Single-Enzyme Kinetics of CALB-Catalyzed Hydrolysis

Integrating Enzymes with Supramolecular Polymers for Recyclable Photobiocatalytic Catalysis

Chemical modifications of enzymes excel in the realm of enzyme engineering due to its directness, robustness, and efficiency; however, challenges persist in devising versatile and effective strategies. In this study, we introduce a supramolecular modification methodology that amalgamates a supramolecular polymer with Candida antarctica lipase B (CalB) to create supramolecular enzymes (SupEnzyme). This approach features the straightforward preparation of a supramolecular amphiphilic polymer (β-CD@SMA), which was subsequently conjugated to the enzyme, resulting in a SupEnzyme capable of self-assembly into supramolecular nanoparticles. The resulting SupEnzyme nanoparticles can form micron-scale supramolecular aggregates through supramolecular and electrostatic interactions with guest entities, thus enhancing catalyst recycling. Remarkably, these aggregates maintain 80 % activity after seven cycles, outperforming Novozym 435. Additionally, they can effectively initiate photobiocatalytic cascade reactions using guest photocatalysts. As a consequence, our SupEnzyme methodology exhibits noteworthy adaptability in enzyme modification, presenting a versatile platform for various polymer, enzyme, and biocompatible catalyst pairings, with potential applications in the fields of chemistry and biology.

A minimal kinetic model for the interpretation of complex catalysis in single enzyme molecules

Multi-exponential waiting-time distribution and randomness parameter greater than unity ascribe dynamic disorder in single-enzyme catalysis corroborated to the interplay of transforming conformers [English et al., Nat. Chem. Biol., 2006, 2, 87]. The associated multi-state model of enzymatic turnovers with statically heterogeneous catalytic rates misdescribes the non-linear uprising of the randomness parameter from unity in relation to the attributes of the fall-offs of the waiting-time distribution at different substrate concentrations. To resolve this crucial issue, we first employ a comprehensive stochastic reaction scenario and further rationalize and work out the minimal indispensable dynamic-disorder model that ensures the foregoing relationship upon comparison with the data. We elucidate that specific disregard for the transition rate coefficients in the multi-state model on account of the especially slow conformational transitions is the underlying reason for not achieving interrelation between the observables.

Dynamic single-molecule sensing by actively tuning binding kinetics for ultrasensitive biomarker detection

SignificanceThe detection of low-abundance molecular biomarkers is key to the liquid-biopsy-based disease diagnosis. Existing methods are limited by the affinity and specificity of recognition probes and the mass transportation of analyte molecules onto the sensor surfaces, resulting in insufficient sensitivity and long assay time. This work establishes a rapid and ultrasensitive approach by actively tuning binding kinetics and accelerating the mass transportation via nanoparticle micromanipulations. This is significant because it permits extremely sensitive measurements within clinically acceptable assay time. It is incubation-free, washing-free, and compatible with low- and high-affinity probes.

Microchamber-Free Digital Flow Cytometric Analysis of T4 Polynucleotide Kinase Phosphatase Based on Single-Enzyme-to-Single-Bead Space-Confined Reaction

Digital bioassays have attracted extensive attention in biomedical applications due to their ultrahigh sensitivity. However, traditional digital bioassays require numerous microchambers such as droplets or microwells, which restricts their application scope. Herein, we propose a microchamber-free flow cytometric method for the digital quantification of T4 polynucleotide kinase phosphatase (T4 PNKP) based on an unprecedented phenomenon that each T4 PNKP molecule-catalyzed reaction can be spatially self-confined on a single microbead, which ultimately enables the one-target-to-one-fluorescence-positive microbead digital signal transduction. The digital signal-readout mode can clearly detect T4 PNKP concentrations as low as 1.28 × 10^-10 U/μL, making it most sensitive method to date. Significantly, T4 PNKP can be specifically distinguished from other phosphatases and nucleases in complex samples by digitally counting the fluorescence-positive microbeads, which cannot be realized by traditional bulk measurement-based methods. Taking advantage of the novel space-confined enzymatic feature of T4 PNKP, this digital mechanism can use T4 PNKP as the enzyme label to fabricate digital sensing systems toward various biomolecules such as digital enzyme-linked immunosorbent assay (ELISA). Therefore, this work not only enlarges the toolbox for high-sensitivity biomolecule detection but also opens new gates to fabricate next-generation digital assays.

