Substrate catalysis enhances single-enzyme diffusion

Active dynamics of charged macromolecules

We study the role of active coupling on the transport properties of homogeneously charged macromolecules in an infinitely dilute solution. An enzyme becomes actively bound to a segment of the macromolecule, exerting an electrostatic force on it. Eventually, thermal fluctuations cause it to become unbound, introducing active coupling into the system. We study the mean-squared displacement (MSD) and find a new scaling regime compared to the thermal counterpart in the presence of hydrodynamic and segment-segment electrostatic interactions. Furthermore, the study of segment-segment equal-time correlation reveals the swelling of the macromolecule. Further, we derive the concentration equation of the macromolecule with active binding and study how the cooperative diffusivity of the macromolecules get modified by its environment, including the macromolecules itself. It turns out that these active fluctuations enhance the effective diffusivity of the macromolecules. The derived closed-form expression for diffusion constant is pertinent to the accurate interpretation of light scattering data in multi-component systems with binding-unbinding equilibria.

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.

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.

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.

Enzyme Catalysis Causes Fluid Flow, Motility, and Directional Transport on Supported Lipid Bilayers

The dynamic interplay between the composition of lipid membranes and the behavior of membrane-bound enzymes is critical to the understanding of cellular function and viability, and the design of membrane-based biosensing platforms. While there is a significant body of knowledge about how lipid composition and dynamics affect membrane-bound enzymes, little is known about how enzyme catalysis influences the motility and lateral transport on lipid membranes. Using enzyme-attached lipids in supported bilayers (SLBs), we provide direct evidence of catalysis-induced fluid flow that underlies the observed motility on SLBs. Additionally, by using active enzyme patches, we demonstrate the directional transport of tracer particles on SLBs. As expected, enhancing the membrane viscosity by incorporating cholesterol into the bilayer suppresses the overall movement. These are the first steps in understanding diffusion and transport on lipid membranes due to active, out-of-equilibrium processes that are the hallmark of living systems. In general, our study demonstrates how active enzymes can be used to control diffusion and transport in confined 2-D environments.

Traveling wave solution and the stability of critical points of an enzyme-inhibitor system under diffusion effects: with special reference to dimer molecule

Enzymes are absolutely essential biological catalysts in human body that catalyze all cellular processes in physiological network. However, there are certain low molecular weight chemical compounds known as inhibitors, that reduce or completely inhibit the enzyme catalytic activity. Mathematical modeling plays a key role in the control and stability of metabolic enzyme inhibition. Enzyme stability is an important issue for protein engineers, because of its great importance and impact on optimal utility of material in biological tissues. In this outlook, we have first determined the existence of traveling wave solution for the enzyme-inhibitor system and then emphasized the stability of critical points that arise in the reactions. The study of traveling wave solution of an enzyme-inhibitor system with reaction diffusion equations involve quite complex mathematical analysis. The results obtained in this model indicate that the traveling wave solution may give a well explained method for improving enzyme kinetic stability. The present study will be helpful in understanding the stability of critical points of an enzyme-inhibitor system to give an idea about the inhibition of less stable enzymes. Moreover, the role of diffusion on the enzyme activity has been exhaustively discussed using mathematical tools related to eigen values and eigen function analysis.

Motility of Synthetic Cells from Engineered Lipids

Synthetic cells are artificial systems that resemble natural cells. Significant efforts have been made over the years to construct synthetic protocells that can mimic biological mechanisms and perform various complex processes. These include compartmentalization, metabolism, energy supply, communication, and gene reproduction. Cell motility is also of great importance, as nature uses elegant mechanisms for intracellular trafficking, immune response, and embryogenesis. In this review, we discuss the motility of synthetic cells made from lipid vesicles and relevant molecular mechanisms. Synthetic cell motion may be classified into surface-based or solution-based depending on whether it involves interactions with surfaces or movement in fluids. Collective migration behaviors have also been demonstrated. The swarm motion requires additional mechanisms for intercellular signaling and directional motility that enable communication and coordination among the synthetic vesicles. In addition, intracellular trafficking for molecular transport has been reconstituted in minimal cells with the help of DNA nanotechnology. These efforts demonstrate synthetic cells that can move, detect, respond, and interact. We envision that new developments in protocell motility will enhance our understanding of biological processes and be instrumental in bioengineering and therapeutic applications.

Self-Propelled Proteomotors with Active Cell-Free mtDNA Clearance for Enhanced Therapy of Sepsis-Associated Acute Lung Injury

Acute lung injury (ALI) is a frequent and serious complication of sepsis with limited therapeutic options. Gaining insights into the inflammatory dysregulation that causes sepsis-associated ALI can help develop new therapeutic strategies. Herein, the crucial role of cell-free mitochondrial DNA (cf-mtDNA) in the regulation of alveolar macrophage activation during sepsis-associated ALI is identified. Most importantly, a biocompatible hybrid protein nanomotor (NM) composed of recombinant deoxyribonuclease I (DNase-I) and human serum albumin (HSA) via glutaraldehyde-mediated crosslinking is prepared to obtain an inhalable nanotherapeutic platform targeting pulmonary cf-mtDNA clearance. The synthesized DNase-I/HSA NMs are endowed with self-propulsive capability and demonstrate superior performances in stability, DNA hydrolysis, and biosafety. Pulmonary delivery of DNase-I/HSA NMs effectively eliminates cf-mtDNAs in the lungs, and also improves sepsis survival by attenuating pulmonary inflammation and lung injury. Therefore, pulmonary cf-mtDNA clearance strategy using DNase-I/HSA NMs is considered to be an attractive approach for sepsis-associated ALI.

Single-Molecule Tracking of Reagent Diffusion during Chemical Reactions

Recent experiments have shown that the diffusion of reagent molecules is inconsistent with what the Stokes-Einstein equation predicts during a chemical reaction. Here, we used single-molecule tracking to observe the diffusion of reactive reagent molecules during click and Diels-Alder (DA) reactions. We found that the diffusion coefficient of the reagents remained unchanged within the experimental uncertainty upon the DA reaction. Yet, diffusion of reagent molecules is faster than predicted during the click reaction when the reagent concentration and catalyst concentration exceed a threshold. A stepwise analysis suggested that the fast diffusion scenario is due to the reaction but not the involvement of the tracer with the reaction itself. The present results provide experimental evidence on the faster-than-expected reagent diffusion during a CuAAC reaction in specific conditions and propose new insights into understanding this unexpected behavior.

A Universal Chemotactic Targeted Delivery Strategy for Inflammatory Diseases

Above 50% of deaths can be attributed to chronic inflammatory diseases; thus, the construction of drug delivery systems based on effective interaction of inflammatory factors with chemotactic nanoparticles is meaningful. Herein, a zwitterion-based artificial chemotactic nanomotor is proposed for universal precise targeting strategy in vivo, where the high level of reactive oxygen species (ROS) and inducible nitric oxide synthase (iNOS) in inflammatory sites are used as a chemoattractant. Multidimensional static models, dynamic models, and in vivo models are established to evaluate chemotactic performance. The results show that the upregulated ROS and iNOS can induce the chemotaxis of nanomotors to diseased tissues in inflammation-related disease models. Further, mesoscale hydrodynamics simulations are performed to explain the chemotactic behavior of the nanomotors. Such a chemotactic delivery strategy is expected to improve delivery efficiency and may be applicable to a variety of inflammatory diseases.

Protein Condensation, Cellular Organization, and Spatiotemporal Regulation of Cytoplasmic Properties

The cytoplasm is an aqueous, highly crowded solution of active macromolecules. Its properties influence the behavior of proteins, including their folding, motion, and interactions. In particular, proteins in the cytoplasm can interact to form phase-separated assemblies, so-called biomolecular condensates. The interplay between cytoplasmic properties and protein condensation is critical in a number of functional contexts and is the subject of this review. The authors first describe how cytoplasmic properties can affect protein behavior, in particular condensate formation, and then describe the functional implications of this interplay in three cellular contexts, which exemplify how protein self-organization can be adapted to support certain physiological phenotypes. The authors then describe the formation of RNA-protein condensates in highly polarized cells such as neurons, where condensates play a critical role in the regulation of local protein synthesis, and describe how different stressors trigger extensive reorganization of the cytoplasm, both through signaling pathways and through direct stress-induced changes in cytoplasmic properties. Finally, the authors describe changes in protein behavior and cytoplasmic properties that may occur in extremophiles, in particular organisms that have adapted to inhabit environments of extreme temperature, and discuss the implications and functional importance of these changes.

Fluid Field Modulation in Mass Transfer for Efficient Photocatalysis

Mass transfer is an essential factor determining photocatalytic performance, which can be modulated by fluid field via manipulating the kinetic characteristics of photocatalysts and photocatalytic intermediates. Past decades have witnessed the efforts and achievements made in manipulating mass transfer based on photocatalyst structure and composition design, and thus, a critical survey that scrutinizes the recent progress in this topic is urgently necessitated. This review examines the basic principles of how mass transfer behavior impacts photocatalytic activity accompanying with the discussion on theoretical simulation calculation including fluid flow speed and pattern. Meanwhile, newly emerged viable photocatalytic micro/nanomotors with self-thermophoresis, self-diffusiophoresis, and bubble-propulsion mechanisms as well as magnet-actuated photocatalytic artificial cilia for facilitating mass transfer will be covered. Furthermore, their applications in photocatalytic hydrogen evolution, carbon dioxide reduction, organic pollution degradation, bacteria disinfection and so forth are scrutinized. Finally, a brief summary and future outlook are presented, providing a viable guideline to those working in photocatalysis, mass transfer, and other related fields.

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.

Response to Comment on "Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion" and "Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question"

In their Comment (DOI: 10.1021/jacs.2c02965) on two related publications by our group (J. Am. Chem. Soc.2022, 144, 1380–1388; DOI: 10.1021/jacs.1c11754) and another (J. Am. Chem. Soc.2021, 143, 20884–20890; DOI: 10.1021/jacs.1c09455), Huang and Granick refer to the diffusion NMR measurements of molecules during a copper-catalyzed azide–alkyne cycloaddition (CuAAC) “click” reaction. Here we respond to their comments and maintain that no measurable diffusion enhancement was observed during the reaction. We expand on the physical arguments presented in our original JACS Article regarding the appropriate reference state for the diffusion coefficient and present new data showing that the use of other reference states, as suggested by Huang and Granick, will still support our conclusion that the two reactants and one product of the CuAAC reaction do not exhibit boosted mobility during the reaction.

Synthesis of Candida Antarctica Lipase B (CALB) enzyme-powered magnetite nanomotor based on PCL/Chitosan Janus nanostructure

In this work, we report the design and synthesis of internal energy-driven Janus nanomotors (JNMs), which are composed of certain reactive materials that are capable of converting chemical energy in the backbone of nanomotors into kinetic energy. For this purpose, superparamagnetic iron oxide nanoparticles (SPIONs) with the anisotropic surface were obtained via a Pickering emulsion. Modified chitosan (as hydrophilic polymer) and functionalized polycaprolactone (as hydrophobic domain) were covalently linked to the surface of bi-functional SPIONs to produce Janus nanoparticles (JNPs). Then, the CALB enzyme was loaded in the PCL hemisphere of JNPs to form the Janus nanomotor. When nanomotors are placed in the phosphate-buffered saline solution, the driving force for motion is provided by the decomposition of polyester into monomers and oligomers on one side of the JNMs. The trajectories of the nanomotors were recorded under different circumstances by a video microscope and analyzed by the mean squared displacement. The results show that the velocity of JNMs increases with an increasing percentage of the loaded enzyme. In addition, the diffusion coefficient enhances up to 87.67% in compared with nanoparticles without enzyme. Controlling the motion direction of JNMs by an external magnetic field is also possible, due to the presence of SPIONs.

