Hidden Markov model analysis of multichromophore photobleaching

FluoroTensor: Identification and tracking of colocalised molecules and their stoichiometries in multi-colour single molecule imaging via deep learning

The identification of photobleaching steps in single molecule fluorescence imaging is a well-established procedure for analysing the stoichiometries of molecular complexes. Nonetheless, the method is challenging with protein fluorophores because of the high levels of noise, rapid bleaching and highly variable signal intensities, all of which complicate methods based on statistical analyses of intensities to identify bleaching steps. It has recently been shown that deep learning by convolutional neural networks can yield an accurate analysis with a relatively short computational time. We describe here an improved use of such an approach that detects bleaching events even in the first time point of observation, and we have included this within an integrated software package incorporating fluorescence spot detection, colocalisation, tracking, FRET and photobleaching step analyses of single molecules or complexes. This package, known as FluoroTensor, is written in Python with a self-explanatory user interface.

Unlicensed origin DNA melting by MCV and SV40 polyomavirus LT proteins is independent of ATP-dependent helicase activity

Cellular eukaryotic replication initiation helicases are first loaded as head-to-head double hexamers on double-stranded (ds) DNA origins and then initiate S-phase DNA melting during licensed (once per cell cycle) replication. Merkel cell polyomavirus (MCV) large T (LT) helicase oncoprotein similarly binds and melts its own 98-bp origin but replicates multiple times in a single cell cycle. To examine the actions of this unlicensed viral helicase, we quantitated multimerization of MCV LT molecules as they assembled on MCV DNA origins using real-time single-molecule microscopy. MCV LT formed highly stable double hexamers having 17-fold longer mean lifetime (τ, >1,500 s) on DNA than single hexamers. Unexpectedly, partial MCV LT assembly without double-hexamer formation was sufficient to melt origin dsDNA as measured by RAD51, RPA70, or S1 nuclease cobinding. DNA melting also occurred with truncated MCV LT proteins lacking the helicase domain, but was lost from a protein without the multimerization domain that could bind only as a monomer to DNA. SV40 polyomavirus LT also multimerized to the MCV origin without forming a functional hexamer but still melted origin DNA. MCV origin melting did not require ATP hydrolysis and occurred for both MCV and SV40 LT proteins using the nonhydrolyzable ATP analog, adenylyl-imidodiphosphate (AMP-PNP). LT double hexamers formed in AMP-PNP, and melted DNA, consistent with direct LT hexamer assembly around single-stranded (ss) DNA without the energy-dependent dsDNA-to-ssDNA melting and remodeling steps used by cellular helicases. These results indicate that LT multimerization rather than helicase activity is required for origin DNA melting during unlicensed virus replication.

Amino acid sequence assignment from single molecule peptide sequencing data using a two-stage classifier

We present a machine learning-based interpretive framework (whatprot) for analyzing single molecule protein sequencing data produced by fluorosequencing, a recently developed proteomics technology that determines sparse amino acid sequences for many individual peptide molecules in a highly parallelized fashion. Whatprot uses Hidden Markov Models (HMMs) to represent the states of each peptide undergoing the various chemical processes during fluorosequencing, and applies these in a Bayesian classifier, in combination with pre-filtering by a k-Nearest Neighbors (kNN) classifier trained on large volumes of simulated fluorosequencing data. We have found that by combining the HMM based Bayesian classifier with the kNN pre-filter, we are able to retain the benefits of both, achieving both tractable runtimes and acceptable precision and recall for identifying peptides and their parent proteins from complex mixtures, outperforming the capabilities of either classifier on its own. Whatprot's hybrid kNN-HMM approach enables the efficient interpretation of fluorosequencing data using a full proteome reference database and should now also enable improved sequencing error rate estimates.

