Functional conformational motions in the turnover cycle of cholesterol oxidase

Aqueous ionic liquids redistribute local enzyme stability via long-range perturbation pathways

Ionic liquids (IL) and aqueous ionic liquids (aIL) are attractive (co-)solvents for biocatalysis due to their unique properties. On the other hand, the incubation of enzymes in IL or aIL often reduces enzyme activity. Recent studies proposed various aIL-induced effects to explain the reduction, classified as direct effects, e.g., local dehydration or competitive inhibition, and indirect effects, e.g., structural perturbations or disturbed catalytic site integrity. However, the molecular origin of indirect effects has largely remained elusive. Here we show by multi-μs long molecular dynamics simulations, free energy computations, and rigidity analyses that aIL favorably interact with specific residues of Bacillus subtilis Lipase A (BsLipA) and modify the local structural stability of this model enzyme by inducing long-range perturbations of noncovalent interactions. The perturbations percolate over neighboring residues and eventually affect the catalytic site and the buried protein core. Validation against a complete experimental site saturation mutagenesis library of BsLipA (3620 variants) reveals that the residues of the perturbation pathways are distinguished sequence positions where substitutions highly likely yield significantly improved residual activity. Our results demonstrate that identifying these perturbation pathways and specific IL ion-residue interactions there effectively predicts focused variant libraries with improved aIL tolerance.

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.

Insulin fibrillation: toward strategies for attenuating the process

The environmental factors affecting the rate of insulin fibrillation. The factors are representative.

Modeling of Nanomachine/Micromachine Crowds: Interplay between the Internal State and Surroundings

The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as enzymes. The working cycles of these machines are often coupled with their internal motion (conformational changes). In the crowded environment of a cell, motion interference between neighboring molecules is not negligible, and this interference can affect the reaction dynamics through machine operation. To simulate such a situation, we propose a reaction-diffusion model consisting of particles whose shape depends on an internal state variable, for crowds of nano- to micromachines. The interference between nearby particles is naturally introduced through excluded volume repulsion. In the simulations, we observed segregation and flow-like patterns enhanced by crowding out of relevant molecules, as well as molecular synchronization waves and phase transitions. The presented model is simple and extensible for diverse molecular machinery and may serve as a framework to study the interplay between the mechanical stress/strain network and the chemical reaction network in the cell. Applications to more macroscopic systems, e.g., crowds of cells, are also discussed.

Correlating Structural and Functional Heterogeneity of Immobilized Enzymes

Many nanobiotechnology applications rely on stable and efficient integration of functional biomacromolecules with synthetic nanomaterials. Unfortunately, the reasons for the ubiquitous loss of activity of immobilized enzymes remain poorly understood due to the difficulty in distinguishing between distinct molecular-level mechanisms. Here, we employ complementary single-molecule fluorescence methods that independently measure the impact of immobilization on the structure and function ( i. e., substrate binding kinetics) of nitroreductase (NfsB). Stochastic statistical modeling methods were used to unambiguously quantify the effects of immobilized NfsB structural dynamics on function, allowing us to explicitly separate effects due to conformation and accessibility. Interestingly, we found that nonspecifically tethered NfsB exhibited enhanced stability compared to site-specifically tethered NfsB; however, the folded state of site-specifically tethered NfsB had faster substrate binding rates, suggesting improved active site accessibility. This demonstrated an unexpected intrinsic trade-off associated with competing bioconjugation methods, suggesting that it may be necessary to balance conformational stability versus active site accessibility. This nuanced view of the impact of immobilization will facilitate a rational approach to the integration of enzymes with synthetic nanomaterials.