Study Enhanced Enzyme Diffusion with High-Speed Single Nanoparticle Rotational and Translational Tracking

Catalytic enzymes exhibiting enhanced motion have drawn extensive attention over the past decade; nevertheless, little is known about the effect on the environment induced by enzymes. Herein, we studied the active urease system by simultaneously monitoring the diffusion of single anisotropic gold nanorods (AuNRs) with high speed dark-field imaging. We found both the translational and the rotational diffusion coefficients of AuNRs were enhanced but with inconsistent degrees, indicating the catalytic reaction had a minor effect on the physiochemical properties of the environment according to the Stokes-Einstein equation. With the increase of substrate concentration, the diffusion of AuNRs showed increased spatial but decreased temporal heterogeneity. Additionally, high speed imaging revealed AuNRs could experience intermittent ballistic motion for tens of milliseconds. These results imply inhomogeneous distribution of enzymes in free solution induced by active enzymatic reactions.

Enhanced diffusivity in microscopically reversible active matter

The physics of self-propelled objects at the nanoscale is a rapidly developing research field where recent experiments have focused on the motion of individual catalytic enzymes. Contrary to the experimental advancements, theoretical understanding of the possible self-propulsion mechanisms at these scales is limited. A particularly puzzling question concerns the origins of the reportedly high diffusivities of the individual enzymes. Here we start with the fundamental principle of microscopic reversibility (MR) of chemical reactions powering self-propulsion and demonstrate that MR can lead to an increase of the particle mobility and of the short- and long-time diffusion coefficients as compared to dynamics where MR is neglected. Furthermore, the derived diffusion coefficients are enhanced due to the action of an external force. These results can shed new light on interpretations of the measured diffusivities and help to test the relevance of MR for the active motion of individual nanoswimmers.

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.

Photothermal interference urease-powered polydopamine nanomotor for enhanced propulsion and synergistic therapy

Enzyme-powered nanomotors with active motion have opened a new door in design of biocompatible drug delivery systems for cancer treatment. However, the movement of them still faces huge challenges due to the viscous physiological environment. To address this issue, we developed a photothermal interference (PTI) urease-modified polydopamine (PDA) nanomotor (PDA@HSA@Ur) for deeper-penetration of doxorubicin (DOX) through improved motion. The urease-powered nanomotors can generate self-propulsion via catalyzing decomposition of biocompatible urea into carbon dioxide and ammonia through a self-diffusiophoretic. Meanwhile, when exposed to near-infrared (NIR) laser, the increased temperature of tumors microenvironment from nanomotors can not only induce tumor cell apoptosis but also enhance the biocatalytic activity of urease to improve the motion of nanomotors. Compared to the nanomotors propelled only by urea, PTI nanomotors realize highly effective self-propulsion with improved cellular uptake in vitro. Furthermore, PTI nanomotors display an enhanced anticancer efficiency owing to synergistic photothermal and chemotherapy effect. The PTI reported in this manuscript is the first to provide a thermally assisted method for highly efficient cancer treatment with urease-powered nanomotors in a complex physiological environment through enhanced motion and synergistic therapy.

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.

Generic Rules for Distinguishing Autophoretic Colloidal Motors

Distinguishing the operating mechanisms of nano- and micromotors powered by chemical gradients, i.e. "autophoresis", holds the key for fundamental and applied reasons. In this article, we propose and experimentally confirm that the speeds of a self-diffusiophoretic colloidal motor scale inversely to its population density but not for self-electrophoretic motors, because the former is an ion source and thus increases the solution ionic strength over time while the latter does not. They also form clusters in visually distinguishable and quantifiable ways. This pair of rules is simple, powerful, and insensitive to the specific material composition, shape or size of a colloidal motor, and does not require any measurement beyond typical microscopy. These rules are not only useful in clarifying the operating mechanisms of typical autophoretic micromotors, but also in predicting the dynamics of unconventional ones that are yet to be experimentally realized, even those involving enzymes.

Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question

Micrometer-sized objects are widely known to exhibit chemically driven motility in systems away from equilibrium. Experimental observation of reaction-induced motility or enhancement in diffusivity at the much shorter length scale of small molecules is, however, still a matter of debate. Here, we investigate the molecular diffusivity of reactants, catalyst, and product of a model reaction, the copper-catalyzed azide-alkyne cycloaddition click reaction, and develop new NMR diffusion approaches that allow the probing of reaction-induced diffusion enhancement in nanosized molecular systems with higher accuracy than the state of the art. Following two different approaches that enable the accounting of time-dependent concentration changes during NMR experiments, we closely monitored the diffusion coefficient of reaction components during the reaction. The reaction components showed distinct changes in the diffusivity: while the two reactants underwent a time-dependent decrease in their diffusivity, the diffusion coefficient of the product gradually increased and the catalyst showed only slight diffusion enhancement within the range expected for reaction-induced sample heating. The decrease in diffusion coefficient of the alkyne, one of the two reactants of click reaction, was not reproduced during its copper coordination when the second reactant, azide, was absent. Our results do not support the catalysis-induced diffusion enhancement of the components of the click reaction and, instead, point to the role of a relatively large intermediate species within the reaction cycle with diffusivity lower than that of both the reactants and product molecule.

Active matter dynamics in confined microfluidic environments

The field of active matter is a nascent area of research in soft condensed matter physics, which is drawing on the expertise of researchers from diverse disciplines. Small scale active particles-both inorganic and biological-display non-trivial emergent dynamics and interactions that could help us understand complex biological processes and phenomena. Recently, using microfluidic technologies, several research groups have performed important experimental and theoretical studies to understand the behavior of self-propelled particles and molecular active matter within confined environments-to glean a fundamental understanding of the cellular processes occurring under ultra-low Reynolds number conditions. In this chapter, we would like to review applications of microfluidics in active matter research, highlighting a few important theoretical and experimental investigations. We will conclude the discussion with a note on the future of this field mentioning a few open questions that are at the forefront of our minds.

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.

Relative Diffusivities of Bound and Unbound Protein Can Control Chemotactic Directionality

Enzyme-based systems have been shown to undergo chemotactic motion in response to their substrate gradient. This phenomenon has been exploited to direct the motion of enzymes and enzyme-attached particles to specific locations in space. Here, we propose a new kinetic model to analyze the directional movement of an ensemble of protein molecules in response to a gradient of the ligand. We also formulate a separate model to probe the motion of enzyme molecules in response to a gradient of the substrate under catalytic conditions. The only input for the new enzymatic model is the Michaelis-Menten constant which is the relevant measurable constant for enzymatic reactions. We show how our model differs from previously proposed models in a significant manner. For both binding and catalytic reactions, a net movement up the ligand/substrate gradient is predicted when the diffusivity of the ligand/substrate-bound protein is lower than that of the unbound protein (positive chemotaxis). Conversely, movement down the ligand/substrate gradient is expected when the diffusivity of the ligand/substrate-bound protein is higher than that of the unbound protein (negative chemotaxis). However, there is no net movement of protein/enzyme when the diffusivities of the bound and free species are equal. The work underscores the critical importance of measuring the diffusivity of the bound protein and comparing it with that of the free protein.

