Role of Differential Transport in an Oscillatory Enzyme Reaction

Artificial Homeostasis Systems Based on Feedback Reaction Networks: Design Principles and Future Promises

Feedback-controlled chemical reaction networks (FCRNs) are indispensable for various biological processes, such as cellular mechanisms, patterns, and signaling pathways. Through the intricate interplay of many feedback loops (FLs), FCRNs maintain a stable internal cellular environment. Currently, creating minimalistic synthetic cells is the long-term objective of systems chemistry, which is motivated by such natural integrity. The design, kinetic optimization, and analysis of FCRNs to exhibit functions akin to those of a cell still pose significant challenges. Indeed, reaching synthetic homeostasis is essential for engineering synthetic cell components. However, maintaining homeostasis in artificial systems against various agitations is a difficult task. Several biological events can provide us with guidelines for a conceptual understanding of homeostasis, which can be further applicable in designing artificial synthetic systems. In this regard, we organize our review with artificial homeostasis systems driven by FCRNs at different length scales, including homogeneous, compartmentalized, and soft material systems. First, we stretch a quick overview of FCRNs in different molecular and supramolecular systems, which are the essential toolbox for engineering different nonlinear functions and homeostatic systems. Moreover, the existing history of synthetic homeostasis in chemical and material systems and their advanced functions with self-correcting, and regulating properties are also emphasized.

Design of oscillatory dynamics in numerical simulations of compartment-based enzyme systems

Enzymatic reactions that yield non-neutral products are known to involve feedback due to the bell-shaped pH-rate curve of the enzyme. Compartmentalizing the reaction has been shown to lead to transport-driven oscillations in theory; however, there have been few reproducible experimental examples. Our objective was to determine how the conditions could be optimized to achieve pH oscillations. We employed numerical simulations to investigate the hydrolysis of ethyl acetate in a confined esterase enzyme system, examining the influence of key factors on its behavior. Specific parameter ranges that lead to bistability and self-sustained pH oscillations and the importance of fast base transport for oscillations in this acid-producing system are highlighted. Suggestions are made to expand the parameter space for the occurrence of oscillations, including modifying the maximum of the enzyme pH-rate curve and increasing the negative feedback rate. This research not only sheds light on the programmable nature of enzyme-driven pH regulation but also furthers knowledge on the optimal design of such feedback systems for experimentalists.

pH-feedback systems to program autonomous self-assembly and material lifecycles

pH-responsive systems have gained importance for the development of smart materials and for biomedical applications because they can switch between different states by simple acid/base triggers. However, such equilibrium systems lack the autonomous behaviour that is so ubiquitous in living systems that self-regulate out of equilibrium. As a contribution to the emerging field of autonomous chemical systems, we have developed pH-feedback systems (pH-FS) based on the coupling of acid- and base-producing steps in chemical reaction networks. The resulting autonomous nonlinear pH curves can be coupled with a variety of pH-sensitive building blocks to program the lifecycles of the associated transient state at the level of self-assemblies and material systems. In this article, we discuss the different generations of such pH-feedback systems, the principles of their coupling to self-assemblies with lifecycles and highlight emerging concepts for the design of autonomous functional materials. The specificity, robustness, and flexible operation of such pH-FS can also be used to realize chemo-structural and chemo-mechanical feedbacks that extend the behaviour of such materials systems toward complex and functional life-like systems.

Collective Behavior of Urease pH Clocks in Nano- and Microvesicles Controlled by Fast Ammonia Transport

The transmission of chemical signals via an extracellular solution plays a vital role in collective behavior in cellular biological systems and may be exploited in applications of lipid vesicles such as drug delivery. Here, we investigated chemical communication in synthetic micro- and nanovesicles containing urease in a solution of urea and acid. We combined experiments with simulations to demonstrate that the fast transport of ammonia to the external solution governs the pH-time profile and synchronizes the timing of the pH clock reaction in a heterogeneous population of vesicles. This study shows how the rate of production and emission of a small basic product controls pH changes in active vesicles with a distribution of sizes and enzyme amounts, which may be useful in bioreactor or healthcare applications.

Stochastic pH Oscillations in a Model of the Urea-Urease Reaction Confined to Lipid Vesicles

The urea-urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.