Deep learning in single-molecule imaging and analysis: recent advances and prospects

Single-molecule microscopy is advantageous in characterizing heterogeneous dynamics at the molecular level. However, there are several challenges that currently hinder the wide application of single molecule imaging in bio-chemical studies, including how to perform single-molecule measurements efficiently with minimal run-to-run variations, how to analyze weak single-molecule signals efficiently and accurately without the influence of human bias, and how to extract complete information about dynamics of interest from single-molecule data. As a new class of computer algorithms that simulate the human brain to extract data features, deep learning networks excel in task parallelism and model generalization, and are well-suited for handling nonlinear functions and extracting weak features, which provide a promising approach for single-molecule experiment automation and data processing. In this perspective, we will highlight recent advances in the application of deep learning to single-molecule studies, discuss how deep learning has been used to address the challenges in the field as well as the pitfalls of existing applications, and outline the directions for future development.

Toward high-throughput oligomer detection and classification for early-stage aggregation of amyloidogenic protein

Aggregation kinetics of proteins and peptides have been studied extensively due to their significance in many human diseases, including neurodegenerative disorders, and the roles they play in some key physiological processes. However, most of these studies have been performed as bulk measurements using Thioflavin T or other fluorescence turn-on reagents as indicators of fibrillization. Such techniques are highly successful in making inferences about the nucleation and growth mechanism of fibrils, yet cannot directly measure assembly reactions at low protein concentrations which is the case for amyloid-β (Aβ) peptide under physiological conditions. In particular, the evolution from monomer to low-order oligomer in early stages of aggregation cannot be detected. Single-molecule methods allow direct access to such fundamental information. We developed a high-throughput protocol for single-molecule photobleaching experiments using an automated fluorescence microscope. Stepwise photobleaching analysis of the time profiles of individual foci allowed us to determine stoichiometry of protein oligomers and probe protein aggregation kinetics. Furthermore, we investigated the potential application of supervised machine learning with support vector machines (SVMs) as well as multilayer perceptron (MLP) artificial neural networks to classify bleaching traces into stoichiometric categories based on an ensemble of measurable quantities derivable from individual traces. Both SVM and MLP models achieved a comparable accuracy of more than 80% against simulated traces up to 19-mer, although MLP offered considerable speed advantages, thus making it suitable for application to high-throughput experimental data. We used our high-throughput method to study the aggregation of Aβ₄₀ in the presence of metal ions and the aggregation of α-synuclein in the presence of gold nanoparticles.

Gold Ion Beam Milled Gold Zero-Mode Waveguides

Zero-mode waveguides (ZMWs) are widely used in single molecule fluorescence microscopy for their enhancement of emitted light and the ability to study samples at physiological concentrations. ZMWs are typically produced using photo or electron beam lithography. We report a new method of ZMW production using focused ion beam (FIB) milling with gold ions. We demonstrate that ion-milled gold ZMWs with 200 nm apertures exhibit similar plasmon-enhanced fluorescence seen with ZMWs fabricated with traditional techniques such as electron beam lithography.

Inhibition of calcium-triggered secretion by hydrocarbon-stapled peptides

Membrane fusion triggered by Ca²⁺ is orchestrated by a conserved set of proteins to mediate synaptic neurotransmitter release, mucin secretion and other regulated exocytic processes^1–4. For neurotransmitter release, the Ca²⁺ sensitivity is introduced by interactions between the Ca²⁺ sensor synaptotagmin and the SNARE complex⁵, and sequence conservation and functional studies suggest that this mechanism is also conserved for mucin secretion⁶. Disruption of Ca²⁺-triggered membrane fusion by a pharmacological agent would have therapeutic value for mucus hypersecretion as it is the major cause of airway obstruction in the pathophysiology of respiratory viral infection, asthma, chronic obstructive pulmonary disease and cystic fibrosis^7–11. Here we designed a hydrocarbon-stapled peptide that specifically disrupts Ca²⁺-triggered membrane fusion by interfering with the so-called primary interface between the neuronal SNARE complex and the Ca²⁺-binding C2B domain of synaptotagmin-1. In reconstituted systems with these neuronal synaptic proteins or with their airway homologues syntaxin-3, SNAP-23, VAMP8, synaptotagmin-2, along with Munc13-2 and Munc18-2, the stapled peptide strongly suppressed Ca²⁺-triggered fusion at physiological Ca²⁺ concentrations. Conjugation of cell-penetrating peptides to the stapled peptide resulted in efficient delivery into cultured human airway epithelial cells and mouse airway epithelium, where it markedly and specifically reduced stimulated mucin secretion in both systems, and substantially attenuated mucus occlusion of mouse airways. Taken together, peptides that disrupt Ca²⁺-triggered membrane fusion may enable the therapeutic modulation of mucin secretory pathways.