Molecules, the Ultimate Nanomotor: Linking Chemical Reaction Intermediates to their Molecular Diffusivity

The intellectual community focused on nanomotors has recently become interested in extending these concepts to individual molecules. Here, we study a chemical reaction according to whose mechanism some intermediate species should speed up while others slow down in predictable ways, if the nanomotor hypothesis of boosted diffusion holds. Accordingly, we scrutinize the absolute diffusion coefficient (D) during intermediate steps of the catalytic cycle for the CuAAC reaction (copper-catalyzed azide-alkyne cycloaddition click reaction), using proton pulsed field-gradient nuclear magnetic resonance to discriminate between the diffusion of various reaction intermediates. We observe time-dependent diffusion that is enhanced for some intermediate molecular species and depressed for those whose size increases owing to complex formation. These findings point to the failure of the conventional Stokes-Einstein equation to fully explain diffusivity during chemical reaction. Without attempting a firm explanation, this paper highlights aspects of the physics of chemical reactions that are imperfectly understood and presents systematic data that can be used to assess hypotheses.

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.

Single-particle diffusional fingerprinting: A machine-learning framework for quantitative analysis of heterogeneous diffusion

Single-particle tracking (SPT) analysis of individual biomolecules is an indispensable tool for extracting quantitative information from dynamic biological processes, but often requires some a priori knowledge of the system. Here we present “single-particle diffusional fingerprinting,” a more general approach for extraction of diffusional patterns in SPT independently of the biological system. This method extracts a set of descriptive features for each SPT trajectory, which are ranked upon classification to yield mechanistic insights for the species under comparison. We demonstrate its capacity to yield a dictionary of diffusional traits across multiple systems (e.g., lipases hydrolyzing fat, transcription factors diffusing in cells, and nanoparticles in mucus), supporting its use on multiple biological phenomena (e.g., drug delivery, receptor dynamics, and virology).

Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of systems such as receptor localization, enzyme propulsion, bacteria motility, and drug nanocarrier delivery. The inherently complex diffusion in such biological systems can vary drastically both in time and across systems, consequently imposing considerable analytical challenges, and currently requires an a priori knowledge of the system. Here we introduce a method for SPT data analysis, processing, and classification, which we term “diffusional fingerprinting.” This method allows for dissecting the features that underlie diffusional behavior and establishing molecular identity, regardless of the underlying diffusion type. The method operates by isolating 17 descriptive features for each observed motion trajectory and generating a diffusional map of all features for each type of particle. Precise classification of the diffusing particle identity is then obtained by training a simple logistic regression model. A linear discriminant analysis generates a feature ranking that outputs the main differences among diffusional features, providing key mechanistic insights. Fingerprinting operates by both training on and predicting experimental data, without the need for pretraining on simulated data. We found this approach to work across a wide range of simulated and experimentally diverse systems, such as tracked lipases on fat substrates, transcription factors diffusing in cells, and nanoparticles diffusing in mucus. This flexibility ultimately supports diffusional fingerprinting’s utility as a universal paradigm for SPT diffusional analysis and prediction.

Nonreciprocality of a micromachine driven by a catalytic chemical reaction

We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechanochemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechanochemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical timescales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called "nonreciprocality" and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two timescales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.

Thermophoretic Random Walks and Enhancement of Diffusion

The contribution of the stochastic thermodiffusion to the diffusion enhancement is studied. The thermodiffusion of particles suspended in a liquid may hold place when the spontaneous endo- or exothermal nanoscale events similar to elementary acts of enzymatic reactions occur as the random series in the space and time. In these events, the energy can be emitted or absorbed at nanoscale during few to hundreds of picoseconds. It may cause local spontaneous temperature spikes spreading quickly in the space and decaying with time. The random local temperature spikes create local transient temperature gradients, where thermodiffusion of the molecules and particles holds place as well as the change in the physical properties of the suspending medium due to heating. These thermodiffusion random walks may appear as the enhanced usual Stokes-Einstein diffusion when the energy absorption/generation is high enough. The evaluated relative contribution of the mentioned effect to the molecular mobility is shown to be in agreement with experimental data on enzymatic reactions from the literature.

