Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer

The roughness of the protein energy landscape results in anomalous diffusion of the polypeptide backbone

Recombination of photolysed protein disulfide bonds confirms subdiffusional backbone motion and measures the roughness of the protein's energy landscape.

Insight into the catalytic mechanism of meta-cleavage product hydrolase BphD: a quantum mechanics/molecular mechanics study

The catalytic mechanism of BphD (the fourth enzyme of the biphenyl catabolic pathway) toward its natural substrate 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoic acid (HOPDA) was investigated in atomistic detail by QM/MM approach.

Computational insights into the charge relaying properties of β-turn peptides in protein charge transfers

Density functional theory calculations suggest that β-turn peptide segments can act as a novel dual-relay elements to facilitate long-range charge hopping transport in proteins, with the N terminus relaying electron hopping transfer and the C terminus relaying hole hopping migration. The electron- or hole-binding ability of such a β-turn is subject to the conformations of oligopeptides and lengths of its linking strands. On the one hand, strand extension at the C-terminal end of a β-turn considerably enhances the electron-binding of the β-turn N terminus, due to its unique electropositivity in the macro-dipole, but does not enhance hole-forming of the β-turn C terminus because of competition from other sites within the β-strand. On the other hand, strand extension at the N terminal end of the β-turn greatly enhances hole-binding of the β-turn C terminus, due to its distinct electronegativity in the macro-dipole, but does not considerably enhance electron-binding ability of the N terminus because of the shared responsibility of other sites in the β-strand. Thus, in the β-hairpin structures, electron- or hole-binding abilities of both termini of the β-turn motif degenerate compared with those of the two hook structures, due to the decreased macro-dipole polarity caused by the extending the two terminal strands. In general, the high polarity of a macro-dipole always plays a principal role in determining charge-relay properties through modifying the components and energies of the highest occupied and lowest unoccupied molecular orbitals of the β-turn motif, whereas local dipoles with low polarity only play a cooperative assisting role. Further exploration is needed to identify other factors that influence relay properties in these protein motifs.

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

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

Silicon photon-counting avalanche diodes for single-molecule fluorescence spectroscopy

Solution-based single-molecule fluorescence spectroscopy is a powerful experimental tool with applications in cell biology, biochemistry and biophysics. The basic feature of this technique is to excite and collect light from a very small volume and work in a low concentration regime resulting in rare burst-like events corresponding to the transit of a single molecule. Detecting photon bursts is a challenging task: the small number of emitted photons in each burst calls for high detector sensitivity. Bursts are very brief, requiring detectors with fast response time and capable of sustaining high count rates. Finally, many bursts need to be accumulated to achieve proper statistical accuracy, resulting in long measurement time unless parallelization strategies are implemented to speed up data acquisition. In this paper we will show that silicon single-photon avalanche diodes (SPADs) best meet the needs of single-molecule detection. We will review the key SPAD parameters and highlight the issues to be addressed in their design, fabrication and operation. After surveying the state-of-the-art SPAD technologies, we will describe our recent progress towards increasing the throughput of single-molecule fluorescence spectroscopy in solution using parallel arrays of SPADs. The potential of this approach is illustrated with single-molecule Förster resonance energy transfer measurements.

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

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

Scale-free fluctuations in behavioral performance: delineating changes in spontaneous behavior of humans with induced sleep deficiency

The timing and dynamics of many diverse behaviors of mammals, e.g., patterns of animal foraging or human communication in social networks exhibit complex self-similar properties reproducible over multiple time scales. In this paper, we analyze spontaneous locomotor activity of healthy individuals recorded in two different conditions: during a week of regular sleep and a week of chronic partial sleep deprivation. After separating activity from rest with a pre-defined activity threshold, we have detected distinct statistical features of duration times of these two states. The cumulative distributions of activity periods follow a stretched exponential shape, and remain similar for both control and sleep deprived individuals. In contrast, rest periods, which follow power-law statistics over two orders of magnitude, have significantly distinct distributions for these two groups and the difference emerges already after the first night of shortened sleep. We have found steeper distributions for sleep deprived individuals, which indicates fewer long rest periods and more turbulent behavior. This separation of power-law exponents is the main result of our investigations, and might constitute an objective measure demonstrating the severity of sleep deprivation and the effects of sleep disorders.

