Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer

Fast and robust two-dimensional inverse Laplace transformation of single-molecule fluorescence lifetime data

Fluorescence spectroscopy at the single-molecule scale has been indispensable for studying conformational dynamics and rare states of biological macromolecules. Single-molecule two-dimensional (2D) fluorescence lifetime correlation spectroscopy is an emerging technique that holds promise for the study of protein and nucleic acid dynamics, as the technique is 1) capable of resolving conformational dynamics using a single chromophore, 2) resolves forward and reverse transitions independently, and 3) has a dynamic window ranging from microseconds to seconds. However, the calculation of a 2D fluorescence relaxation spectrum requires an inverse Laplace transform (ILT), which is an ill-conditioned inversion that must be estimated numerically through a regularized minimization. Current methods for performing ILTs of fluorescence relaxation can be computationally inefficient, sensitive to noise corruption, and difficult to implement. Here, we adopt an approach developed for NMR spectroscopy (T1-T2 relaxometry) to perform one-dimensional (1D) and 2D-ILTs on single-molecule fluorescence spectroscopy data using singular-valued decomposition and Tikhonov regularization. This approach provides fast, robust, and easy to implement Laplace inversions of single-molecule fluorescence data. We compare this approach to the widely used maximal entropy method.

Ultrafast dynamics of fully reduced flavin in catalytic structures of thymidylate synthase ThyX

Thymidylate is a vital DNA precursor synthesized by thymidylate synthases. ThyX is a flavin-dependent thymidylate synthase found in several human pathogens and absent in humans, which makes it a potential target for antimicrobial drugs. This enzyme methylates the 2'-deoxyuridine 5'-monophosphate (dUMP) to 2'-deoxythymidine 5'-monophosphate (dTMP) using a reduced flavin adenine dinucleotide (FADH^-) as prosthetic group and (6R)-N₅,N₁₀-methylene-5,6,7,8-tetrahydrofolate (CH₂THF) as a methylene donor. Recently, it was shown that ThyX-catalyzed reaction is a complex process wherein FADH^- promotes both methylene transfer and reduction of the transferred methylene into a methyl group. Here, we studied the dynamic and photophysics of FADH^- bound to ThyX, in several substrate-binding states (no substrate, in the presence of dUMP or folate or both) by femtosecond transient absorption spectroscopy. This methodology provides valuable information about the ground-state configuration of the isoalloxazine moiety of FADH^- and the rigidity of its local environment, through spectra shape and excited-state lifetime parameters. In the absence of substrate, the environment of FADH^- in ThyX is only mildly more constrained than that of free FADH^- in solution. The addition of dUMP however narrows the distribution of ground-state configurations and increases the constraints on the butterfly bending motion in the excited state. Folate binding results in the selection of new ground-state configurations, presumably located at a greater distance from the conical intersection where excited-state decay occurs. When both substrates are present, the ground-state configuration appears on the contrary rather limited to a geometry close to the conical intersection, which explains the relatively fast excited-state decay (100 ps on the average), even if the environment of the isoalloxazine is densely packed. Hence, although the environment of the flavin is dramatically constrained, FADH^- retains a dynamic necessary to shuttle carbon from folate to dUMP. Our study demonstrates the high sensitivity of FADH^- photophysics to the constraints exerted by its immediate surroundings.

Red-Emitting Fluorophores as Local Water-Sensing Probes

Fluorescent probes are known for their ability to sense changes in their direct environment. We introduce here the idea that common red-emitting fluorophores recommended for biological labeling and typically used for simple visualization of biomolecules can also act as reporters of the water content in their first solvent sphere by a simple measurement of their fluorescence lifetime. Using fluorescence spectroscopy, we investigated the excited-state dynamics of seven commercially available fluorophores emitting between 650 and 800 nm that are efficiently quenched by H₂O. The amount of H₂O in their direct surrounding was modulated in homogeneous H₂O-D₂O mixtures or, in heterogeneous systems, by confining them into reverse micelles, by encapsulating them into host-guest complexes with cyclodextrins, or by attaching them to peptides and proteins. We found that their fluorescence properties can be rationalized in terms of the amount of H₂O in their direct surroundings, which provides a general mechanism for protein-induced fluorescence enhancements of red-emitting dyes and opens perspectives for directly counting water molecules in key biological environments or in polymers.

Time-squeezing and time-expanding transformations in harmonic force fields

A variety of real life phenomena exhibit complex time-inhomogeneous nonlinear diffusive motion in the presence of an external harmonic force. In capturing the characteristics of such dynamics, the class of Ornstein-Uhlenbeck processes, with its physical time appropriately modulated, has long been regarded as the most relevant model on the basis of its mean reversion property. In this paper, we contrast two similar, yet definitely different, time-changing mechanisms in harmonic force fields by systematically deriving and presenting a variety of key properties all at once, that is, whether or not and how those time-changing mechanisms affect the characteristics of mean-reverting diffusion through sample path properties, the marginal probability density function, the asymptotic degeneracy of increments, the stationary law, the second-order structure, and the ensemble- and time-averaged mean square displacements. Some of those properties turn out rather counter-intuitive due to, or irrespective of, possible degeneracy of time-changing mechanisms in the long run. In light of those illustrative comparisons, we examine whether such time-changing operations are worth the additional operational cost, relative to physically relevant characteristics induced, and deduce practical implications and precautions from modeling and inference perspectives, for instance, on the experimental setup involving those anomalous diffusion processes, such as the observation start time and stepsize when measuring mean square displacements, so as to preclude potentially misleading results and paradoxical interpretations.

Factors underlying asymmetric pore dynamics of disaggregase and microtubule-severing AAA+ machines

Disaggregation and microtubule-severing nanomachines from the AAA+ (ATPases associated with various cellular activities) superfamily assemble into ring-shaped hexamers that enable protein remodeling by coupling large-scale conformational changes with application of mechanical forces within a central pore by loops protruding within the pore. We probed the asymmetric pore motions and intraring interactions that support them by performing extensive molecular dynamics simulations of single-ring severing proteins and the double-ring disaggregase ClpB. Simulations reveal that dynamic stability of hexameric pores of severing proteins and of the nucleotide-binding domain 1 (NBD1) ring of ClpB, which belong to the same clade, involves a network of salt bridges that connect conserved motifs of central pore loops. Clustering analysis of ClpB highlights correlated motions of domains of neighboring protomers supporting strong interprotomer collaboration. Severing proteins have weaker interprotomer coupling and stronger intraprotomer stabilization through salt bridges involving pore loops. Distinct mechanisms are identified in the NBD2 ring of ClpB involving weaker interprotomer coupling through salt bridges formed by noncanonical loops and stronger intraprotomer coupling. Analysis of collective motions of PL1 loops indicates that the largest amplitude motions in the spiral complex of spastin and ClpB involve axial excursions of the loops, whereas for katanin they involve opening and closing of the central pore. All three motors execute primarily axial excursions in the ring complex. These results suggest distinct substrate processing mechanisms of remodeling and translocation by ClpB and spastin compared to katanin, thus providing dynamic support for the differential action of the two severing proteins. Relaxation dynamics of the distance between the PL1 loops and the center of mass of protomers reveals observation-time-dependent dynamics, leading to predicted relaxation times of tens to hundreds of microseconds on millisecond experimental timescales. For ClpB, the predicted relaxation time is in excellent agreement with the extracted time from smFRET experiments.