Feedback and Communication in Active Hydrogel Spheres with pH Fronts: Facile Approaches to Grow Soft Hydrogel Structures

Compartmentalized reaction networks regulating signal processing, communication and pattern formation are central to living systems. Towards achieving life-like materials, we compartmentalized urea-urease and more complex urea-urease/ester-esterase pH-feedback reaction networks into hydrogel spheres and investigate how fuel-driven pH fronts can be sent out from these spheres and regulated by internal reaction networks. Membrane characteristics are installed by covering urease spheres with responsive hydrogel shells. We then encapsulate the two networks (urea-urease and ester-esterase) separately into different hydrogel spheres to devise communication, pattern formation and attraction. Moreover, these pH fronts and patterns can be used for self-growing hydrogels, and for developing complex geometries from non-injectable hydrogels without 3D printing tools. This study opens possibilities for compartmentalized feedback reactions and their use in next generation materials fabrication.

Stimuli responsive dynamic transformations in supramolecular gels

Supramolecular gels are formed by the self-assembly of small molecules under the influence of various non-covalent interactions. As the interactions are individually weak and reversible, it is possible to perturb the gels easily, which in turn enables fine tuning of their properties. Synthetic supramolecular gels are kinetically trapped and usually do not show time variable changes in material properties after formation. However, such materials potentially become switchable when exposed to external stimuli like temperature, pH, light, enzyme, redox, and chemical analytes resulting in reconfiguration of gel matrix into a different type of network. Such transformations allow gel-to-gel transitions while the changes in the molecular aggregation result in alteration of physical and chemical properties of the gel with time. Here, we discuss various methods that have been used to achieve gel-to-gel transitions by modifying a pre-formed gel material through external perturbation. We also describe methods that allow time-dependent autonomous switching of gels into different networks enabling synthesis of next generation functional materials. Dynamic modification of gels allows construction of an array of supramolecular gels with various properties from a single material which eventually extend the limit of applications of the gels. In some cases, gel-to-gel transitions lead to materials that cannot be accessed directly. Finally, we point out the necessity and possibility of further exploration of the field.

Programming properties of transient hydrogels by an enzymatic reaction

Supramolecular gels are usually stable in time as they are formed under thermodynamic equilibrium or at least in a deep well of a kinetically trapped state. However, artificial construction of kinetically controlled transient supramolecular gels is an interesting challenge. In these systems, usually a kinetically trapped transient aggregate is formed by active building blocks that leads to gelation; the gel then typically returns to the solution state. In this work, we show that such transient aggregation can occur by successive formation of two distinctly different kinetically controlled metastable states. Control over the first metastable state allows us to achieve significant control over the stability and properties of the second metastable state.

Modelling Bacteria-Inspired Dynamics with Networks of Interacting Chemicals

One approach to understanding how life-like properties emerge involves building synthetic cellular systems that mimic certain dynamical features of living cells such as bacteria. Here, we developed a model of a reaction network in a cellular system inspired by the ability of bacteria to form a biofilm in response to increasing cell density. Our aim was to determine the role of chemical feedback in the dynamics. The feedback was applied through the enzymatic rate dependence on pH, as pH is an important parameter that controls the rates of processes in cells. We found that a switch in pH can be used to drive base-catalyzed gelation or precipitation of a substance in the external solution. A critical density of cells was required for gelation that was essentially independent of the pH-driven feedback. However, the cell pH reached a higher maximum as a result of the appearance of pH oscillations with feedback. Thus, we conclude that while feedback may not play a vital role in some density-dependent behavior in cellular systems, it nevertheless can be exploited to activate internally regulated cell processes at low cell densities.

Influence of reaction-induced convection on quorum sensing in enzyme-loaded agarose beads

In theory, groups of enzyme-loaded particles producing an acid or base may show complex behavior including dynamical quorum sensing, the appearance of synchronized oscillations above a critical number or density of particles. Here, experiments were performed with the enzyme urease loaded into mm-sized agarose beads and placed in a solution of urea, resulting in an increase in pH. This behavior was found to be dependent upon the number of beads present in the array; however, reaction-induced convection occurred and plumes of high pH developed that extended to the walls of the reactor. The convection resulted in the motion of the mm-sized particles and conversion of the solution to high pH. Simulations in a simple model of the beads demonstrated the suppression of dynamical quorum sensing in the presence of flow.

