Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor

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.

Periodic Nucleation of Calcium Phosphate in a Stirred Biocatalytic Reaction

Highly ordered superstructures composed of inorganic nanoparticles appear in natural and synthetic systems, however the mechanisms of non-equilibrium self-organization that may be involved are still poorly understood. Herein, we performed a kinetic investigation of the precipitation of calcium phosphate using a process widely found in microorganisms: the hydrolysis of urea by enzyme urease. With high initial ratio of calcium ion to phosphate, periodic precipitation was obtained accompanied by pH oscillations in a well-stirred, closed reactor. We propose that an internal pH-regulated change in the concentration of phosphate ion is the driving force for periodicity. A simple model involving the biocatalytic reaction network coupled with burst nucleation of nanoparticles above a critical supersaturation reproduced key features of the experiments. These findings may provide insight to the self-organization of nanoparticles in biomineralization and improve design strategies of biomaterials for medical applications.

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.

Towards feedback-controlled nanomedicines for smart, adaptive delivery

IMPACT STATEMENT

The timing and rate of release of pharmaceuticals from advanced drug delivery systems is an important property that has received considerable attention in the scientific literature. Broadly, these mostly fall into two classes: controlled release with a prolonged release rate or triggered release where the drug is rapidly released in response to an environmental stimulus. This review aims to highlight the potential for developing adaptive release systems that more subtlety modulate the drug release profile through continuous communication with its environment facilitated through feedback control. By reviewing the key elements of this approach in one place (fundamental principles of nanomedicine, enzymatic nanoreactors for medical therapies and feedback-controlled chemical systems) and providing additional motivating case studies in the context of chronobiology, we hope to inspire innovative development of novel "chrononanomedicines."

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.

Drug treatment efficiency depends on the initial state of activation in nonlinear pathways

An accurate prediction of the outcome of a given drug treatment requires quantitative values for all parameters and concentrations involved as well as a detailed characterization of the network of interactions where the target molecule is embedded. Here, we present a high-throughput in silico screening of all potential networks of three interacting nodes to study the effect of the initial conditions of the network in the efficiency of drug inhibition. Our study shows that most network topologies can induce multiple dose-response curves, where the treatment has an enhanced, reduced or even no effect depending on the initial conditions. The type of dual response observed depends on how the potential bistable regimes interplay with the inhibition of one of the nodes inside a nonlinear pathway architecture. We propose that this dependence of the strength of the drug on the initial state of activation of the pathway may be affecting the outcome and the reproducibility of drug studies and clinical trials.

Modeling and simulation of enzymatic gluconic acid production using immobilized enzyme and CSTR-PFTR circulation reaction system

OBJECTIVES

Production of gluconic acid by using immobilized enzyme and continuous stirred tank reactor-plug flow tubular reactor (CSTR-PFTR) circulation reaction system.

RESULTS

A production system is constructed for gluconic acid production, which consists of a continuous stirred tank reactor (CSTR) for pH control and liquid storage and a plug flow tubular reactor (PFTR) filled with immobilized glucose oxidase (GOD) for gluconic acid production. Mathematical model is developed for this production system and simulation is made for the enzymatic reaction process. The pH inhibition effect on GOD is modeled by using a bell-type curve.

CONCLUSIONS

Gluconic acid can be efficiently produced by using the reaction system and the mathematical model developed for this system can simulate and predict the process well.

Materials learning from life: concepts for active, adaptive and autonomous molecular systems

A broad overview of functional aspects in biological and synthetic out-of-equilibrium systems.

Nested arithmetic progressions of oscillatory phases in Olsen's enzyme reaction model

We report some regular organizations of stability phases discovered among self-sustained oscillations of a biochemical oscillator. The signature of such organizations is a nested arithmetic progression in the number of spikes of consecutive windows of periodic oscillations. In one of them, there is a main progression of windows whose consecutive number of spikes differs by one unit. Such windows are separated by a secondary progression of smaller windows whose number of spikes differs by two units. Another more complex progression involves a fan-like nested alternation of stability phases whose number of spikes seems to grow indefinitely and to accumulate methodically in cycles. Arithmetic progressions exist abundantly in several control parameter planes and can be observed by tuning just one among several possible rate constants governing the enzyme reaction.

Effects of tyramine and 4-aminophenol on the oscillating peroxidase-oxidase reaction

The peroxidase-oxidase oscillator, a model of biological oscillations, is usually studied in conjunction with the effector molecule, 2,4-dichlorophenol. In this account, we present evidence of the effects of a naturally occurring phenol, tyramine, on the reaction, and also those of the structurally similar 4-aminophenol. Whereas 2,4-dichlorophenol gives rise to sustained oscillations at 40 μM, it was discovered that tyramine promotes damped oscillations at a concentration of 120 μM. Oxidation of NADH was completely inhibited by 4-aminophenol and ascorbate. In separate experiments, the peroxidase-catalyzed ring coupling of tyramine and 4-aminophenol was observed, which in the case of tyramine, may provide an explanation for the damping of oscillations.

