stoechiometric and dynamical autocatalysis for diluted chemical reaction networks

Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Recently, Blokhuis et al. (PNAS 117(41):25230-25236, 2020) gave a stoechiometric definition of autocatalysis for reaction networks, stating the existence of a combination of reactions such that the balance for all autocatalytic species is strictly positive, and investigated minimal autocatalytic networks, called autocatalytic cores. By contrast, spontaneous autocatalysis-namely, exponential amplification of all species internal to a reaction network, starting from a diluted regime, i.e. low concentrations-is a dynamical property. We introduce here a topological condition (Top) for autocatalysis, namely: restricting the reaction network description to highly diluted species, we assume existence of a strongly connected component possessing at least one reaction with multiple products (including multiple copies of a single species). We find this condition to be necessary and sufficient for stoechiometric autocatalysis. When degradation reactions have small enough rates, the topological condition further ensures dynamical autocatalysis, characterized by a strictly positive Lyapunov exponent giving the instantaneous exponential growth rate of the system. The proof is generally based on the study of auxiliary Markov chains. We provide as examples general autocatalytic cores of Type I and Type III in the typology of Blokhuis et al. (PNAS 117(41):25230-25236, 2020) . In a companion article (Unterberger in Dynamical autocatalysis for autocatalytic cores, 2021), Lyapunov exponents and the behavior in the growth regime are studied quantitatively beyond the present diluted regime .

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.

Light-activated photodeformable supramolecular dissipative self-assemblies

Dissipative self-assembly, one of fundamentally important out-of-equilibrium self-assembly systems, can serve as a controllable platform to exhibit temporal processes for various non-stimulus responsive properties. However, construction of light-fueled dissipative self-assembly structures with transformable morphology to modulate non-photoresponsive properties remains a great challenge. Here, we report a light-activated photodeformable dissipative self-assembly system in aqueous solution as metastable fluorescent palette. Zwitterionic sulfonato-merocyanine is employed as a light-induced amphiphile to co-assemble with polyethyleneimine after light irradiation. The formed spherical nanoparticles spontaneously transform into cuboid ones in the dark with simultaneous variation of the particle sizes. Then the two kinds of nanoparticles can reversibly interconvert to each other by periodical light irradiation and thermal relaxation. Furthermore, after loading different fluorophores exhibiting red, green, blue emissions and their mixtures, all these fluorescent dissipative deformable nanoparticles display time-dependent fluorescence variation with wide range of colors. Owing to the excellent performance of photodeformable dissipative assembly platform, the light-controlled fluorescence has achieved a 358-fold enhancement. Therefore, exposing the nanoparticles loaded with fluorophores to light in a spatially controlled manner allows us to draw multicolored fluorescent images that spontaneously disappeared after a specific period of time.

Dissipative self-assembly can serve as a controllable platform to exhibit temporal processes for various non-stimulus responsive properties but construction of light-fueled dissipative self-assembly structures with transformable morphology to modulate non-photoresponsive properties remains a challenge. Here, the authors report a light-activated photodeformable dissipative self-assembly system in aqueous solution as metastable fluorescent platform.

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.

Nonequilibrium Catalytic Supramolecular Assemblies of Melamine- and Imidazole-Based Dynamic Building Blocks

The development of synthetic nonequilibrium systems has gathered increasing attention due to their potential to illustrate the dynamic, complex, and emergent traits of biological systems. Simple building blocks capable of interacting via dynamic covalent chemistry and physical assembly in a reaction network under nonequilibrium conditions can contribute to our understanding of complex systems of life and its origin. Herein, we have demonstrated the nonequilibrium generation of catalytic supramolecular assemblies from simple heterocycle melamine driven by a thermodynamically activated ester. Utilizing a reversible covalent linkage, an imidazole moiety was recruited by the assemblies to access a catalytic transient state that dissipated energy via accelerated hydrolysis of the activated ester. The nonequilibrium assemblies were further capable of temporally binding to a hydrophobic guest to modulate its photophysical properties. Notably, the presence of an exogenous aromatic base augmented the lifetime of the catalytic microphases, reflecting their higher kinetic stability.

Energetic scaling in microbial growth

Microbial growth is a clear example of organization and structure arising in nonequilibrium conditions. Due to the complexity of the microbial metabolic network, elucidating the fundamental principles governing microbial growth remains a challenge. Here, we present a systematic analysis of microbial growth thermodynamics, leveraging an extensive dataset on energy-limited monoculture growth. A consistent thermodynamic framework based on reaction stoichiometry allows us to quantify how much of the available energy microbes can efficiently convert into new biomass while dissipating the remaining energy into the environment and producing entropy. We show that dissipation mechanisms can be linked to the electron donor uptake rate, a fact leading to the central result that the thermodynamic efficiency is related to the electron donor uptake rate by the scaling law [Formula: see text] and to the growth yield by [Formula: see text] These findings allow us to rederive the Pirt equation from a thermodynamic perspective, providing a means to compute its coefficients, as well as a deeper understanding of the relationship between growth rate and yield. Our results provide rather general insights into the relation between mass and energy conversion in microbial growth with potentially wide application, especially in ecology and biotechnology.