Sensing Enzyme Activation Heat Capacity at the Single-Molecule Level Using Gold-Nanorod-Based Optical Whispering Gallery Modes

Here, we report a label-free gold nanoparticle-based single-molecule optical platform to study the immobilization, activity, and thermodynamics of single enzymes. The sensor uses plasmonic gold nanoparticles coupled to optical whispering gallery modes (WGMs) to probe enzyme conformational dynamics during turnover at a microsecond time resolution. Using a glucosidase enzyme as the model system, we explore the temperature dependence of the enzyme turnover at the single-molecule (SM) level. A recent physical model for understanding enzyme temperature dependencies (macromolecular rate theory; MMRT) has emerged as a powerful tool to study the relationship between enzyme turnover and thermodynamics. Using WGMs, SM enzyme measurements enable us to accurately track turnover as a function of conformational changes and therefore to quantitatively probe the key feature of the MMRT model, the activation heat capacity, at the ultimate level of SM. Our data shows that WGMs are extraordinarily sensitive to protein conformational change and can discern both multiple steps with turnover as well as microscopic conformational substates within those steps. The temperature dependence studies show that the MMRT model can be applied to a range of steps within turnover at the SM scale that is associated with conformational change. Our study validates the notion that MMRT captures differences in dynamics between states. The WGM sensors provide a platform for the quantitative analysis of SM activation heat capacity, applying MMRT to the label-free sensing of microsecond substates of active enzymes.

Single enzyme electroanalysis

Traditional studies of enzymatic activity rely on the combined kinetics of millions of enzyme molecules to produce a product, an experimental approach that may wash out heterogeneities that exist between individual enzymes. Evaluating these properties on an enzyme-by-enzyme basis represents an unambiguous means of elucidating heterogeneities; however, the quantification of enzymatic activity at the single-enzyme level is fundamentally limited by the maximum catalytic rate, k_cat, inherent to a given enzyme. For electrochemical methods measuring current, single enzymes must turn over greater than 10⁷ molecules per second to produce a measurable signal on the order of 10^-12 A. Enzymes with this capability are extremely rare in nature, with typical k_cat values for biologically relevant enzymes falling between 1 and 10 000 s^-1. Thus, clever amplification strategies are necessary to electrochemically detect the vast majority of enzymes. This review details the progress toward the electroanalytical detection and evaluation of single enzyme kinetics largely focused on the nanoimpact method, a chronoamperometric detection strategy that monitors the change in the current-time profile associated with stochastic collisions of freely diffusing entities (e.g., enzymes) onto a microelectrode or nanoelectrode surface. We discuss the experimental setups and methods developed in the last decade toward the quantification of single molecule enzymatic rates. Special emphasis is given to the limitations of measurement science in the observation of single enzyme activity and feasible methods of signal amplification with reasonable bandwidth.

Direct observation of Thermomyces lanuginosus lipase diffusional states by Single Particle Tracking and their remodeling by mutations and inhibition