Enzyme Kinetics in Femtoliter Arrays

Over the last decade, femtoliter arrays have been used as a simple and robust way to encapsulate and monitor the kinetics of single enzyme molecules. Encapsulating individual enzyme molecules within a femtoliter-sized reaction chamber does not require immobilization of the enzyme molecules or fluorescent tagging of the enzyme molecules, which offers the unique advantage of observing unmodified single enzyme molecules free in solution. Several fascinating details about enzyme kinetics have been revealed using these femtoliter arrays, which were unattainable from traditional ensemble experiments. Here, we discuss various considerations to take into account when developing single-molecule enzyme assays in femtoliter arrays and the advantages and disadvantages of various protocols.

Adaptive Heat Engine

A major limitation of many heat engines is that their functioning demands on-line control and/or an external fitting between the environmental parameters (e.g., temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence, no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that make the bath temperatures closer. We determine resources of adaptation and relate them to the prior information available about the environment.

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.

Probing protein multidimensional conformational fluctuations by single-molecule multiparameter photon stamping spectroscopy

Conformational motions of proteins are highly dynamic and intrinsically complex. To capture the temporal and spatial complexity of conformational motions and further to understand their roles in protein functions, an attempt is made to probe multidimensional conformational dynamics of proteins besides the typical one-dimensional FRET coordinate or the projected conformational motions on the one-dimensional FRET coordinate. T4 lysozyme hinge-bending motions between two domains along α-helix have been probed by single-molecule FRET. Nevertheless, the domain motions of T4 lysozyme are rather complex involving multiple coupled nuclear coordinates and most likely contain motions besides hinge-bending. It is highly likely that the multiple dimensional protein conformational motions beyond the typical enzymatic hinged-bending motions have profound impact on overall enzymatic functions. In this report, we have developed a single-molecule multiparameter photon stamping spectroscopy integrating fluorescence anisotropy, FRET, and fluorescence lifetime. This spectroscopic approach enables simultaneous observations of both FRET-related site-to-site conformational dynamics and molecular rotational (or orientational) motions of individual Cy3-Cy5 labeled T4 lysozyme molecules. We have further observed wide-distributed rotational flexibility along orientation coordinates by recording fluorescence anisotropy and simultaneously identified multiple intermediate conformational states along FRET coordinate by monitoring time-dependent donor lifetime, presenting a whole picture of multidimensional conformational dynamics in the process of T4 lysozyme open-close hinge-bending enzymatic turnover motions under enzymatic reaction conditions. By analyzing the autocorrelation functions of both lifetime and anisotropy trajectories, we have also observed the dynamic and static inhomogeneity of T4 lysozyme multidimensional conformational fluctuation dynamics, providing a fundamental understanding of the enzymatic reaction turnover dynamics associated with overall enzyme as well as the specific active-site conformational fluctuations that are not identifiable and resolvable in the conventional ensemble-averaged experiment.

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

Electrochemical tunnelling sensors and their potential applications

The quantum-mechanical tunnelling effect allows charge transport across nanometre-scale gaps between conducting electrodes. Application of a voltage between these electrodes leads to a measurable tunnelling current, which is highly sensitive to the gap size, the voltage applied and the medium in the gap. Applied to liquid environments, this offers interesting prospects of using tunnelling currents as a sensitive tool to study fundamental interfacial processes, to probe chemical reactions at the single-molecule level and to analyse the composition of biopolymers such as DNA, RNA or proteins. This offers the possibility of a new class of sensor devices with unique capabilities.

Probing single-molecule enzyme active-site conformational state intermittent coherence

The relationship between protein conformational dynamics and enzymatic reactions has been a fundamental focus in modern enzymology. Using single-molecule fluorescence resonance energy transfer (FRET) with a combined statistical data analysis approach, we have identified the intermittently appearing coherence of the enzymatic conformational state from the recorded single-molecule intensity-time trajectories of enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in catalytic reaction. The coherent conformational state dynamics suggests that the enzymatic catalysis involves a multistep conformational motion along the coordinates of substrate-enzyme complex formation and product releasing, presenting as an extreme dynamic behavior intrinsically related to the time bunching effect that we have reported previously. The coherence frequency, identified by statistical results of the correlation function analysis from single-molecule FRET trajectories, increases with the increasing substrate concentrations. The intermittent coherence in conformational state changes at the enzymatic reaction active site is likely to be common and exist in other conformation regulated enzymatic reactions. Our results of HPPK interaction with substrate support a multiple-conformational state model, being consistent with a complementary conformation selection and induced-fit enzymatic loop-gated conformational change mechanism in substrate-enzyme active complex formation.