Peptides that disrupt Ca²⁺-triggered membrane fusion may enable the therapeutic modulation of mucin secretory pathways.

Analyzing protein dynamics from fluorescence intensity traces using unsupervised deep learning network

We propose an unsupervised deep learning network to analyze the dynamics of membrane proteins from the fluorescence intensity traces. This system was trained in an unsupervised manner with the raw experimental time traces and synthesized ones, so neither predefined state number nor pre-labelling were required. With the bidirectional Long Short-Term Memory (biLSTM) networks as the hidden layers, both the past and future context can be used fully to improve the prediction results and can even extract information from the noise distribution. The method was validated with the synthetic dataset and the experimental dataset of monomeric fluorophore Cy5, and then applied to extract the membrane protein interaction dynamics from experimental data successfully.

Amyloid-β oligomerization monitored by single-molecule stepwise photobleaching

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Method enables investigation of amyloid-β oligomer stoichiometry without requiring extrinsic fluorescent probes.

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Uses single-molecule stepwise photobleaching in vitro.

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Unveils heterogeneity within populations of oligomers.

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Assays oligomer-induced dysregulation of intracellular Ca²⁺ homeostasis in living cells.

A major hallmark of Alzheimer’s disease is the misfolding and aggregation of the amyloid- β peptide (Aβ). While early research pointed towards large fibrillar- and plaque-like aggregates as being the most toxic species, recent evidence now implicates small soluble Aβ oligomers as being orders of magnitude more harmful. Techniques capable of characterizing oligomer stoichiometry and assembly are thus critical for a deeper understanding of the earliest stages of neurodegeneration and for rationally testing next-generation oligomer inhibitors. While the fluorescence response of extrinsic fluorescent probes such as Thioflavin-T have become workhorse tools for characterizing large Aβ aggregates in solution, it is widely accepted that these methods suffer from many important drawbacks, including an insensitivity to oligomeric species. Here, we integrate several biophysics techniques to gain new insight into oligomer formation at the single-molecule level. We showcase single-molecule stepwise photobleaching of fluorescent dye molecules as a powerful method to bypass many of the traditional limitations, and provide a step-by-step guide to implementing the technique in vitro. By collecting fluorescence emission from single Aβ(1–42) peptides labelled at the N-terminal position with HiLyte Fluor 555 via wide-field total internal reflection fluorescence (TIRF) imaging, we demonstrate how to characterize the number of peptides per single immobile oligomer and reveal heterogeneity within sample populations. Importantly, fluorescence emerging from Aβ oligomers cannot be easily investigated using diffraction-limited optical microscopy tools. To assay oligomer activity, we also demonstrate the implementation of another biophysical method involving the ratiometric imaging of Fura-2-AM loaded cells which quantifies the rate of oligomer-induced dysregulation of intracellular Ca²⁺ homeostasis. We anticipate that the integrated single-molecule biophysics approaches highlighted here will develop further and in principle may be extended to the investigation of other protein aggregation systems under controlled experimental conditions.

Single-Molecule Imaging of Protein Interactions and Dynamics

Live-cell single-molecule fluorescence imaging has become a powerful analytical tool to investigate cellular processes that are not accessible to conventional biochemical approaches. This has greatly enriched our understanding of the behaviors of single biomolecules in their native environments and their roles in cellular events. Here, we review recent advances in fluorescence-based single-molecule bioimaging of proteins in living cells. We begin with practical considerations of the design of single-molecule fluorescence imaging experiments such as the choice of imaging modalities, fluorescent probes, and labeling methods. We then describe analytical observables from single-molecule data and the associated molecular parameters along with examples of live-cell single-molecule studies. Lastly, we discuss computational algorithms developed for single-molecule data analysis.