Lipases are interfacially activated enzymes that catalyze the hydrolysis of ester bonds and constitute prime candidates for industrial and biotechnological applications ranging from detergent industry, to chiral organic synthesis. As a result, there is an incentive to understand the mechanisms underlying lipase activity at the molecular level, so as to be able to design new lipase variants with tailor-made functionalities. Our understanding of lipase function primarily relies on bulk assay averaging the behavior of a high number of enzymes masking structural dynamics and functional heterogeneities. Recent advances in single molecule techniques based on fluorogenic substrate analogues revealed the existence of lipase functional states, and furthermore so how they are remodeled by regulatory cues. Single particle studies of lipases on the other hand directly observed diffusional heterogeneities and suggested lipases to operate in two different modes. Here to decipher how mutations in the lid region controls Thermomyces lanuginosus lipase (TLL) diffusion and function we employed a Single Particle Tracking (SPT) assay to directly observe the spatiotemporal localization of TLL and rationally designed mutants on native substrate surfaces. Parallel imaging of thousands of individual TLL enzymes and HMM analysis allowed us to observe and quantify the diffusion, abundance and microscopic transition rates between three linearly interconverting diffusional states for each lipase. We proposed a model that correlate diffusion with function that allowed us to predict that lipase regulation, via mutations in lid region or product inhibition, primarily operates via biasing transitions to the active states.

Renaissance Distribution for Statistically Failed Experiments

Much of the experimental data, especially in life sciences, is considered to be useless if it demonstrates a large standard deviation from the mean value. The Renaissance distribution, as presented in this study, allows one to extract true values from such statistical data with large noise. To obtain proof of the Renaissance distribution, high-throughput synthesis of deep substitutions for a target amino acid sequence was performed, and the known epitope was identified in assay with human serum antibodies. In addition, the Renaissance distribution was shown to approach the epitope affinity maturation by the deep alanine substitution. The Renaissance distribution may have an impact in the development of novel specific drugs.

Plasmon-Enhanced Single-Molecule Enzymology

We present a numerical study on plasmon-enhanced single-molecule enzymology. We combine Brownian dynamics and electromagnetic simulations to calculate the enhancement of fluorescence signals of fluorogenic substrate converted by an enzyme conjugated to a plasmonic particle. We simulate the Brownian motion of a fluorescent product away from the active site of the enzyme, and calculate the photon detection rate taking into account modifications of the excitation and emission processes by coupling to the plasmon. We show that plasmon enhancement can boost the signal-to-noise ratio (SNR) of single turnovers by up to 100 fold compared to confocal microscopy. This enhancement factor is a trade-off between the reduced residence time in the near-field of the particle, and the enhanced emission intensity due to coupling to the plasmon. The enhancement depends on the size, shape and material of the particle and the photophysical properties of the fluorescent product. Our study provides guidelines on how to enhance the SNR of single-molecule enzyme studies and may aid in further understanding and quantifying static and dynamic heterogeneity.

Direct observation of multiple conformational states in Cytochrome P450 oxidoreductase and their modulation by membrane environment and ionic strength

Cytochrome P450 oxidoreductase (POR) is the primary electron donor in eukaryotic cytochrome P450 (CYP) containing systems. A wealth of ensemble biophysical studies of Cytochrome P450 oxidoreductase (POR) has reported a binary model of the conformational equilibrium directing its catalytic efficiency and biomolecular recognition. In this study, full length POR from the crop plant Sorghum bicolor was site-specifically labeled with Cy3 (donor) and Cy5 (acceptor) fluorophores and reconstituted in nanodiscs. Our single molecule fluorescence resonance energy transfer (smFRET) burst analyses of POR allowed the direct observation and quantification of at least three dominant conformational sub-populations, their distribution and occupancies. Moreover, the state occupancies were remodeled significantly by ionic strength and the nature of reconstitution environment, i.e. phospholipid bilayers (nanodiscs) composed of different lipid head group charges vs. detergent micelles. The existence of conformational heterogeneity in POR may mediate selective activation of multiple downstream electron acceptors and association in complexes in the ER membrane.

