Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems

A Catalysis-Driven Dual Molecular Motor

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

Minimal catalytic dissipative assemblies via cooperation of an amino acid, a nucleobase precursor and a cofactor

Functions arising from cooperation between protobiopolymers have fueled the chemical emergence of living matter, which requires a continuous supply of energy to exist in a far-from-equilibrium state. Non-equilibrium conditions imparted by available energy sources have played critical roles in the appearance of complex co-assembled architectures, which exploit the properties of different classes of biopolymers. Such co-assemblies formed from mixtures of nitrogenous heterocycles as protonucleobases and peptide precursors might have acted as early versions of catalytic machinery, capable of sustaining chemical reaction networks. Herein, we show the generation of catalytic non-equilibrium networks from a mixture of a nitrogenous heterocycle, an amino acid and a cofactor driven by an aromatic substrate. The cooperation, a result of supramolecular interactions between different components, rendered the assemblies capable of activating the cofactor towards oxidative degradation of the substrate, which resulted in autonomous disassembly (negative feedback). Furthermore, utilising promiscuous hydrolytic capability, the transient co-assemblies could metabolise a precursor to generate additional amounts of the substrate, enhancing the lifetime (positive feedback) of the assemblies.

Beyond Single-Cycle Autonomous Molecular Machines: Light-Powered Shuttling in a Multi-Cycle Reaction Network

Biomolecular machines autonomously convert energy into functions, driving systems away from thermodynamic equilibrium. This energy conversion is achieved by leveraging complex, kinetically asymmetric chemical reaction networks that are challenging to characterize precisely. In contrast, all known synthetic molecular systems in which kinetic asymmetry has been quantified are well described by simple single-cycle networks. Here, we report on a unique light-driven [2]rotaxane that enables the autonomous operation of a synthetic molecular machine with a multi-cycle chemical reaction network. Unlike all prior systems, the present one exploits a photoactive macrocycle, which features a different photoreactivity depending on the binding sites at which it resides. Furthermore, E to Z isomerization reverses the relative affinity of the macrocycle for two binding sites on the axle, resulting in a multi-cycle network. Building on the most recent theoretical advancements, this work quantifies kinetic asymmetry in a multi-cycle network for the first time. Our findings represent the simplest rotaxane capable of autonomous shuttling developed so far and offer a general strategy to generate and quantify kinetic asymmetry beyond single-cycle systems.

Power Strokes in Molecular Motors: Predictive, Irrelevant, or Somewhere in Between?

For several decades, molecular motor directionality has been rationalized in terms of the free energy of molecular conformations visited before and after the motor takes a step, a so-called power stroke mechanism with analogues in macroscopic engines. Despite theoretical and experimental demonstrations of its flaws, the power stroke language is quite ingrained, and some communities still value power stroke intuition. By building a catalysis-driven motor into simulated numerical experiments, we here systematically report on how directionality responds when the motor is modified accordingly to power stroke intuition. We confirm that the power stroke mechanism generally does not predict motor directionality. Nevertheless, the simulations illustrate that the relative stability of molecular conformations should be included as a potential design element to adjust the motor directional bias. Though power strokes are formally unimportant for determining directionality, we show that practical attempts to alter a power stroke have side effects that can in fact alter the bias. The change in the bias can align with what power stroke intuition would have suggested, offering a potential explanation for why the flawed power stroke mechanism can retain apparent utility when engineering specific systems.

Design principles, growth laws, and competition of minimal autocatalysts

The difficulty of designing simple autocatalysts that grow exponentially in the absence of enzymes, external drives or ingenious internal mechanisms severely constrains scenarios for the emergence of evolution by natural selection in chemical and physical systems. Here, we systematically analyze these difficulties in the simplest and most generic autocatalyst: a dimeric molecule that duplicates by templated ligation. We show that despite its simplicity, such an autocatalyst can achieve exponential growth autonomously. We also show, however, that it is possible to design as simple sub-exponential autocatalysts that have an advantage over exponential autocatalysts when competing for a common resource. We reach these conclusions by developing a theoretical framework based on kinetic barrier diagrams. Besides challenging commonly accepted assumptions in the field of the origin of life, our results provide a blueprint for the experimental realization of elementary autocatalysts exhibiting a form of natural selection, whether on a molecular or colloidal scale.