Analyzing the Dynamics of Single TBP-DNA-NC2 Complexes Using Hidden Markov Models

Single-pair Förster resonance energy transfer (spFRET) has become an important tool for investigating conformational dynamics in biological systems. To extract dynamic information from the spFRET traces measured with total internal reflection fluorescence microscopy, we extended the hidden Markov model (HMM) approach. In our extended HMM analysis, we incorporated the photon-shot noise from camera-based systems into the HMM. Thus, the variance in Förster resonance energy transfer (FRET) efficiency of the various states, which is typically a fitted parameter, is explicitly included in the analysis estimated from the number of detected photons. It is also possible to include an additional broadening of the FRET state, which would then only reflect the inherent flexibility of the dynamic biological systems. This approach is useful when comparing the dynamics of individual molecules for which the total intensities vary significantly. We used spFRET with the extended HMM analysis to investigate the dynamics of TATA-box-binding protein (TBP) on promoter DNA in the presence of negative cofactor 2 (NC2). We compared the dynamics of two promoters as well as DNAs of different length and labeling location. For the adenovirus major late promoter, four FRET states were observed; three states correspond to different conformations of the DNA in the TBP-DNA-NC2 complex and a four-state model in which the complex has shifted along the DNA. The HMM analysis revealed that the states are connected via a linear, four-well model. For the H2B promoter, more complex dynamics were observed. By clustering the FRET states detected with the HMM analysis, we could compare the general dynamics observed for the two promoter sequences. We observed that the dynamics from a stretched DNA conformation to a bent conformation for the two promoters were similar, whereas the bent conformation of the TBP-DNA-NC2 complex for the H2B promoter is approximately three times more stable than for the adenovirus major late promoter.

Enzyme-Mediated Directional Transport of a Small-Molecule Walker With Chemically Identical Feet

We describe a small-molecule "walker" that uses enzyme catalysis to discriminate between the relative positions of its "feet" on a track and thereby move with net directionality. The bipedal walker has identical carboxylic acid feet, and "steps" along an isotactic hydroxyl-group-derivatized polyether track by the formation/breakage of ester linkages. Lipase AS catalyzes the selective hydrolysis of the rear foot of macrocyclized walkers (an information ratchet mechanism), the rear foot producing an (R)-stereocenter at its point of attachment to the track. If the hydrolyzed foot reattaches to the track in front of the bound foot it forms an (S)-stereocenter, which is resistant to enzymatic hydrolysis. Only macrocyclic walker-track conjugates are efficiently hydrolyzed by the enzyme, leading to high processivity of the walker movement along the track. Conventional chemical reagents promote formation of the ester bonds between the walker and the track. Iterative macrocyclization and hydrolysis reactions lead to 68% of walkers taking two steps directionally along a three-foothold track.

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.

State aggregation for fast likelihood computations in molecular evolution

Motivation

Codon models are widely used to identify the signature of selection at the molecular level and to test for changes in selective pressure during the evolution of genes encoding proteins. The large size of the state space of the Markov processes used to model codon evolution makes it difficult to use these models with large biological datasets. We propose here to use state aggregation to reduce the state space of codon models and, thus, improve the computational performance of likelihood estimation on these models.

Results

We show that this heuristic speeds up the computations of the M0 and branch-site models up to 6.8 times. We also show through simulations that state aggregation does not introduce a detectable bias. We analyzed a real dataset and show that aggregation provides highly correlated predictions compared to the full likelihood computations. Finally, state aggregation is a very general approach and can be applied to any continuous-time Markov process-based model with large state space, such as amino acid and coevolution models. We therefore discuss different ways to apply state aggregation to Markov models used in phylogenetics.

Availability and Implementation

The heuristic is implemented in the godon package (https://bitbucket.org/Davydov/godon) and in a version of FastCodeML (https://gitlab.isb-sib.ch/phylo/fastcodeml).

Contact

nicolas.salamin@unil.ch

Supplementary Information

Supplementary data are available at Bioinformatics online.