Recent progress on single-molecule nanocatalysis based on single-molecule fluorescence microscopy

Understanding the heterogeneous catalytic properties of nanoparticles is of great significance for the development of high efficient nanocatalysts, but the intrinsic heterogeneities of nanocatalysts were always covered in traditional ensemble studies. This issue can be overcome if one can follow the catalysis of individual nanoparticles in real time. This paper mainly summarizes recent developments in single-molecule nanocatalysis at single particle level in Changchun Institute of Applied Chemistry, Chinese Academy of Sciences. These developments include the revealing of catalytic kinetics of different types (plane & edge) of surface atoms on individual Pd nanocubes, the observing of in situ deactivation of individual carbon-supported Pt nanoparticles during the electrocatalytic hydrogen-oxidation reaction, and the measurement of catalytic activation energies on single nanocatalysts for both product formation process and dissociation process, etc. These studies further indicate the advantages or unique abilities of single-molecule methods in the studies of nanocatalysis or even chemical reactions.

Chemistry at the square nanometer: reactivity at liquid/solid interfaces revealed with an STM

An overview is given of single molecule reactivity at a liquid/solid interface employing a scanning tunneling microscope.

Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm—Variational Bayes-double chain Markov model (VB-DCMM)—to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na⁺ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA.

We have developed a new algorithm to better decode single molecule data with dynamic disorder. Our new algorithm, which represents a substantial improvement over other methodologies, can detect the presence of dynamic disorder in each trajectory and quantify the kinetic characteristics of underlying energy landscape. As a model system, we applied our algorithm to the single molecule FRET time traces of H-DNA. While duplex-triplex transitions of H-DNA are conventionally interpreted in terms of two-state kinetics, slowly varying dynamic patterns corresponding to hidden internal states can also be identified from the individual time traces. Our algorithm reveals that at least 4 distinct internal states are required to correctly interpret the data.

Shedding light on protein folding, structural and functional dynamics by single molecule studies

The advent of advanced single molecule measurements unveiled a great wealth of dynamic information revolutionizing our understanding of protein dynamics and behavior in ways unattainable by conventional bulk assays. Equipped with the ability to record distribution of behaviors rather than the mean property of a population, single molecule measurements offer observation and quantification of the abundance, lifetime and function of multiple protein states. They also permit the direct observation of the transient and rarely populated intermediates in the energy landscape that are typically averaged out in non-synchronized ensemble measurements. Single molecule studies have thus provided novel insights about how the dynamic sampling of the free energy landscape dictates all aspects of protein behavior; from its folding to function. Here we will survey some of the state of the art contributions in deciphering mechanisms that underlie protein folding, structural and functional dynamics by single molecule fluorescence microscopy techniques. We will discuss a few selected examples highlighting the power of the emerging techniques and finally discuss the future improvements and directions.

Enzyme molecules in solitary confinement

Large arrays of homogeneous microwells each defining a femtoliter volume are a versatile platform for monitoring the substrate turnover of many individual enzyme molecules in parallel. The high degree of parallelization enables the analysis of a statistically representative enzyme population. Enclosing individual enzyme molecules in microwells does not require any surface immobilization step and enables the kinetic investigation of enzymes free in solution. This review describes various microwell array formats and explores their applications for the detection and investigation of single enzyme molecules. The development of new fabrication techniques and sensitive detection methods drives the field of single molecule enzymology. Here, we introduce recent progress in single enzyme molecule analysis in microwell arrays and discuss the challenges and opportunities.

Resonant plasmonic enhancement of single-molecule fluorescence by individual gold nanorods

Enhancing the fluorescence of a weak emitter is important to further extend the reach of single-molecule fluorescence imaging to many unexplored systems. Here we study fluorescence enhancement by isolated gold nanorods and explore the role of the surface plasmon resonance (SPR) on the observed enhancements. Gold nanorods can be cheaply synthesized in large volumes, yet we find similar fluorescence enhancements as literature reports on lithographically fabricated nanoparticle assemblies. The fluorescence of a weak emitter, crystal violet, can be enhanced more than 1000-fold by a single nanorod with its SPR at 629 nm excited at 633 nm. This strong enhancement results from both an excitation rate enhancement of ∼130 and an effective emission enhancement of ∼9. The fluorescence enhancement, however, decreases sharply when the SPR wavelength moves away from the excitation laser wavelength or when the SPR has only a partial overlap with the emission spectrum of the fluorophore. The reported measurements of fluorescence enhancement by 11 nanorods with varying SPR wavelengths are consistent with numerical simulations.