Significant expansion of fluorescent protein sensing ability through the genetic incorporation of superior photo-induced electron-transfer quenchers

Photo-induced electron transfer (PET) is ubiquitous for photosynthesis and fluorescent sensor design. However, genetically coded PET sensors are underdeveloped, due to the lack of methods to site-specifically install PET probes on proteins. Here we describe a family of acid and Mn(III) turn-on fluorescent protein (FP) sensors, named iLovU, based on PET and the genetic incorporation of superior PET quenchers in the fluorescent flavoprotein iLov. Using the iLovU PET sensors, we monitored the cytoplasmic acidification process, and achieved Mn(III) fluorescence sensing for the first time. The iLovU sensors should be applicable for studying pH changes in living cells, monitoring biogentic Mn(III) in the environment, and screening for efficient manganese peroxidase, which is highly desirable for lignin degradation and biomass conversion. Our work establishes a platform for many more protein PET sensors, facilitates the de novo design of metalloenzymes harboring redox active residues, and expands our ability to probe protein conformational dynamics.

Sinc-Chebyshev collocation method for a class of fractional diffusion-wave equations

This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed.

Single molecule conformational memory extraction: p5ab RNA hairpin

Extracting kinetic models from single molecule data is an important route to mechanistic insight in biophysics, chemistry, and biology. Data collected from force spectroscopy can probe discrete hops of a single molecule between different conformational states. Model extraction from such data is a challenging inverse problem because single molecule data are noisy and rich in structure. Standard modeling methods normally assume (i) a prespecified number of discrete states and (ii) that transitions between states are Markovian. The data set is then fit to this predetermined model to find a handful of rates describing the transitions between states. We show that it is unnecessary to assume either (i) or (ii) and focus our analysis on the zipping/unzipping transitions of an RNA hairpin. The key is in starting with a very broad class of non-Markov models in order to let the data guide us toward the best model from this very broad class. Our method suggests that there exists a folding intermediate for the P5ab RNA hairpin whose zipping/unzipping is monitored by force spectroscopy experiments. This intermediate would not have been resolved if a Markov model had been assumed from the onset. We compare the merits of our method with those of others.

Picosecond-resolved fluorescent probes at functionally distinct tryptophans within a thermophilic alcohol dehydrogenase: relationship of temperature-dependent changes in fluorescence to catalysis

Two single-tryptophan variants were generated in a thermophilic alcohol dehydrogenase with the goal of correlating temperature-dependent changes in local fluorescence with the previously demonstrated catalytic break at ca. 30 °C (Kohen et al., Nature 1999, 399, 496). One tryptophan variant, W87in, resides at the active site within van der Waals contact of bound alcohol substrate; the other variant, W167in, is a remote-site surface reporter located >25 Å from the active site. Picosecond-resolved fluorescence measurements were used to analyze fluorescence lifetimes, time-dependent Stokes shifts, and the extent of collisional quenching at Trp87 and Trp167 as a function of temperature. A subnanosecond fluorescence decay rate constant has been detected for W87in that is ascribed to the proximity of the active site Zn(2+) and shows a break in behavior at 30 °C. For the remainder of the reported lifetime measurements, there is no detectable break between 10 and 50 °C, in contrast with previously reported hydrogen/deuterium exchange experiments that revealed a temperature-dependent break analogous to catalysis (Liang et al., Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 9556). We conclude that the motions that lead to the rigidification of ht-ADH below 30 °C are likely to be dominated by global processes slower than the picosecond to nanosecond motions measured herein. In the case of collisional quenching of fluorescence by acrylamide, W87in and W167in behave in a similar manner that resembles free tryptophan in water. Stokes shift measurements, by contrast, show distinctive behaviors in which the active-site tryptophan relaxation is highly temperature-dependent, whereas the solvent-exposed tryptophan's dynamics are temperature-independent. These data are concluded to reflect a significantly constrained environment surrounding the active site Trp87 that both increases the magnitude of the Stokes shift and its temperature-dependence. The results are discussed in the context of spatially distinct differences in enthalpic barriers for protein conformational sampling that may be related to catalysis.

Modified surface plasmon polaritons for the nanoconcentration and long-range propagation of optical energy

We propose a new surface plasmon polariton concept for the nanoconcentration and long-range propagation of optical energy. The propagation loss from the mode can be greatly decreased, and the mode nanoconfinement can be simultaneously maintained, by appropriately modifying the field distribution of the surface plasmon polaritons. Furthermore, we present a metal nanowire placed in a dielectric hole to guide the mode and achieve both a 26 nm beam radius and a 24 mm propagation distance. We expect the modified surface plasmon polaritons to motivate many important applications in nanophotonics, biophotonics, and highly integrated photonic circuits.

