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

Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems

The intricate and complex features of enzymatic reaction networks (ERNs) play a key role in the emergence and sustenance of life. Constructing such networks in vitro enables stepwise build up in complexity and introduces the opportunity to control enzymatic activity using physicochemical stimuli. Rational design and modulation of network motifs enable the engineering of artificial systems with emergent functionalities. Such functional systems are useful for a variety of reasons such as creating new-to-nature dynamic materials, producing value-added chemicals, constructing metabolic modules for synthetic cells, and even enabling molecular computation. In this review, we offer insights into the chemical characteristics of ERNs while also delving into their potential applications and associated challenges.

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.

Mean-field models for the chemical fueling of transient soft matter states

The chemical fueling of transient states (CFTS) is a powerful process to control the nonequilibrium structuring and the homeostatic function of adaptive soft matter systems. Here, we introduce a simple mean-field model of CFTS based on the activation of metastable equilibrium states in a tilted 'Landau' bistable energy landscape along a coarse-grained reaction coordinate (or 'order parameter') triggered by a nonmonotonic two-step chemical fueling reaction. Evaluation of the model in the quasi-static (QS) limit-valid for fast system relaxation-allows us to extract useful analytical laws for the critical activation concentration and duration of the transient states in dependence of physical parameters, such as rate constants, fuel concentrations, and the system's distance to its equilibrium transition point. We apply our model in the QS limit explicitly to recent experiments of CFTS of collapsing responsive microgels and find a very good performance with only a few global and physically interpretable fitting parameters, which can be employed for programmable material design. Moreover, our model framework also allows a thermodynamic analysis of the energy and performed work in the system. Finally, we go beyond the QS limit, where the system's response is slow and retarded versus the chemical reaction, using an overdamped Smoluchowski approach. The latter demonstrates how internal system time scales can be used to tune the time-dependent behavior and programmed delay of the transient states in full nonequilibrium.

Synergistic chemomechanical dynamics of feedback-controlled microreactors

The experimental control of synergistic chemomechanical dynamics of catalytically active microgels (microreactors) is a key prerequisite for the design of adaptive and biomimetic materials. Here, we report a minimalistic model of feedback-controlled microreactors based on the coupling between the hysteretic polymer volume phase transition and a volume-controlled permeability for the internal chemical conversion. We categorize regimes of mono- and bistability, excitability, damped oscillations, as well as sustained oscillatory states with tunable amplitude, as indicated by experiments and representable by the FitzHugh-Nagumo dynamics for neurons. We summarize the features of such a "colloidal neuron" in bifurcation diagrams with respect to microgel design parameters, such as permeability and relaxation times, as a guide for experimental synthesis.

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.