A single molecule perspective on the functional diversity of in vitro evolved β-glucuronidase

The mechanisms that drive the evolution of new enzyme activity have been investigated by comparing the kinetics of wild-type and in vitro evolved β-glucuronidase (GUS) at the single molecule level. Several hundred single GUS molecules were separated in large arrays of 62,500 ultrasmall reaction chambers etched into the surface of a fused silica slide to observe their individual substrate turnover rates in parallel by fluorescence microscopy. Individual GUS molecules feature long-lived but divergent activity states, and their mean activity is consistent with classic Michaelis-Menten kinetics. The large number of single molecule substrate turnover rates is representative of the activity distribution within an entire enzyme population. Partially evolved GUS displays a much broader activity distribution among individual enzyme molecules than wild-type GUS. The broader activity distribution indicates a functional division of work between individual molecules in a population of partially evolved enzymes that-as so-called generalists-are characterized by their promiscuous activity with many different substrates.

INSIGHTS IN ENZYME FUNCTIONAL DYNAMICS AND ACTIVITY REGULATION BY SINGLE MOLECULE STUDIES

The advent of advanced single molecule measurements heralded the arrival of a wealth of dynamic information revolutionizing our understanding of protein dynamics and behavior in ways not deducible by conventional bulk assays. They offered the direct observation and quantification of the abundance and life time of multiple states and transient intermediates in the energy landscape that are typically averaged out in non-synchronized ensemble measurements, thus providing unprecedented insights into complex biological processes. Here we survey the current state of the art in single-molecule fluorescence microscopy methodology for studying the mechanism of enzymatic activity and the insights on protein functional dynamics. We will initially discuss the strategies employed to date, their limitations and possible ways to overcome them, and finally how single enzyme kinetics can advance our understanding on mechanisms underlying function and regulation of proteins.

[Formula: see text]Special Issue Comment: This review focuses on functional dynamics of individual enzymes and is related to the review on ion channels by Lu,44 the reviews on mathematical treatment of Flomenbom45 and Sach et al.,46 and review on FRET by Ruedas-Rama et al.41

MATHEMATICAL TREATMENTS THAT SOLVE SINGLE MOLECULES

In this article, we talk about the ways that scientists can solve single molecule trajectories. Solving single molecules, that is, finding the model from the data, is complicated at least as much as measuring single molecules. We must filter the noise and take care of every step in the analysis when constructing the most accurate model from the data. Here, we present valuable solutions. Ways that solve clean discrete data are first presented. We review here our reduced dimensions forms (RDFs): unique models that are canonical forms of discrete data, and the statistical and numerical toolbox that builds a RDF from finite, clean, two-state data. We then review our most recent filter that "tackles" the noise when measuring two state noisy photon trajectories. The filter is a numerical algorithm with various special statistical treatments that is based on a general likelihood function that we have developed recently. We show the strengths of the filter (also over other approaches) and talk about its various new variants. This filter (with minor adjustments) can solve the noise in any discrete state trajectories, yet, extensions are needed in "tackling" the noise from other data, e.g. continuous data. Only the combined procedures enable creating the most accurate model from noisy discrete trajectories from single molecules. These concepts and methods (with adjustments) are valuable also when solving continuous trajectories and fluorescence resonance energy transfer trajectories. We also present a set of simple methods that can help any scientist with treating the trajectory perhaps encouraging applying the involved methods. The involved methods will appear in software that we are developing now, helping therefore the experimentalists utilizing these methods on real data. Comparisons with other known methods in this field are made.

[Formula: see text]Special Issue Comment: This article about mathematical treatments when solving single molecules is related to the reviews in this Special Issue about measuring enzymes67 and about FRET experiments2 and about the software QUB.6

Elucidating the relationship between substrate and inhibitor binding to the active sites of tetrameric β-galactosidase

The stochastic binding and release of two different inhibitors from a tetrameric enzyme is described at the single molecule level.