Extensive use of FRET in biological imaging

Förster resonance energy transfer (FRET) is a phenomenon used for bioimaging ranging from single molecules to in vivo scale. A large variety of organic dyes and fluorescent proteins are available for FRET probes. In this review, we introduce the representative pairs of FRET probes developed thus far. The efficiency of FRET is depending on the spectral overlap of donor emission and acceptor absorption, the orientation of donor and acceptor and their distance. For FRET-based indicators composed of fluorescent proteins, their orientation and dimeric property of donor and acceptor largely affect the FRET efficiency, indicating the effect for the performance of indicators. In addition, three major applications of FRET, including genetically encoded indicators, single-molecule FRET, and enhancement of chemiluminescent proteins, have been introduced and their functions have also been discussed.

Stretching of single poly-ubiquitin molecules revisited: dynamic disorder in the non-exponential unfolding kinetics

A theoretical framework based on a generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and a power-law memory kernel is presented to describe the non-exponential kinetics of the unfolding of a single poly-ubiquitin molecule under a constant force [T.-L. Kuo, S. Garcia-Manyes, J. Li, I. Barel, H. Lu, B. J. Berne, M. Urbakh, J. Klafter, and J. M. Fernández, Proc. Natl. Acad. Sci. U.S.A. 107, 11336 (2010)]. Such a GLE-fGn strategy is made on the basis that the pulling coordinate variable x undergoes subdiffusion, usually resulting from conformational fluctuations, over a one-dimensional force-modified free-energy surface U(x, F). By using the Kramers' rate theory, we have obtained analytical formulae for the time-dependent rate coefficient k(t, F), the survival probability S(t, F) as well as the waiting time distribution function f(t, F) as functions of time t and force F. We find that our results can fit the experimental data of f(t, F) perfectly in the whole time range with a power-law exponent γ = 1/2, the characteristic of typical anomalous subdiffusion. In addition, the fitting of the survival probabilities for different forces facilitates us to reach rather reasonable estimations for intrinsic properties of the system, such as the free-energy barrier and the distance between the native conformation and the transition state conformation along the reaction coordinate, which are in good agreements with molecular dynamics simulations in the literatures. Although static disorder has been implicated in the original work of Kuo et al., our work suggests a sound and plausible alternative interpretation for the non-exponential kinetics in the stretching of poly-ubiquitin molecules, associated with dynamic disorder.

Slow diffusion underlies alternation of fast and slow growth periods of microtubule assembly

In vitro microtubule assembly exhibits a rhythmic phenomenon, that is, fast growth periods alternating with slow growth periods. Mechanism underlying this phenomenon is unknown. Here a simple diffusion mechanism coupled with small diffusion coefficients is proposed to underlie this phenomenon. Calculations based on previously published results demonstrate that such a mechanism can explain the differences in the average duration of the interval encompassing a fast growth period and a slow growth period in in vitro microtubule assembly experiments in different conditions. Because no parameter unique to the microtubule assembly process is involved in the analysis, the proposed mechanism is expected to be generally applicable to heterogeneous chemical reactions. Also because biological systems are characterized by heterogeneous chemical reactions, the diffusion-based rhythmic characteristic of heterogeneous reactions is postulated to be a fundamental element in generating rhythmic behaviors in biological systems.

Electron transfer-based single molecule fluorescence as a probe for nano-environment dynamics

Electron transfer (ET) is one of the most important elementary processes that takes place in fundamental aspects of biology, chemistry, and physics. In this review, we discuss recent research on single molecule probes based on ET. We review some applications, including the dynamics of glass-forming systems, surface binding events, interfacial ET on semiconductors, and the external field-induced dynamics of polymers. All these examples show that the ET-induced changes of fluorescence trajectory and lifetime of single molecules can be used to sensitively probe the surrounding nano-environments.

1/ f Fluctuations of amino acids regulate water transportation in aquaporin 1

Aquaporins (AQPs), which transport water molecules across cell membranes, are involved in many physiological processes. Recently, it is reported that the water-water interactions within the channel are broken at the aromatic/arginine selectivity filter (ar/R region), which prevents proton transportation [U. K. Eriksson et al., Science 340, 1346 (2013)]. However, the effects of the conformational fluctuations of amino acids on water transportation remain unclear. Using all-atom molecular dynamics simulations, we analyze water transportation and fluctuations of amino acids within AQP1. The amino acids exhibit 1/f fluctuations, indicating possession of long-term memory. Moreover, we find that water molecules crossing the ar/R region obey a non-Poisson process. To investigate the effect of 1/f fluctuations on water transportation, we perform restrained molecular dynamics simulations of AQP1 and simple Langevin stochastic simulations. As a result, we confirm that 1/f fluctuations of amino acids contribute to water transportation in AQP1. These findings appreciably enhance our understanding of AQPs and suggest possibilities for developing biomimetic nanopores.

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

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

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

MATHEMATICAL TREATMENTS THAT SOLVE SINGLE MOLECULES

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

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

Probing backbone dynamics with hydrogen/deuterium exchange mass spectrometry

Protein dynamics can be probed by the solution technique amide hydrogen/deuterium exchange. The exchange rate of hydrogen for deuterium along a peptide backbone is dependent on the extent of hydrogen bonding from secondary structure, accessibility by D2O, and protein motions. Both global and local conformational changes that alter bonding or structure will lead to changes in the amount of deuterium incorporated. The deuterium can be localized via pepsin digestion of the protein and quantified by electrospray ionization mass spectrometry through the mass shifts of the resulting peptides. The technique is emerging as an essential tool to study protein structure in solution due to the exceptional capability of examining both dynamic and structural changes related to protein function.

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

This Perspective summarises the properties of a variety of anomalous diffusion processes and provides the necessary tools to analyse and interpret recorded anomalous diffusion data.

Statistics and Related Topics in Single-Molecule Biophysics

Since the universal acceptance of atoms and molecules as the fundamental constituents of matter in the early twentieth century, molecular physics, chemistry and molecular biology have all experienced major theoretical breakthroughs. To be able to actually "see" biological macromolecules, one at a time in action, one has to wait until the 1970s. Since then the field of single-molecule biophysics has witnessed extensive growth both in experiments and theory. A distinct feature of single-molecule biophysics is that the motions and interactions of molecules and the transformation of molecular species are necessarily described in the language of stochastic processes, whether one investigates equilibrium or nonequilibrium living behavior. For laboratory measurements following a biological process, if it is sampled over time on individual participating molecules, then the analysis of experimental data naturally calls for the inference of stochastic processes. The theoretical and experimental developments of single-molecule biophysics thus present interesting questions and unique opportunity for applied statisticians and probabilists. In this article, we review some important statistical developments in connection to single-molecule biophysics, emphasizing the application of stochastic-process theory and the statistical questions arising from modeling and analyzing experimental data.

Observation time scale, free-energy landscapes, and molecular symmetry

When structures that interconvert on a given time scale are lumped together, the corresponding free-energy surface becomes a function of the observation time. This view is equivalent to grouping structures that are connected by free-energy barriers below a certain threshold. We illustrate this time dependence for some benchmark systems, namely atomic clusters and alanine dipeptide, highlighting the connections to broken ergodicity, local equilibrium, and "feasible" symmetry operations of the molecular Hamiltonian.

BOBA FRET: bootstrap-based analysis of single-molecule FRET data

Time-binned single-molecule Förster resonance energy transfer (smFRET) experiments with surface-tethered nucleic acids or proteins permit to follow folding and catalysis of single molecules in real-time. Due to the intrinsically low signal-to-noise ratio (SNR) in smFRET time traces, research over the past years has focused on the development of new methods to extract discrete states (conformations) from noisy data. However, limited observation time typically leads to pronounced cross-sample variability, i.e., single molecules display differences in the relative population of states and the corresponding conversion rates. Quantification of cross-sample variability is necessary to perform statistical testing in order to assess whether changes observed in response to an experimental parameter (metal ion concentration, the presence of a ligand, etc.) are significant. However, such hypothesis testing has been disregarded to date, precluding robust biological interpretation. Here, we address this problem by a bootstrap-based approach to estimate the experimental variability. Simulated time traces are presented to assess the robustness of the algorithm in conjunction with approaches commonly used in thermodynamic and kinetic analysis of time-binned smFRET data. Furthermore, a pair of functionally important sequences derived from the self-cleaving group II intron Sc.ai5γ (d3'EBS1*/IBS1*) is used as a model system. Through statistical hypothesis testing, divalent metal ions are shown to have a statistically significant effect on both thermodynamic and kinetic aspects of their interaction. The Matlab source code used for analysis (bootstrap-based analysis of smFRET data, BOBA FRET), as well as a graphical user interface, is available via http://www.aci.uzh.ch/rna/.

