Absolute diffusion measurements of active enzyme solutions by NMR

Activity-induced diffusion recovery in crowded colloidal suspensions

We show that the forces generated by active enzyme molecules are strong enough to influence the dynamics of their surroundings under artificial crowded environments. We measured the behavior of polymer microparticles in a quasi-two-dimensional system under aqueous environment, at various area fraction values of particles. In the presence of enzymatic activity, not only was the diffusion of the suspended particles enhanced at shorter time-scales, but the system also showed a transition from subdiffusive to diffusive dynamics at longer time-scale limits. Similar observations were also recorded with enzyme-functionalized microparticles. Brownian dynamics simulations have been performed to support the experimental observations.

Enzymatic micro/nanomotors in biomedicine: from single motors to swarms

Micro/nanomotors (MNMs) have evolved from single self-propelled entities to versatile systems capable of performing one or multiple biomedical tasks. When single MNMs self-assemble into coordinated swarms, either under external control or triggered by chemical reactions, they offer advantages that individual MNMs cannot achieve. These benefits include intelligent multitasking and adaptability to changes in the surrounding environment. Here, we provide our perspective on the evolution of MNMs, beginning with the development of enzymatic MNMs since the first theoretical model was proposed in 2005. These enzymatic MNMs hold immense promise in biomedicine due to their advantages in biocompatibility and fuel availability. Subsequently, we introduce the design and application of single motors in biomedicine, followed by the control of MNM swarms and their biomedical applications. In the end, we propose viable solutions for advancing the development of MNM swarms and anticipate valuable insights into the creation of more intelligent and controllable MNM swarms for biomedical applications.

Diffusion coefficient and power spectrum of active particles with a microscopically reversible mechanism of self-propelling

Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused by a limited understanding of specifics of self-propulsion mechanisms at the nanoscale. Here, we study a generic model of a self-propelled nanoparticle that does not rely on a particular mechanism. Instead, its main assumption is the fundamental symmetry of microscopic dynamics of chemical reactions: the principle of microscopic reversibility. Significant consequences of this assumption arise if we subject the particle to an action of an external time-periodic force. The particle diffusion coefficient is then enhanced compared to the unbiased dynamics. The enhancement can be controlled by the force amplitude and frequency. We also derive the power spectrum of particle trajectories. Among new effects stemming from the microscopic reversibility are the enhancement of the spectrum at all frequencies and sigmoid-shaped transitions and a peak at characteristic frequencies of rotational diffusion and external forcing. The microscopic reversibility is a generic property of a broad class of chemical reactions, therefore we expect that the presented results will motivate new experimental studies aimed at testing of our predictions. This could provide new insights into dynamics of catalytic macromolecules.

Perspective: a stirring role for metabolism in cells

Based on recent findings indicating that metabolism might be governed by a limit on the rate at which cells can dissipate Gibbs energy, in this Perspective, we propose a new mechanism of how metabolic activity could globally regulate biomolecular processes in a cell. Specifically, we postulate that Gibbs energy released in metabolic reactions is used to perform work, allowing enzymes to self‐propel or to break free from supramolecular structures. This catalysis‐induced enzyme movement will result in increased intracellular motion, which in turn can compromise biomolecular functions. Once the increased intracellular motion has a detrimental effect on regulatory mechanisms, this will establish a feedback mechanism on metabolic activity, and result in the observed thermodynamic limit. While this proposed explanation for the identified upper rate limit on cellular Gibbs energy dissipation rate awaits experimental validation, it offers an intriguing perspective of how metabolic activity can globally affect biomolecular functions and will hopefully spark new research.

Displacement Statistics of Unhindered Single Molecules Show no Enhanced Diffusion in Enzymatic Reactions

Recent studies have sparked debate over whether catalytic reactions enhance the diffusion coefficients D of enzymes. Through high statistics of the transient (600 μs) displacements of unhindered single molecules freely diffusing in common buffers, we here quantify D for four enzymes under catalytic turnovers. We thus formulate how ∼ ±1% precisions may be achieved for D, and show no changes in diffusivity for catalase, urease, aldolase, and alkaline phosphatase under the application of wide concentration ranges of substrates. Our single-molecule approach thus overcomes potential limitations and artifacts underscored by recent studies to show no enhanced diffusion in enzymatic reactions.

Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion

The reported changes in self-diffusion of small molecules during reactions have been attributed to "boosted mobility". We demonstrate the critical role of changing concentrations of paramagnetic ions on nuclear magnetic resonance (NMR) signal intensities, which led to erroneous measurements of diffusion coefficients. We present simple methods to overcome this problem. The use of shuffled gradient amplitudes allows accurate diffusion NMR measurements, even with time-dependent relaxation rates caused by changing concentrations of paramagnetic ions. The addition of a paramagnetic relaxation agent allows accurate determination of both diffusion coefficients and reaction kinetics during a single experiment. We analyze a copper-catalyzed azide-alkyne cycloaddition "click" reaction, for which boosted mobility has been claimed. With our methods, we accurately measure the diffusive behavior of the solvent, starting materials, and product and find no global increase in diffusion coefficients during the reaction. We overcome NMR signal overlap using an alternative reducing agent to improve the accuracy of the diffusion measurements. The alkyne reactant diffuses slower as the reaction proceeds due to binding to the copper catalyst during the catalytic cycle. The formation of this intermediate was confirmed by complementary NMR techniques and density functional theory calculations. Our work calls into question recent claims that molecules actively propel or swim during reactions and establishes that time-resolved diffusion NMR measurements can provide valuable insight into reaction mechanisms.

A simple theory for molecular chemotaxis driven by specific binding interactions

Recent experiments have suggested that enzymes and other small molecules chemotax toward their substrates. However, the physical forces driving this chemotaxis are currently debated. In this work, we consider a simple thermodynamic theory for molecular chemotaxis that is based on the McMillan-Mayer theory of dilute solutions and Schellman's theory for macromolecular binding. Even in the absence of direct interactions, the chemical binding equilibrium introduces a coupling term into the relevant free energy, which then reduces the chemical potential of both enzymes and their substrates. Assuming a local thermodynamic equilibrium, this binding contribution to the chemical potential generates an effective thermodynamic force that promotes chemotaxis by driving each solute toward its binding partner. Our numerical simulations demonstrate that, although small, this thermodynamic force is qualitatively consistent with several experimental studies. Thus, our study may provide additional insight into the role of the thermodynamic binding free energy for molecular chemotaxis.

Oxygen Generation Using Catalytic Nano/Micromotors

Gaseous oxygen plays a vital role in driving the metabolism of living organisms and has multiple agricultural, medical, and technological applications. Different methods have been discovered to produce oxygen, including plants, oxygen concentrators and catalytic reactions. However, many such approaches are relatively expensive, involve challenges, complexities in post-production processes or generate undesired reaction products. Catalytic oxygen generation using hydrogen peroxide is one of the simplest and cleanest methods to produce oxygen in the required quantities. Chemically powered micro/nanomotors, capable of self-propulsion in liquid media, offer convenient and economic platforms for on-the-fly generation of gaseous oxygen on demand. Micromotors have opened up opportunities for controlled oxygen generation and transport under complex conditions, critical medical diagnostics and therapy. Mobile oxygen micro-carriers help better understand the energy transduction efficiencies of micro/nanoscopic active matter by careful selection of catalytic materials, fuel compositions and concentrations, catalyst surface curvatures and catalytic particle size, which opens avenues for controllable oxygen release on the level of a single catalytic microreactor. This review discusses various micro/nanomotor systems capable of functioning as mobile oxygen generators while highlighting their features, efficiencies and application potentials in different fields.

Enzyme aggregation and fragmentation induced by catalysis relevant species

It is usually assumed that enzymes retain their native structure during catalysis. However, the aggregation and fragmentation of proteins can be difficult to detect and sometimes conclusions are drawn based on the assumption that the protein is in its native form. We have examined three model enzymes, alkaline phosphatase (AkP), hexokinase (HK) and glucose oxidase (GOx). We find that these enzymes aggregate or fragment after addition of chemical species directly related to their catalysis. We used several independent techniques to study this behavior. Specifically, we found that glucose oxidase and hexokinase fragment in the presence of D-glucose but not L-glucose, while hexokinase aggregates in the presence of Mg²⁺ ion and either ATP or ADP at low pH. Alkaline phosphatase aggregates in the presence of Zn²⁺ ion and inorganic phosphate. The aggregation of hexokinase and alkaline phosphatase does not appear to attenuate their catalytic activity. Our study indicates that specific multimeric structures of native enzymes may not be retained during catalysis and suggests pathways for different enzymes to associate or separate over the course of substrate turnover.

Chemically-powered swimming and diffusion in the microscopic world

The past decade has seen intriguing reports and heated debates concerning the chemically-driven enhanced motion of objects ranging from small molecules to millimetre-size synthetic robots. These objects, in solutions in which chemical reactions were occurring, were observed to diffuse (spread non-directionally) or swim (move directionally) at rates exceeding those expected from Brownian motion alone. The debates have focused on whether observed enhancement is an experimental artefact or a real phenomenon. If the latter were true, then we would also need to explain how the chemical energy is converted into mechanical work. In this Perspective, we summarize and discuss recent observations and theories of active diffusion and swimming. Notably, the chemomechanical coupling and magnitude of diffusion enhancement are strongly size-dependent and should vanish as the size of the swimmers approaches the molecular scale. We evaluate the reliability of common techniques to measure diffusion coefficients and finish by considering the potential applications and chemical to mechanical energy conversion efficiencies of typical nanoswimmers and microswimmers.

Comment on “Boosted molecular mobility during common chemical reactions”

The apparent “boosted mobility” observed by Wang et al. (Reports, 31 July 2020, p. 537) is the result of a known artifact. When signal intensities are changing during a nuclear magnetic resonance (NMR) diffusion measurement for reasons other than diffusion, the use of monotonically increasing gradient amplitudes produces erroneous diffusion coefficients. We show that no boosted molecular mobility is observed when shuffled gradient amplitudes are applied.

Fundamentals and applications of enzyme powered micro/nano-motors

Micro/nanomotors (MNMs) are miniaturized machines that can convert many kinds of energy into mechanical motion. Over the past decades, a variety of driving mechanisms have been developed, which have greatly extended the application scenarios of MNMs. Enzymes exist in natural organisms which can convert chemical energy into mechanical force. It is an innovative attempt to utilize enzymes as biocatalyst providing driving force for MNMs. The fuels for enzymatic reactions are biofriendly as compared to traditional counterparts, which makes enzyme-powered micro/nanomotors (EMNMs) of great value in biomedical field for their nature of biocompatibility. Until now, EMNMs with various shapes can be propelled by catalase, urease and many others. Also, they can be endowed with multiple functionalities to accomplish on-demand tasks. Herein, combined with the development process of EMNMs, we are committed to present a comprehensive understanding of EMNMs, including their types, propelling principles, and potential applications. In this review, we will introduce single enzyme that can be used as motor, enzyme powered molecule motors and other micro/nano-architectures. The fundamental mechanism of energy conversion process of EMNMs and crucial factors that affect their movement behavior will be discussed. The current progress of proof-of-concept applications of EMNMs will also be elaborated in detail. At last, we will summarize and prospect the opportunities and challenges that EMNMs will face in their future development.

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Clear classification and description of different enzyme-powered micro/nanomotors (EMNMs).

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Discussion of the fundamental mechanism of energy conversion process of EMNMs and their movement influence factors.

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Introduction of the current progress of proof-of-concept applications of EMNMs.

Master curve of boosted diffusion for 10 catalytic enzymes

The literature is inconsistent regarding evidence for boosted molecular mobility during enzyme catalysis, a phenomenon that challenges the common tenet that enzyme mobility is governed solely by Brownian motion. This paper surveys 10 different catalytic enzymes and shows that magnitude of enhanced diffusion scales with energy release rate, the Gibbs free energy of reaction multiplied by the Michaelis–Menten reaction rate. A practical implication is that boosted effective diffusivity can be used to determine the energetics associated with enzyme action, since effective enzyme diffusivity is simply proportional to the change in free energy associated with the biochemical conversion. This master curve to predict the magnitude of boosted molecular mobility may be useful for estimating the effect in as-yet untested enzymes.

Molecular agitation more rapid than thermal Brownian motion is reported for cellular environments, motor proteins, synthetic molecular motors, enzymes, and common chemical reactions, yet that chemical activity coupled to molecular motion contrasts with generations of accumulated knowledge about diffusion at equilibrium. To test the limits of this idea, a critical testbed is the mobility of catalytically active enzymes. Sentiment is divided about the reality of enhanced enzyme diffusion, with evidence for and against. Here a master curve shows that the enzyme diffusion coefficient increases in proportion to the energy release rate—the product of Michaelis-Menten reaction rate and Gibbs free energy change (ΔG)—with a highly satisfactory correlation coefficient of 0.97. For 10 catalytic enzymes (urease, acetylcholinesterase, seven enzymes from the glucose cascade cycle, and one other), our measurements span from a roughly 40% enhanced diffusion coefficient at a high turnover rate and negative ΔG to no enhancement at a slow turnover rate and positive ΔG. Moreover, two independent measures of mobility show consistency, provided that one avoids undesirable fluorescence photophysics. The master curve presented here quantifies the limits of both ideas, that enzymes display enhanced diffusion and that they do not within instrumental resolution, and has possible implications for understanding enzyme mobility in cellular environments. The striking linear dependence of ΔG for the exergonic enzymes (ΔG <0), together with the vanishing effect for endergonic enzyme (ΔG >0), are consistent with a physical picture in which the mechanism boosting the diffusion is an active one, utilizing the available work from the chemical reaction.