Breaking the concentration limit of optical single-molecule detection

Over the last decade, single-molecule detection has been successfully utilized in the life sciences and materials science. Yet, single-molecule measurements only yield meaningful results when working in a suitable, narrow concentration range. On the one hand, diffraction limits the minimal size of the observation volume in optical single-molecule measurements and consequently a sample must be adequately diluted so that only one molecule resides within the observation volume. On the other hand, at ultra-low concentrations relevant for sensing, the detection volume has to be increased in order to detect molecules in a reasonable timespan. This in turn results in the loss of an optimal signal-to-noise ratio necessary for single-molecule detection. This review discusses the requirements for effective single-molecule fluorescence applications, reflects on the motivation for the extension of the dynamic concentration range of single-molecule measurements and reviews various approaches that have been introduced recently to solve these issues. For the high-concentration limit, we identify four promising strategies including molecular confinement, optical observation volume reduction, temporal separation of signals and well-conceived experimental designs that specifically circumvent the high concentration limit. The low concentration limit is addressed by increasing the measurement speed, parallelization, signal amplification and preconcentration. The further development of these ideas will expand our possibilities to interrogate research questions with the clarity and precision provided only by the single-molecule approach.

Exploration of the spontaneous fluctuating activity of single enzyme molecules

Single enzyme molecules display inevitable, stochastic fluctuations in their catalytic activity. In metabolism, for instance, the stochastic activity of individual enzymes is averaged out due to their high copy numbers per single cell. However, many processes inside cells rely on single enzyme activity, such as transcription, replication, translation, and histone modifications. Here we introduce the main theoretical concepts of stochastic single-enzyme activity starting from the Michaelis-Menten enzyme mechanism. Next, we discuss stochasticity of multi-substrate enzymes, of enzymes and receptors with multiple conformational states and finally, how fluctuations in receptor activity arise from fluctuations in signal concentration. This paper aims to introduce the exciting field of single-molecule enzyme kinetics and stochasticity to a wider audience of biochemists and systems biologists.

Single molecule kinetics of horseradish peroxidase exposed in large arrays of femtoliter-sized fused silica chambers

Large arrays of femtoliter-sized chambers were etched into the surface of fused silica slides to enclose and observe hundreds of single horseradish peroxidase (HRP) molecules in parallel. Individual molecules of HRP oxidize the fluorogenic substrate Amplex Red to fluorescent resorufin in separate chambers, which was monitored by fluorescence microscopy. Photooxidation of Amplex Red and photobleaching of resorufin have previously limited the analysis of HRP in femtoliter arrays. We have strongly reduced these effects by optimizing the fluorescence excitation and detection scheme to yield accurate single molecule substrate turnover rates. We demonstrate the presence of long-lived kinetic states of single HRP molecules that are individually different for each molecule in the array. The large number of molecules investigated in parallel provides excellent statistics on the activity distribution in the enzyme population, which is similar to that reported for other enzymes such as β-galactosidase. We have further confirmed that the product formation of HRP in femtoliter chambers is 10-fold lower than that in the bulk solution due to the particular two-step redox reaction mechanism of HRP.

Single-enzyme analysis in a droplet-based micro- and nanofluidic system

The kinetic activity of individual enzyme molecules was determined in aqueous droplets generated in a nano- and microfluidic device. To avoid high background noise, the enzyme and substrate solution was confined into femtoliter carriers, achieving high product concentrations from single-molecule encapsulation. The tiny droplets (φ ~ 2.5-3 μm) generated from this fluidic system were highly monodisperse, beneficial for an analysis of single enzyme activity. The method presented here allows to follow large numbers of individual droplets over time. The instrumental requirements are furthermore modest, since the small droplet size allows to use of standard microscope and standard Pyrex glass chips as well as the use of relatively high enzyme concentrations (nM range) for single molecule encapsulation.