Proteins in action: femtosecond to millisecond structural dynamics of a photoactive flavoprotein

Living systems are fundamentally dependent on the ability of proteins to respond to external stimuli. The mechanism, the underlying structural dynamics, and the time scales for regulation of this response are central questions in biochemistry. Here we probe the structural dynamics of the BLUF domain found in several photoactive flavoproteins, which is responsible for light activated functions as diverse as phototaxis and gene regulation. Measurements have been made over 10 decades of time (from 100 fs to 1 ms) using transient vibrational spectroscopy. Chromophore (flavin ring) localized dynamics occur on the pico- to nanosecond time scale, while subsequent protein structural reorganization is observed over microseconds. Multiple time scales are observed for the dynamics associated with different vibrations of the protein, suggesting an underlying hierarchical relaxation pathway. Structural evolution in residues directly H-bonded to the chromophore takes place more slowly than changes in more remote residues. However, a point mutation which suppresses biological function is shown to 'short circuit' this structural relaxation pathway, suppressing the changes which occur further away from the chromophore while accelerating dynamics close to it.

Fluorescent silver nanoclusters as DNA probes

Fluorescent silver nanoclusters (few atoms, quantum sized) have attracted much attention as promising substitutes for conventional fluorophores. Due to their unique environmental sensitivities, new fluorescent probes have been developed based on silver nanoclusters for the sensitive and specific detection of DNA. In this review we present the recent discoveries of activatable and color-switchable properties of DNA-templated silver nanoclusters and discuss the strategies to use these new properties in DNA sensing.

Photo-induced conformational flexibility in single solution-phase peridinin-chlorophyll-proteins

The peridinin-chlorophyll-protein (PCP) is an accessory light-harvesting complex found in red-tide dinoflagellates. PCP absorbs photons primarily in the blue-green spectral region via peridinin (Per) carotenoid pigments which then transfer excitations to chlorophyll (Chl) and ultimately downstream to photosystem II (PSII). Whereas the ultrafast dynamics of PCP are well-studied, much less is known about slower protein dynamics on time scales of milliseconds and seconds. Previous single-molecule studies of spectral emission and intensity have attached PCP to surfaces, but the native environment of PCP is in the lumen, meaning that a surface-attached environment could perturb its native conformations. To address this concern, we use the anti-Brownian electrokinetic (ABEL) trap to study single PCP monomers in solution for several seconds each. We measure, for the first time, simultaneous single-molecule intensity, lifetime, and spectral emission shifts for each trapped PCP monomer. The rate of reversible spectral redshifts depends linearly on irradiance over a factor of 30, indicating a light-induced mechanism which we attribute to a protein conformational change. Independent of these spectral shifts, our measurements of intensity and lifetime show reversible Chl quenching. In contrast to previous work, we show that this quenching cannot result from isolated photobleaching of Chl. These independent mechanisms arise from distinct conformational changes which maintain relatively stable fluorescence emission.

Aggregated markov model using time series of single molecule dwell times with minimum excessive information

Statistics of the dwell times, the stationary state distributions (SSDs), are often studied to infer the underlying kinetics from a single molecule finite-level time series. However, it is well known that the underlying kinetic scheme, a hidden Markov model (HMM), cannot be identified uniquely from the SSDs because some features of the underlying HMM are hidden by finite-level measurements. Here, we quantify the amount of excessive information in a given HMM that is not warranted by the measured SSDs and extract the HMM with minimum excessive information as the most objective representation of the data. The method is applied to a single molecule enzymatic turnover experiment, and the origin of dynamic disorder is discussed in terms of the network properties of the HMM.

Kinetic response of a photoperturbed allosteric protein

By covalently linking an azobenzene photoswitch across the binding groove of a PDZ domain, a conformational transition, similar to the one occurring upon ligand binding to the unmodified domain, can be initiated on a picosecond timescale by a laser pulse. The protein structures have been characterized in the two photoswitch states through NMR spectroscopy and the transition between them through ultrafast IR spectroscopy and molecular dynamics simulations. The binding groove opens on a 100-ns timescale in a highly nonexponential manner, and the molecular dynamics simulations suggest that the process is governed by the rearrangement of the water network on the protein surface. We propose this rearrangement of the water network to be another possible mechanism of allostery.

Numerical construction of estimators for single-molecule fluorescence measurements

A novel scheme to estimate the values of the underlying physical quantity and those of any functions of the quantity from measured observable(s) contaminated with stochastic noise is presented for any arbitrary probability distribution. The constructed estimators can either maximize the unbiasedness (i.e., minimize the amount of the deviation of the expectation value from the true value buried in the measurement) or minimize the risk (the average deviation from the true value) depending on the relative priority of unbiasedness and risk in the data analysis. The performance of the constructed estimators is demonstrated with computer simulations of Förster-type resonance energy transfer (FRET) measurements and also with FRET experimental data of the agonist-binding domain of the GluA2 subunit of AMPA receptors with agonists chloro- and iodo-willardiines and with adenylate kinase both in the apo form and with substrates AMP-PNP and AMP. It is shown that the estimators constructed by the present method can quantify faithfully not only the physical quantity to be monitored but also the functions of that quantity for a wide range of values.

Ultrafast fluorescence quenching dynamics of Atto655 in the presence of N-acetyltyrosine and N-acetyltryptophan in aqueous solution: proton-coupled electron transfer versus electron transfer

We studied the ultrafast fluorescence quenching dynamics of Atto655 in the presence of N-acetyltyrosine (AcTyr) and N-acetyltryptophan (AcTrp) in aqueous solution with femtosecond transient absorption spectroscopy. We found that the charge-transfer rate between Atto655 and AcTyr is about 240 times smaller than that between Atto655 and AcTrp. The pH value and D2O dependences of the excited-state decay kinetics of Atto655 in the presence of AcTyr and AcTrp reveal that the quenching of Atto655 fluorescence by AcTyr in aqueous solution is via a proton-coupled electron-transfer (PCET) process and that the quenching of Atto655 fluorescence by AcTrp in aqueous solution is via an electron-transfer process. With the version of the semiclassical Marcus ET theory, we derived that the electronic coupling constant for the PCET reaction between Atto655 and AcTyr in aqueous solution is 8.3 cm(-1), indicating that the PCET reaction between Atto655 and AcTyr in aqueous solution is nonadiabatic.

Kinetics of molecular transitions with dynamic disorder in single-molecule pulling experiments

Macromolecular transitions are subject to large fluctuations of rate constant, termed as dynamic disorder. The individual or intrinsic transition rates and activation free energies can be extracted from single-molecule pulling experiments. Here we present a theoretical framework based on a generalized Langevin equation with fractional Gaussian noise and power-law memory kernel to study the kinetics of macromolecular transitions to address the effects of dynamic disorder on barrier-crossing kinetics under external pulling force. By using the Kramers' rate theory, we have calculated the fluctuating rate constant of molecular transition, as well as the experimentally accessible quantities such as the force-dependent mean lifetime, the rupture force distribution, and the speed-dependent mean rupture force. Particular attention is paid to the discrepancies between the kinetics with and without dynamic disorder. We demonstrate that these discrepancies show strong and nontrivial dependence on the external force or the pulling speed, as well as the barrier height of the potential of mean force. Our results suggest that dynamic disorder is an important factor that should be taken into account properly in accurate interpretations of single-molecule pulling experiments.

Ultrafast real-time visualization of active site flexibility of flavoenzyme thymidylate synthase ThyX