Rapid-prototyping a Brownian particle in an active bath

Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) by kicks, and quantifying heat dissipation to maintain the non-equilibrium steady state in an active bath. The model reproduces experimental results of tracer mobility in an active bath of swimming algal cells. It can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding, owing to the generic framework of the protocol.

Single-molecule diffusometry reveals no catalysis-induced diffusion enhancement of alkaline phosphatase as proposed by FCS experiments

Recent experiments have suggested that the energy released by a chemical reaction can propel its enzyme catalyst (for example, alkaline phosphatase). However, this topic remains controversial, partially due to the indirect and ensemble nature of existing measurements. Here, we used recently developed single-molecule approaches to monitor directly the motions of individual proteins in aqueous solution and find that single alkaline phosphatase enzymes do not diffuse faster under catalysis. Instead, we demonstrate that interactions between the fluorescent dye and the enzyme’s substrate can produce the signature of apparent diffusion enhancement in fluorescence correlation spectroscopy, the standard ensemble assay currently used to study enzyme diffusion and indicate that single-molecule approaches provide a more robust means to investigate diffusion at the nanoscale.

Theoretical and experimental observations that catalysis enhances the diffusion of enzymes have generated exciting implications about nanoscale energy flow, molecular chemotaxis, and self-powered nanomachines. However, contradictory claims on the origin, magnitude, and consequence of this phenomenon continue to arise. To date, experimental observations of catalysis-enhanced enzyme diffusion have relied almost exclusively on fluorescence correlation spectroscopy (FCS), a technique that provides only indirect, ensemble-averaged measurements of diffusion behavior. Here, using an anti-Brownian electrokinetic (ABEL) trap and in-solution single-particle tracking, we show that catalysis does not increase the diffusion of alkaline phosphatase (ALP) at the single-molecule level, in sharp contrast to the ∼20% enhancement seen in parallel FCS experiments using p-nitrophenyl phosphate (pNPP) as substrate. Combining comprehensive FCS controls, ABEL trap, surface-based single-molecule fluorescence, and Monte Carlo simulations, we establish that pNPP-induced dye blinking at the ∼10-ms timescale is responsible for the apparent diffusion enhancement seen in FCS. Our observations urge a crucial revisit of various experimental findings and theoretical models––including those of our own––in the field, and indicate that in-solution single-particle tracking and ABEL trap are more reliable means to investigate diffusion phenomena at the nanoscale.

Revealing the initial steps in homogeneous photocatalysis by time-resolved spectroscopy

Photocatalysis attracts currently intense research since it can provide efficient routes for generating solar fuels and allows to apply sunlight for an environmentally friendly synthesis of valuable chemical compounds. Accordingly, in future photocatalysis may contribute significantly to a sustainable economy. However, up to now photocatalysis has made it only into some niche applications. The reasons are manifold including too low yields, insufficient stability, and scarce availability of the precious metals and rare earths used in most cases. The design of better systems is the goal of many research activities. They call for a detailed knowledge of the individual steps and the microscopic mechanisms. Time-resolved spectroscopy is a powerful tool to improve our understanding of the individual steps of a photocatalytic process and of the efficiencies and losses associated with them. This allows to address specific weaknesses of the components of a photocatalytic system and to pursue a rational design of the corresponding compounds. In this review an overview is given about what insights can be gained by time-resolved spectroscopy referring mostly to our own results while it has to be stressed that many other groups are also highly successfully working in this area. We restrict ourselves to homogeneous systems which are often easier to analyze and focus on the primary steps occurring after optical excitation. This includes intramolecular relaxation and intersystem crossing in the photosensitizer as well as the first electron transfer step resulting from the interaction of the sensitizer with other components of the system. Ultrafast pump-probe spectroscopy turns out to be particularly helpful in analyzing new photosensitizers based on abundant metals, i.e. copper and iron. These sensitizers can suffer from short lifetimes of the metal-to-ligand charge transfer states which are typically involved in the intermolecular charge transfer processes. The latter are investigated on the pico- to microsecond timescale by quenching experiments making use of a streak camera and by pump-probe spectroscopy applying a YAG-laser system for excitation. The experiments with the streak camera allow to discriminate between oxidative and reductive pathways and to determine the corresponding bimolecular quenching rates which are compared to their diffusion limit to obtain a measure for the quenching efficiency. By applying transient absorption spectroscopy, it is furthermore possible to observe appearing charge transfer products and to determine their concentrations. In this way the efficiency of the electron transfer itself can be deduced and the relevance of lossy quenching events can be estimated.