Accounting for the instantaneous disorder in the enzyme-substrate Michaelis complex to calculate the Gibbs free energy barrier of an enzyme reaction

Many enzyme reactions present instantaneous disorder. These dynamic fluctuations in the enzyme-substrate Michaelis complexes generate a wide range of energy barriers that cannot be experimentally observed, but that determine the measured kinetics of the reaction. These individual energy barriers can be calculated using QM/MM methods, but then the problem is how to deal with this dispersion of energy barriers to provide kinetic information. So far, the most usual procedure has implied the so-called exponential average of the energy barriers. In this paper, we discuss the foundations of this method, and we use the free energy perturbation theory to derive an alternative equation to get the Gibbs free energy barrier of the enzyme reaction. In addition, we propose a practical way to implement it. We have chosen four enzyme reactions as examples. In particular, we have studied the hydrolysis of a glycosidic bond catalyzed by the enzyme Thermus thermophilus β-glycosidase, and the mutant Y284P Ttb-gly, and the hydrogen abstraction reactions from C13 and C7 of arachidonic acid catalyzed by the enzyme rabbit 15-lipoxygenase-1.

Structural Stability and Conformational Dynamics of Cytochrome c in Hydrated Deep Eutectic Solvents

Many deep eutectic solvents (DESs) are currently being explored as environment-friendly media for biorelated applications. As an understanding of the effect of these solvents on the structure of biomolecules is crucial for these applications, we study how two DESs comprising trimethylglycine (TMG) and ethylene glycol (EG) or glycerol (GL) influence the structural stability and conformational dynamics of cytochrome c (Cytc) using single-molecule-based fluorescence correlation spectroscopy (FCS) technique and several other ensemble-based biophysical methods. The FCS studies on A488-labeled Cytc enable an estimation of the size (20.5 ± 1.5 Å) of the protein and capture its conformational dynamics (54 ± 2 μs) in aqueous buffered solution. It is observed that both size and conformational dynamics of the protein are influenced in the presence of the DESs, but this effect is more pronounced in the case of TMG-EG. The ensemble measurements on both labeled and wild-type Cytc reveal that the protein structure is unfolded completely by TMG-EG, whereas the structure is slightly altered by TMG-GL. The results suggest that the behavior of Cytc in hydrated DESs is determined by the strength of interactions between the DES constituents as well as that between the constituents and the water molecules present in the system.

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.

Photochemical processes in flavo-enzymes as a probe for active site dynamics: TrmFO of Thermus thermophilus

Quenching of flavin fluorescence by electron transfer from neighboring aromatic residues is ubiquitous in flavoproteins. Apart from constituting a functional process in specific light-active systems, time-resolved spectral characterization of the process can more generally be employed as a probe for the active site configuration and dynamics. In the C51A variant of the bacterial RNA-transforming flavoenzyme TrmFO from the bacterium Thermus thermophilus, fluorescence is very short-lived (~ 1 ps), and close-by Tyr343 is known to act as the main quencher, as confirmed here by the very similar dynamics observed in protein variants with modified other potential quenchers, Trp283 and Trp214. When Tyr343 is modified to redox-inactive phenylalanine, slower and highly multiphasic kinetics are observed on the picosecond-nanosecond timescale, reflecting heterogeneous electron donor-acceptor configurations. We demonstrate that Trp214, which is located on a potentially functional flexible loop, contributes to electron donor quenching in this variant. Contrasting with observations in other nucleic acid-transforming enzymes, these kinetics are strikingly temperature-independent. This indicates (a) near-barrierless electron transfer reactions and (b) no exchange between different configurations on the timescale up to at least 2 ns, despite the presumed flexibility of Trp214. Results of extensive molecular dynamics simulations are presented to explain this unexpected finding in terms of slowly exchanging protein configurations.

Effect of Memory and Inertial Contribution on Transition-Time Distributions: Theory and Simulations

Transition paths refer to the time taken by molecules to cross a barrier separating two molecular conformations. In this work, we study how memory, as well as inertial contribution in the dynamics along a reaction coordinate, can affect the distribution of the transition-path time. We use a simple model of dynamics governed by a generalized Langevin equation with a power-law memory along with the inertial term, which was neglected in previous studies, where memory effects were explored only in the overdamped limit. We derive an approximate expression for the transit-time distribution and discuss our results for the short- and long-time limits and also compare it with known results in the high friction (overdamped) limit as well as in the Markovian limit. We have developed a numerical algorithm to test our theoretical results against extensive numerical simulations.

Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3  nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.

Characterization of Light-Induced, Short-Lived Interacting Radicals in the Active Site of Flavoprotein Ferredoxin-NADP+ Oxidoreductase

Radicals of flavin adenine dinucleotide (FAD), as well as tyrosine and tryptophan, are widely involved as key reactive intermediates during electron-transfer (ET) reactions in flavoproteins. Due to the high reactivity of these species and their corresponding short lifetime, characterization of these intermediates in functional processes of flavoproteins is usually challenging but can be achieved by ultrafast spectroscopic studies of light-activatable flavoproteins. In ferredoxin-NADP⁺ oxidoreductase from Bacillus subtilis (BsFNR), fluorescence of the FAD cofactor that very closely interacts with a neighboring tyrosine residue (Tyr50) is strongly quenched. Here we study short-lived photoproducts of this enzyme and its variants, with Tyr50 replaced by tryptophan or glycine. Using time-resolved fluorescence and absorption spectroscopies, we show that, upon the excitation of WT BsFNR, ultrafast ET from Tyr50 to the excited FAD cofactor occurs in ∼260 fs, an order of magnitude faster than the decay by charge recombination, facilitating the characterization of the reaction intermediates in the charge-separated state with respect to other recently studied systems. These studies are corroborated by experiments on the Y50W mutant protein, which yield photoproducts qualitatively similar to those observed in other tryptophan-bearing flavoproteins. By combining the experimental results with molecular dynamics simulations and quantum mechanics calculations, we investigate in detail the effects of protein environment and relaxations on the spectral properties of those radical intermediates and demonstrate that the spectral features of radical anionic FAD are highly sensitive to its environment, and in particular to the dynamics and nature of the counterions formed in the photoproducts. Altogether, comprehensive characterizations are provided for important radical intermediates that are generally involved in functional processes of flavoproteins.