A novel method to accurately locate and count large numbers of steps by photobleaching

Photobleaching event counting is a single-molecule fluorescence technique that is increasingly being used to determine the stoichiometry of protein and RNA complexes composed of many subunits in vivo as well as in vitro. By tagging protein or RNA subunits with fluorophores, activating them, and subsequently observing as the fluorophores photobleach, one obtains information on the number of subunits in a complex. The noise properties in a photobleaching time trace depend on the number of active fluorescent subunits. Thus, as fluorophores stochastically photobleach, noise properties of the time trace change stochastically, and these varying noise properties have created a challenge in identifying photobleaching steps in a time trace. Although photobleaching steps are often detected by eye, this method only works for high individual fluorophore emission signal-to-noise ratios and small numbers of fluorophores. With filtering methods or currently available algorithms, it is possible to reliably identify photobleaching steps for up to 20-30 fluorophores and signal-to-noise ratios down to ∼1. Here we present a new Bayesian method of counting steps in photobleaching time traces that takes into account stochastic noise variation in addition to complications such as overlapping photobleaching events that may arise from fluorophore interactions, as well as on-off blinking. Our method is capable of detecting ≥50 photobleaching steps even for signal-to-noise ratios as low as 0.1, can find up to ≥500 steps for more favorable noise profiles, and is computationally inexpensive.

Counting tagged molecules one by one: Quantitative photoactivation and bleaching of photoactivatable fluorophores

Determining the number of molecules in a given assembly, such as the number of proteins in a toxic aggregate, is often critical to understanding chemistry and function. Herein, we report a variation of a limitless method for counting photoactivatable fluorescent dyes in which single dye molecules are photoswitched to a fluorescent state, counted, and then irreversibly photobleached. We use this method to count the number of CAGE 552 covalently bound to the surface of 500 nm polystyrene beads. Activation of CAGE 552 was achieved with a 405 nm laser pulse. Once activated, the dye was excited with 532 nm light, and the fluorescence emission was collected with a CCD camera. The results from the fluorescence experiments were then compared to bulk fluorescence measurements to assess the error in counting. There are other ways of counting molecules, such as photobleaching and statistical analysis of reversible switchable chromophores. The method reported here provides a lower bound to the number of chromophores, with no upper limit to the number of molecules that can be quantified.

Long-lived intracellular single-molecule fluorescence using electroporated molecules

Studies of biomolecules in vivo are crucial to understand their function in a natural, biological context. One powerful approach involves fusing molecules of interest to fluorescent proteins to study their expression, localization, and action; however, the scope of such studies would be increased considerably by using organic fluorophores, which are smaller and more photostable than their fluorescent protein counterparts. Here, we describe a straightforward, versatile, and high-throughput method to internalize DNA fragments and proteins labeled with organic fluorophores into live Escherichia coli by employing electroporation. We studied the copy numbers, diffusion profiles, and structure of internalized molecules at the single-molecule level in vivo, and were able to extend single-molecule observation times by two orders of magnitude compared to green fluorescent protein, allowing continuous monitoring of molecular processes occurring from seconds to minutes. We also exploited the desirable properties of organic fluorophores to perform single-molecule Förster resonance energy transfer measurements in the cytoplasm of live bacteria, both for DNA and proteins. Finally, we demonstrate internalization of labeled proteins and DNA into yeast Saccharomyces cerevisiae, a model eukaryotic system. Our method should broaden the range of biological questions addressable in microbes by single-molecule fluorescence.

Analyzing conformational dynamics of single P-glycoprotein transporters by Förster resonance energy transfer using hidden Markov models

Single-molecule Förster resonance energy (smFRET) transfer has become a powerful tool for observing conformational dynamics of biological macromolecules. Analyzing smFRET time trajectories allows to identify the state transitions occuring on reaction pathways of molecular machines. Previously, we have developed a smFRET approach to monitor movements of the two nucleotide binding domains (NBDs) of P-glycoprotein (Pgp) during ATP hydrolysis driven drug transport in solution. One limitation of this initial work was that single-molecule photon bursts were analyzed by visual inspection with manual assignment of individual FRET levels. Here a fully automated analysis of Pgp smFRET data using hidden Markov models (HMM) for transitions up to 9 conformational states is applied. We propose new estimators for HMMs to integrate the information of fluctuating intensities in confocal smFRET measurements of freely diffusing lipid bilayer bound membrane proteins in solution. HMM analysis strongly supports that under conditions of steady state turnover, conformational states with short NBD distances and short dwell times are more populated compared to conditions without nucleotide or transport substrate present.

