Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer

Adhesion of a polymer-grafted nanoparticle to cells explored using generalized Langevin dynamics

We model a polymer-grafted stealth nanoparticle (SNP) as a composite system consisting of a spherical core coated with a porous polymeric brush with end-ligands. Adjacent to target cells, the near-wall hydrodynamics, thermal fluctuations, and thermodynamic adhesive interactions simultaneously impact the transient motion of the SNP. Employing both the Langevin framework for the effective hard sphere dynamics and the coupled generalized Langevin framework for the nanoparticle-polymer dynamics, we comprehensively investigate the velocity and position temporal relaxations of the SNP in the absence and presence of end-to-end distance fluctuations for the tethered polymer. We demonstrate that polymer structural relaxations substantially impact the SNP adhesive dynamics, especially when the grafted polymer is more flexible. Moreover, a long-time tail with t-3/2 scaling due to polymer chain-length fluctuations is observed in the velocity autocorrelation for a bound SNP. Finally, the thermodynamic effects of membrane morphology on SNP adhesion are explored by modifying the membrane-mediated binding potential of mean force.

Characterizing highly dynamic conformational states: The transcription bubble in RNAP-promoter open complex as an example

Bio-macromolecules carry out complicated functions through structural changes. To understand their mechanism of action, the structure of each step has to be characterized. While classical structural biology techniques allow the characterization of a few "structural snapshots" along the enzymatic cycle (usually of stable conformations), they do not cover all (and often fast interconverting) structures in the ensemble, where each may play an important functional role. Recently, several groups have demonstrated that structures of different conformations in solution could be solved by measuring multiple distances between different pairs of residues using single-molecule Förster resonance energy transfer (smFRET) and using them as constrains for hybrid/integrative structural modeling. However, this approach is limited in cases where the conformational dynamics is faster than the technique's temporal resolution. In this study, we combine existing tools that elucidate sub-millisecond conformational dynamics together with hybrid/integrative structural modeling to study the conformational states of the transcription bubble in the bacterial RNA polymerase-promoter open complex (RPo). We measured microsecond alternating laser excitation-smFRET of differently labeled lacCONS promoter dsDNA constructs. We used a combination of burst variance analysis, photon-by-photon hidden Markov modeling, and the FRET-restrained positioning and screening approach to identify two conformational states for RPo. The experimentally derived distances of one conformational state match the known crystal structure of bacterial RPo. The experimentally derived distances of the other conformational state have characteristics of a scrunched RPo. These findings support the hypothesis that sub-millisecond dynamics in the transcription bubble are responsible for transcription start site selection.

Direct single-molecule counting for immunoassay applications

Single-molecule methods offer specificity in studying complex systems and dynamics, but they also offer high sensitivity for basic enumeration. We apply single-molecule TIRF to immunoassays by counting the number of target molecules captured on a streptavidin surface. We demonstrate the utility of using single-molecule counting on eluted detection conjugate, following the capture and sandwich formation portions of the assay having been completed on microparticles. This approach is simple and effective, and creates the opportunity for a universal detection platform that can be used to perform a variety of diagnostic and blood screening assays. We take advantage of the low volume requirements of single-molecule detection and apply a sample reloading approach to concentrate sample onto the detection surface. Due to the high affinity of the streptavidin-biotin reaction, concentration through reloading is both quick and robust. These findings are demonstrated on a model system and in an HIV p24 antigen assay. Single-molecule detection techniques do not need to be complex to exhibit power and flexibility, and so can become valuable in the field of immunoassay diagnostics.

Single-molecule photoredox catalysis

Photocatalytic dehalogenation by a common dyestuff under aqueous conditions is driven by energy-additive absorption of two photons on the single-molecule level.