Inference of Joint Conformational Distributions from Separately Acquired Experimental Measurements

Flexible proteins serve vital roles in a multitude of biological processes. However, determining their full conformational ensembles is extremely difficult because this requires detailed knowledge about the heterogeneity of the protein's degrees of freedom. Label-based experiments such as double electron-electron resonance (DEER) are very useful in studying flexible proteins, as they provide distributional data on heterogeneity. These experiments are typically performed separately, so information about correlation between distributions is lost. We have developed a method to recover correlation information using nonequilibrium work estimates in molecular dynamics refinement. We tested this method on a simple model of an alternating-access transporter for which the true joint distributions are known, and it successfully recovered the true joint distribution. We also applied our method to the protein syntaxin-1a, where it discarded physically implausible conformations. Our method thus provides a way to recover correlation structure in separate experimental measurements of conformational ensembles and refines the resulting structural ensemble.

Single-Molecule Study of Redox Reaction Kinetics by Observing Fluorescence Blinking

Recent advances in fluorescence microscopy allow us to track chemical reactions at the single-molecule level. Single-molecule measurements make it possible to minimize the amount of sample needed for analysis and diagnosis. Signal amplification is often applied to ultralow-level biomarker detection. Polymerase chain reaction (PCR) is used to detect DNA/RNA, and enzyme-linked immunosorbent assay (ELISA) can sensitively probe antigen-antibody interactions. While these techniques are brilliant and will continue to be used in the future, single-molecule-level measurements would allow us to reduce the time and cost needed to amplify signals.The kinetics of chemical reactions have been studied mainly using ensemble-averaged methods. However, they can hardly distinguish time-dependent fluctuations and static heterogeneity of the kinetics. The information hidden in ensemble-averaged measurements would be extractable from a single-molecule experiment. Thus, single-molecule measurement would provide unique opportunities to investigate unrevealed phenomena and to elucidate the questions in chemistry, physics, and life sciences. Redox reaction, which is triggered by electron transfer, is among the most fundamental and ubiquitous chemical reactions. The redox reaction of a fluorescent molecule results in the formation of radical ions, which are normally nonemissive. In single-molecule-level measurements, the redox reaction causes the fluctuation of fluorescence signals between the bright ON-state and the dark OFF-state, in a phenomenon called blinking. The duration of the OFF-state (τ_OFF) corresponds to the lifetime of the radical ion state, and its reaction kinetics can be measured as 1/τ_OFF. Thus, the kinetics of redox reactions of fluorescent molecules can be accessed at the single-molecule level by monitoring fluorescence blinking. One of the key aspects of single-molecule analysis based on blinking is its robustness. A blinking signal with a certain regular pattern enables single fluorescent molecules to be distinguished and resolved from the random background signal.In this Account, we summarize the recent studies on the single-molecule measurement of redox reaction kinetics, with a focus on our group's recent progress. We first introduce the control of redox blinking to increase the photostability of fluorescent molecules. We then demonstrate the control of redox blinking, which allows us to detect target DNA by monitoring the function of a molecular beacon-type probe, and we investigate antigen-antibody interactions at the single-molecule level. By tracing the time-dependent changes in blinking patterns, redox blinking is shown to be adaptable to tracking the structural switching dynamics of RNA, the preQ₁ riboswitch. This Account ends with a discussion of our ongoing work on the control of fluorescent blinking. We also discuss the development of devices that allow single-molecule-level analysis in a high-throughput fashion.

The docking of synaptic vesicles on the presynaptic membrane induced by α-synuclein is modulated by lipid composition

α-Synuclein (αS) is a presynaptic disordered protein whose aberrant aggregation is associated with Parkinson’s disease. The functional role of αS is still debated, although it has been involved in the regulation of neurotransmitter release via the interaction with synaptic vesicles (SVs). We report here a detailed characterisation of the conformational properties of αS bound to the inner and outer leaflets of the presynaptic plasma membrane (PM), using small unilamellar vesicles. Our results suggest that αS preferentially binds the inner PM leaflet. On the basis of these studies we characterise in vitro a mechanism by which αS stabilises, in a concentration-dependent manner, the docking of SVs on the PM by establishing a dynamic link between the two membranes. The study then provides evidence that changes in the lipid composition of the PM, typically associated with neurodegenerative diseases, alter the modes of binding of αS, specifically in a segment of the sequence overlapping with the non-amyloid component region. Taken together, these results reveal how lipid composition modulates the interaction of αS with the PM and underlie its functional and pathological behaviours in vitro.

α-Synuclein is a presynaptic protein whose aberrant aggregation is associated with Parkinson’s disease. Here, the authors show how αSynuclein-induced docking of synaptic vesicles is modulated by the lipid composition changes typically observed in neurodegeneration using an in vitro system.

QM/MM Investigation of the Spectroscopic Properties of the Fluorophore of Bacterial Luciferase

We employ replica-exchange molecular dynamics (REMD) and a hybrid ab initio multiconfigurational quantum mechanics/molecular mechanics (QM/MM) approach to model the absorption and fluorescence properties of bacterial luciferin-luciferase. Specifically, we employ complete active space perturbation theory (CASPT2) and study the effect of active space, basis set, and IPEA shift on the computed energies. We discuss the effect of the protein environment on the fluorophore's excited-state potential energy surface and the role that the protein plays in enhancing the fluorescence quantum yield in bacterial bioluminescence.

Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes

Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.

How Useful can the Voigt Profile be in Protein Folding Processes?

The analytical expression for the Voigt profile, along with its simplified forms for the Gaussian and Lorentzian dominance, is presented. The applicability of the Voigt profile in the description of anomalous diffusion phenomena, ubiquitous in different fields of science including protein folding, is discussed. It is shown that the Voigt profile is a good descriptor of the processes occurring in protein folding and in the native state. The usefulness of the Voigt profile in deriving important information of the diffusive motions in proteins from a quasielastic incoherent neutron scattering experiments is illustrated.