Allosteric Control of the Catalytic Properties of Dipeptide-Based Supramolecular Assemblies

Allostery, as seen in extant biology, governs the activity regulation of enzymes through the redistribution of conformational equilibria upon binding an effector. Herein, a minimal design is demonstrated where a dipeptide can exploit dynamic imine linkage to condense with simple aldehydes to access spherical aggregates as catalytically active states, which facilitates an orthogonal reaction due to the closer proximity of catalytic residues (imidazoles). The allosteric site (amine) of the minimal catalyst can concomitantly bind to an inhibitor via a dynamic exchange, which leads to the alternation of the energy landscape of the self-assembled state, resulting in downregulation of catalytic activity. Further, temporal control over allosteric regulation is realized via a feedback-controlled autonomous reaction network that utilizes the hydrolytic activity of the (in)active state as a function of time.

A role for conformational changes in enzyme catalysis

The role played by conformational changes in enzyme catalysis is controversial. In addition to examining specific enzymes, studying formal models can help identify the conditions under which conformational changes promote catalysis. Here, we present a model demonstrating how conformational changes can break a generic trade-off due to the conflicting requirements of successive steps in catalytic cycles, namely high specificity for the transition state to accelerate the chemical transformation and low affinity for the products to favor their release. The mechanism by which the trade-off is broken is a transition between conformations with different affinities for the substrate. The role of the effector that induces the transition is played by a substrate "handle," a part of the substrate that is not chemically transformed but whose interaction with the enzyme is nevertheless essential to rapidly complete the catalytic cycle. A key element of the model is the formalization of the constraints causing the trade-off that the presence of multiple states breaks, which we attribute to the strong chemical similarity between successive reaction states-substrates, transition states, and products. For the sake of clarity, we present our model for irreversible one-step unimolecular reactions. In this context, we demonstrate how the different forms that chemical similarities between reaction states can take impose limits on the overall catalytic turnover. We first analyze catalysts without internal degrees of freedom and then show how two-state catalysts can overcome their limitations. Our results recapitulate previous proposals concerning the role of conformational changes and substrate handles in a formalism that makes explicit the constraints that elicit these features. In addition, our approach establishes links with studies in the field of heterogeneous catalysis, where the same trade-offs are observed and where overcoming them is a well-recognized challenge.

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.

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.

Temporal (Dis)Assembly of Peptide Nanostructures Dictated by Native Multistep Catalytic Transformations

Emergence of complex catalytic machinery via simple building blocks under non-equilibrium conditions can contribute toward the system level understanding of the extant biocatalytic reaction network that fuels metabolism. Herein, we report temporal (dis)assembly of peptide nanostructures in presence of a cofactor dictated by native multistep cascade transformations. The short peptide can form a dynamic covalent bond with the thermodynamically activated substrate and recruit cofactor hemin to access non-equilibrium catalytic nanostructures (positive feedback). The neighboring imidazole and hemin moieties in the assembled state rapidly converted the substrate to product(s) via a two-step cascade reaction (hydrolase-peroxidase like) that subsequently triggered the disassembly of the catalytic nanostructures (negative feedback). The feedback coupled reaction cycle involving intrinsic catalytic prowess of short peptides to realize the advanced trait of two-stage cascade degradation of a thermodynamically activated substrate foreshadows the complex non-equilibrium protometabolic networks that might have preceded the chemical emergence of life.

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.

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.

On the Emergence of Autonomous Chemical Systems through Dissipation Kinetics

This work addresses the kinetic requirements for compensating the entropic cost of self-organization and natural selection, thereby revealing a fundamental principle in biology. Metabolic and evolutionary features of life cannot therefore be separated from an origin of life perspective. Growth, self-organization, evolution and dissipation processes need to be metabolically coupled and fueled by low-entropy energy harvested from the environment. The evolutionary process requires a reproduction cycle involving out-of-equilibrium intermediates and kinetic barriers that prevent the reproductive cycle from proceeding in reverse. Model analysis leads to the unexpectedly simple relationship that the system should be fed energy with a potential exceeding a value related to the ratio of the generation time to the transition state lifetime, thereby enabling a process mimicking natural selection to take place. Reproducing life's main features, in particular its Darwinian behavior, therefore requires satisfying constraints that relate to time and energy. Irreversible reaction cycles made only of unstable entities reproduce some of these essential features, thereby offering a physical/chemical basis for the possible emergence of autonomy. Such Emerging Autonomous Systems (EASs) are found to be capable of maintaining and reproducing their kind through the transmission of a stable kinetic state, thereby offering a physical/chemical basis for what could be deemed an epigenetic process.

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.