What is special about autocatalysis?

Kinetics and coexistence of autocatalytic reaction cycles

Biological reproduction rests ultimately on chemical autocatalysis. Autocatalytic chemical cycles are thought to have played an important role in the chemical complexification en route to life. There are two, related issues: what chemical transformations allow such cycles to form, and at what speed they are operating. Here we investigate the latter question for solitary as well as competitive autocatalytic cycles in resource-unlimited batch and resource-limited chemostat systems. The speed of growth tends to decrease with the length of a cycle. Reversibility of the reproductive step results in parabolic growth that is conducive to competitive coexistence. Reversibility of resource uptake also slows down growth. Unilateral help by a cycle of its competitor tends to favour the competitor (in effect a parasite on the helper), rendering coexistence unlikely. We also show that deep learning is able to predict the outcome of competition just from the topology and the kinetic rate constants, provided the training set is large enough. These investigations pave the way for studying autocatalytic cycles with more complicated coupling, such as mutual catalysis.

The emerging chemistry of self-electrified water interfaces

Water is known for dissipating electrostatic charges, but it is also a universal agent of matter electrification, creating charged domains in any material contacting or containing it. This new role of water was discovered during the current century. It is proven in a fast-growing number of publications reporting direct experimental measurements of excess charge and electric potential. It is indirectly verified by its success in explaining surprising phenomena in chemical synthesis, electric power generation, metastability, and phase transition kinetics. Additionally, electrification by water is opening the way for developing green technologies that are fully compatible with the environment and have great potential to contribute to sustainability. Electrification by water shows that polyphasic matter is a charge mosaic, converging with the Maxwell-Wagner-Sillars effect, which was discovered one century ago but is still often ignored. Electrified sites in a real system are niches showing various local electrochemical potentials for the charged species. Thus, the electrified mosaics display variable chemical reactivity and mass transfer patterns. Water contributes to interfacial electrification from its singular structural, electric, mixing, adsorption, and absorption properties. A long list of previously unexpected consequences of interfacial electrification includes: "on-water" reactions of chemicals dispersed in water that defy current chemical wisdom; reactions in electrified water microdroplets that do not occur in bulk water, transforming the droplets in microreactors; and lowered surface tension of water, modifying wetting, spreading, adhesion, cohesion, and other properties of matter. Asymmetric capacitors charged by moisture and water are now promising alternative equipment for simultaneously producing electric power and green hydrogen, requiring only ambient thermal energy. Changing surface tension by interfacial electrification also modifies phase-change kinetics, eliminating metastability that is the root of catastrophic electric discharges and destructive explosions. It also changes crystal habits, producing needles and dendrites that shorten battery life. These recent findings derive from a single factor, water's ability to electrify matter, touching on the most relevant aspects of chemistry. They create tremendous scientific opportunities to understand the matter better, and a new chemistry based on electrified interfaces is now emerging.

On the exclusion of exponential autocatalysts by sub-exponential autocatalysts

Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially, can coexist. Here we consider competitions between autocatalytic species with different growth laws and make the simple yet counterintuitive observation that sub-exponential species can exclude exponential ones while the reverse is, in principle, impossible. This observation has implications for scenarios pertaining to the emergence of natural selection.

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.

Exactly solvable toy model of autocatalysis: Irreversible relaxation after a quantum quench

A resolvable quantum many-body Hamiltonian is introduced that mimics the behavior of the autocatalytic chemical reaction A+B⇄2B involving two different molecular species, A and B. The model also describes two nonlinearly coupled modes of an optical cavity. Consistent with the current understanding of the relaxation dynamics of integrable systems in isolation, the wave function following a quantum quench exhibits irreversibility with retention of the memory about its initial conditions. Salient features of the model include a marked similarity with conventional quantum decay and a total B-to-A conversion, with associated classical-like behavior of the wave function, when the initial state does not contain A-type molecules.

Conditions for the origin of homochirality in primordial catalytic reaction networks

We study the generation of homochirality in a general chemical model (based on the homogeneous, fully connected Smoluchowski aggregation-fragmentation model) that obeys thermodynamics and can be easily mapped onto known origin of life models (e.g. autocatalytic sets, hypercycles, etc.), with essential aspects of origin of life modeling taken into consideration. Using a combination of theoretical modeling and numerical simulations, we look for minimal conditions for which our general chemical model exhibits spontaneous mirror symmetry breaking. We show that our model spontaneously breaks mirror symmetry in various catalytic configurations that only involve a small number of catalyzed reactions and nothing else. Of particular importance is that mirror symmetry breaking occurs in our model without the need for single-step autocatalytis or mutual inhibition, which may be of relevance for prebiotic chemistry.