Effect of the PHY Domain on the Photoisomerization Step of the Forward Pr →Pfr Conversion of a Knotless Phytochrome

Phytochrome photoreceptors operate via photoisomerization of a bound bilin chromophore. Their typical architecture consists of GAF, PAS and PHY domains. Knotless phytochromes lack the PAS domain, while retaining photoconversion abilities, with some being able to photoconvert with just the GAF domain. Therefore, we investigated the ultrafast photoisomerization of the Pr state of a knotless phytochrome to reveal the effect of the PHY domain and its "tongue" region on the transduction of the light signal. We show that the PHY domain does not affect the initial conformational dynamics of the chromophore. However, it significantly accelerates the consecutively induced reorganizational dynamics of the protein, necessary for the progression of the photoisomerization. Consequently, the PHY domain keeps the bilin and its binding pocket in a more reactive conformation, which decreases the extent of protein reorganization required for the chromophore isomerization. Thereby, less energy is lost along nonproductive reaction pathways, resulting in increased efficiency.

Origin of subdiffusions in proteins: Insight from peptide systems

Subdiffusive kinetics are popular in proteins and peptides as observed in experiments and simulations. For protein systems with diverse interactions, are there multiple mechanisms to produce the common subdiffusion behavior? To approach this problem, long trajectories of two model peptides are simulated to study the mechanism of subdiffusion and the relations with their interactions. The free-energy profiles and the subdiffusive kinetics are observed for these two peptides. A hierarchical plateau analysis is employed to extract the features of the landscape from the mean square of displacement. The mechanism of subdiffusions can be postulated by comparing the exponents by simulations with those based on various models. The results indicate that the mechanisms of these two peptides are different and are related to the characteristics of their energy landscapes. The subdiffusion of the flexible peptide is mainly caused by depth distribution of traps on the energy landscape, while the subdiffusion of the helical peptide is attributed to the fractal topology of local minima on the landscape. The emergence of these different mechanisms reflects different kinetic scenarios in peptide systems though the peptides behave in a similar way of diffusion. To confirm these ideas, the transition networks between various conformations of these peptides are generated. Based on the network description, the controlled kinetics based only on the topology of the networks are calculated and compared with the results based on simulations. For the flexible peptide, the feature of controlled diffusion is distinct from that of simulation, and for the helical peptide, two kinds of kinetics have a similar exponent of subdiffusion. These results further exemplify the importance of the landscape topology in the kinetics of structural proteins and the effect of depth distribution of traps for the subdiffusion of disordered peptides.

Anharmonic Molecular Motion Drives Resonance Energy Transfer in peri-Arylene Dyads

Spectral and dynamical properties of molecular donor-acceptor systems strongly depend on the steric arrangement of the constituents with exciton coupling J as a key control parameter. In the present work we study two peri-arylene based dyads with orthogonal and parallel transition dipoles for donor and acceptor moieties, respectively. We show that the anharmonic multi-well character of the orthogonal dyad's intramolecular potential explains findings from both stationary and time-resolved absorption experiments. While for a parallel dyad, standard quantum chemical estimates of J at 0 K are in good agreement with experimental observations, J becomes vanishingly small for the orthogonal dyad, in contrast to its ultrafast experimental transfer times. This discrepancy is not resolved even by accounting for harmonic fluctuations along normal coordinates. We resolve this problem by supplementing quantum chemical approaches with dynamical sampling of fluctuating geometries. In contrast to the moderate Gaussian fluctuations of J for the parallel dyad, fluctuations for the orthogonal dyad are found to follow non-Gaussian statistics leading to significantly higher effective J in good agreement with experimental observations. In effort to apply a unified framework for treating the dynamics of optical coherence and excitonic populations of both dyads, we employ a vibronic approach treating electronic and selected vibrational degrees on an equal footing. This vibronic model is used to model absorption and fluorescence spectra as well as donor-acceptor transport dynamics and covers the more traditional categories of Förster and Redfield transport as limiting cases.

Fluoroacetate dehalogenase catalyzed dehalogenation of halogenated carboxylic acids: A QM/MM approach

Dehalogenation is one of the most important reactions in environmental pollution control, for instance, the degradation of persistent organic pollutants (POPs). Recently, fluoroacetate dehalogenase (FAcD) has been reported to catalyze the dehalogenation reactions, which shows great potential in treating halogenated pollutants. Here the dehalogenation mechanism catalyzed by FAcD was fully deciphered with the aid of quantum mechanics/molecular mechanics method. The results show that FAcD catalyzed dehalogenation efficiency follows the order of defluorination > dechlorination > debromination. The corresponding Boltzmann-weighted average barriers are 10.1, 19.7, and 20.9 kcal mol^-1. Positive/negative correlations between activation barriers and structural parameters (e.g. distance and angle) for FAcD catalyzed dechlorination and debromination were established. Based on the structure-energy relationship, we propose that mutation of the binding pocket amino acids (e.g. His155, Trp156, Tyr219) to smaller proton donor amino acids (e.g. Serine, Threonine, Cysteine, Asparagine) may increase the efficiency for dechlorination and debromination. The results may of practical value for the efficient degradation of chlorined and bromined pollutants by harnessing FAcD.

Highly precise characterization of the hydration state upon thermal denaturation of human serum albumin using a 65 GHz dielectric sensor

The biological functions of proteins depend on harmonization with hydration water surrounding them. Indeed, the dynamical transition of proteins, such as thermal denaturation, is dependent on the changes in the mobility of hydration water. However, the role of hydration water during dynamical transition is yet to be fully understood due to technical limitations in precisely characterizing the amount of hydration water. A state-of-the-art CMOS dielectric sensor consisting of 65 GHz LC resonators addressed this issue by utilizing the feature that oscillation frequency sensitively shifts in response to the complex dielectric constant at 65 GHz with extremely high precision. This study aimed to establish an analytical algorithm to derive the hydration number from the measured frequency shift and to demonstrate the transition of hydration number upon the thermal denaturation of human serum albumin. The determined hydration number in the native state drew a "global" hydration picture beyond the first solvation shell, with substantially reduced uncertainty of the hydration number (about ±1%). This allowed the detection of a rapid increase in the hydration number at about 55 °C during the heating process, which was in excellent phase with the irreversible rupture of the α-helical structure into solvent-exposed extended chains, whereas the hydration number did not trace the forward path in the subsequent cooling process. Our result indicates that the weakening of water hydrogen bonds trigger the unfolding of the protein structure first, followed by the changes in the number of hydration water as a consequence of thermal denaturation.

Super-resolution Surface-Enhanced Raman Scattering Imaging of Single Particles in Cells

The ability to locate and identify molecular interactions in cells has significant importance for understanding protein function and molecular biology. Functionalized metallic nanoparticles have been used as probes for protein tracking and drug delivery because of their ability to carry therapeutic agents and readily functionalized surfaces. In this work, we present a super-resolution surface-enhanced Raman scattering (SERS) approach for imaging and tracking membrane receptors interacting with peptide-functionalized gold nanostars (AuNS). The αvβ3 integrin receptors in colon cancer cells are successfully targeted and imaged using AuNS with the high-affinity amino acid sequence arginine-glycine-aspartic acid-phenylalanine-cysteine (RGDFC) attached. The RGDFC peptide interaction with the integrin receptor provides a bright and fluctuating SERS signal that can be analyzed with localization microscopy algorithms. Additionally, the observed SERS spectrum is used to confirm protein-peptide interaction. Experiments with functionalized and bare AuNS illustrate specific and nonspecific binding events. Specific binding is monitored with a localization precision of ∼6 nm. The observed spatial resolution is associated with tight binding, which was confirmed by the slower diffusion coefficient measured from 4.4 × 10-11 cm2/s for the AuNS-RGDFC compared to 7.8 × 10-10 cm2/s for the bare AuNS. Super-resolution SERS images at different focal planes show evidence of internalized particles and suggest insights into protein orientation on the surface of cells. Our work demonstrates super-resolution SERS imaging to probe membrane receptor interactions in cells, providing chemical information and spatial resolution with potential for diverse applications in life science and biomedicine.

The interplay between chromophore and protein determines the extended excited state dynamics in a single-domain phytochrome

Phytochromes are a diverse family of bilin-binding photoreceptors that regulate a wide range of physiological processes. Their photochemical properties make them attractive for applications in optogenetics and superresolution microscopy. Phytochromes undergo reversible photoconversion triggered by the Z ⇄ E photoisomerization about the double bond in the bilin chromophore. However, it is not fully understood at the molecular level how the protein framework facilitates the complex photoisomerization dynamics. We have studied a single-domain bilin-binding photoreceptor All2699g1 (Nostoc sp. PCC 7120) that exhibits photoconversion between the red light-absorbing (P_r) and far red-absorbing (P_fr) states just like canonical phytochromes. We present the crystal structure and examine the photoisomerization mechanism of the P_r form as well as the formation of the primary photoproduct Lumi-R using time-resolved spectroscopy and hybrid quantum mechanics/molecular mechanics simulations. We show that the unusually long excited state lifetime (broad lifetime distribution centered at ∼300 picoseconds) is due to the interactions between the isomerizing pyrrole ring D and an adjacent conserved Tyr142. The decay kinetics shows a strongly distributed character which is imposed by the nonexponential protein dynamics. Our findings offer a mechanistic insight into how the quantum efficiency of the bilin photoisomerization is tuned by the protein environment, thereby providing a structural framework for engineering bilin-based optical agents for imaging and optogenetics applications.

Luminescence Activity Decreases When v-coelenterazine Replaces Coelenterazine in Calcium-Regulated Photoprotein-A Theoretical and Experimental Study

Calcium-regulated photoproteins are found in at least five phyla of organisms. The light emitted by those photoproteins can be tuned by mutating the photoprotein and/or by modifying the substrate coelenterazine (CTZ). Thirty years ago, Shimomura observed that the luminescence activity of aequorin was dramatically reduced when the substrate CTZ was replaced by its analog v-CTZ. The latter is formed by adding a phenyl ring to the π-conjugated moiety of CTZ. The decrease in luminescence activity has not been understood until now. In this paper, through combined quantum mechanics and molecular mechanics calculations as well as molecular dynamics simulations, we discovered the reason for this observation. Modification of the substrate changes the conformation of nearby aromatic residues and enhances the π-π stacking interactions between the conjugated moiety of v-CTZ and the residues, which weakens the charge transfer to form light emitter and leads to a lower luminescence activity. The microenvironments of CTZ in obelin and in aequorin are very similar, so we predicted that the luminescence activity of obelin will also dramatically decrease when CTZ is replaced by v-CTZ. This prediction has received strong evidence from currently theoretical calculations and has been verified by experiments.

Dissecting the Dynamics during Enzyme Catalysis: A Case Study of Pin1 Peptidyl-Prolyl Isomerase

Free energy surfaces have played a central role in studying protein conformational changes and enzymatic reactions over decades. Yet, free energy barriers and kinetics are highly dependent on the coordinates chosen to define the surface, and furthermore, the dynamics during the reactions are often overlooked. Our recent study on the Pin1-catalyzed isomerization reaction has indicated that the isomerization transition events remarkably deviate from the free energy path, highlighting the need to understand the reaction dynamics in more detail. To this end, here we investigate the reaction coordinates that describe the transition states of the free energy and transition pathways by minimizing the cross-entropy function. We show that the isomerization transition events can be expressed by the concerted changes in the improper torsion angle ζ and nearby backbone torsional angles of the ligand, whereas the transition state of the free energy surface involves changes in a broad range of coordinates including multiple protein-ligand interactions. The current result supports the previous finding that the isomerization transitions occur quickly from the conformational excited states, which is in sharp contrast to the slow and collective changes suggested from the free energy path. Our results further indicate that the coordinates derived from the transition trajectories are not sufficient for finding the transition states on the free energy surfaces due to the lack of information from conformational excited states.

Single-molecule transport kinetics of a glutamate transporter homolog shows static disorder

Kinetic properties of membrane transporters are typically poorly defined because high-resolution functional assays analogous to single-channel recordings are lacking. Here, we measure single-molecule transport kinetics of a glutamate transporter homolog from Pyrococcus horikoshii, GltPh, using fluorescently labeled periplasmic amino acid binding protein as a fluorescence resonance energy transfer-based sensor. We show that individual transporters can function at rates varying by at least two orders of magnitude that persist for multiple turnovers. A gain-of-function mutant shows increased population of the fast-acting transporters, leading to a 10-fold increase in the mean transport rate. These findings, which are broadly consistent with earlier single-molecule measurements of GltPh conformational dynamics, suggest that GltPh transport is defined by kinetically distinct populations that exhibit long-lasting "molecular memory."