Michaelis-Menten equation and detailed balance in enzymatic networks

Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis-Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis-Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of the substrate dependence in the mean turnover time of complex enzymatic reactions and identify detailed balance (i.e., the lack of unbalanced conformational current) as a sufficient condition for the Michaelis-Menten equation to describe the substrate concentration dependence of the turnover rate in an enzymatic network. This prediction can be verified in single-molecule event-averaged measurements using the recently proposed signatures of detailed balance violations. The finding helps analyze recent single-molecule studies of enzymatic networks and can be applied to other external variables, such as force-dependence and voltage-dependence.

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.

Seeing the forest for the trees: fluorescence studies of single enzymes in the context of ensemble experiments

Enzymes are remarkable molecular machines that make many difficult biochemical reactions possible under mild biological conditions with incredible precision and efficiency. Our understanding of the working principles of enzymes, however, has not reached the level where one can readily deduce the mechanism and the catalytic rates from an enzyme's structure. Resolving the dynamics that relate the three-dimensional structure of an enzyme to its function has been identified as a key issue. While still challenging to implement, single-molecule techniques have emerged as one of the most useful methods for studying enzymes. We review enzymes studied using single-molecule fluorescent methods but placing them in the context of results from other complementary experimental work done on bulk samples. This review primarily covers three enzyme systems--flavoenzymes, dehydrofolate reductase, and adenylate kinase--with additional enzymes mentioned where appropriate. When the single-molecule experiments are discussed together with other methods aiming at the same scientific question, the weakness, strength, and unique contributions become clear.

Bunching effect in single-molecule T4 lysozyme nonequilibrium conformational dynamics under enzymatic reactions

The bunching effect, implying that conformational motion times tend to bunch in a finite and narrow time window, is observed and identified to be associated with substrate-enzyme complex formation in T4 lysozyme conformational dynamics under enzymatic reactions. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. On the basis of the single-molecule spectroscopic results, molecular dynamics simulation, and a random walk model analysis, multiple intermediate states have been estimated in the evolution of T4 lysozyme enzymatic reaction active complex formation (Chen, Y.; Hu, D.; Vorpagel, E. R.; Lu, H. P. Probing single-molecule T4 lysozyme conformational dynamics by intramolecular fluorescence energy transfer. J. Phys. Chem. B 2003, 107, 7947-7956). In this Article, we report progress on the analysis of the reported experimental results, and we have identified the bunching effect of the substrate-enzyme active complex formation time in T4 lysozyme enzymatic reactions. We show that the bunching effect, a dynamic behavior observed for the catalytic hinge-bending conformational motions of T4 lysozyme, is a convoluted outcome of multiple consecutive Poisson rate processes that are defined by protein functional motions under substrate-enzyme interactions; i.e., convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. We suggest that the bunching effect is likely common in protein conformational dynamics involved in conformation-gated protein functions.

Fluorescence and single molecule analysis in cell biology

An overview is presented which describes the development of fluorescence spectroscopy at the cellular level from its beginning as a quantitative tool to determine the content of cellular components to its present use. Analysis of individual biomolecules, their transport and kinetics within a single cell is now possible.

Single-biomolecule kinetics: the art of studying a single enzyme

The potential of single-enzyme studies to unravel the complex energy landscape of these polymeric catalysts is the next critical step in enzymology. From its inception in Rotman's emulsion experiments in the 1960s, the field of single-molecule enzymology has now advanced into the time-resolved age. Technological advances have enabled individual enzymatic turnover reactions to be observed with a millisecond time resolution. A number of initial studies have revealed the underlying static and dynamic disorder in the catalytic rates originating from conformational fluctuations. Although these experiments are still in their infancy, they may be able to relate the topography of the energy landscape to the biological function and regulation of enzymes. This review summarizes some of the experimental techniques and data-analysis methods that have been used to study individual enzyme molecules in search of a deeper understanding of their kinetics.

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

Cholesterol oxidase: biochemistry and structural features

Cholesterol oxidases are bifunctional flavoenzymes that catalyze the oxidation of steroid substrates which have a hydroxyl group at the 3beta position of the steroid ring system. The enzyme is found, in a wide range of bacterial species, in two forms: one with the FAD cofactor bound noncovalently to the enzyme; and one with the cofactor linked covalently to the protein. Here we discuss, compare and contrast the salient biochemical properties of the two forms of the enzyme. Specifically, the structural features are discussed that affect the redox potentials of the flavin cofactor, the chemical mechanism of substrate dehydrogenation by active-center amino acid residues, the kinetic parameters of both types of enzymes and the reactivity of reduced enzymes with molecular dioxygen. The presence of a molecular tunnel that is proposed to serve in the access of dioxygen to the active site and mechanisms of its control by a 'gate' formed by amino acid residues are highlighted.

Two-dimensional reaction free energy surfaces of catalytic reaction: effects of protein conformational dynamics on enzyme catalysis

We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

Multiple-state reactions between the epidermal growth factor receptor and Grb2 as observed by using single-molecule analysis

Phosphorylation of the cytoplasmic tyrosine residues of the epidermal growth factor receptor (EGFR) upon binding of EGF induces recognition of various intracellular signaling molecules, including Grb2. Here, the reaction kinetics between EGFR and Grb2 was analyzed by visualizing single molecules of Grb2 conjugated to the fluorophore Cy3 (Cy3-Grb2). The plasma membrane fraction was purified from human epithelial carcinoma A431 cells after stimulation with EGF and attached to coverslips. Unitary events of association and dissociation of Cy3-Grb2 on the EGFR in the membrane fraction were observed at different concentrations of Grb2 (0.1-100 nM). The dissociation kinetics could be explained by using a multiple-exponential function with a major (>90%) dissociation rate of 8 s(-1) and a few minor components, suggesting the presence of multiple bound states. In contrast, the association kinetics could be described by a stretched exponential function, suggesting the presence of multiple reaction channels from many unbound substates. Transitions between the unbound substates were also suggested. Unexpectedly, the rate of association was not proportional to the Grb2 concentration: an increase in Cy3-Grb2 concentration by a factor of 10 induced an increase in the reaction frequency approximately by a factor of three. This effect can compensate for fluctuation of the signal transduction from EGFR to Grb2 caused by variations in the expression level of Grb2 in living cells.

Time-dependent molecular memory in single voltage-gated sodium channel

Excitability in neurons is associated with firing of action potentials and requires the opening of voltage-gated sodium channels with membrane depolarization. Sustained membrane depolarization, as seen in pathophysiological conditions like epilepsy, can have profound implications on the biophysical properties of voltage-gated ion channels. Therefore, we sought to characterize the effect of sustained membrane depolarization on single voltage-gated Na+ channels. Single-channel activity was recorded in the cell-attached patch-clamp mode from the rNa(v)1.2 alpha channels expressed in CHO cells. Classical statistical analysis revealed complex nonlinear changes in channel dwell times and unitary conductance of single Na+ channels as a function of conditioning membrane depolarization. Signal processing tools like weighted wavelet Z (WWZ) and discrete Fourier transform analyses attributed a "pseudo-oscillatory" nature to the observed nonlinear variation in the kinetic parameters. Modeling studies using the hidden Markov model (HMM) illustrated significant changes in kinetic states and underlying state transition rate constants upon conditioning depolarization. Our results suggest that sustained membrane depolarization induces novel nonlinear properties in voltage-gated Na+ channels. Prolonged membrane depolarization also induced a "molecular memory" phenomenon, characterized by clusters of dwell time events and strong autocorrelation in the dwell time series similar to that reported recently for single enzyme molecules. The persistence of such molecular memory was found to be dependent on the duration of depolarization. Voltage-gated Na+ channel with the observed time-dependent nonlinear properties and the molecular memory phenomenon may determine the functional state of the channel and, in turn, the excitability of a neuron.