The chemistry of life is founded on light, so is it appropriate to think of light as a chemical substance? Planck's quantization offers a metric analogous to Avogadro's number to relate the number of particles to an effective reaction of single molecules and photons to form a new compound. A rhodamine dye molecule serves as a dehalogenating photocatalyst in a consecutive photoelectron transfer (conPET) process which adds the energy of two photons, with the first photon inducing radical formation and the second photon triggering PET to the substrate molecule. Rather than probing catalytic heterogeneity and dynamics on the single-molecule level, single-photon synthesis is demonstrated: the light quantum constitutes a reactant for the single substrate molecule in a dye–driven reaction. The approach illustrates that molecular diffusion and excited-state internal conversion are not limiting factors in conPET reaction kinetics because of catalyst–substrate preassociation. The effect could be common to photoredox catalysis, removing the conventional requirement of long excited-state lifetimes.

Insights into the catalytic mechanism of dehydrogenase BphB: A quantum mechanics/molecular mechanics study

The present study delineated the dehydrogenation mechanism of cis-2,3-dihydro-2,3-dihydroxybiphenyl (2,3-DDBPH) and cis-2,3-dihydro-2,3-dihydroxy-4,4'-dichlorobiphenyl (2,3-DD-4,4'-DBPH) by Pandoraea pnomenusa strain B-356 cis-2,3-dihydro-2,3-dihydroxybiphenyl dehydrogenase (BphB) in atomistic detail. The enzymatic process was investigated by a combined quantum mechanics/molecular mechanics (QM/MM) approach. Five different snapshots were extracted and calculated, which revealed that the Boltzmann-weighted average barriers of 2,3-DDBPH and 2,3-DD-4,4'-DBPH dehydrogenation processes are 10.7 and 11.5 kcal mol^-1, respectively. The established dehydrogenation mechanism provides new insight into the degradation processes of other chlorinated 2,3-DDBPH. In addition to Asn115, Ser142, and Lys149, the importance of Ile 89, Asn143, Pro184, Met 187, Thr189, and Lue 191 during the dehydrogenation process of 2,3-DDBPH and 2,3-DD-4,4'-DBPH were also highlighted to search for promising mutation targets for improving the catalytic efficiency of BphB.

Single-molecule studies of flavivirus envelope dynamics: Experiment and computation

Flaviviruses are simple enveloped viruses exhibiting complex structural and functional heterogeneities. Decades of research have provided crucial basic insights, antiviral medication and moderately successful gene therapy trials. The most infectious particle is, however, not always the most abundant one in a population, questioning the utility of classic ensemble-averaging virology approaches. Indeed, viral replication is often not particularly efficient, prone to errors or containing parallel routes. Here, we review different single-molecule sensitive fluorescence methods that are employed to investigate flaviviruses. In particular, we review how (i) time-resolved Förster resonance energy transfer (trFRET) was applied to probe dengue envelope conformations; (ii) FRET-fluorescence correlation spectroscopy to investigate dengue envelope intrinsic dynamics and (iii) single particle tracking to follow the path of dengue viruses in cells. We also discuss how such methods may be supported by molecular dynamics (MD) simulations over a range of spatio-temporal scales, to provide complementary data on the structure and dynamics of flaviviral systems. We describe recent improvements in multiscale MD approaches that allowed the simulation of dengue particle envelopes in near-atomic resolution. We hope this review is an incentive for setting up and applying similar single-molecule studies and combine them with MD simulations to investigate structural dynamics of entire flavivirus particles over the nanosecond-to-millisecond time-scale and follow viruses during infection in cells over milliseconds to minutes.

Viscoelastic subdiffusion in a random Gaussian environment

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short-range exponentially decaying and algebraically slow decaying with an infinite correlation length, both for a moderate (several k_BT, in the units of thermal energy), and strong (5-10k_BT) disorder. For a moderate disorder, it is shown that on the ensemble level viscoelastic subdiffusion can easily overcome the medium's disorder. Asymptotically, it is not distinguishable from the disorder-free subdiffusion. However, a strong scatter in single-trajectory averages is nevertheless seen even for a moderate disorder. It features a weak ergodicity breaking, which occurs on a very long yet transient time scale. Furthermore, for a strong disorder, a very long transient regime of logarithmic, Sinai-type diffusion emerges. It can last longer and be faster in the absolute terms for weakly decaying correlations as compared with the short-range correlations. Residence time distributions in a finite spatial domain are of a generalized log-normal type and are reminiscent also of a stretched exponential distribution. They can be easily confused for power-law distributions in view of the observed weak ergodicity breaking. This suggests a revision of some experimental data and their interpretation.