Mechanical Unfolding of Single Polyubiquitin Molecules Reveals Evidence of Dynamic Disorder

Mechanical unfolding of single polyubiquitin molecules subjected to a constant stretching force showed nonexponentiality in the measured probability density of unfolding (waiting time distribution) and the survival probability of the folded state during the course of the measurements. These observations explored the relevance of disorder present in the system under study with implications for a static disorder approach to rationalize the experimental results. Here, an approach for dynamic disorder is presented based on Zwanzig's fluctuating bottleneck (FB) model, in which the rate of the reaction is controlled by the passage through the cross-sectional area of the bottleneck. The radius of the latter undergoes stochastic fluctuations that in turn is described in terms of the end-to-end distance fluctuations of the Rouse-like dynamics using a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise. Our results are comprised of analytical expressions for the survival probability and waiting time distribution, which show excellent agreement with the experimental data throughout the range of the applied forces. In addition, by fitting the survival probabilities at different stretching forces, we quantify two system parameters, namely, the average free energy ΔG _av and the average distance to the transition state Δx _av, both perfectly recovered the experimental estimates. These agreements validate the present model of polymer dynamics, which captures the very essence of dynamic disorder in single-molecule pulling experiments.

High-Fidelity Single Molecule Quantification in a Flow Cytometer Using Multiparametric Optical Analysis

Microfluidic techniques are widely used for high-throughput quantification and discrete analysis of micron-scale objects but are difficult to apply to molecular-scale targets. Instead, single-molecule methods primarily rely on low-throughput microscopic imaging of immobilized molecules. Here we report that commercial-grade flow cytometers can detect single nucleic acid targets following enzymatic extension and dense labeling with multiple distinct fluorophores. We focus on microRNAs, short nucleic acids that can be extended by rolling circle amplification (RCA). We labeled RCA-extended microRNAs with multicolor fluorophores to generate repetitive nucleic acid products with submicron sizes and tunable multispectral profiles. By cross-correlating the multiparametric optical features, signal-to-background ratios were amplified 1600-fold to allow single-molecule detection across 4 orders of magnitude of concentration. The limit of detection was measured to be 47 fM, which is 100-fold better than gold-standard methods based on polymerase chain reaction. Furthermore, multiparametric analysis allowed discrimination of different microRNA sequences in the same solution using distinguishable optical barcodes. Barcodes can apply both ratiometric and colorimetric signatures, which could facilitate high-dimensional multiplexing. Because of the wide availability of flow cytometers, we anticipate that this technology can provide immediate access to high-throughput multiparametric single-molecule measurements and can further be adapted to the diverse range of molecular amplification methods that are continually emerging.

Non-Markov bond model for dynamic force spectroscopy

Single-molecule force spectroscopy data are conventionally analyzed using a schematic model, wherein a molecular bond is represented as a virtual particle diffusing in a one-dimensional free-energy landscape. However, this simple and efficient approach is unable to account for the "anomalous" bond-breaking kinetics increasingly observed in force spectroscopy experiments and simulations, e.g., in the form of non-exponential distributions of bond lifetimes under constant load. Here, we show that such characteristic traits arise naturally in a rigorous extension of the one-dimensional theory that accounts for the transient dynamics of a generic set of coupled degrees of freedom. These "hidden modes" affect the reaction dynamics in various ways, depending on their relaxation spectrum and the loading protocol, giving rise, in particular, to apparent static and dynamic disorder. In two complementary asymptotic limits, we are able to find exact analytical expressions for pertinent experimental observables, such as the mean rupture force and the rupture-force distribution. Intriguingly, our asymptotic results become unconditionally exact at high loading rates, thus providing us with a microscopically consistent theory of rapid force spectroscopy that avoids the usual Markov assumption.

Electron Transfer in a Naphthalene Diimide System Studied by Single-Molecule Delayed Fluorescence

Electron transfer (ET) is a key chemical reaction in nature and has been extensively studied in bulk systems, but remains challenging to investigate at the single-molecule level. A previously reported naphthalene diimide (NDI)-based system (Higginbotham et al., Chem. Commun. 2013, 49, 5061–5063) displays delayed fluorescence with good quantum yield (~0.5) and long-lived (nanoseconds) prompt and delayed fluorescence lifetimes, providing an opportunity to interrogate the underlying ET processes in single molecules. Time-resolved single-molecule fluorescence measurements enabled forward and reverse ET rate constants to be calculated for 45 individual molecules embedded in poly(methylmethacrylate) (PMMA) film. Interpretation of the results within the framework of Marcus–Hush theory for ET demonstrates that variation in both the electronic coupling and the driving force for ET is occurring from molecule to molecule within the PMMA film and over time for individual molecules.

A quantitative analysis of memory effects in the viscously coupled dynamics of optically trapped Brownian particles

We provide a quantitative description of the memory effects existing in the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity to each other such that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the memory effects, we quantify the storage of energy in terms of various system parameters and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects are maximized at a certain trap stiffness ratio, and reduce with increasing particle separation. The technique can be generally used to determine the effective viscoelastic parameters of any such fluid-particle systems, and can thus help understand the interactions between active particles mediated by simple or complex fluids.

Single electron transfer events and dynamical heterogeneity in the small protein azurin from Pseudomonas aeruginosa

Monitoring the fluorescence of single-dye-labeled azurin molecules, we observed the reaction of azurin with hexacyanoferrate under controlled redox potential yielding data on the timing of individual (forward and backward) electron transfer (ET) events. Change-point analysis of the time traces demonstrates significant fluctuations of ET rates and of mid-point potential E 0. These fluctuations are a signature of dynamical heterogeneity, here observed on a 14 kDa protein, the smallest to date. By correlating changes in forward and backward reaction rates we found that 6% of the observed change events could be explained by a change in midpoint potential, while for 25% a change of the donor-acceptor coupling could explain the data. The remaining 69% are driven by variations in complex association constants or structural changes that cause forward and back ET rates to vary independently. Thus, the observed spread in individual ET rates could be related in a unique way to variations in molecular parameters. The relevance for the understanding of metabolic processes is briefly discussed.

Role of hydration water in the onset of protein structural dynamics

Proteins are the molecular workhorses in a living organism. Their 3D structures are animated by a multitude of equilibrium fluctuations and specific out-of-equilibrium motions that are required for proteins to be biologically active. When studied as a function of temperature, functionally relevant dynamics are observed at and above the so-called protein dynamical transition (~240 K) in hydrated, but not in dry proteins. In this review we present and discuss the main experimental and computational results that provided evidence for the dynamical transition, with a focus on the role of hydration water dynamics in sustaining functional protein dynamics. The coupling and mutual influence of hydration water dynamics and protein dynamics are discussed and the hypotheses illustrated that have been put forward to explain the physical origin of their onsets.