Substrate induced generation of transient self-assembled catalytic systems

Living matter is sustained under non-equilibrium conditions via continuous expense of energy which is coordinated by complex organized events. Spatiotemporal control over exquisite functions arises from chemical complexity under non-equilibrium conditions. For instance, extant biology often uses substrate binding events to access temporally stable protein conformations which show acceleration of catalytic rates to subsequently degrade the substrate. Furthermore, thermodynamically activated but kinetically stable esters (GTP) induce the change of conformation of cytoskeleton proteins (microtubules) which leads to rapid polymerization and triggers an augmentation of catalytic rates to subsequently degrade the ester. Importantly, high-energy assemblies composed of non-activated building blocks (GDP-tubulin) are accessed utilizing the energy dissipated from the catalytic conversion of GTP to GDP from the assembled state. Notably, some experimental studies with simple self-assembled systems have elegantly mimicked the phenomena of substrate induced transient generation of catalytic conformations. Through this review, we endeavour to highlight those select studies which have used simple building blocks to demonstrate substrate induced self-assemblies that subsequently show rate acceleration to convert the substrate into waste. The concept of substrate induced self-assembly of building blocks and rate acceleration from the assembled state has the potential to play a predominant role in the preparation of non-equilibrium systems. The design strategies covered in this review can inspire the possibilities of accessing high energy self-assembled structures that are seen in living systems.

This review highlights the studies which show substrate induced generation of transient catalytic moieties. Examples have been discussed with keeping an eye on the design strategies for development of non-equilibrium high energy assemblies as seen in Nature.

Chemical engines: driving systems away from equilibrium through catalyst reaction cycles

Biological systems exhibit a range of complex functions at the micro- and nanoscales under non-equilibrium conditions (for example, transportation and motility, temporal control, information processing and so on). Chemists also employ out-of-equilibrium systems, for example in kinetic selection during catalysis, self-replication, dissipative self-assembly and synthetic molecular machinery, and in the form of chemical oscillators. Key to non-equilibrium behaviour are the mechanisms through which systems are able to extract energy from the chemical reactants ('fuel') that drive such processes. In this Perspective we relate different examples of such powering mechanisms using a common conceptual framework. We discuss how reaction cycles can be coupled to other dynamic processes through positive (acceleration) or negative (inhibition) catalysis to provide the thermodynamic impetus for diverse non-equilibrium behaviour, in effect acting as a 'chemical engine'. We explore the way in which the energy released from reaction cycles is harnessed through kinetic selection in a series of what have sometimes been considered somewhat disparate fields (systems chemistry, molecular machinery, dissipative assembly and chemical oscillators), highlight common mechanistic principles and the potential for the synchronization of chemical reaction cycles, and identify future challenges for the invention and application of non-equilibrium systems. Explicit recognition of the use of fuelling reactions to power structural change in catalysts may stimulate the investigation of known catalytic cycles as potential elements for chemical engines, a currently unexplored area of catalysis research.

Nonequilibrium thermodynamics of light-induced reactions

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

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 Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties-that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics-can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes-required to sustain complex dissipative structures-might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.

Robust Dynamics of Synthetic Molecular Systems as a Consequence of Broken Symmetry

The construction of molecular robot-like objects that imitate living things is an important challenge for current chemists. Such molecular devices are expected to perform their duties robustly to carry out mechanical motion, process information, and make independent decisions. Dissipative self-organization plays an essential role in meeting these purposes. To produce a micro-robot that can perform the above tasks autonomously as a single entity, a function generator is required. Although many elegant review articles featuring chemical devices that mimic biological mechanical functions have been published recently, the dissipative structure, which is the minimum requirement for mimicking these functions, has not been sufficiently discussed. This article aims to show clearly that dissipative self-organization is a phenomenon involving autonomy, robustness, mechanical functions, and energy transformation. Moreover, it reports the results of recent experiments with an autonomous light-driven molecular device that achieves all of these features. In addition, a chemical model of cell-amplification is also discussed to focus on the generation of hierarchical movement by dissipative self-organization. By reviewing this research, it may be perceived that mainstream approaches to synthetic chemistry have not always been appropriate. In summary, the author proposes that the integration of catalytic functions is a key issue for the creation of autonomous microarchitecture.

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.

Strong current response to slow modulation: A metabolic case-study

We study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviation approach that allows us to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks.