Molecular propulsion: chemical sensing and chemotaxis of DNA driven by RNA polymerase

Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts

Mixtures of particles that interact through phoretic effects are known to aggregate if they belong to species that exhibit attractive self-interactions. We study self-organization in a model metabolic cycle composed of three species of catalytically active particles that are chemotactic toward the chemicals that define their connectivity network. We find that the self-organization can be controlled by the network properties, as exemplified by a case where a collapse instability is achieved by design for self-repelling species. Our findings highlight a possibility for controlling the intricate functions of metabolic networks by taking advantage of the physics of phoretic active matter.

Self-organization of primitive metabolic cycles due to non-reciprocal interactions

One of the greatest mysteries concerning the origin of life is how it has emerged so quickly after the formation of the earth. In particular, it is not understood how metabolic cycles, which power the non-equilibrium activity of cells, have come into existence in the first instances. While it is generally expected that non-equilibrium conditions would have been necessary for the formation of primitive metabolic structures, the focus has so far been on externally imposed non-equilibrium conditions, such as temperature or proton gradients. Here, we propose an alternative paradigm in which naturally occurring non-reciprocal interactions between catalysts that can partner together in a cyclic reaction lead to their recruitment into self-organized functional structures. We uncover different classes of self-organized cycles that form through exponentially rapid coarsening processes, depending on the parity of the cycle and the nature of the interaction motifs, which are all generic but have readily tuneable features.

On the utility of microfluidic systems to study protein interactions: advantages, challenges, and applications

Within the complex milieu of a cell, which comprises a large number of different biomolecules, interactions are critical for function. In this post-reductionist era of biochemical research, the 'holy grail' for studying biomolecular interactions is to be able to characterize them in native environments. While there are a limited number of in situ experimental techniques currently available, there is a continuing need to develop new methods for the analysis of biomolecular complexes that can cope with the additional complexities introduced by native-like solutions. We think approaches that use microfluidics allow researchers to access native-like environments for studying biological problems. This review begins with a brief overview of the importance of studying biomolecular interactions and currently available methods for doing so. Basic principles of diffusion and microfluidics are introduced and this is followed by a review of previous studies that have used microfluidics to measure molecular diffusion and a discussion of the advantages and challenges of this technique.

Accounts of applied molecular rotors and rotary motors: recent advances

Molecular machines are nanoscale devices capable of performing mechanical works at molecular level. These systems could be a single molecule or a collection of component molecules that interrelate with one another to produce nanomechanical movements and resulting performances. The design of the components of molecular machine with bioinspired traits results in various nanomechanical motions. Some known molecular machines are rotors, motors, nanocars, gears, elevators, and so on based on their nanomechanical motion. The conversion of these individual nanomechanical motions to collective motions via integration into suitable platforms yields impressive macroscopic output at varied sizes. Instead of limited experimental acquaintances, the researchers demonstrated several applications of molecular machines in chemical transformation, energy conversion, gas/liquid separation, biomedical use, and soft material fabrication. As a result, the development of new molecular machines and their applications has accelerated over the previous two decades. This review highlights the design principles and application scopes of several rotors and rotary motor systems because these machines are used in real applications. This review also offers a systematic and thorough overview of current advancements in rotary motors, providing in-depth knowledge and predicting future problems and goals in this area.

Pair dynamics of active force dipoles in an odd-viscous fluid

We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible fluid with an odd viscosity, while the force dipole (representing an active protein or enzyme) induces a dipolar flow. Taking into account the momentum decay in the 2D fluid, we obtain analytically the mobility tensor that depends on the odd viscosity and includes nonreciprocal hydrodynamic interactions. We find that the particle pair shows spiral behavior due to the transverse flow induced by the odd viscosity. When the magnitude of the odd viscosity is large as compared with the shear viscosity, two types of oscillatory behaviors are seen. One of them can be understood as arising from closed orbits in dynamical systems, and its circular trajectories are determined by the ratio between the magnitude of the odd viscosity and the force dipole. In addition, the phase diagrams of the particle dipolar angles are obtained numerically. Our findings reveal that the nonreciprocal response leads to complex dynamics of active particles embedded in an active fluid with odd viscosity.

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.

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.

Spatiotemporal dynamics of self-assembled structures in enzymatically induced agonistic and antagonistic conditions

Predicting and designing systems with dynamic self-assembly properties in a spatiotemporal fashion is an important research area across disciplines ranging from understanding the fundamental non-equilibrium features of life to the fabrication of next-generation materials with life-like properties. Herein, we demonstrate a spatiotemporal dynamics pattern in the self-assembly behavior of a surfactant from an unorganized assembly, induced by adenosine triphosphate (ATP) and enzymes responsible for the degradation or conversion of ATP. We report the different behavior of two enzymes, alkaline phosphatase (ALP) and hexokinase (HK), towards adenosine triphosphate (ATP)-driven surfactant assembly, which also results in contrasting spatiotemporal dynamic assembly behavior. Here, ALP acts antagonistically, resulting in transient self-assemblies, whereas HK shows agonistic action with the ability to sustain the assemblies. This dynamic assembly behavior was then used to program the time-dependent emergence of a self-assembled structure in a two-dimensional space by maintaining concentration gradients of the enzymes and surfactant at different locations, demonstrating a new route for obtaining 'spatial' organizational adaptability in a self-organized system of interacting components for the incorporation of programmed functionality.

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.

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.

Non-equilibrium phase separation in mixtures of catalytically active particles: size dispersity and screening effects

Biomolecular condensates in cells are often rich in catalytically active enzymes. This is particularly true in the case of the large enzymatic complexes known as metabolons, which contain different enzymes that participate in the same catalytic pathway. One possible explanation for this self-organization is the combination of the catalytic activity of the enzymes and a chemotactic response to gradients of their substrate, which leads to a substrate-mediated effective interaction between enzymes. These interactions constitute a purely non-equilibrium effect and show exotic features such as non-reciprocity. Here, we analytically study a model describing the phase separation of a mixture of such catalytically active particles. We show that a Michaelis-Menten-like dependence of the particles' activities manifests itself as a screening of the interactions, and that a mixture of two differently sized active species can exhibit phase separation with transient oscillations. We also derive a rich stability phase diagram for a mixture of two species with both concentration-dependent activity and size dispersity. This work highlights the variety of possible phase separation behaviours in mixtures of chemically active particles, which provides an alternative pathway to the passive interactions more commonly associated with phase separation in cells. Our results highlight non-equilibrium organizing principles that can be important for biologically relevant liquid-liquid phase separation.

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.

Biophysics and the Genomic Sciences

It is now rare to find biological, or genetic investigations that do not rely on the tools, data, and thinking drawn from the genomic sciences. Much of this revolution is powered by contemporary sequencing approaches that readily deliver large, genome-wide data sets that not only provide genetic insights but also uniquely report molecular outcomes from experiments that biophysicists are increasingly using for potentiating structural and mechanistic investigations. In this perspective, I describe a path of how biophysical thinking greatly contributed to this revolution in ways that parallel advancements in computer science through discussion of several key inventions, described as "foundational devices." These discussions also point at the future of how biophysics and the genomic sciences may become more finely integrated for empowering new measurement paradigms for biological investigations.

Direct Single Molecule Imaging of Enhanced Enzyme Diffusion

Recent experimental results have shown that enzymes can diffuse faster when they are in the presence of their reactants (substrate). This faster diffusion has been termed enhanced diffusion. Fluorescence correlation spectroscopy (FCS), which has been employed as the only method to make these measurements, relies on analyzing the fluctuations in fluorescence intensity to measure the diffusion coefficient of particles. Recently, artifacts in FCS measurements due to its sensitivity to environmental conditions have been evaluated, calling prior enhanced diffusion results into question. It behooves us to adopt complementary and direct methods to measure the mobility of enzymes. Herein, we use a technique of direct single molecule imaging to observe the diffusion of individual enzymes in solution. This technique is less sensitive to intensity fluctuations and deduces the diffusion coefficient directly based on the trajectory of the enzyme. Our measurements recapitulate that enzyme diffusion is enhanced in the presence of its substrate and find that the relative increase in diffusion of a single enzyme is even higher than those previously reported using FCS. We also use this complementary method to test if the total enzyme concentration affects the relative increase in diffusion and if the enzyme oligomerization state changes during its catalytic turnover. We find that the diffusion increase is independent of the total concentration of enzymes and the presence of substrate does not change the oligomerization state of enzymes.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Enhanced Diffusion of Catalytically Active Enzymes

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

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

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

Absolute diffusion measurements of active enzyme solutions by NMR

The diffusion of enzymes is of fundamental importance for many biochemical processes. Enhanced or directed enzyme diffusion can alter the accessibility of substrates and the organization of enzymes within cells. Several studies based on fluorescence correlation spectroscopy report enhanced diffusion of enzymes upon interaction with their substrate or inhibitor. In this context, major importance is given to the enzyme fructose-bisphosphate aldolase, for which enhanced diffusion has been reported even though the catalysed reaction is endothermic. Additionally, enhanced diffusion of tracer particles surrounding the active aldolase enzymes has been reported. These studies suggest that active enzymes can act as chemical motors that self-propel and give rise to enhanced diffusion. However, fluorescence studies of enzymes can, despite several advantages, suffer from artefacts. Here, we show that the absolute diffusion coefficients of active enzyme solutions can be determined with Pulsed Field Gradient Nuclear Magnetic Resonance (PFG-NMR). The advantage of PFG-NMR is that the motion of the molecule of interest is directly observed in its native state without the need for any labelling. Furthermore, PFG-NMR is model-free and thus yields absolute diffusion constants. Our PFG-NMR experiments of solutions containing active fructose-bisphosphate aldolase from rabbit muscle do not show any diffusion enhancement for the active enzymes, nor the surrounding molecules. Additionally, we do not observe any diffusion enhancement of aldolase in the presence of its inhibitor pyrophosphate.

Chemical and hydrodynamic alignment of an enzyme

Motivated by the implications of the complex and dynamic modular geometry of an enzyme on its motion, we investigate the effect of combining long-range internal and external hydrodynamic interactions due to thermal fluctuations with short-range surface interactions. An asymmetric dumbbell consisting of two unequal subunits, in a nonuniform suspension of a solute with which it interacts via hydrodynamic interactions as well as non-contact surface interactions, is shown to have two alignment mechanisms due to the two types of interactions. In addition to alignment, the chemical gradient results in a drift velocity that is modified by hydrodynamic interactions between the constituents of the enzyme.

Metabolon formation by chemotaxis

Enzymes that participate in reaction cascades have been shown to assemble into metabolons, in the presence of the first enzyme's substrate. However, the mechanism of metabolon formation is still an open question. We applied microfluidic and fluorescent spectroscopy techniques to study the coordinated movement of the first four enzymes of the glycolysis cycle: hexokinase, phosphoglucose isomerase, phosphofructokinase, and aldolase and showed that each enzyme independently follows its own specific substrate gradient, which is produced by the preceding enzymatic reaction. The extent of enzyme migration is proportional to the time the enzyme is exposed to the substrate gradient. Significantly, the chemotactic migration of enzymes is fairly rapid even under conditions that mimic cytosolic crowding. The observed rate was very similar to the reported rate of enzyme diffusion in living cells. Thus, chemotaxis may be a basis for the organization of metabolic networks in the cytosol of the cell.

Reaction induced diffusio-phoresis of ordinary catalytic particles

Catalytic particles phoretically migrate due to the reactant concentration gradients that they form.

Aldolase Does Not Show Enhanced Diffusion in Dynamic Light Scattering Experiments

Recent experimental studies have measured a 30-80% increase of the diffusion coefficient when various enzymes, including aldolase, are catalytically active. This observation has been supported by several theoretical explanations; however, other theoretical studies argue against the possibility of enhanced diffusion, and two of them ascribe the experimental observations to potential artifacts arising in fluorescence correlation spectroscopy (FCS) measurements. Here, we utilized dynamic light scattering (DLS) to measure the diffusion coefficient of aldolase in the absence and presence of its substrate. The DLS measurements have an experimental error of 3% and do not find a statistically significant change of the aldolase diffusion coefficient even at a saturating substrate concentration. This finding lends support to the contention that photophysical artifacts may have affected the FCS measurements and challenges the idea that enzymes can be self-propelled by their catalytic activity.

Catalytic enzymes are active matter

Catalysis and mobility of reactants in fluid are normally thought to be decoupled. Violating this classical paradigm, this paper presents the catalyst laws of motion. Comparing experimental data to the theory presented here, we conclude that part of the free energy released by chemical reaction is channeled into driving catalysts to execute wormlike trajectories by piconewton forces performing work of a few k_BT against fluid viscosity, where the rotational diffusion rate dictates the trajectory persistence length. This active motion agitates the fluid medium and produces antichemotaxis, the migration of catalyst down the gradient of the reactant concentration. Alternative explanations of enhanced catalyst mobility are examined critically.

Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements—performed across four orders of magnitude of substrate concentration, with emphasis on the biologically relevant regime around or below the Michaelis–Menten constant—show that catalysis boosts the motion of enzymes to be superdiffusive for a few microseconds, enhancing their effective diffusivity over longer timescales. Occurring at the catalytic turnover rate, these fast ballistic leaps maintain direction over a duration limited by rotational diffusion, driving enzymes to execute wormlike trajectories by piconewton forces performing work of a few k_BT against viscosity. The boosts are more frequent at high substrate concentrations, biasing the trajectories toward substrate-poor regions, thus exhibiting antichemotaxis, demonstrated here experimentally over a wide range of aqueous concentrations. Alternative noncatalytic, passive mechanisms that predict chemotaxis, cross-diffusion, and phoresis, are critically analyzed. We examine the physical interpretation of our findings, speculate on the underlying mechanism, and discuss the avenues they open with biological and technological implications. These findings violate the classical paradigm that chemical reaction and motility are distinct processes, and suggest reaction–motion coupling as a general principle of catalysis.

Enhanced Diffusion and Chemotaxis at the Nanoscale

Enzymes have been recently proposed to have mechanical activity associated with their chemical activity. In a number of recent studies, it has been reported that enzymes undergo enhanced diffusion in the presence of their corresponding substrate when this substrate is uniformly distributed in solution. Moreover, if the concentration of the substrate is nonuniform, enzymes and other small molecules have been reported to show chemotaxis (biased stochastic movement in the direction of the substrate gradient), typically toward higher concentrations of this substrate, with a few exceptions. The underlying physical mechanisms responsible for enhanced diffusion and chemotaxis at the nanoscale, however, are still not well understood. Understanding these processes is important both for fundamental biological research, for example, in the context of spatial organization of enzymes in metabolic pathways (metabolon formation), as well as for engineering applications, such as in the design of new vehicles for targeted drug delivery. In this Account, we will review the available experimental observations of both enhanced diffusion and chemotaxis, and we will discuss critically the different theories that have been proposed to explain the two. We first focus on enhanced diffusion, beginning with an overview of the experimental results. We then discuss the two main types of mechanisms that have been proposed, namely, active mechanisms relying on the catalytic step of the enzymatic reaction and equilibrium mechanisms, which consider the reversible binding and unbinding of the substrate to the enzyme. We put particular emphasis on an equilibrium model recently introduced by us, which describes how the diffusion of dumbbell-like modular enzymes can be enhanced in the presence of substrate thanks to a binding-induced reduction of the internal fluctuations of the enzyme. We then turn to chemotaxis, beginning with an overview of the experimental evidence for the chemotaxis of enzymes and small molecules, followed by a description of a number of shortcomings and pitfalls in the thermodynamic and phenomenological models for chemotaxis introduced in those and other works in the literature. We then discuss a microscopic model for chemotaxis including both noncontact interactions and specific binding between enzyme and substrate recently developed by us, which overcomes many of these shortcomings and is consistent with the experimental observations of chemotaxis. Finally, we show that the results of this model may be used to engineer chemically active macromolecules that are directed in space via patterning of the concentrations of their substrates.

Powering Motion with Enzymes

Enzymes are ubiquitous in living systems. Apart from traditional motor proteins, the function of enzymes was assumed to be confined to the promotion of biochemical reactions. Recent work shows that free swimming enzymes, when catalyzing reactions, generate enough mechanical force to cause their own movement, typically observed as substrate-concentration-dependent enhanced diffusion. Preliminary indication is that the impulsive force generated per turnover is comparable to the force produced by motor proteins and is within the range to activate biological adhesion molecules responsible for mechanosensation by cells, making force generation by enzymatic catalysis a novel mechanobiology-relevant event. Furthermore, when exposed to a gradient in substrate concentration, enzymes move up the gradient: an example of chemotaxis at the molecular level. The driving force for molecular chemotaxis appears to be the lowering of chemical potential due to thermodynamically favorable enzyme-substrate interactions and we suggest that chemotaxis promotes enzymatic catalysis by directing the motion of the catalyst and substrates toward each other. Enzymes that are part of a reaction cascade have been shown to assemble through sequential chemotaxis; each enzyme follows its own specific substrate gradient, which in turn is produced by the preceding enzymatic reaction. Thus, sequential chemotaxis in catalytic cascades allows time-dependent, self-assembly of specific catalyst particles. This is an example of how information can arise from chemical gradients, and it is tempting to suggest that similar mechanisms underlie the organization of living systems. On a practical level, chemotaxis can be used to separate out active catalysts from their less active or inactive counterparts in the presence of their respective substrates and should, therefore, find wide applicability. When attached to bigger particles, enzyme ensembles act as "engines", imparting motility to the particles and moving them directionally in a substrate gradient. The impulsive force generated by enzyme catalysis can also be transmitted to the surrounding fluid and molecular and colloidal tracers, resulting in convective fluid pumping and enhanced tracer diffusion. Enzyme-powered pumps that transport fluid directionally can be fabricated by anchoring enzymes onto a solid support and supplying the substrate. Thus, enzyme pumps constitute a novel platform that combines sensing and microfluidic pumping into a single self-powered microdevice. Taken in its entirety, force generation by active enzymes has potential applications ranging from nanomachinery, nanoscale assembly, cargo transport, drug delivery, micro- and nanofluidics, and chemical/biochemical sensing. We also hypothesize that, in vivo, enzymes may be responsible for the stochastic motion of the cytoplasm, the organization of metabolons and signaling complexes, and the convective transport of fluid in cells. A detailed understanding of how enzymes convert chemical energy to directional mechanical force can lead us to the basic principles of fabrication, development, and monitoring of biological and biomimetic molecular machines.

A Theory of Enzyme Chemotaxis: From Experiments to Modeling

Enzymes show two distinct transport behaviors in the presence of their substrates in solution. First, their diffusivity enhances with an increasing substrate concentration. In addition, enzymes perform directional motion toward regions with a high substrate concentration, termed as chemotaxis. While a variety of enzymes has been shown to undergo chemotaxis, there remains a lack of quantitative understanding of the phenomenon. Here, we derive a general expression for the active movement of an enzyme in a concentration gradient of its substrate. The proposed model takes into account both the substrate-binding and catalytic turnover step, as well as the enhanced diffusion of the enzyme. We have experimentally measured the chemotaxis of a fast and a slow enzyme: urease under catalytic conditions and hexokinase for both full catalysis and for simple noncatalytic substrate binding. There is good agreement between the proposed model and the experiments. The model is general, has no adjustable parameters, and only requires three experimentally defined constants to quantify chemotaxis: enzyme-substrate binding affinity ( K_d), Michaelis-Menten constant ( K_M), and level of diffusion enhancement in the associated substrate (α).

Progress toward Catalytic Micro- and Nanomotors for Biomedical and Environmental Applications

Synthetic micro- and nanomotors (MNMs) are tiny objects that can autonomously move under the influence of an appropriate source of energy, such as a chemical fuel, magnetic field, ultrasound, or light. Chemically driven MNMs are composed of or contain certain reactive material(s) that convert chemical energy of a fuel into kinetic energy (motion) of the particles. Several different materials have been explored over the last decade for the preparation of a wide variety of MNMs. Here, the discovery of materials and approaches to enhance the efficiency of chemically driven MNMs are reviewed. Several prominent applications of the MNMs, especially in the fields of biomedicine and environmental science, are also discussed, as well as the limitations of existing materials and future research directions.

Phoresis and Enhanced Diffusion Compete in Enzyme Chemotaxis

Chemotaxis of enzymes in response to gradients in the concentration of their substrate has been widely reported in recent experiments, but a basic understanding of the process is still lacking. Here, we develop a microscopic theory for chemotaxis that is valid for enzymes and other small molecules. Our theory includes both nonspecific interactions between enzyme and substrate as well as complex formation through specific binding between the enzyme and the substrate. We find that two distinct mechanisms contribute to enzyme chemotaxis: a diffusiophoretic mechanism due to the nonspecific interactions and a new type of mechanism due to binding-induced changes in the diffusion coefficient of the enzyme. The latter chemotactic mechanism points toward lower substrate concentration if the substrate enhances enzyme diffusion and toward higher substrate concentration if the substrate inhibits enzyme diffusion. For a typical enzyme, attractive phoresis and binding-induced enhanced diffusion will compete against each other. We find that phoresis dominates above a critical substrate concentration, whereas binding-induced enhanced diffusion dominates for low substrate concentration. Our results resolve an apparent contradiction regarding the direction of urease chemotaxis observed in experiments and, in general, clarify the relation between the enhanced diffusion and the chemotaxis of enzymes. Finally, we show that the competition between the two distinct chemotactic mechanisms may be used to engineer nanomachines that move toward or away from regions with a specific substrate concentration.

Determining if DNA Stained with a Cyanine Dye Can Be Digested with Restriction Enzymes

Visualization of DNA for fluorescence microscopy utilizes a variety of dyes such as cyanine dyes. These dyes are utilized due to their high affinity and sensitivity for DNA. In order to determine if the DNA molecules are full length after the completion of the experiment, a method is required to determine if the stained molecules are full length by digesting DNA with restriction enzymes. However, stained DNA may inhibit the enzymes, so a method is needed to determine what enzymes one could use for fluorochrome stained DNA. In this method, DNA is stained with a cyanine dye overnight to allow the dye and DNA to equilibrate. Next, stained DNA is digested with a restriction enzyme, loaded into a gel and electrophoresed. The experimental DNA digest bands are compared to an in silico digest to determine the restriction enzyme activity. If there is the same number of bands as expected, then the reaction is complete. More bands than expected indicate partial digestion and less bands indicate incomplete digestion. The advantage of this method is its simplicity and it uses equipment that a scientist would need for a restriction enzyme assay and gel electrophoresis. A limitation of this method is that the enzymes available to most scientists are commercially available enzymes; however, any restriction enzymes could be used.

Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States

Theoretical analysis, which maps single-molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1, whose dynamics is confined on one-dimensional tracks, is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers a thermodynamic basis to understand the heat-enhanced self-diffusion of exothermic enzymes.

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

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

Enzyme Catalysis To Power Micro/Nanomachines

Enzymes play a crucial role in many biological processes which require harnessing and converting free chemical energy into kinetic forces in order to accomplish tasks. Enzymes are considered to be molecular machines, not only because of their capability of energy conversion in biological systems but also because enzymatic catalysis can result in enhanced diffusion of enzymes at a molecular level. Enlightened by nature's design of biological machinery, researchers have investigated various types of synthetic micro/nanomachines by using enzymatic reactions to achieve self-propulsion of micro/nanoarchitectures. Yet, the mechanism of motion is still under debate in current literature. Versatile proof-of-concept applications of these enzyme-powered micro/nanodevices have been recently demonstrated. In this review, we focus on discussing enzymes not only as stochastic swimmers but also as nanoengines to power self-propelled synthetic motors. We present an overview on different enzyme-powered micro/nanomachines, the current debate on their motion mechanism, methods to provide motion and speed control, and an outlook of the future potentials of this multidisciplinary field.

Chemistry pumps: a review of chemically powered micropumps

Lab-on-a-chip devices have over recent years attracted a significant amount of attention in both the academic circle and industry, due to their promise in delivering versatile functionalities with high throughput and low sample amount. Typically, mechanical or electrokinetic micropumps are used in the majority of lab-on-a-chip devices that require powered fluid flow, but the technical challenges and the requirement of external power associated with these pumping devices hinder further development and miniaturization of lab-on-a-chip devices. Self-powered micropumps, especially those powered by chemical reactions, have been recently designed and can potentially address some of these issues. In this review article, we provide a detailed introduction to four types of chemically powered micropumps, with particular focus on their respective structures, operating mechanisms and practical usefulness as well as limitations. We then discuss the various functionalities and controllability demonstrated by these micropumps, ending with a brief discussion of how they can be improved in the future. Due to the absence of external power sources, versatile activation methods and sensitivity to environmental cues, chemically powered micropumps could find potential applications in a wide range of lab-on-a-chip devices.

Self-propulsion and interactions of catalytic particles in a chemically active medium

Enzymatic "machines," such as catalytic rods or colloids, can self-propel and interact by generating gradients of their substrates. We theoretically investigate the behaviors of such machines in a chemically active environment where their catalytic substrates are continuously synthesized and destroyed, as occurs in living cells. We show how the kinetic properties of the medium modulate self-propulsion and pairwise interactions between machines, with the latter controlled by a tunable characteristic interaction range analogous to the Debye screening length in an electrolytic solution. Finally, we discuss the effective force arising between interacting machines and possible biological applications, such as partitioning of bacterial plasmids.

Krebs cycle metabolon formation: metabolite concentration gradient enhanced compartmentation of sequential enzymes

Dynamics of metabolon formation in mitochondria was probed by studying diffusional motion of two sequential Krebs cycle enzymes in a microfluidic channel. Enhanced directional co-diffusion of both enzymes against a substrate concentration gradient was observed in the presence of intermediate generation. This reveals a metabolite directed compartmentation of metabolic pathways.

From one to many: dynamic assembly and collective behavior of self-propelled colloidal motors

The assembly of complex structures from simpler, individual units is a hallmark of biology. Examples include the pairing of DNA strands, the assembly of protein chains into quaternary structures, the formation of tissues and organs from cells, and the self-organization of bacterial colonies, flocks of birds, and human beings in cities. While the individual behaviors of biomolecules, bacteria, birds, and humans are governed by relatively simple rules, groups assembled from many individuals exhibit complex collective behaviors and functions that do not exist in the absence of the hierarchically organized structure. Self-assembly is a familiar concept to chemists who study the formation and properties of monolayers, crystals, and supramolecular structures. In chemical self-assembly, disorder evolves to order as the system approaches equilibrium. In contrast, living assemblies are typically characterized by two additional features: (1) the system constantly dissipates energy and is not at thermodynamic equilibrium; (2) the structure is dynamic and can transform or disassemble in response to stimuli or changing conditions. To distinguish them from equilibrium self-assembled structures, living (or nonliving) assemblies of objects with these characteristics are referred to as active matter. In this Account, we focus on the powered assembly and collective behavior of self-propelled colloids. These nano- and microparticles, also called nano- and micromotors or microswimmers, autonomously convert energy available in the environment (in the form of chemical, electromagnetic, acoustic, or thermal energy) into mechanical motion. Collections of these colloids are a form of synthetic active matter. Because of the analogy to living swimmers of similar size such as bacteria, the dynamic interactions and collective behavior of self-propelled colloids are interesting in the context of understanding biological active matter and in the development of new applications. The progression from individual particle motion to pairwise interactions, and then to multiparticle behavior, can be studied systematically with colloidal particles. Colloidal particles are also amenable to designs (in terms of materials, shapes, and sizes) that are not readily available in, for example, microbial systems. We review here our efforts and those of other groups in studying these fundamental interactions and the collective behavior that emerges from them. Although this field is still very new, there are already unique and interesting applications in analysis, diagnostics, separations, and materials science that derive from our understanding of how powered colloids interact and assemble.

The heat released during catalytic turnover enhances the diffusion of an enzyme

Recent studies have shown that the diffusivity of enzymes increases in a substrate-dependent manner during catalysis. Although this observation has been reported and characterized for several different systems, the precise origin of this phenomenon is unknown. Calorimetric methods are often used to determine enthalpies from enzyme-catalysed reactions and can therefore provide important insight into their reaction mechanisms. The ensemble averages involved in traditional bulk calorimetry cannot probe the transient effects that the energy exchanged in a reaction may have on the catalyst. Here we obtain single-molecule fluorescence correlation spectroscopy data and analyse them within the framework of a stochastic theory to demonstrate a mechanistic link between the enhanced diffusion of a single enzyme molecule and the heat released in the reaction. We propose that the heat released during catalysis generates an asymmetric pressure wave that results in a differential stress at the protein-solvent interface that transiently displaces the centre-of-mass of the enzyme (chemoacoustic effect). This novel perspective on how enzymes respond to the energy released during catalysis suggests a possible effect of the heat of reaction on the structural integrity and internal degrees of freedom of the enzyme.