Confinement-Free Wide-Field Ratiometric Tracking of Single Fluorescent Molecules

Single-molecule fluorescence has been highly instrumental in elucidating interactions and dynamics of biological molecules in the past two decades. Single-molecule fluorescence experiments usually rely on one of two detection geometries, either confocal point-detection or wide-field area detection, typically in a total internal reflection fluorescence (TIRF) format. However, each of these techniques suffers from fundamental drawbacks that limit their application. In this work, we present a new technique, solution wide-field imaging (SWiFi) of diffusing molecules, as an alternative to the existing methods. SWiFi is a simple extension to existing objective-type TIRF microscopes that allows wide-field observations of fast-diffusing molecules down to single fluorophores without the need of tethering the molecules to the surface. We demonstrate that SWiFi enables high-throughput ratiometric measurements with several thousands of individual data points per minute on double-stranded DNA standard (dsDNA) samples containing Förster resonance energy transfer pairs. We further display the capabilities of SWiFi by reporting on mobility and ratiometric characterization of fluorescent nanodiamonds, DNA Holliday junctions, and protein-DNA interactions. The ability of SWiFi for high-throughput, ratiometric measurements of fast-diffusing species renders it a valuable tool for the single-molecule research community by bridging between confocal and TIRF detection geometries in a simple and efficient way.

Harnessing fluoroacetate dehalogenase for defluorination of fluorocarboxylic acids: in silico and in vitro approach

Widely distributed fluorocarboxylic acids have aroused worldwide environmental concerns due to its toxicity, persistence, and bioaccumulation. Enzyme-based eco-friendly biodegradation techniques have become increasingly important in treating fluorocarboxylic acids. Here we utilized in silico and in vitro approaches to investigate the defluorination mechanism of fluoroacetate dehalogenase (FAcD) toward monofluoropropionic acids at atomic-level. The experimentally determined k_cat and k_M for defluorination of 2-fluoropropionic acid are 330 ± 60 min^-1 and 6.12 ± 0.13 mM. The in silico results demonstrated positive/negative correlations between activation barriers and structural parameters (e.g. distance and angle) under different enzymatic conformations. We also screened computationally and tested in vitro (enzyme assay and kinetic study) the catalytic proficiency of FAcD toward polyfluoropropionic acids and perfluoropropionic acids which are known to be challenging for enzymatic degradation. The results revealed potential degradation activity of FAcD enzyme toward 2,3,3,3-tetrafluoropropionic acids. Our work will initiate the development of a new "integrated approach" for enzyme engineering to degrade environmentally persistent fluorocarboxylic acids.

Hemocompatibility of Super-Repellent surfaces: Current and Future

Virtually all blood-contacting medical implants and devices initiate immunological events in the form of thrombosis and inflammation. Typically, patients receiving such implants are also given large doses of anticoagulants, which pose a high risk and a high cost to the patient. Thus, the design and development of surfaces with improved hemocompatibility and reduced dependence on anticoagulation treatments is paramount for the success of blood-contacting medical implants and devices. In the past decade, the hemocompatibility of super-repellent surfaces (i.e., surfaces that are extremely repellent to liquids) has been extensively investigated because such surfaces greatly reduce the blood-material contact area, which in turn reduces the area available for protein adsorption and blood cell or platelet adhesion, thereby offering the potential for improved hemocompatibility. In this review, we critically examine the progress made in characterizing the hemocompatibility of super-repellent surfaces, identify the unresolved challenges and highlight the opportunities for future research on developing medical implants and devices with super-repellent surfaces.

Microsecond Conformational Dynamics of Biopolymers Revealed by Dynamic-Quenching Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy with Single Dye Labeling

The single-molecule Förster resonance energy transfer (smFRET) technique is widely used for studying conformational dynamics of biopolymers. However, smFRET requires double dye labeling and is usually utilized for detecting dynamics on slow time scales (≳ milliseconds). In this Letter, we report dynamic-quenching two-dimensional fluorescence lifetime correlation spectroscopy (DQ 2D FLCS) that can elucidate the microsecond conformational dynamics of biopolymers with only single dye labeling. In DQ 2D FLCS, the difference in solvent accessibility of the labeled dye makes the fluorescence lifetime different, which is used for distinguishing different conformers. By applying DQ 2D FLCS to a singly labeled DNA hairpin, we successfully detect microsecond interconversion dynamics between the open and closed forms and evaluate the state-specific solvent accessibility of each form with Stern-Volmer analysis. Because DQ 2D FLCS is sensitive to the local structural change, it is complementary to FRET-based 2D FLCS and thus is a new, powerful tool for studying structural dynamics of biopolymers.

TCR-pMHC bond conformation controls TCR ligand discrimination

A major unanswered question is how a TCR discriminates between foreign and self-peptides presented on the APC surface. Here, we used in situ fluorescence resonance energy transfer (FRET) to measure the distances of single TCR–pMHC bonds and the conformations of individual TCR–CD3ζ receptors at the membranes of live primary T cells. We found that a TCR discriminates between closely related peptides by forming single TCR–pMHC bonds with different conformations, and the most potent pMHC forms the shortest bond. The bond conformation is an intrinsic property that is independent of the binding affinity and kinetics, TCR microcluster formation, and CD4 binding. The bond conformation dictates the degree of CD3ζ dissociation from the inner leaflet of the plasma membrane via a positive calcium signaling feedback loop to precisely control the accessibility of CD3ζ ITAMs for phosphorylation. Our data revealed the mechanism by which a TCR deciphers the structural differences among peptides via the TCR–pMHC bond conformation.

Transport and escape in a deformable channel driven by fractional Gaussian noise

Fractional Gaussian noise (FGN) with the Hurst exponent H is an important tool to model various phenomena in biophysical systems, like subdiffusion in a single protein molecule. Considering that there also exists a confined structure which can be modeled as a channel in these systems, transport and escape driven by FGN in a deformable channel are investigated in this paper. By calculating the mean velocity, and the mean first passage time (MFPT) for crossing the nearest bottleneck and the probability distribution of the final position, effects of FGN and channel structure on the system dynamics are illustrated. Our results indicate that FGN has a complex influence mechanism under different combinations of H and the noise intensity. For a persistence case (H>0.5), the mean velocity decreases but MFPT increases with the increase of the noise intensity and H. While for an antipersistence case (H<0.5), when H is small, the relationships among the mean velocity, MFPT and the noise intensity are exactly the opposite to persistence cases. When H has a large value, the mean velocity tends to first decrease and then increase. Moreover, effects of the bottleneck and channel asymmetry are investigated. It is shown that a small H and a large channel width can lead to a large mean velocity and fast crossing. Besides, a channel asymmetry can affect the system dynamics by inducing asymmetric structure and adjusting the width of bottleneck. However, the effect of the bottleneck is the main factor. Therefore, a combination of channel with wide bottleneck and FGN in an antipersistence regime is the optimal choice to promote the transport and escape. These results provide a basis for the explanation of molecular activity in living organisms and the design of particle mixture separators.