In many bacteria the flavoenzyme thymidylate synthase ThyX produces the DNA nucleotide deoxythymidine monophosphate from dUMP, using methylenetetrahydrofolate as carbon donor and NADPH as hydride donor. Because all three substrates bind in close proximity to the catalytic flavin adenine dinucleotide group, substantial flexibility of the ThyX active site has been hypothesized. Using femtosecond time-resolved fluorescence spectroscopy, we have studied the conformational heterogeneity and the conformational interconversion dynamics in real time in ThyX from the hyperthermophilic bacterium Thermotoga maritima. The dynamics of electron transfer to excited flavin adenine dinucleotide from a neighboring tyrosine residue are used as a sensitive probe of the functional dynamics of the active site. The fluorescence decay spanned a full three orders of magnitude, demonstrating a very wide range of conformations. In particular, at physiological temperatures, multiple angstrom cofactor-residue displacements occur on the picoseconds timescale. These experimental findings are supported by molecular dynamics simulations. Binding of the dUMP substrate abolishes this flexibility and stabilizes the active site in a configuration where dUMP closely interacts with the flavin cofactor and very efficiently quenches fluorescence itself. Our results indicate a dynamic selected-fit mechanism where binding of the first substrate dUMP at high temperature stabilizes the enzyme in a configuration favorable for interaction with the second substrate NADPH, and more generally have important implications for the role of active site flexibility in enzymes interacting with multiple poly-atom substrates and products. Moreover, our data provide the basis for exploring the effect of inhibitor molecules on the active site dynamics of ThyX and other multisubstrate flavoenzymes.

Electronic measurements of single-molecule catalysis by cAMP-dependent protein kinase A

Single-molecule studies of enzymes open a window into their dynamics and kinetics. A single molecule of the catalytic domain of cAMP-dependent protein kinase A (PKA) was attached to a single-walled carbon nanotube device for long-duration monitoring. The electronic recording clearly resolves substrate binding, ATP binding, and cooperative formation of PKA's catalytically functional, ternary complex. Using recordings of a single PKA molecule extending over 10 min and tens of thousands of binding events, we determine the full transition probability matrix and conversion rates governing formation of the apo, intermediate, and closed enzyme configurations. We also observe kinetic rates varying over 2 orders of magnitude from one second to another. Anti-correlation of the on and off rates for PKA binding to the peptide substrate, but not ATP, demonstrates that regulation of enzyme activity results from altering the stability of the PKA-substrate complex, not its binding to ATP. The results depict a highly dynamic enzyme offering dramatic possibilities for regulated activity, an attribute useful for an enzyme with crucial roles in cell signaling.

Ensemble-based characterization of unbound and bound states on protein energy landscape

Physicochemical description of numerous cell processes is fundamentally based on the energy landscapes of protein molecules involved. Although the whole energy landscape is difficult to reconstruct, increased attention to particular targets has provided enough structures for mapping functionally important subspaces associated with the unbound and bound protein structures. The subspace mapping produces a discrete representation of the landscape, further called energy spectrum. We compiled and characterized ensembles of bound and unbound conformations of six small proteins and explored their spectra in implicit solvent. First, the analysis of the unbound-to-bound changes points to conformational selection as the binding mechanism for four proteins. Second, results show that bound and unbound spectra often significantly overlap. Moreover, the larger the overlap the smaller the root mean square deviation (RMSD) between the bound and unbound conformational ensembles. Third, the center of the unbound spectrum has a higher energy than the center of the corresponding bound spectrum of the dimeric and multimeric states for most of the proteins. This suggests that the unbound states often have larger entropy than the bound states. Fourth, the exhaustively long minimization, making small intrarotamer adjustments (all-atom RMSD ≤ 0.7 Å), dramatically reduces the distance between the centers of the bound and unbound spectra as well as the spectra extent. It condenses unbound and bound energy levels into a thin layer at the bottom of the energy landscape with the energy spacing that varies between 0.8-4.6 and 3.5-10.5 kcal/mol for the unbound and bound states correspondingly. Finally, the analysis of protein energy fluctuations showed that protein vibrations itself can excite the interstate transitions, including the unbound-to-bound ones.

Temperature Dependence of Logarithmic-like Relaxational Dynamics of Hydrated tRNA

The dynamics of RNA within the β-relaxation region of 10 ps to 1 ns is crucial to its biological function. Because of its simpler chemical building blocks and the lack of the side methyl groups, faster relaxational dynamics of RNA compared to proteins can be expected. However, the situation is actually opposite. In this work, the relaxational dynamics of tRNA is measured by quasielastic neutron scattering and analyzed using the mode coupling theory, originally developed for glass-forming liquids. Our results reveal that the dynamics of tRNA follows a log-decay within the β-relaxation region, which is an important trait demonstrated by the dynamics of proteins. The dynamics of hydrated tRNA and lysozyme compared in the time domain further demonstrate that the slower dynamics of tRNA relative to proteins originates from the difference in the folded states of tRNA and proteins, as well as the influence of their hydration water.