Chemotactic separation of enzymes

We demonstrate a procedure for the separation of enzymes based on their chemotactic response toward an imposed substrate concentration gradient. The separation is observed within a two-inlet, five-outlet microfluidic network, designed to allow mixtures of active (ones that catalyze substrate turnover) and inactive (ones that do not catalyze substrate turnover) enzymes, labeled with different fluorophores, to flow through one of the inlets. Substrate solution prepared in phosphate buffer was introduced through the other inlet of the device at the same flow rate. The steady-state concentration profiles of the enzymes were obtained at specific positions within the outlets of the microchannel using fluorescence microscopy. In the presence of a substrate concentration gradient, active enzyme molecules migrated preferentially toward the substrate channel. The excess migration of the active enzyme molecules was quantified in terms of an enrichment coefficient. Experiments were carried out with different pairs of enzymes. Coupling the physics of laminar flow of liquid and molecular diffusion, multiphysics simulations were carried out to estimate the extent of the chemotactic separation. Our results show that, with appropriate microfluidic arrangement, molecular chemotaxis leads to spontaneous separation of active enzyme molecules from their inactive counterparts of similar charge and size.

Enzymatically induced motion at nano- and micro-scales

In contrast to adenosine triphosphate (ATP)-dependent motor enzymes, other enzymes are little-known as "motors" or "pumps", that is, for their ability to induce motion. The enhanced diffusive movement of enzyme molecules, the self-propulsion of enzyme-based nanomotors, and liquid pumping with enzymatic micropumps were indeed only recently reported. Enzymatically induced motion can be achieved in mild conditions and without the use of external fields. It is thus better suited for use in living systems (from single-cell to whole-body) than most other ways to achieve motion at small scales. Enzymatically induced motion is thus not only new but also important. Therefore, the present work reviews the most significant discoveries in enzymatically induced motion. As we will learn, freely diffusing enzymes enhance their diffusive movement by nonreciprocal conformational changes which parallel their catalytic cycles. Meanwhile, enzyme-modified nano- and micro-objects turn chemical energy into kinetic energy through mechanisms such as bubble recoil propulsion, self-electrophoresis, and self-diffusiophoresis. Enzymatically induced motion of small objects ranges from enhanced diffusive movement to directed motion at speeds as high as 1 cm s(-1). In spite of the progress made in understanding how the energy of enzyme reactions is turned into motion, most enzymatically powered devices remain inefficient and need improvements before we will witness their application in real world environments.

Self-powered enzyme micropumps

Non-mechanical nano- and microscale pumps that function without the aid of an external power source and provide precise control over the flow rate in response to specific signals are needed for the development of new autonomous nano- and microscale systems. Here we show that surface-immobilized enzymes that are independent of adenosine triphosphate function as self-powered micropumps in the presence of their respective substrates. In the four cases studied (catalase, lipase, urease and glucose oxidase), the flow is driven by a gradient in fluid density generated by the enzymatic reaction. The pumping velocity increases with increasing substrate concentration and reaction rate. These rechargeable pumps can be triggered by the presence of specific analytes, which enables the design of enzyme-based devices that act both as sensor and pump. Finally, we show proof-of-concept enzyme-powered devices that autonomously deliver small molecules and proteins in response to specific chemical stimuli, including the release of insulin in response to glucose.

DNA polymerase as a molecular motor and pump

DNA polymerase is responsible for synthesizing DNA, a key component in the running of biological machinery. Using fluorescence correlation spectroscopy, we demonstrate that the diffusive movement of a molecular complex of DNA template and DNA polymerase enhances during nucleotide incorporation into the growing DNA template. The diffusion coefficient of the complex also shows a strong dependence on its inorganic cofactor, Mg2+ ions. When exposed to gradients of either nucleotide or cofactor concentrations, an ensemble of DNA polymerase complex molecules shows collective movement toward regions of higher concentrations. By immobilizing the molecular complex on a patterned gold surface, we demonstrate the fabrication of DNA polymerase-powered fluid pumps. These miniature pumps are capable of transporting fluid and tracer particles in a directional manner with the pumping speed increasing in the presence of the cofactor. The role of DNA polymerase as a micropump opens up avenues for designing miniature fluid pumps using enzymes as engines.

A catalytically driven organometallic molecular motor

We have observed by NMR spectroscopy that the diffusive movement of a ruthenium-based Grubbs' catalyst increases during ring-closing metathesis as a function of the substrate concentration. This is one of the smallest single molecule motors to exhibit catalytically driven motion.