Immobilization adjusted clock reaction in the urea–urease–H+ reaction system

The bell-shaped reactivity-pH curve is the fundamental reason that the temporal programmable kinetic switch in clock reactions can be obtained in bio-competitive enzymatic reactions. In this work, urease was loaded on small resin particles through ionic binding. Experimental results reveal that the immobilization not only increased the stability of the enzyme and the reproducibility of the clock reaction, but also shifted the bell-shaped activity curve to lower pHs. The latter change enables the clock reaction to occur from an initial pH of 2.3, where the free enzyme had already lost its activity. Two mechanisms explain the influence of the immobilization on the clock reaction. Immobilization modified the pH sensitive functional groups on the enzyme, shifting the activity curve to a more acidic region, and reduced diffusion alters the enzyme dynamics.

The reported immobilization shifts the bell-shaped reactivity-pH curve to lower pHs and enables the clock reaction to occur from a very low initial pH, where the free enzyme had already lost its activity.

Oscillations of pH in the urea–urease system in a membrane reactor

Urea–urease reaction in an open reservoir–membrane–reactor system displays regular spontaneous oscillations of pH.

Reaction fronts of the autocatalytic hydrogenase reaction

We have built a model to describe the hydrogenase catalyzed, autocatalytic, reversible hydrogen oxidation reaction where one of the enzyme forms is the autocatalyst. The model not only reproduces the experimentally observed front properties, but also explains the found hydrogen ion dependence. Furthermore, by linear stability analysis, two different front types are found in good agreement with the experiments.

Switches induced by quorum sensing in a model of enzyme-loaded microparticles

Quorum sensing refers to the ability of bacteria and other single-celled organisms to respond to changes in cell density or number with population-wide changes in behaviour. Here, simulations were performed to investigate quorum sensing in groups of diffusively coupled enzyme microparticles using a well-characterized autocatalytic reaction which raises the pH of the medium: hydrolysis of urea by urease. The enzyme urease is found in both plants and microorganisms, and has been widely exploited in engineering processes. We demonstrate how increases in group size can be used to achieve a sigmoidal switch in pH at high enzyme loading, oscillations in pH at intermediate enzyme loading and a bistable, hysteretic switch at low enzyme loading. Thus, quorum sensing can be exploited to obtain different types of response in the same system, depending on the enzyme concentration. The implications for microorganisms in colonies are discussed, and the results could help in the design of synthetic quorum sensing for biotechnology applications such as drug delivery.

Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory

Despite the usefulness of curly arrows in chemistry, their relationship with real electron density flows is still imprecise, and even their direct connection to quantum chemistry is still controversial. The paradigmatic description - from first principles - of the mechanistic aspects of a given chemical process is based mainly on the relative energies and geometrical changes at the stationary points of the potential energy surface along the reaction pathway; however, it is not sufficient to describe chemical systems in terms of bonding aspects. Probing the electron density distribution during a chemical reaction can provide important insights, enabling us to understand and control chemical reactions. This aim has required an extension of the relationships between the concepts of traditional chemistry and those of quantum mechanics. Bonding evolution theory (BET), which combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT), provides a powerful method that offers insight into the molecular mechanism of chemical rearrangements. In agreement with the laws of physical and aspects of quantum theory, BET can be considered an appropriate tool to tackle chemical reactivity with a wide range of possible applications. In this work, BET is applied to address a long-standing problem: the ability to monitor the flow of electron density. BET analysis shows a connection between quantum mechanics and bond making/forming processes. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds and provides detailed physical grounds for this type of representation. We demonstrate this procedure using the test set of prototypical examples of thermal ring apertures, and the degenerated Cope rearrangement of semibullvalene.

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.