When does the Michaelis-Menten equation hold for fluctuating enzymes?

Enzymes are dynamic entities: both their conformation and catalytic activity fluctuate over time. When such fluctuations are relatively fast, it is not surprising that the classical Michaelis-Menten (MM) relationship between the steady-state enzymatic velocity and the substrate concentration still holds. However, recent single-molecule experiments have shown that this is the case even for an enzyme whose catalytic activity fluctuates on the 10(-4)-10 s range. The purpose of this paper is to examine various scenarios in which slowly fluctuating enzymes would still obey the MM relationship. Specifically, we consider (1) the quasi-static condition (e.g., the conformational fluctuation of the enzyme-substrate complex is much slower than binding, catalysis, and the conformational fluctuations of the free enzyme), (2) the quasi-equilibrium condition (when the substrate dissociation is much faster than catalysis, irrespective of the time scales or amplitudes of conformational fluctuations), and (3) the conformational-equilibrium condition (when the dissociation and catalytic rates depend on the conformational coordinate in the same way). For each of these scenarios, the physical meaning of the apparent Michaelis constant and catalytic rate constant is provided. Finally, as an example, the theoretical analysis of a recent single-molecule enzyme assay is considered in light of the perspectives presented in this paper.

Molecular synchronization waves in arrays of allosterically regulated enzymes

Spatiotemporal pattern formation in a product-activated enzymic reaction at high enzyme concentrations is investigated. Stochastic simulations show that catalytic turnover cycles of individual enzymes can become coherent and that complex wave patterns of molecular synchronization can develop. The analysis based on the mean-field approximation indicates that the observed patterns result from the presence of Hopf and wave bifurcations in the considered system.

Nonlinear relaxation dynamics in elastic networks and design principles of molecular machines

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well defined internal mechanical motions to various initial deformations and that these motions are robust against external perturbations. We show that this behavior is not characteristic for random elastic networks. However, special network architectures with such properties can be designed by evolutionary optimization methods. Using them, an example of an artificial elastic network, operating as a cyclic machine powered by ligand binding, is constructed.

Manipulating single enzymes by an external harmonic force

We study a Michaelis-Menten reaction for a single two-state enzyme molecule, whose transition rates between the two conformations are modulated by an harmonically oscillating external force. In particular, we obtain a range of optimal driving frequencies for changing the conformation of the enzyme, thereby controlling the enzymatic activity (i.e., product formation). This analysis demonstrates that it is, in principle, possible to obtain information about particular rates within the kinetic scheme.

Testing for Renewal and Detailed Balance Violations in Single-Molecule Blinking Processes

This paper examines methods to test one- and two-dimensional histograms for several features including the renewal properties, detailed balance violations, and experimental condition dependences. The tests are simple to implement and allow rigorous statistical determination of the existence of these kinetic features. The tests are used to determine the lower bound on the number of measurements necessary to differentiate underlying kinetic models.

Do enzymes sleep and work?

Single-enzyme studies suggest that dynamic disorder is a general characteristic of enzyme catalysis.

Synthesis and single enzyme activity of a clicked lipase–BSA hetero-dimer

Click chemistry is used to construct a novel lipase-BSA hetero-dimer, in which the latter protein acts as a foot enabling the anchoring of the enzyme onto the surface for single enzyme studies.

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited

Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.