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.

Emerging tools for studying single entity electrochemistry

Electrochemistry studies charge transfer and related processes at various microscopic structures (atomic steps, islands, pits and kinks on electrodes), and mesoscopic materials (nanoparticles, nanowires, viruses, vesicles and cells) made by nature and humans, involving ions and molecules. The traditional approach measures averaged electrochemical quantities of a large ensemble of these individual entities, including the microstructures, mesoscopic materials, ions and molecules. There is a need to develop tools to study single entities because a real system is usually heterogeneous, e.g., containing nanoparticles with different sizes and shapes. Even in the case of "homogeneous" molecules, they bind to different microscopic structures of an electrode, assume different conformations and fluctuate over time, leading to heterogeneous reactions. Here we highlight some emerging tools for studying single entity electrochemistry, discuss their strengths and weaknesses, and provide personal views on the need for tools with new capabilities for further advancing single entity electrochemistry.

Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding

Recent single-molecule experiments probed transition paths of biomolecular folding and, in particular, measured the time biomolecules spend while crossing their free energy barriers. A surprising finding from these studies is that the transition barriers crossed by transition paths, as inferred from experimentally observed transition path times, are often lower than the independently determined free energy barriers. Here we explore memory effects leading to anomalous diffusion as a possible origin of this discrepancy. Our analysis of several molecular dynamics trajectories shows that the dynamics of common reaction coordinates used to describe protein folding is subdiffusive, at least at sufficiently short times. We capture this effect using a one-dimensional fractional Brownian motion (FBM) model, in which the system undergoes a subdiffusive process in the presence of a potential of mean force, and show that this model yields much broader distributions of transition path times with stretched exponential long-time tails. Without any adjustable parameters, these distributions agree well with the transition path times computed directly from protein trajectories. We further discuss how the FBM model can be tested experimentally.

Probing Activated and Non-Activated Single Calmodulin Molecules under a Piconewton Compressive Force

Interrogating the protein structure-function inter-relationship under a piconewton force manipulation has been highly promising and informative. Although protein conformational changes under pulling force manipulations have been extensively studied, protein conformational changes under a compressive force have not been explored in detail. Using our home-modified sensitive and high signal-to-noise atomic force microscopy (AFM) approach, we have applied a piconewton compressive force, manipulating a Calmodulin (CaM) molecule to characterize two different forms of CaM, the Ca²⁺-ligated activated form and the Ca²⁺ free non-activated form (apo-CaM). We observed sudden and spontaneous structural rupture of apo-CaM under compressive force applied by an AFM tip, though no such events were recorded in the case of Ca²⁺-ligated activated CaM form. The sudden spontaneous structural rupture under a piconewton force compression has never been reported before, which presents an unexplored function that is likely important for protein-protein interactions and cell signaling functions.

Revealing Abrupt and Spontaneous Ruptures of Protein Native Structure under picoNewton Compressive Force Manipulation

Manipulating protein conformations for exploring protein structure-function relationship has shown great promise. Although protein conformational changes under pulling force manipulation have been extensively studied, protein conformation changes under a compressive force have not been explored quantitatively. The latter is even more biologically significant and relevant in revealing protein functions in living cells associated with protein crowdedness, distribution fluctuations, and cell osmotic stress. Here we report our experimental observations on abrupt ruptures of protein native structures under compressive force, demonstrated and studied by single-molecule AFM-FRET spectroscopic nanoscopy. Our results show that the protein ruptures are abrupt and spontaneous events occurred when the compressive force reaches a threshold of 12-75 pN, a force amplitude accessible from thermal fluctuations in a living cell. The abrupt ruptures are sensitive to local environment, likely a general and important pathway of protein unfolding in living cells.

Dynamic Neutron Scattering by Biological Systems

Dynamic neutron scattering directly probes motions in biological systems on femtosecond to microsecond timescales. When combined with molecular dynamics simulation and normal mode analysis, detailed descriptions of the forms and frequencies of motions can be derived. We examine vibrations in proteins, the temperature dependence of protein motions, and concepts describing the rich variety of motions detectable using neutrons in biological systems at physiological temperatures. New techniques for deriving information on collective motions using coherent scattering are also reviewed.

Microsecond resolved single-molecule FRET time series measurements based on the line confocal optical system combined with hybrid photodetectors

Single-molecule (sm) fluorescence time series measurements based on the line confocal optical system are a powerful strategy for the investigation of the structure, dynamics, and heterogeneity of biological macromolecules. This method enables the detection of more than several thousands of fluorescence photons per millisecond from single fluorophores, implying that the potential time resolution for measurements of the fluorescence resonance energy transfer (FRET) efficiency is 10 μs. However, the necessity of using imaging photodetectors in the method limits the time resolution in the FRET efficiency measurements to approximately 100 μs. In this investigation, a new photodetector called a hybrid photodetector (HPD) was incorporated into the line confocal system to improve the time resolution without sacrificing the length of the time series detection. Among several settings examined, the system based on a slit width of 10 μm and a high-speed counting device made the best of the features of the line confocal optical system and the HPD. This method achieved a time resolution of 10 μs and an observation time of approximately 5 ms in the sm-FRET time series measurements. The developed device was used for the native state of the B domain of protein A.

Anomalous pressure effects on the photoreaction of a light-sensor protein from Synechocystis, PixD (Slr1694), and the compressibility change of its intermediates

SyPixD (Slr1694) is a blue-light receptor that contains a BLUF (blue-light sensor using a flavin chromophore) domain for the function of phototaxis. The key reaction of this protein is a light-induced conformational change and subsequent dissociation reaction from the decamer to the dimer. In this study, anomalous effects of pressure on this reaction were discovered, and changes in the compressibility of its short-lived intermediates were investigated. While the absorption spectra of the dark and light states are not sensitive to pressure, the formation yield of the first intermediate decreases with pressure to about 40% at 150 MPa. Upon blue-light illumination with a sufficiently strong intensity, the transient grating signal, which represents the dissociation of the SyPixD decamer, was observed at 0.1 MPa, and the signal intensity significantly decreased with increasing pressure. This behavior shows that the dissociation of the decamer from the second intermediate state is suppressed by pressure. However, while the decamer undergoes no dissociation upon excitation of one monomer unit at 0.1 MPa, dissociation is gradually induced with increasing pressure. For solving this strange behavior, the compressibility changes of the intermediates were measured as a function of pressure at weak light intensity. Interestingly, the compressibility change was negative at low pressure, but became positive with increasing pressure. Because the compressibility is related to the volume fluctuation, this observation suggests that the driving force for this reaction is fluctuation of the protein. The relationship between the cavities at the interfaces of the monomer units and the reactivity was also discussed.

Toward dynamic structural biology: Two decades of single-molecule Förster resonance energy transfer

Classical structural biology can only provide static snapshots of biomacromolecules. Single-molecule Förster resonance energy transfer (smFRET) paved the way for studying dynamics in macromolecular structures under biologically relevant conditions. Since its first implementation in 1996, smFRET experiments have confirmed previously hypothesized mechanisms and provided new insights into many fundamental biological processes, such as DNA maintenance and repair, transcription, translation, and membrane transport. We review 22 years of contributions of smFRET to our understanding of basic mechanisms in biochemistry, molecular biology, and structural biology. Additionally, building on current state-of-the-art implementations of smFRET, we highlight possible future directions for smFRET in applications such as biosensing, high-throughput screening, and molecular diagnostics.

Fluorescence Correlation Spectroscopy of Labeled Azurin Reveals Photoinduced Electron Transfer between Label and Cu Center

Fluorescent labeling of biomacromolecules enjoys increasing popularity for structural, mechanistic, and microscopic investigations. Its success hinges on the ability of the dye to alternate between bright and dark states. Förster resonance energy transfer (FRET) is an important source of fluorescence modulation. Photo-induced electron transfer (PET) may occur as well, but is often considered only when donor and acceptor are in van der Waals contact. In this study, PET is shown between a label and redox centers in oxidoreductases, which may occur over large distances. In the small blue copper protein azurin, labeled with ATTO655, PET is observed when the label is at 18.5 Å, but not when it is at 29.1 Å from the Cu. For Cu^II , PET from label to Cu occurs at a rate of (4.8±0.3)×10⁴  s^-1 and back at (0.7±0.1)×10³  s^-1 . With Cu^I the numbers are (3.3±0.7)×10⁶  s^-1 and (1.0±0.1)×10⁴  s^-1 . Reorganization energies and electronic coupling elements are in the range of 0.8-1.2 eV and 0.02-0.5 cm^-1 , respectively. These data are compatible with electron transfer (ET) along a through-bond pathway although transient complex formation followed by ET cannot be ruled out. The outcome of this study is a useful guideline for experimental designs in which oxidoreductases are labelled with fluorescent dyes, with particular attention to single molecule investigations. The labelling position for FRET can be optimized to avoid reactions like PET by evaluating the structure and thermodynamics of protein and label.

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.

Origins of Enzyme Catalysis: Experimental Findings for C-H Activation, New Models, and Their Relevance to Prevailing Theoretical Constructs

The physical basis for enzymatic rate accelerations is a subject of great fundamental interest and of direct relevance to areas that include the de novo design of green catalysts and the pursuit of new drug regimens. Extensive investigations of C-H activating systems have provided considerable insight into the relationship between an enzyme's overall structure and the catalytic chemistry at its active site. This Perspective highlights recent experimental data for two members of distinct, yet iconic C-H activation enzyme classes, lipoxygenases and prokaryotic alcohol dehydrogenases. The data necessitate a reformulation of the dominant textbook definition of biological catalysis. A multidimensional model emerges that incorporates a range of protein motions that can be parsed into a combination of global stochastic conformational thermal fluctuations and local donor-acceptor distance sampling. These motions are needed to achieve a high degree of precision with regard to internuclear distances, geometries, and charges within the active site. The available model also suggests a physical framework for understanding the empirical enthalpic barrier in enzyme-catalyzed processes. We conclude by addressing the often conflicting interface between computational and experimental chemists, emphasizing the need for computation to predict experimental results in advance of their measurement.

Quantifying Microsecond Transition Times Using Fluorescence Lifetime Correlation Spectroscopy

Many complex luminescent emitters such as fluorescent proteins exhibit multiple emitting states that result in rapid fluctuations of their excited-state lifetime. Here, we apply fluorescence lifetime correlation spectroscopy (FLCS) to resolve the photophysical state dynamics of the prototypical fluorescence protein enhanced green fluorescent protein (EGFP). We quantify the microsecond transition rates between its two fluorescent states, which have otherwise highly overlapping emission spectra. We relate these transitions to a room-temperature angstrom-scale rotational isomerism of an amino acid next to its fluorescent center. With this study, we demonstrate the power of FLCS for studying the rapid transition dynamics of a broad range of light-emitting systems with complex multistate photophysics, which cannot be easily done by other methods.

Single-Molecule Monitoring of the Structural Switching Dynamics of Nucleic Acids through Controlling Fluorescence Blinking

Single-molecule fluorescence resonance energy transfer (smFRET) is a powerful tool to investigate the dynamics of biomolecular events in real time. However, it requires two fluorophores and can be applied only to dynamics that accompany large changes in distance between the molecules. Herein, we introduce a method for kinetic analysis based on control of fluorescence blinking (KACB), a general approach to investigate the dynamics of biomolecules by using a single fluorophore. By controlling the kinetics of the redox reaction the blinking kinetics or pattern can be controlled to be affected by microenvironmental changes around a fluorophore (rKACB), thereby enabling real-time single-molecule measurement of the structure-changing dynamics of nucleic acids.

Fluorescence lifetime imaging ophthalmoscopy

Imaging techniques based on retinal autofluorescence have found broad applications in ophthalmology because they are extremely sensitive and noninvasive. Conventional fundus autofluorescence imaging measures fluorescence intensity of endogenous retinal fluorophores. It mainly derives its signal from lipofuscin at the level of the retinal pigment epithelium. Fundus autofluorescence, however, can not only be characterized by the spatial distribution of the fluorescence intensity or emission spectrum, but also by a characteristic fluorescence lifetime function. The fluorescence lifetime is the average amount of time a fluorophore remains in the excited state following excitation. Fluorescence lifetime imaging ophthalmoscopy (FLIO) is an emerging imaging modality for in vivo measurement of lifetimes of endogenous retinal fluorophores. Recent reports in this field have contributed to our understanding of the pathophysiology of various macular and retinal diseases. Within this review, the basic concept of fluorescence lifetime imaging is provided. It includes technical background information and correlation with in vitro measurements of individual retinal metabolites. In a second part, clinical applications of fluorescence lifetime imaging and fluorescence lifetime features of selected retinal diseases such as Stargardt disease, age-related macular degeneration, choroideremia, central serous chorioretinopathy, macular holes, diabetic retinopathy, and retinal artery occlusion are discussed. Potential areas of use for fluorescence lifetime imaging ophthalmoscopy will be outlined at the end of this review.

Identification of the TyrOH•+ Radical Cation in the Flavoenzyme TrmFO

Tyrosine (TyrOH) and tryptophan radicals play important roles as intermediates in biochemical charge-transfer reactions. Tryptophanyl radicals have been observed both in their protonated cation form and in their unprotonated neutral form, but to date, tyrosyl radicals have only been observed in their unprotonated form. With a genetically modified form of the flavoenzyme TrmFO as a suitable model system and using ultrafast fluorescence and absorption spectroscopy, we characterize its protonated precursor TyrOH^•+, and we show this species to have a distinct visible absorption band and a transition moment that we suggest to lie close to the phenol symmetry axis. TyrOH^•+ is formed in ∼1 ps by electron transfer to excited flavin and decays in ∼3 ps by charge recombination. These findings imply that TyrOH oxidation does not necessarily induce its concerted deprotonation. Our results will allow disentangling of photoproduct states in flavoproteins in often-encountered complex situations and more generally are important for understanding redox chains relying on tyrosyl intermediates.

DNA-Endonuclease Complex Dynamics by Simultaneous FRET and Fluorophore Intensity in Evanescent Field

The single-molecule Förster resonance energy transfer (FRET) is a powerful tool to study interactions and conformational changes of biological molecules in the distance range from a few to 10 nm. In this study, we demonstrate a method to augment this range with longer distances. The method is based on the intensity changes of a tethered fluorophore, diffusing in the exponentially decaying evanescent excitation field. In combination with FRET it allowed us to reveal and characterize the dynamics of what had been inaccessible conformations of the DNA-protein complex. Our model system, restriction enzyme Ecl18kI, interacts with a FRET pair-labeled DNA fragment to form two different DNA loop conformations. The DNA-protein interaction geometry is such that the efficient FRET is expected for one of these conformations-"antiparallel" loop. In the alternative "parallel" loop, the expected distance between the dyes is outside the range accessible by FRET. Therefore, "antiparallel" looping is observed in a single-molecule time trajectory as discrete transitions to a state of high FRET efficiency. At the same time, transitions to a high-intensity state of the directly excited acceptor fluorophore on a DNA tether are due to a change of its average position in the evanescent field of excitation and can be associated with a loop of either "parallel" or "antiparallel" configuration. Simultaneous analysis of FRET and acceptor intensity trajectories then allows us to discriminate different DNA loop conformations and access the average lifetimes of different states.

Coexisting origins of subdiffusion in internal dynamics of proteins

Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.

Single Particle Tracking: From Theory to Biophysical Applications

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

Time-resolved fluctuation during the photochemical reaction of a photoreceptor protein: phototropin1LOV2-linker

Although the relationship between structural fluctuations and reactions is important for elucidating reaction mechanisms, experimental data describing such fluctuations of reaction intermediates are sparse. In order to investigate structural fluctuations during a protein reaction, the compressibilities of intermediate species after photoexcitation of a phot1LOV2-linker, which is a typical LOV domain protein with the C-terminal linker including the J-α helix and used recently for optogenetics, were measured in the time-domain by the transient grating and transient lens methods with a high pressure optical cell. The yield of covalent bond formation between the chromophore and a Cys residue (S state formation) relative to that at 0.1 MPa decreased very slightly with increasing pressure. The fraction of the reactive species that yields the T state (linker-unfolded state) decreased almost proportionally with pressure (0.1-200 MPa) to about 65%. Interestingly, the volume change associated with the reaction was much more pressure sensitive. By combining these data, the compressibility changes for the short lived intermediate (S state) and the final product (T state) formation were determined. The compressibility of the S state was found to increase compared with the dark (D) state, and the compressibility decreased during the transition from the S state to the T state. The compressibility change is discussed in terms of cavities inside the protein. By comparing the crystal structures of the phot1LOV2-linker at dark and light states, we concluded that the cavity volumes between the LOV domain and the linker domain increase in the S state, which explains the enhanced compressibility.

On the generality of Michaelian kinetics

The reversible Michaelis-Menten equation is shown to follow from a very broad class of steady-state kinetic models involving enzymes that adopt a unique free (i.e., not complexed to substrate/product) state in solution. In the case of enzymes with multiple free states/conformations (e.g., fluctuating, hysteretic, or co-operative monomeric enzymes), Michaelian behavior is still assured if the relative steady-state populations of free enzyme states are independent of substrate and product concentration. Prior models for Michaelian behavior in multiple conformer enzymes are shown to be special cases of this single condition.

Quantum ergodicity breaking in semi-classical electron transfer dynamics

Strange statistics of single-electron transfer events in a classically adiabatic electron transfer with strictly exponential ensemble kinetics.

Decoding Single Molecule Time Traces with Dynamic Disorder

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

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

Single-molecule fluorescence resonance energy transfer in molecular biology

Single-molecule fluorescence resonance energy transfer (smFRET) is a powerful technique for studying the conformation dynamics and interactions of individual biomolecules. In this review, we describe the concept and principle of smFRET, illustrate general instrumentation and microscopy settings for experiments, and discuss the methods and algorithms for data analysis. Subsequently, we review applications of smFRET in protein conformational changes, ion channel open-close properties, receptor-ligand interactions, nucleic acid structure regulation, vesicle fusion, and force induced conformational dynamics. Finally, we discuss the main limitations of smFRET in molecular biology.

Quantitative FRET studies and integrative modeling unravel the structure and dynamics of biomolecular systems

Förster Resonance Energy Transfer (FRET) combined with single-molecule spectroscopy probes macromolecular structure and dynamics and identifies coexisting conformational states. We review recent methodological developments in integrative structural modeling by satisfying spatial restraints on networks of FRET pairs (hybrid-FRET). We discuss procedures to incorporate prior structural knowledge and to obtain optimal distance networks. Finally, a workflow for hybrid-FRET is presented that automates integrative structural modeling and experiment planning to put hybrid-FRET on rails. To test this workflow, we simulate realistic single-molecule experiments and resolve three protein conformers, exchanging at 30μs and 10ms, with accuracies of 1-3Å RMSD versus the target structure. Incorporation of data from other spectroscopies and imaging is also discussed.

Superconducting nanowire single-photon detectors with non-periodic dielectric multilayers

We present superconducting nanowire single-photon detectors (SSPDs) on non-periodic dielectric multilayers, which enable us to design a variety of wavelength dependences of optical absorptance by optimizing the dielectric multilayer. By adopting a robust simulation to optimize the dielectric multilayer, we designed three types of SSPDs with target wavelengths of 500 nm, 800 nm, and telecom range respectively. We fabricated SSPDs based on the optimized designs for 500 and 800 nm, and evaluated the system detection efficiency at various wavelengths. The results obtained confirm that the designed SSPDs with non-periodic dielectric multilayers worked well. This versatile device structure can be effective for multidisciplinary applications in fields such as the life sciences and remote sensing that require high efficiency over a precise spectral range and strong signal rejection at other wavelengths.