Temporal Control of Gelation and Polymerization Fronts Driven by an Autocatalytic Enzyme Reaction

Chemical systems that remain kinetically dormant until activated have numerous applications in materials science. Herein we present a method for the control of gelation that exploits an inbuilt switch: the increase in pH after an induction period in the urease-catalyzed hydrolysis of urea was used to trigger the base-catalyzed Michael addition of a water-soluble trithiol to a polyethylene glycol diacrylate. The time to gelation (minutes to hours) was either preset through the initial concentrations or the reaction was initiated locally by a base, thus resulting in polymerization fronts that converted the mixture from a liquid into a gel (ca. 0.1 mm min(-1)). The rate of hydrolytic degradation of the hydrogel depended on the initial concentrations, thus resulting in a gel lifetime of hours to months. In this way, temporal programming of gelation was possible under mild conditions by using the output of an autocatalytic enzyme reaction to drive both the polymerization and subsequent degradation of a hydrogel.

Temporal Control of Gelation and Polymerization Fronts Driven by an Autocatalytic Enzyme Reaction

Chemical systems that remain kinetically dormant until activated have numerous applications in materials science. Herein we present a method for the control of gelation that exploits an inbuilt switch: the increase in pH after an induction period in the urease-catalyzed hydrolysis of urea was used to trigger the base-catalyzed Michael addition of a water-soluble trithiol to a polyethylene glycol diacrylate. The time to gelation (minutes to hours) was either preset through the initial concentrations or the reaction was initiated locally by a base, thus resulting in polymerization fronts that converted the mixture from a liquid into a gel (ca. 0.1 mm min-1). The rate of hydrolytic degradation of the hydrogel depended on the initial concentrations, thus resulting in a gel lifetime of hours to months. In this way, temporal programming of gelation was possible under mild conditions by using the output of an autocatalytic enzyme reaction to drive both the polymerization and subsequent degradation of a hydrogel.

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation

The displacement of the nuclei along the reaction path provides an explanatory interpretation of the electron density transfers making possible to understand chemical reactions.

Inquiry of the electron density transfers in chemical reactions: a complete reaction path for the denitrogenation process of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives

A detailed study on all stages associated with the reaction mechanisms for the denitrogenation of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives (DBX, with X substituents at the methano-bridge carbon atom, X = H and OH) is presented. In particular, we have characterized the processes leading to cycloalkene derivatives through migration-type mechanisms as well as the processes leading to cyclopentil-1,3-diradical species along concerted or stepwise pathways. The reaction mechanisms have been further analysed within the bonding evolution theory framework at B3LYP and M05-2X/6-311+G(2d,p) levels of theory. Analysis of the results allows us to obtain the intimate electronic mechanism for the studied processes, providing a new topological picture of processes underlying the correlation between the experimental measurements obtained by few-optical-cycle visible pulse radiation and the quantum topological analysis of the electron localization function (ELF) in terms of breaking/forming processes along this chemical rearrangement. The evolution of the population of the disynaptic basin V(N1,N2) can be related to the experimental observation associated with the N=N stretching mode evolution, relative to the N2 release, along the reaction process. This result allows us to determine why the N2 release is easier for the DBH case via a concerted mechanism compared to the stepwise mechanism found in the DBOH system. This holds the key to unprecedented insight into the mapping of the electrons making/breaking the bonds while the bonds change.

Spatiotemporal behavior induced by differential diffusion in Landolt systems

The spatiotemporal dynamics of Landolt type reactions, for instance reactions between sulfite ions and strong oxidants, performed in a medium fed by the diffusion from a boundary is investigated numerically by using a simple general reaction scheme. In these conditions, the model can generate various spatiotemporal phenomena, e.g., spatial bistability, simple and complex oscillations, birhythmicity, and chaos, even though in a spatially homogeneous open reactor only steady-state bistability can develop. The model consists of two reactions, a protonation equilibrium of the reductant and an oxidation step that is autoactivated by hydrogen ions. The rich dynamics is the result of two factors: (i) long-range activation, through the rapidly diffusing hydrogen ions, (ii) the presence of two parallel autocatalytic pathways. Long range activation provides the necessary negative feedback, whereas the dual nature of the autocatalysis leads to the appearance of two different oscillatory modes. The presence of a second-order term in the rate law of the autocatalytic reaction is linked to a large amplitude oscillations that affect the system as a whole, whereas the third-order one gives rise to localized front oscillations. The complex phenomena, like mixed mode and chaotic oscillations are observed at the meeting of these different oscillatory modes.