Reply to Comment on "Using NMR to Test Molecular Mobility during a Chemical Reaction"

Reports of boosted diffusion during chemical and enzymatic reactions have inspired a loyal community of scientists who find them so counterintuitive that they must be artifact. This second Comment on the subject by these authors is about technicalities of how to analyze data we deposited online regarding J. Phys. Chem. Lett. 2021 12, 2370 and Science 2020 369, 537. Now that their own data is also online, one apparent discrepancy can be resolved: we demonstrate that the authors' data agrees with ours because their first Comment on this subject reported only truncated short-time excerpts of the longer time series they deposited online (zenodo.org/record/4628353). This second Comment adds five additional objections, four of which are too technical to change the qualitative conclusion. The fifth objection errs because it omits recognizing intermediate states of the click reaction during which one reactant complexes with the catalyst to form an object of larger size. Elsewhere we analyzed in great detail the respective influences of boosted diffusion and this hydrodynamic effect (DOI: 10.26434/chemrxiv.14740563.v1). The factual evidence and reasoning in this Reply strongly support this laboratory's earlier conclusions regarding boosted diffusion during common chemical reactions.

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.

Interconnectivity between Surface Reactivity and Self-Assembly of Kemp Elimination Catalyzing Nanorods

Understanding the fundamental facts behind dynamicity of catalytic processes has been a longstanding quest across disciplines. Herein, we report self-assembly of catalytically active gold nanorods that can be regulated by tuning its reactivity towards a proton transfer reaction at different pH. Unlike substrate-induced templating and co-operativity, the enhanced aggregation rate is due to alteration of catalytic surface charge only during reactivity as negatively charged transition state of reactant (5-nitrobenzisoxazole) is formed on positively charged nanorod while undergoing a concerted E2-pathway. Herein, enhanced diffusivity during catalytic processes might also act as an additional contributing factor. Furthermore, we have also shown that nanosized hydrophobic cavities of clustered nanorods can also efficiently accelerate the rate of an aromatic nucleophilic substitution reaction, which also demonstrates a catalytic phenomenon that can lead to cascading of other reactions where substrates and products of the starting reactions are not directly involved.

Experimental insight into enzyme catalysis and dynamics: A review on applications of state of art spectroscopic methods

Enzymes are dynamic in nature and understanding their activity depends on exploring their overall structural fluctuation as well as transformation at the active site in free state as well as turnover conditions. In this chapter, the application of several different spectroscopy techniques viz. single molecule spectroscopy, ultrafast spectroscopy and Raman spectroscopy in the context of enzyme dynamics and catalysis are discussed. The importance of such studies are significant in the understanding of new discoveries of drugs, cure for some lethal diseases, gene modification as well as in industrial applications.

Enzyme-driven micro/nanomotors: Recent advances and biomedical applications

Micro/nanomotors (MNMs), both self-propelled actuators and external fields-promoted machines, have joined forces in the past decade to accomplish versatile tasks such as precise detection and targeted cargo delivery with adequate propulsion and desirable locomotion. Amongst, enzyme-driven MNMs have been able to differentiate themselves from others owing to their distinct characteristics, such as absence of chemical fuel, enhanced cellular uptake and the possibility to be easily conjugated with many therapeutics, including both small molecules and biologics, displaying superior efficacy, enhanced specificity and diminished side effects. In the present review, we aim to highlight and summarize recent advances in enzyme-driven MNMs, particularly to provide an in-depth discussion focusing on the enzyme linking approaches onto those MNMs and motion control strategies of such MNMs with advantages and limitations thereof. Conclusions and future perspectives are also provided in brief.

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.

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.