Passage through a sub-diffusing geometrical bottleneck

The usual Kramers theory of reaction rates in condensed media predict the rate to have an inverse dependence on the viscosity of the medium, η. However, experiments on ligand binding to proteins, performed long ago, showed the rate to have η^-ν dependence, with ν in the range of 0.4-0.8. Zwanzig [J. Chem. Phys. 97, 3587 (1992)] suggested a model in which the ligand has to pass through a fluctuating opening to reach the binding site. This fluctuating gate model predicted the rate to be proportional to η^-1/2. More recently, experiments performed by Xie et al. [Phys. Rev. Lett. 93, 180603 (2004)] showed that the distance between two groups in a protein undergoes not normal diffusion, but subdiffusion. Hence, in this paper, we suggest and solve a generalization of the Zwanzig model, viz., passage through an opening, whose size undergoes subdiffusion. Our solution shows that the rate is proportional to η^-ν with ν in the range of 0.5-1, and hence, the subdiffusion model can explain the experimental observations.

Short-Lived Radical Intermediates in the Photochemistry of Glucose Oxidase

Glucose oxidase is a flavoprotein that is relatively well-studied as a physico-chemical model system. The flavin cofactor is surrounded by several aromatic acid residues that can act as direct and indirect electron donors to photoexcited flavin. Yet, the identity of the photochemical product states is not well established. We present a detailed full spectral reinvestigation of this issue using femtosecond fluorescence and absorption spectroscopy. Based on a recent characterization of the unstable tyrosine cation radical TyrOH^•+ , we now propose that the primary photoproduct involves this species, which was previously not considered. Formation of this product is followed by competing charge recombination and radical pair stabilization reactions that involve proton transfer and radical transfer to tryptophan. A minimal kinetic model is proposed, including a fraction of TyrOH^.+ that is stabilized up to the tens of picoseconds timescale, suggesting a potential role of this species as intermediate in biochemical electron transfer reactions.

Whispering-gallery mode (WGM) sensors: review of established and WGM-based techniques to study protein conformational dynamics

Monitoring the conformational dynamics of proteins is crucial for a better understanding of their biological functions. To observe the structural dynamics of proteins, it is often necessary to study each molecule individually. To this end, single-molecule techniques have been developed such as Förster resonance energy transfer and optical tweezers. However, although powerful, these techniques do have their limitations, for example, limited temporal resolution, or necessity for fluorescent labelling, and they can often only access a limited set of all protein motions. Here, within the context of established structural biology techniques, we review a new class of highly sensitive optical devices based on WGM, which characterise protein dynamics on previously inaccessible timescales, visualise motions throughout a protein, and track movements of single atoms.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

Estimation of Shape, Volume, and Dipole Moment of Individual Proteins Freely Transiting a Synthetic Nanopore

This paper demonstrates that high-bandwidth current recordings in combination with low-noise silicon nitride nanopores make it possible to determine the molecular volume, approximate shape, and dipole moment of single native proteins in solution without the need for labeling, tethering, or other chemical modifications of these proteins. The analysis is based on current modulations caused by the translation and rotation of single proteins through a uniform electric field inside of a nanopore. We applied this technique to nine proteins and show that the measured protein parameters agree well with reference values but only if the nanopore walls were coated with a nonstick fluid lipid bilayer. One potential challenge with this approach is that an untethered protein is able to diffuse laterally while transiting a nanopore, which generates increasingly asymmetric disruptions in the electric field as it approaches the nanopore walls. These "off-axis" effects add an additional noise-like element to the electrical recordings, which can be exacerbated by nonspecific interactions with pore walls that are not coated by a fluid lipid bilayer. We performed finite element simulations to quantify the influence of these effects on subsequent analyses. Examining the size, approximate shape, and dipole moment of unperturbed, native proteins in aqueous solution on a single-molecule level in real time while they translocate through a nanopore may enable applications such as identifying or characterizing proteins in a mixture, or monitoring the assembly or disassembly of transient protein complexes based on their shape, volume, or dipole moment.

Fractional electron transfer kinetics and a quantum breaking of ergodicity

The dissipative curve-crossing problem provides a paradigm for electron-transfer (ET) processes in condensed media. It establishes the simplest conceptual test bed to study the influence of the medium's dynamics on ET kinetics both on the ensemble level, and on the level of single particles. Single electron description is particularly important for nanoscaled systems like proteins, or molecular wires. Especially insightful is this framework in the semiclassical limit, where the environment can be treated classically, and an exact analytical treatment becomes feasible. Slow medium's dynamics is capable of enslaving ET and bringing it on the ensemble level from a quantum regime of nonadiabatic tunneling to the classical adiabatic regime, where electrons follow the nuclei rearrangements. This classical adiabatic textbook picture contradicts, however, in a very spectacular fashion to the statistics of single electron transitions, even in the Debye, memoryless media, also named Ohmic in the parlance of the famed spin-boson model. On the single particle level, ET always remains quantum, and this was named a quantum breaking of ergodicity in the adiabatic ET regime. What happens in the case of subdiffusive, fractional, or sub-Ohmic medium's dynamics, which is featured by power-law decaying dynamical memory effects typical, e.g., for protein macromolecules, and other viscoelastic media? Such a memory is vividly manifested by anomalous Cole-Cole dielectric response in such media. We address this question based both on accurate numerics and analytical theory. The ensemble theory remarkably agrees with the numerical dynamics of electronic populations, revealing a power-law relaxation tail even in a profoundly nonadiabatic electron transfer regime. In other words, ET in such media should typically display fractional kinetics. However, a profound difference with the numerically accurate results occurs for the distribution of residence times in the electronic states, both on the ensemble level and the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case. Our results question the applicability of all the existing and widely accepted ensemble theories of electron transfer in fractional, sub-Ohmic environments, on the level of single molecules, and provide a real challenge to face, both for theorists and experimentalists.