Network nonlinearities in drug treatment

Despite major achievements in the understanding of human disease, there is a general perception that the drug development industry has failed to meet the expectations that recent advances in biotechnology should drive. One of the potential sources of failure of many next generation drugs is that their targets are embedded in highly nonlinear signaling pathways and gene networks with multiple negative and positive feedback loops of regulation. There is increasing evidence that this complex network shapes the response to external perturbations in the form of drug treatment, originating bistability, hypersensitivity, robustness, complex dose-response curves or schedule dependent activity. This review focuses on the effect of nonlinearities on signaling and gene networks involved in human disease, using tools from Nonlinear Dynamics to discuss the implications and to overcome the effects of the nonlinearities on regulatory networks.

A nanoliter-scale open chemical reactor

An open chemical reactor is a container that exchanges matter with the exterior. Well-mixed open chemical reactors, called continuous stirred tank reactors (CSTR), have been instrumental for investigating the dynamics of out-of-equilibrium chemical processes, such as oscillations, bistability, and chaos. Here, we introduce a microfluidic CSTR, called μCSTR, that reduces reagent consumption by six orders of magnitude. It consists of an annular reactor with four inlets and one outlet fabricated in PDMS using multi-layer soft lithography. A monolithic peristaltic pump feeds fresh reagents into the reactor through the inlets. After each injection the content of the reactor is continuously mixed with a second peristaltic pump. The efficiency of the μCSTR is experimentally characterized using a bromate, sulfite, ferrocyanide pH oscillator. Simulations accounting for the digital injection process are in agreement with experimental results. The low consumption of the μCSTR will be advantageous for investigating out-of-equilibrium dynamics of chemical processes involving biomolecules. These studies have been scarce so far because a miniaturized version of a CSTR was not available.

pH wave-front propagation in the urea-urease reaction

The urease-catalyzed hydrolysis of urea displays feedback that results in a switch from acid (pH ~3) to base (pH ~9) after a controllable period of time (from 10 to >5000 s). Here we show that the spatially distributed reaction can support pH wave fronts propagating with a speed of the order of 0.1-1 mm min(-1). The experimental results were reproduced qualitatively in reaction-diffusion simulations including a Michaelis-Menten expression for the urease reaction with a bell-shaped rate-pH dependence. However, this model fails to predict that at lower enzyme concentrations, the unstirred reaction does not always support fronts when the well-stirred reaction still rapidly switches to high pH.

Periodic orbits in glycolytic oscillators: from elliptic orbits to relaxation oscillations

We consider the Sel'kov model of glycolytic oscillator for a quantitative study of the limit cycle oscillations in the system. We identify a region of parameter space where perturbation theory holds and use both Linstedt Poincaré technique and harmonic balance to obtain the shape and frequency of the limit cycle. The agreement with the numerically obtained result is excellent. We also find a different extreme, where the limit cycle is of the relaxation oscillator variety, has a large time period and it is seen that, as a particular parameter in the model is varied, the time period increases indefinitely. We characterize this divergence numerically. A calculational method is devised to capture the divergence approximately.

Nonlinear Dynamics in the Uncatalyzed Bromate–Pyrocatechol Reaction

Spontaneous chemical oscillations are uncovered in the uncatalyzed bromate–pyrocatechol reaction conducted in a stirred batch reactor. Phase diagrams show that the oscillatory behavior is more sensitive to the ratio of [bromate]/[pyrocatechol] than their actual concentrations. The long induction time observed in the system is insensitive to the initial presence of brominated pyrocatechol species. Quenching experiments illustrate that the studied chemical oscillator is both bromide and radical controlled. In addition, this new uncatalyzed bromate oscillator exhibits both light-induced and light-quenched oscillatory behaviors. Preliminary mechanistic characterization with UV/vis absorption method and mass spectrometry suggests the formation of bromo-1,2-benzoquinone through the reaction between pyrocatechol and bromine.

Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase

Waves and patterns in living systems are often driven by biochemical reactions with enzymes as catalysts and regulators. We present a reaction-diffusion system catalyzed by the enzyme glucose oxidase that exhibits traveling wave patterns in a spatially extended medium. Fronts and pulses propagate as a result of the coupling between the enzyme-catalyzed autocatalytic production and diffusion of hydrogen ions. A mathematical model qualitatively explains the experimental observations.