Photon-HDF5: An Open File Format for Timestamp-Based Single-Molecule Fluorescence Experiments

We introduce Photon-HDF5, an open and efficient file format to simplify exchange and long-term accessibility of data from single-molecule fluorescence experiments based on photon-counting detectors such as single-photon avalanche diode, photomultiplier tube, or arrays of such detectors. The format is based on HDF5, a widely used platform- and language-independent hierarchical file format for which user-friendly viewers are available. Photon-HDF5 can store raw photon data (timestamp, channel number, etc.) from any acquisition hardware, but also setup and sample description, information on provenance, authorship and other metadata, and is flexible enough to include any kind of custom data. The format specifications are hosted on a public website, which is open to contributions by the biophysics community. As an initial resource, the website provides code examples to read Photon-HDF5 files in several programming languages and a reference Python library (phconvert), to create new Photon-HDF5 files and convert several existing file formats into Photon-HDF5. To encourage adoption by the academic and commercial communities, all software is released under the MIT open source license.

Path statistics, memory, and coarse-graining of continuous-time random walks on networks

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states (for example, those employed in studies of molecular kinetics) or spatial disorder can give rise to memory and non-exponential distributions of waiting times and first-passage statistics. However, existing methods for analyzing CTRWs on complex energy landscapes do not address these effects. Here we use statistical mechanics of the nonequilibrium path ensemble to characterize first-passage CTRWs on networks with arbitrary connectivity, energy landscape, and waiting time distributions. Our approach can be applied to calculating higher moments (beyond the mean) of path length, time, and action, as well as statistics of any conservative or non-conservative force along a path. For homogeneous networks, we derive exact relations between length and time moments, quantifying the validity of approximating a continuous-time process with its discrete-time projection. For more general models, we obtain recursion relations, reminiscent of transfer matrix and exact enumeration techniques, to efficiently calculate path statistics numerically. We have implemented our algorithm in PathMAN (Path Matrix Algorithm for Networks), a Python script that users can apply to their model of choice. We demonstrate the algorithm on a few representative examples which underscore the importance of non-exponential distributions, memory, and coarse-graining in CTRWs.

Bioluminophore and Flavin Mononucleotide Fluorescence Quenching of Bacterial Bioluminescence-A Theoretical Study

Bacterial bioluminescence with continuous glow has been applied to the fields of environmental toxin monitoring, drug screening, and in vivo imaging. Nonetheless, the chemical form of the bacterial bioluminophore is still a bone of contention. Flavin mononucleotide (FMN), one of the light-emitting products, and 4a-hydroxy-5-hydro flavin mononucleotide (HFOH), an intermediate of the chemical reactions, have both been assumed candidates for the light emitter because they have similar molecular structures and fluorescence wavelengths. The latter is preferred in experiments and was assigned in our previous density functional study. HFOH displays weak fluorescence in solutions, but exhibits strong bioluminescence in the bacterial luciferase. FMN shows the opposite behavior; its fluorescence is quenched when it is bound to the luciferase. This is the first example of flavin fluorescence quenching observed in bioluminescent systems and is merely an observation, both the quenching mechanism and quencher are still unclear. Based on theoretical analysis of high-level quantum mechanics (QM), combined QM and molecular mechanics (QM/MM), and molecular dynamics (MD), this paper confirms that HFOH in its first singlet excited state is the bioluminophore of bacterial bioluminescence. More importantly, the computational results indicate that Tyr110 in the luciferase quenches the FMN fluorescence via an electron-transfer mechanism.

Theory of Acoustic Raman Modes in Proteins

We present a theoretical analysis that associates the resonances of extraordinary acoustic Raman (EAR) spectroscopy [Wheaton et al., Nat. Photonics 9, 68 (2015)] with the collective modes of proteins. The theory uses the anisotropic elastic network model to find the protein acoustic modes, and calculates Raman intensity by treating the protein as a polarizable ellipsoid. Reasonable agreement is found between EAR spectra and our theory. Protein acoustic modes have been extensively studied theoretically to assess the role they play in protein function; this result suggests EAR spectroscopy as a new experimental tool for studies of protein acoustic modes.