Shear viscosity of two-state enzyme solutions

We discuss the shear viscosity of a Newtonian solution of catalytic enzymes and substrate molecules. The enzyme is modeled as a two-state dimer consisting of two spherical domains connected with an elastic spring. The enzymatic conformational dynamics is induced by the substrate binding and such a process is represented by an additional elastic spring. Employing the Boltzmann distribution weighted by the waiting times of enzymatic species in each catalytic cycle, we obtain the shear viscosity of dilute enzyme solutions as a function of substrate concentration and its physical properties. The substrate affinity distinguishes between fast and slow enzymes, and the corresponding viscosity expressions are obtained. Furthermore, we connect the obtained viscosity with the diffusion coefficient of a tracer particle in enzyme solutions.

Enhanced Diffusion and Chemotaxis of Enzymes

Many enzymes appear to diffuse faster in the presence of substrate and to drift either up or down a concentration gradient of their substrate. Observations of these phenomena, termed enhanced enzyme diffusion (EED) and enzyme chemotaxis, respectively, lead to a novel view of enzymes as active matter. Enzyme chemotaxis and EED may be important in biology and could have practical applications in biotechnology and nanotechnology. They are also of considerable biophysical interest; indeed, their physical mechanisms are still quite uncertain. This review provides an analytic summary of experimental studies of these phenomena and of the mechanisms that have been proposed to explain them and offers a perspective on future directions for the field.

Self-Propulsion Strategies for Artificial Cell-Like Compartments

Reconstitution of life-like properties in artificial cells is a current research frontier in synthetic biology. Mimicking metabolism, growth, and sensing are active areas of investigation; however, achieving motility and directional taxis are also challenging in the context of artificial cells. To tackle this problem, recent progress has been made that leverages the tools of active matter physics in synthetic biology. This review surveys the most significant achievements in designing motile cell-like compartments. In this context, strategies for self-propulsion are summarized, including, compartmentalization of catalytically active particles, phoretic propulsion of vesicles and emulsion droplet motion driven by Marangoni flows. This work showcases how the realization of motile protocells may impact biomedical engineering while also aiming at answering fundamental questions in locomotion of prebiotic cells.

Enhanced Diffusion of Catalytically Active Enzymes

The past decade has seen an increasing number of investigations into enhanced diffusion of catalytically active enzymes. These studies suggested that enzymes are actively propelled as they catalyze reactions or bind with ligands (e.g., substrates or inhibitors). In this Outlook, we chronologically summarize and discuss the experimental observations and theoretical interpretations and emphasize the potential contradictions in these efforts. We point out that the existing multimeric forms of enzymes or isozymes may cause artifacts in measurements and that the conformational changes upon substrate binding are usually not sufficient to give rise to a diffusion enhancement greater than 30%. Therefore, more rigorous experiments and a more comprehensive theory are urgently needed to quantitatively validate and describe the enhanced enzyme diffusion.

A Thermodynamic Limit on the Role of Self-Propulsion in Enhanced Enzyme Diffusion

A number of enzymes reportedly exhibit enhanced diffusion in the presence of their substrates, with a Michaelis-Menten-like concentration dependence. Although no definite explanation of this phenomenon has emerged, a physical picture of enzyme self-propulsion using energy from the catalyzed reaction has been widely considered. Here, we present a kinematic and thermodynamic analysis of enzyme self-propulsion that is independent of any specific propulsion mechanism. Using this theory, along with biophysical data compiled for all enzymes so far shown to undergo enhanced diffusion, we show that the propulsion speed required to generate experimental levels of enhanced diffusion exceeds the speeds of well-known active biomolecules, such as myosin, by several orders of magnitude. Furthermore, the minimal power dissipation required to account for enzyme enhanced diffusion by self-propulsion markedly exceeds the chemical power available from enzyme-catalyzed reactions. Alternative explanations for the observation of enhanced enzyme diffusion therefore merit stronger consideration.

Brownian dynamics assessment of enhanced diffusion exhibited by ‘fluctuating-dumbbell enzymes’

Numerical simulations show moderate diffusion enhancements for fluctuating-dumbbell enzyme models.