In situ click chemistry: a powerful means for lead discovery

Combinatorial chemistry and parallel synthesis are important and regularly applied tools for lead identification and optimisation, although they are often accompanied by challenges related to the efficiency of library synthesis and the purity of the compound library. In the last decade, novel means of lead discovery approaches have been investigated where the biological target is actively involved in the synthesis of its own inhibitory compound. These fragment-based approaches, also termed target-guided synthesis (TGS), show great promise in lead discovery applications by combining the synthesis and screening of libraries of low molecular weight compounds in a single step. Of all the TGS methods, the kinetically controlled variant is the least well known, but it has the potential to emerge as a reliable lead discovery method. The kinetically controlled TGS approach, termed in situ click chemistry, is discussed in this article.

Stochastic mapping of first order reaction networks: a systematic comparison of the stochastic and deterministic kinetic approaches

Stochastic maps are developed and used for first order reaction networks to decide whether the deterministic kinetic approach is appropriate for a certain evaluation problem or the use of the computationally more demanding stochastic approach is inevitable. On these maps, the decision between the two approaches is based on the standard deviation of the expectation of detected variables: when the relative standard deviation is larger than 1%, the use of the stochastic method is necessary. Four different systems are considered as examples: the irreversible first order reaction, the reversible first order reaction, two consecutive irreversible first order reactions, and the unidirectional triangle reaction. Experimental examples are used to illustrate the practical use of the theoretical results. It is shown that the maps do not only depend on particle numbers, but the influence of parameters such as time, rate constants, and the identity of the detected target variable is also an important factor.

Monogalactopyranosides of fluorescein and fluorescein methyl ester: synthesis, enzymatic hydrolysis by biotnylated β-galactosidase, and determination of translational diffusion coefficient

Fluorescein monoglycosides (D-galactopyranoside (FMG) and D-glucopyranoside) and their methyl ester (MFMG) have been prepared from acetobromoglucose/galactose and fluorescein methyl ester in good yields. Enzymatic hydrolysis experiments (using biotinylated β-galactosidase) of the galacto derivatives have been performed and kinetic parameters were calculated. A 15-20 times increase of the fluorescence intensity has been observed during the hydrolysis. A linear increase of fluorescence has been noted at short time and low concentration of substrate, making these compounds useful and sensitive probes for galactosidases. The magnitude of the Michaelis-Menten constant (K(m)) value for MFMG is higher than that of FMG suggesting a possible conformational change of the fluorogenic substrate. K(m) value for biotinylated β-Gal with FMG is lower than that for the native enzyme. This observation indicates higher substrate affinity of the biotinylated enzyme in comparison to the native enzyme. Translational diffusion coefficients have been measured, for both fluorogenic substrates and both the products, employing fluorescence correlation spectroscopy. Translational diffusion coefficients for fluorogenic substrates and the enzymatic hydrolysis products have been measured to be similar, in the range of 3.5-4.5×10(-10) m(2) s(-1). Thus an enhancement or retardation of the enzymatic kinetics due to difference in translational mobility of substrate and product is not that apparent.

Allosteric inhibition of individual enzyme molecules trapped in lipid vesicles

Enzymatic inhibition by product molecules is an important and widespread phenomenon. We describe an approach to study product inhibition at the single-molecule level. Individual HRP molecules are trapped within surface-tethered lipid vesicles, and their reaction with a fluorogenic substrate is probed. While the substrate readily penetrates into the vesicles, the charged product (resorufin) gets trapped and accumulates inside the vesicles. Surprisingly, individual enzyme molecules are found to stall when a few tens of product molecules accumulate. Bulk enzymology experiments verify that the enzyme is noncompetitively inhibited by resorufin. The initial reaction velocity of individual enzyme molecules and the number of product molecules required for their complete inhibition are broadly distributed and dynamically disordered. The two seemingly unrelated parameters, however, are found to be substantially correlated with each other in each enzyme molecule and over long times. These results suggest that, as a way to counter disorder, enzymes have evolved the means to correlate fluctuations at structurally distinct functional sites.