Coulombic Surface-Ion Interactions Induce Nonlinear and Chemistry-Specific Charging Kinetics

While important for many industrial applications, chemical reactions responsible for the charging of solids in water are often poorly understood. We theoretically investigate the charging kinetics of solid-liquid interfaces and find that the time-dependent equilibration of surface charge contains key information not only on the reaction mechanism, but also on the valency of the reacting ions. We construct a nonlinear differential equation describing surface charging by combining chemical Langmuir kinetics and electrostatic Poisson-Boltzmann theory. Our results reveal a clear distinction between late-time (near-equilibrium) and short-time (far-from-equilibrium) relaxation rates, the ratio of which contains information on the charge valency and ad- or desorption mechanism of the charging process. Similarly, we find that single-ion reactions can be distinguished from two-ion reactions, as the latter show an inflection point during equilibration. Interestingly, such inflection points are characteristic of autocatalytic reactions, and we conclude that the Coulombic ion-surface interaction is an autocatalytic feedback mechanism.

Spontaneous Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models

To explore abiotic theories related to the origin of biomolecular homochirality, we analyze two entirely reversible kinetic models composed of an enantioselective autocatalysis with limited stereoselectivity that is coupled to an enantiomeric mutual inhibition (Frank-like models). The two models differ in their autocatalytic steps in respect to the formation of monomer species in one model and of dimer species in the other. While fully reversible and running in a closed system, spontaneous mirror symmetry breaking (SMSB) gives rise to transient chiral excursions, even when starting from a strictly achiral situation. Before the SMSB, the two models differ in the main dissipative processes. At the SMSB, the entropy production rate reaches its maximum in both models. Here it is the enantioselective autocatalysis with retention of the winner enantiomer that dominates. During the terminal phase, the enantioselective autocatalysis with inversion prevails, while the entropy production rate vanishes, thus fulfilling the conditions of microscopic reversibility. SMSB does not occur if the autocatalytic rate constant is too strong or too weak. However, when the autocatalysis is relatively weak, the temporary chiral excursions last for long periods of time and could be the starting point of a cascade of asymmetric reactions. The realism of such Frank-like models is discussed from the viewpoint of their relevance to prebiotic chemistry.

Early Physical Organic Chemistry: Nikolai Aleksandrovich Menshutkin (1842-1907) and Reaction Velocities

The name of Menshutkin is most frequently associated with his eponymous reaction (the quaternization of tertiary amines with alkyl halides). However, he made encyclopedic contributions to the field of reaction kinetics, where he carried out extensive studies of the effects of reactant structure on the rates of esterification of monohydric, dihydric and trihydric alcohols with monocarboxylic acids, and monobasic and dibasic carboxylic acids and anhydrides with monohydric alcohols. In these studies, he deduced an order of reactivity of alcohols in esterification on the basis of their reactions with acetic acid, and the effects of acid structure on the rates of esterification based on the reaction of the carboxylic acid with isobutyl alcohol. When his attention later turned to the substitution chemistry of amines, he defined the parameters that affected their reactions: anilines were less reactive than alkylamines, secondary more reactive than primary amines, and the reaction was accelerated by replacing benzene as a solvent with alcohols. The wide-ranging work of Menshutkin, the physical organic chemist, is discussed.

Interaction of anions with the surface of a coordination cage in aqueous solution probed by their effect on a cage-catalysed Kemp elimination

