Direct Single Molecule Imaging of Enhanced Enzyme Diffusion

Barrier crossing in a viscoelastic medium under active noise: Predictions of Kramers' flux-over-population method

The biochemical activity inside a cell has recently been suggested to act as a source of hydrodynamic fluctuations that can speed up or slow down enzyme catalysis [Tripathi et al., Commun. Phys. 5, 101 (2022).] The idea has been tested against and largely corroborated by simulations of activated barrier crossing in a simple fluid in the presence of thermal and athermal noise. The present paper attempts a wholly analytic solution to the same noise-driven barrier crossing problem but generalizes it to include viscoelastic memory effects of the kind likely to be present in cellular interiors. A calculation of the model's barrier crossing rate, using Kramers' flux-over-population formalism, reveals that in relation to the case where athermal noise is absent, athermal noise always accelerates barrier crossing, though the extent of enhancement depends on the duration τ0 over which the noise acts. More importantly, there exists a critical τ0-determined by the properties of the medium-at which Kramers' theory breaks down and, on approach to which, the rate grows significantly. The possibility of such a giant enhancement is potentially open to experimental validation using optically trapped nanoparticles in viscoelastic media that are acted on by externally imposed colored noise.

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.

Demixing in Binary Mixtures with Differential Diffusivity at High Density

Spontaneous phase separation, or demixing, is important in biological phenomena such as cell sorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While differential-diffusivity-induced phase separation occurs in mixtures with a packing fraction up to 0.7 [S. N. Weber et al. Binary mixtures of particles with different diffusivities demix, Phys. Rev. Lett. 116, 058301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.058301], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between 0.7 and 1.0 the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram that occurs when phase separation can no longer drive a change in entropy production at high densities. We also find that a confluent Voronoi model for tissues does not phase separate, consistent with particle-based simulations.

Non-specific cargo-filament interactions slow down motor-driven transport

Active, motor-based cargo transport is important for many cellular functions and cellular development. However, the cell interior is complex and crowded and could have many weak, non-specific interactions with the cargo being transported. To understand how cargo-environment interactions will affect single motor cargo transport and multi-motor cargo transport, we use an artificial quantum dot cargo bound with few (~ 1) to many (~ 5-10) motors allowed to move in a dense microtubule network. We find that kinesin-driven quantum dot cargo is slower than single kinesin-1 motors. Excitingly, there is some recovery of the speed when multiple motors are attached to the cargo. To determine the possible mechanisms of both the slow down and recovery of speed, we have developed a computational model that explicitly incorporates multi-motor cargos interacting non-specifically with nearby microtubules, including, and predominantly with the microtubule on which the cargo is being transported. Our model has recovered the experimentally measured average cargo speed distribution for cargo-motor configurations with few and many motors, implying that numerous, weak, non-specific interactions can slow down cargo transport and multiple motors can reduce these interactions thereby increasing velocity.

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.

Intracellularly Self-Assembled 2D Materials Induce Apoptotic Cell Death by Impeding Cytosolic Transport

Using a photochemically isomerizable cucurbit[6]uril derivative as a building block, we succeeded in generating a large number of oversized 2D materials within the cytosol of a living cell via controlled self-assembly. Fluorescence recovery after a photobleaching assay indicated that the resulting 2D material pieces posed discernible hindrance to not only diffusive spreading but also motor-driven motion of intracellular components in the cytosol, which eventually induced apoptotic cell death. Such behavior was seldom observed in previous 2D material-bearing cells prepared by endocytosis, as the total lateral size constituted by the endocytosed 2D materials per cell failed to exceed a threshold level, leading to a tortuosity of transport path inadequate to impede cytosolic transport in an appreciable manner. By varying the initial concentration of the building block, the existence of such a threshold was experimentally demonstrated from the relationship between the flow cytometry side scatter of the treated cells and corresponding cell viability. With the otherwise well-regulated cytosolic transport dynamics of living cells being physically altered, therapeutics with a new mechanism of action that counteracts drug resistance or intracellular platforms that advance our understanding of subcellular pathology of certain intractable diseases are in sight.

Gauging Nanoswimmer Dynamics via the Motion of Large Bodies

Nanoswimmers are ubiquitous in biotechnology and nanotechnology but are extremely challenging to measure due to their minute size and driving forces. A simple method is proposed for detecting the elusive physical features of nanoswimmers by observing how they affect the motion of much larger, easily traceable particles. Modeling the swimmers as hydrodynamic force dipoles, we find direct, easy-to-calibrate relations between the observable power spectrum and diffusivity of the tracers and the dynamic characteristics of the swimmers-their force dipole moment and correlation times.

Anomalous diffusion and transport by a reciprocal convective flow

Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause diffusion enhancement [Koyano et al., Phys. Rev. E 102, 033109 (2020)2470-004510.1103/PhysRevE.102.033109]. In this paper, such cooperative effects are investigated in detail. Numerical simulations based on the convection-diffusion equation revealed that anisotropic diffusion and net shift as well as diffusion enhancement occur under a reciprocal flow. Such anomalous diffusion and transport are theoretically derived by the analyses of the Langevin dynamics.

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 Mobility during Diels-Alder Reaction: Results of Molecular Simulations

Recent measurements indicate enhanced mobility of solvent molecules during Diels-Alder (DA) and other common chemical reactions. We present results of molecular dynamics simulations of the last stages of the DA cycloaddition reaction, from the transition state configuration to product, of furfurylamine and maleimide in acetonitrile at reactant concentrations studied experimentally. We find enhanced mobility of solvent and reactant molecules up to at least a nanometer from the DA product over hundreds of picoseconds. Local heating is ruled out as a factor in the enhanced mobility observed in the simulations, which is instead found to be due to solvent relaxation following the formation of the DA product.

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.

Trade-off between carbohydrates and metal ions regulates the chemotactic directionality of alkaline phosphatase

The role of the Hofmeister interaction in governing the chemotactic behavior of alkaline phosphatase in the presence of carbohydrate and metal ion gradients has been established.

Automating Bayesian inference and design to quantify acoustic particle levitation

Self-propulsion of micro- and nanoparticles powered by ultrasound provides an attractive strategy for the remote manipulation of colloidal matter using biocompatible energy inputs. Quantitative understanding of particle motion and its dependence on size, shape, and composition requires accurate characterization of the acoustic field, which depends sensitively on the experimental setup. Here, we show how automated experiments based on Bayesian inference and design can accurately and efficiently characterize the acoustic field within resonant chambers used to propel acoustic nanomotors. Repeated cycles of observation, inference, and design (OID) are guided by a physical model that describes the rate at which levitating particles approach the nodal plane. Using video microscopy, we observe the relaxation of tracer particles to this plane following the application of the acoustic field. We use sequential Monte Carlo methods to infer model parameters such as the amplitude and frequency of the resonant chamber while accounting for particle-level measurement noise and population-level heterogeneity in the field. Guided by simulated outcomes, we select the optimal design for the next experiment as to maximize the information gain in the relevant parameters. We show how this iterative process serves to discriminate between competing hypotheses and efficiently converges to accurate parameter estimates using only few automated experiments. We discuss the need for model criticism to ensure the validity of the guiding model throughout automated cycles of observation, inference, and design. This work demonstrates how Bayesian methods can learn the parameters of nonlinear, hierarchical models used to describe video microscopy data of active colloids.

Synchronization and Enhanced Catalysis of Mechanically Coupled Enzymes

We examine the stochastic dynamics of two enzymes that are mechanically coupled to each other, e.g., through an elastic substrate or a fluid medium. The enzymes undergo conformational changes during their catalytic cycle, which itself is driven by stochastic steps along a biased chemical free energy landscape. We find conditions under which the enzymes can synchronize their catalytic steps, and discover that the coupling can lead to a significant enhancement in their overall catalytic rate. Both effects can be understood as arising from a global bifurcation in the underlying dynamical system at sufficiently strong coupling. Our findings suggest that, despite their molecular scale, enzymes can be cooperative and improve their performance in metabolic clusters.

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.

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.

Nanoscale Catalyst Chemotaxis Can Drive the Assembly of Functional Pathways

Recent experiments demonstrate molecular chemotaxis or altered diffusion rates of enzymes in the presence of their own substrates. We show here an important implication, namely, that if a nanoscale catalyst A produces a small-molecule ligand product L which is the substrate of another catalyst B, the two catalysts will attract each other. We explore this nonequilibrium producer recruitment force (ProRec) in a reaction-diffusion model. The predicted cat-cat association will be the strongest when A is a fast producer of L and B is a tight binder to it. ProRec is a force that could drive a mechanism (the catpath mechanism) by which catalysts could become spatially localized into functional pathways, such as in the biochemical networks in cells, which can achieve complex goals.

Crowder and surface effects on self-organization of microtubules

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

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.

Mechanochemical enzymes and protein machines as hydrodynamic force dipoles: the active dimer model

Mechanochemically active enzymes change their shapes within every turnover cycle. Therefore, they induce circulating flows in the solvent around them and behave as oscillating hydrodynamic force dipoles. Because of non-equilibrium fluctuating flows collectively generated by the enzymes, mixing in the solution and diffusion of passive particles within it are expected to get enhanced. Here, we investigate the intensity and statistical properties of such force dipoles in the minimal active dimer model of a mechanochemical enzyme. In the framework of this model, novel estimates for hydrodynamic collective effects in solution and in lipid bilayers under rapid rotational diffusion are derived, and available experimental and computational data is examined.

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.

•

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

•

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

•

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.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

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.

Quantifying the non-equilibrium activity of an active colloid

Active matter systems exhibit rich emergent behavior due to constant injection and dissipation of energy at the level of individual agents. Since these systems are far from equilibrium, their dynamics and energetics cannot be understood using the framework of equilibrium statistical mechanics. Recent developments in stochastic thermodynamics extend classical concepts of work, heat, and energy dissipation to fluctuating non-equilibrium systems. We use recent advances in experiment and theory to study the non-thermal dissipation of individual light-activated self-propelled colloidal particles. We focus on characterizing the transition from thermal to non-thermal fluctuations and show that energy dissipation rates on the order of ∼kBT s-1 are measurable from finite time series data.

Cooperatively enhanced reactivity and "stabilitaxis" of dissociating oligomeric proteins

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer on them a functional advantage with respect to nondissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with localized targets. In nonuniform environments with position-dependent association-dissociation, caused by, for example, spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term "stabilitaxis."

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.

Robustness of FCS (Fluorescence Correlation Spectroscopy) with Quenchers Present

Inspired by recent publications doubtful of the FCS technique, we scrutinize how irreversible ("static") and reversible ("dynamic") quenching can influence the interpretation of such data. Textbook presentations often emphasize only how to analyze data in extremes, the absence of quenching or the presence of substantial quenching. Here, we consider intermediate cases where the assessment of photophysics (static quenching, blinking-like triplet-state relaxation) influence on autocorrelation curves can be delicate if dye-labeled objects diffuse on comparably rapid time scales. We used the amino acid, tryptophan, as the quencher. As our example of small-molecule dye that diffuses rapidly, we mix the quencher with the fluorescence dye, Alexa 488. The translational diffusion coefficient, inferred from fit to the standard one-component Fickian diffusion model, speeds up without the loss of quality of fit, but quenching is reflected in the fact that the data become exceptionally noisy. This reflects the bidisperse population of quenched and unquenched dyes when the time scales overlap between the processes of translational diffusion, quenching, and blinking. As our example of the large-molecule dye-labeled object that diffuses relatively slowly, we mixed the quencher with dye-labeled BSA, bovine serum albumin. Diffusion, static quenching, and blinking time scales are now separated. In spite of quenching contribution to the autocorrelation function when the delay time is relatively short, the inferred translational diffusion coefficient now depends weakly on the presence of a quencher. We conclude that when the diffusing molecule is substantially slower to diffuse than the time scale of photophysical processes of the fluorescent dye to which it is attached, the influence of quenching is self-evident and the FCS autocorrelation curves give an appropriate diffusion coefficient if correct fitting functions are chosen in the analysis.