Variational Bayes analysis of a photon-based hidden Markov model for single-molecule FRET trajectories

Single-molecule fluorescence resonance energy transfer (smFRET) measurement is a powerful technique for investigating dynamics of biomolecules, for which various efforts have been made to overcome significant stochastic noise. Time stamp (TS) measurement has been employed experimentally to enrich information within the signals, while data analyses such as the hidden Markov model (HMM) have been successfully applied to recover the trajectories of molecular state transitions from time-binned photon counting signals or images. In this article, we introduce the HMM for TS-FRET signals, employing the variational Bayes (VB) inference to solve the model, and demonstrate the application of VB-HMM-TS-FRET to simulated TS-FRET data. The same analysis using VB-HMM is conducted for other models and the previously reported change point detection scheme. The performance is compared to other analysis methods or data types and we show that our VB-HMM-TS-FRET analysis can achieve the best performance and results in the highest time resolution. Finally, an smFRET experiment was conducted to observe spontaneous branch migration of Holliday-junction DNA. VB-HMM-TS-FRET was successfully applied to reconstruct the state transition trajectory with the number of states consistent with the nucleotide sequence. The results suggest that a single migration process frequently involves rearrangement of multiple basepairs.

A three-compartment chemically-driven molecular information ratchet

We describe a three-compartment rotaxane information ratchet in which the macrocycle can be directionally transported in either direction along an achiral (disregarding isotopic labeling) track. Chiral DMAP-based catalysts promote a benzoylation reaction that ratchets the displacement of the macrocycle, transporting it predominantly to a particular end compartment determined by the handedness of the catalyst.

Near-infrared fluorescent sensors based on single-walled carbon nanotubes for life sciences applications

Many properties of single-walled carbon nanotubes (SWCNTs) make them ideal candidates for sensors, particularly for biological systems. Both their fluorescence in the near-infrared range of 820-1600 nm, where absorption by biological tissues is often minimal, and their inherent photostability are desirable attributes for the design of in vitro and in vivo sensors. The mechanisms by which a target molecule can selectively alter the fluorescent emission include primarily changes in emission wavelength (i.e., solvatochromism) and intensity, including effects such as charge-transfer transition bleaching and exciton quenching. The central challenge lies in engineering the nanotube interface to be selective for the analyte of interest. In this work, we review the recent development in this area over the past few years, and describe the design rules that we have developed for detecting various analytes, ranging from stable small molecules and reactive oxygen species (ROS) or reactive nitrogen species (RNS) to macromolecules. Applications to in vivo sensor measurements using these sensors are also described. In addition, the emerging field of SWCNT-based single-molecule detection using band gap fluorescence and the recent efforts to accurately quantify and utilize this unique class of stochastic sensors are also described in this article.

Measuring, in solution, multiple-fluorophore labeling by combining fluorescence correlation spectroscopy and photobleaching

Determining the number of fluorescent entities that are coupled to a given molecule (DNA, protein, etc.) is a key point of numerous biological studies, especially those based on a single molecule approach. Reliable methods are important, in this context, not only to characterize the labeling process but also to quantify interactions, for instance within molecular complexes. We combined fluorescence correlation spectroscopy (FCS) and photobleaching experiments to measure the effective number of molecules and the molecular brightness as a function of the total fluorescence count rate on solutions of cDNA (containing a few percent of C bases labeled with Alexa Fluor 647). Here, photobleaching is used as a control parameter to vary the experimental outputs (brightness and number of molecules). Assuming a Poissonian distribution of the number of fluorescent labels per cDNA, the FCS-photobleaching data could be easily fit to yield the mean number of fluorescent labels per cDNA strand (approximately = 2). This number could not be determined solely on the basis of the cDNA brightness, because of both the statistical distribution of the number of fluorescent labels and their unknown brightness when incorporated in cDNA. The statistical distribution of the number of fluorophores labeling cDNA was confirmed by analyzing the photon count distribution (with the cumulant method), which showed clearly that the brightness of cDNA strands varies from one molecule to the other. We also performed complementary continuous photobleaching experiments and found that the photobleaching decay rate of Alexa Fluor 647 in the excited state decreases by about 30% when incorporated into cDNA, while its nonradiative decay rate is increased such that the brightness of individual Alexa labels is decreased by 25% compared to free Alexa dyes.