An octanuclear M8L12 coordination cage catalyses the Kemp elimination reaction of 5-nitro-1,2-benzisoxazole (NBI) with hydroxide to give 2-cyano-4-nitrophenolate (CNP) as the product. In contrast to the previously-reported very efficient catalysis of the Kemp elimination reaction of unsubstituted benzisoxazole, which involves the substrate binding inside the cage cavity, the catalysed reaction of NBI with hydroxide is slower and occurs at the external surface of the cage, even though NBI can bind inside the cage cavity. The rate of the catalysed reaction is sensitive to the presence of added anions, which bind to the 16+ cage surface, displacing the hydroxide ions from around the cage which are essential reaction partners in the Kemp elimination. Thus we can observe different binding affinities of anions to the surface of the cationic cage in aqueous solution by the extent to which they displace hydroxide and thereby inhibit the catalysed Kemp elimination and slow down the appearance of CNP. For anions with a -1 charge the observed affinity order for binding to the cage surface is consistent with their ease of desolvation and their ordering in the Hofmeister series. With anions that are significantly basic (fluoride, hydrogen carbonate, carboxylates) the accumulation of the anion around the cage surface accelerates the Kemp elimination compared to the background reaction with hydroxide, which we ascribe to the ability of these anions to participate directly in the Kemp elimination. This work provides valuable mechanistic insights into the role of the cage in co-locating the substrate and the anionic reaction partners in a cage-catalysed reaction.

Thermodynamic Analysis of the Landolt-Type Autocatalytic System

A recent work demonstrated the example of the Landolt-type reaction system and how the simplest autocatalytic loop is described by the kinetic mass action law and proper parametrization of direct and autocatalytic pathways. Using a methodology of non-equilibrium thermodynamics, the thermodynamic consistency of that kinetic model is analyzed and the mass action description is generalized, including an alternative description by the empirical rate equation. Relationships between independent and dependent reactions and their rates are given. The mathematical modeling shows that following the time evolution of reaction rates provides additional insight into autocatalytic behavior. A brief note on thermodynamic driving forces and coupling with diffusion is added. In summary, this work extends and generalizes the kinetic description of the Landolt-type system, placing it within the framework of non-equilibrium thermodynamics and demonstrating its thermodynamic consistency.

Mechanistic Study of Membrane Disruption by Antimicrobial Methacrylate Random Copolymers by the Single Giant Vesicle Method

Cationic amphiphilic polymers have been a platform to create new antimicrobial materials that act by disrupting bacterial cell membranes. While activity characterization and chemical optimization have been done in numerous studies, there remains a gap in our knowledge on the antimicrobial mechanisms of the polymers, which is needed to connect their chemical structures and biological activities. To that end, we used a single giant unilamellar vesicle (GUV) method to identify the membrane-disrupting mechanism of methacrylate random copolymers. The copolymers consist of random sequences of aminoethyl methacrylate and methyl (MMA) or butyl (BMA) methacrylate, with low molecular weights of 1600-2100 g·mol^-1. GUVs consisting of an 8:2 mixture of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1'-rac-glycerol), sodium salt (POPG) and those with only 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) were prepared to mimic the bacterial (Escherichia coli) or mammalian membranes, respectively. The disruption of bacteria and mammalian cell membrane-mimetic lipid bilayers in GUVs reflected the antimicrobial and hemolytic activities of the copolymers, suggesting that the copolymers act by disrupting cell membranes. The copolymer with BMA formed pores in the lipid bilayer, while that with MMA caused GUVs to burst. Therefore, we propose that the mechanism is inherent to the chemical identity or properties of hydrophobic groups. The copolymer with MMA showed characteristic sigmoid curves of the time course of GUV burst. We propose a new kinetic model with a positive feedback loop in the insertion of the polymer chains in the lipid bilayer. The novel finding of alkyl-dependent membrane-disrupting mechanisms will provide a new insight into the role of hydrophobic groups in the optimization strategy for antimicrobial activity and selectivity.

Self-Reproduction and Darwinian Evolution in Autocatalytic Chemical Reaction Systems

Understanding the emergence of life from (primitive) abiotic components has arguably been one of the deepest and yet one of the most elusive scientific questions. Notwithstanding the lack of a clear definition for a living system, it is widely argued that heredity (involving self-reproduction) along with compartmentalization and metabolism are key features that contrast living systems from their non-living counterparts. A minimal living system may be viewed as "a self-sustaining chemical system capable of Darwinian evolution". It has been proposed that autocatalytic sets of chemical reactions (ACSs) could serve as a mechanism to establish chemical compositional identity, heritable self-reproduction, and evolution in a minimal chemical system. Following years of theoretical work, autocatalytic chemical systems have been constructed experimentally using a wide variety of substrates, and most studies, thus far, have focused on the demonstration of chemical self-reproduction under specific conditions. While several recent experimental studies have raised the possibility of carrying out some aspects of experimental evolution using autocatalytic reaction networks, there remain many open challenges. In this review, we start by evaluating theoretical studies of ACSs specifically with a view to establish the conditions required for such chemical systems to exhibit self-reproduction and Darwinian evolution. Then, we follow with an extensive overview of experimental ACS systems and use the theoretically established conditions to critically evaluate these empirical systems for their potential to exhibit Darwinian evolution. We identify various technical and conceptual challenges limiting experimental progress and, finally, conclude with some remarks about open questions.

Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases.

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

Vibrio cholerae biofilm scaffolding protein RbmA shows an intrinsic, phosphate-dependent autoproteolysis activity

Vibrio cholerae is the causative agent of the diarrheal disease cholera, for which biofilm communities are considered to be environmental reservoirs. In endemic regions, and after algal blooms, which may result from phosphate enrichment following agricultural runoff, the bacterium is released from biofilms resulting in seasonal disease outbreaks. However, the molecular mechanism by which V. cholerae senses its environment and switches lifestyles from the biofilm‐bound state to the planktonic state is largely unknown. Here, we report that the major biofilm scaffolding protein RbmA undergoes autocatalytic proteolysis via a phosphate‐dependent induced proximity activation mechanism. Furthermore, we show that RbmA mutants that are defective in autoproteolysis cause V. cholerae biofilms to grow larger and mechanically stronger, correlating well with the observation that RbmA stability directly affects microbial community homeostasis and rheological properties. In conclusion, our biophysical study characterizes a novel phosphate‐dependent breakdown pathway of RbmA, while microbiological data suggest a new, sensory role of this biofilm scaffolding element.

Universal motifs and the diversity of autocatalytic systems

Autocatalysis is essential for the origin of life and chemical evolution. However, the lack of a unified framework so far prevents a systematic study of autocatalysis. Here, we derive, from basic principles, general stoichiometric conditions for catalysis and autocatalysis in chemical reaction networks. This allows for a classification of minimal autocatalytic motifs called cores. While all known autocatalytic systems indeed contain minimal motifs, the classification also reveals hitherto unidentified motifs. We further examine conditions for kinetic viability of such networks, which depends on the autocatalytic motifs they contain and is notably increased by internal catalytic cycles. Finally, we show how this framework extends the range of conceivable autocatalytic systems, by applying our stoichiometric and kinetic analysis to autocatalysis emerging from coupled compartments. The unified approach to autocatalysis presented in this work lays a foundation toward the building of a systems-level theory of chemical evolution.

The SIR dynamic model of infectious disease transmission and its analogy with chemical kinetics

Mathematical models of the dynamics of infectious disease transmission are used to forecast epidemics and assess mitigation strategies. In this article, we highlight the analogy between the dynamics of disease transmission and chemical reaction kinetics while providing an exposition on the classic Susceptible–Infectious–Removed (SIR) epidemic model. Particularly, the SIR model resembles a dynamic model of a batch reactor carrying out an autocatalytic reaction with catalyst deactivation. This analogy between disease transmission and chemical reaction enables the exchange of ideas between epidemic and chemical kinetic modeling communities.

An ecological framework for the analysis of prebiotic chemical reaction networks

It is becoming widely accepted that very early in life's origin, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolution. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed compartments that are subject to constant dilution by a solution with a fixed concentration of input chemicals. Modelling all chemical reactions as fully reversible, we show that seeding an autocatalytic cycle with tiny amounts of one or more of its member chemicals results in logistic growth of all member chemicals in the cycle. This finding justifies drawing an instructive analogy between an autocatalytic cycle and a biological species. We extend this finding to show that pairs of autocatalytic cycles can exhibit competitive, predator-prey, or mutualistic associations just like biological species. Furthermore, when there is stochasticity in the environment, particularly in the seeding of autocatalytic cycles, chemical ecosystems can show complex dynamics that can resemble evolution. The evolutionary character is especially clear when the network architecture results in ecological precedence, which makes a system's trajectory historically contingent on the order in which cycles are seeded. For all its simplicity, the framework developed here helps explain the onset of adaptive evolution in prebiotic chemical reaction networks, and can shed light on the origin of key biological attributes such as thermodynamic irreversibility and genetic encoding.