Self-Propelled Micro/Nanomotors for On-Demand Biomedical Cargo Transportation

Micro/nanomotors (MNMs) are miniaturized machines that can perform assigned tasks at the micro/nanoscale. Over the past decade, significant progress has been made in the design, preparation, and applications of MNMs that are powered by converting different sources of energy into mechanical force, to realize active movement and fulfill on-demand tasks. MNMs can be navigated to desired locations with precise controllability based on different guidance mechanisms. A considerable research effort has gone into demonstrating that MNMs possess the potential of biomedical cargo loading, transportation, and targeted release to achieve therapeutic functions. Herein, the recent advances of self-propelled MNMs for on-demand biomedical cargo transportation, including their self-propulsion mechanisms, guidance strategies, as well as proof-of-concept studies for biological applications are presented. In addition, some of the major challenges and possible opportunities of MNMs are identified for future biomedical applications in the hope that it may inspire future research.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Pseudo-chemotaxis of active Brownian particles competing for food

Active Brownian particles (ABPs) are physical models for motility in simple life forms and easily studied in simulations. An open question is to what extent an increase of activity by a gradient of fuel, or food in living systems, results in an evolutionary advantage of actively moving systems such as ABPs over non-motile systems, which rely on thermal diffusion only. It is an established fact that within confined systems in a stationary state, the activity of ABPs generates density profiles that are enhanced in regions of low activity, which is thus referred to as ‘anti-chemotaxis’. This would suggest that a rather complex sensoric subsystem and information processing is a precondition to recognize and navigate towards a food source. We demonstrate in this work that in non-stationary setups, for instance as a result of short bursts of fuel/food, ABPs do in fact exhibit chemotactic behavior. In direct competition with inactive, but otherwise identical Brownian particles (BPs), the ABPs are shown to fetch a larger amount of food. We discuss this result based on simple physical arguments. From the biological perspective, the ability of primitive entities to move in direct response to the available amount of external energy would, even in absence of any sensoric devices, encompass an evolutionary advantage.

Mechanobiology of dynamic enzyme systems

This Perspective paper advances a hypothesis of mechanosensation by endothelial cells in which the cell is a dynamic crowded system, driven by continuous enzyme activity, that can be shifted from one non-equilibrium state to another by external force. The nature of the shift will depend on the direction, rate of change, and magnitude of the force. Whether force induces a pathophysiological or physiological change in cell biology will be determined by whether the dynamics of a cellular system can accommodate the dynamics and magnitude of the force application. The complex interplay of non-static cytoskeletal structures governs internal cellular rheology, dynamic spatial reorganization, and chemical kinetics of proteins such as integrins, and a flaccid membrane that is dynamically supported; each may constitute the necessary dynamic properties able to sense external fluid shear stress and reorganize in two and three dimensions. The resulting reorganization of enzyme systems in the cell membrane and cytoplasm may drive the cell to a new physiological state. This review focuses on endothelial cell mechanotransduction of shear stress, but may lead to new avenues of investigation of mechanobiology in general requiring new tools for interrogation of mechanobiological systems, tools that will enable the synthesis of large amounts of spatial and temporal data at the molecular, cellular, and system levels.

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.

Enzyme catalysis powered micro/nanomotors for biomedical applications

This review provides insights on enzyme powered motors using fuels present in biological environments for biomedical applications.

Tadpole-like Unimolecular Nanomotor with Sub-100 nm Size Swims in a Tumor Microenvironment Model

Inspired by the natural motors capable of performing multiple tasks in complex living environments, synthetic nanomotors emerge as a potential vehicle for revolutionizing biomedical processes. Yet current motors suffer from decreased and even completely hindered motion in a complex physiological environment, shadowing the future of this booming field. To address this problem, a unimolecular nanomotor based on molecular bottlebrush (MBB) of sub-100 nm size is reported. This motor is constructed precisely via controlled radical polymerization and click chemistry and propelled with biocompatible catalase. Such a molecular nanomotor possesses tadpole-like asymmetry and is able to overcome Brownian motion, and demonstrates strong directional propulsion (linear and coiled cyclic trajectories) in a viscous tumor microenvironment gel model at an ultralow hydrogen peroxide level of 2 mM (0.006%). In addition, the molecular nanomotor exhibits superior stability in serum containing cell medium and good biocompatibility in blood. Such molecular bottlebrush based nanomotors may represent a unique platform for overcoming the tissue penetration barrier.