Hidden markov analysis of short single molecule intensity trajectories

Photon trajectories from single molecule experiments can report on biomolecule structural changes and motions. Hidden Markov models (HMM) facilitate extraction of the sequence of hidden states from noisy data through construction of probabilistic models. Typically, the true number of states is determined by the Bayesian information criteria (BIC); however, constraints resulting from short data sets and Poisson-distributed photons in radiative processes like fluorescence can limit successful application of goodness-of-fit statistics. For single molecule intensity trajectories, additional information criteria such as peak localization error (LE) and chi-square probabilities can incorporate theoretical constraints on experimental data while modifying normal HMM. Chi-square minimization also serves as a stopping point of the iteration in which the system parameters are trained. Peak LE enables exclusion of overfitted and overlapped states. These constraints and criteria are tested against BIC on simulated single molecule trajectories to best identify the true number of emissive levels in any sequence.

Information-theoretical analysis of time-correlated single-photon counting measurements of single molecules

Time-correlated single photon counting allows luminescence lifetime information to be determined on a single molecule level. This paper develops a formalism to allow information theory analysis of the ability of luminescence lifetime measurements to resolve states in a single molecule. It analyzes the information content of the photon stream and the fraction of that information that is relevant to the state determination problem. Experimental losses of information due to instrument response, digitization, and different types of background are calculated and a procedure to determine the optimal value of experimental parameters is demonstrated. This paper shows how to use the information theoretical formalism to evaluate the number of photons required to distinguish dyes that differ only by lifetime. It extends this idea to include distinguishing molecular states that differ in the electron transfer quenching or resonant energy transfer and shows how the differences between the lifetime of signal and background can help distinguish the dye position in an excitation beam.

Stochastic analysis of stepwise fluorescence quenching reactions on single-walled carbon nanotubes: single molecule sensors

The 1D quantum confinement of photogenerated excitons in single-walled carbon nanotubes (SWNT) can amplify the detection of molecular adsorption to where single-molecule discrimination is realizable, even from within living cells and tissues. Toward this aim, we present a type 1 collagen film, similar to those used as 3D cell scaffolds for tissue engineering, containing embedded SWNT capable of reporting single-molecule adsorption of quenching molecules. We utilize hidden Markov modeling to link single-molecule adsorption events to rate constants for H2O2, H+, and Fe(CN)6(3-). Among the three kinds of reactant molecules studied, H2O2 has the highest quenching equilibrium constant of 1.59 at 20 microM, whereas H+ is so insensitive that a similar equilibrium constant is achieved only with a concentration of 0.1 M (pH 1). The results were self-consistent because reverse (unquenching) rate constants (600 micros(-1) for H2O2, 1130 micros(-1) for H+ and 4000 micros(-1) for Fe(CN)6(3-)) were observed to be concentration-independent and the forward (quenching) rate constants varied monotonically with concentration. The quenching rate constants also increased with an increase in the redox potential of the quencher, indicating that electron transfer increases the adsorption equilibrium constant on the nanotube surface and, hence, the dwell time of the quencher. These developments provide the material, analytical, and mechanistic groundwork for SWNT to function as single-molecule stochastic biosensors.

COCIS: Markov processes in single molecule fluorescence

This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.

Protein free energy landscapes remodeled by ligand binding

Glucose/galactose binding protein (GGBP) functions in two different larger systems of proteins used by enteric bacteria for molecular recognition and signaling. Here we report on the thermodynamics of conformational equilibrium distributions of GGBP. Three fluorescence components appear at zero glucose concentration and systematically transition to three components at high glucose concentration. Fluorescence anisotropy correlations, fluorescent lifetimes, thermodynamics, computational structure minimization, and literature work were used to assign the three components as open, closed, and twisted conformations of the protein. The existence of three states at all glucose concentrations indicates that the protein continuously fluctuates about its conformational state space via thermally driven state transitions; glucose biases the populations by reorganizing the free energy profile. These results and their implications are discussed in terms of the two types of specific and nonspecific interactions GGBP has with cytoplasmic membrane proteins.