Step Detection in Single-Molecule Real Time Trajectories Embedded in Correlated Noise

Single-molecule real time trajectories are embedded in high noise. To extract kinetic or dynamic information of the molecules from these trajectories often requires idealization of the data in steps and dwells. One major premise behind the existing single-molecule data analysis algorithms is the Gaussian ‘white’ noise, which displays no correlation in time and whose amplitude is independent on data sampling frequency. This so-called ‘white’ noise is widely assumed but its validity has not been critically evaluated. We show that correlated noise exists in single-molecule real time trajectories collected from optical tweezers. The assumption of white noise during analysis of these data can lead to serious over- or underestimation of the number of steps depending on the algorithms employed. We present a statistical method that quantitatively evaluates the structure of the underlying noise, takes the noise structure into account, and identifies steps and dwells in a single-molecule trajectory. Unlike existing data analysis algorithms, this method uses Generalized Least Squares (GLS) to detect steps and dwells. Under the GLS framework, the optimal number of steps is chosen using model selection criteria such as Bayesian Information Criterion (BIC). Comparison with existing step detection algorithms showed that this GLS method can detect step locations with highest accuracy in the presence of correlated noise. Because this method is automated, and directly works with high bandwidth data without pre-filtering or assumption of Gaussian noise, it may be broadly useful for analysis of single-molecule real time trajectories.     

Stochastic dynamic study of optical transition properties of single GFP-like molecules

Due to high fluctuations and quantum uncertainty, the processes of single-molecules should be treated by stochastic methods. To study fluorescence time series and their statistical properties, we have applied two stochastic methods, one of which is an analytic method to study the off-time distributions of certain fluorescence transitions and the other is Gillespie’s method of stochastic simulations. These methods have been applied to study the optical transition properties of two single-molecule systems, GFPmut2 and a Dronpa-like molecule, to yield results in approximate agreement with experimental observations on these systems. Rigorous oscillatory time series of GFPmut2 before it unfolds in the presence of denaturants have not been obtained based on the stochastic method used, but, on the other hand, the stochastic treatment puts constraints on the conditions under which such oscillatory behavior is possible. Furthermore, a sensitivity analysis is carried out on GFPmut2 to assess the effects of transition rates on the observables, such as fluorescence intensities.     

Fluorescence-based analysis of enzymes at the single-molecule level

Enzymes, and proteins in general, consist of a dynamic ensemble of different conformations, which fluctuate around an average structure. Single-molecule experiments are a powerful tool to obtain information about these conformations and their contributions to the catalytic reaction. In contrast to classical ensemble measurements, which average over the whole population, singlemolecule experiments are able to detect conformational heterogeneities, to identify transient or rare conformations, to follow the time series of conformational changes and to reveal parallel reaction pathways. A number of single-molecule studies with enzymes have proven this potential showing that the activity of individual enzymes varies between different molecules and that the catalytic rate constants fluctuate over time. From a practical point of view this review focuses on fluorescence-based methods that have been used to study enzymes at the single-molecule level. Since the first proof-of-principle experiments a wide range of different methods have been developed over the last 10 years and the methodology now needs to be applied to answer questions of biological relevance, for example about conformational changes induced by allosteric effectors or mutations.     

Analysis of single-molecule FRET trajectories using hidden Markov modeling

The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.     

Fodis: Software for Protein Unfolding Analysis

The folding dynamics of proteins at the single-molecule level has been studied with single-molecule force spectroscopy experiments for 20 years, but a common standardized method for the analysis of the collected data and for sharing among the scientific community members is still not available. We have developed a new open-source tool—Fodis—for the analysis of the force-distance curves obtained in single-molecule force spectroscopy experiments, providing almost automatic processing, analysis, and classification of the obtained data. Our method provides also a classification of the possible unfolding pathways and the structural heterogeneity present during the unfolding of proteins.     

Coordinate-based colocalization analysis of single-molecule localization microscopy data

Colocalization of differently labeled biomolecules is a valuable tool in fluorescence microscopy and can provide information on biomolecular interactions. With the advent of super-resolution microscopy, colocalization analysis is getting closer to molecular resolution, bridging the gap to other technologies such as fluorescence resonance energy transfer. Among these novel microscopic techniques, single-molecule localization-based super-resolution methods offer the advantage of providing single-molecule coordinates that, rather than intensity information, can be used for colocalization analysis. This requires adapting the existing mathematical algorithms for localization microscopy data. Here, we introduce an algorithm for coordinate-based colocalization analysis which is suited for single-molecule super-resolution data. In addition, we present an experimental configuration for simultaneous dual-color imaging together with a robust approach to correct for optical aberrations with an accuracy of a few nanometers. We demonstrate the potential of our approach for cellular structures and for two proteins binding actin filaments.     

Analyzing time series gene expression data

MOTIVATION: Time series expression experiments are an increasingly popular method for studying a wide range of biological systems. However, when analyzing these experiments researchers face many new computational challenges. Algorithms that are specifically designed for time series experiments are required so that we can take advantage of their unique features (such as the ability to infer causality from the temporal response pattern) and address the unique problems they raise (e.g. handling the different non-uniform sampling rates). RESULTS: We present a comprehensive review of the current research in time series expression data analysis. We divide the computational challenges into four analysis levels: experimental design, data analysis, pattern recognition and networks. For each of these levels, we discuss computational and biological problems at that level and point out some of the methods that have been proposed to deal with these issues. Many open problems in all these levels are discussed. This review is intended to serve as both, a point of reference for experimental biologists looking for practical solutions for analyzing their data, and a starting point for computer scientists interested in working on the computational problems related to time series expression analysis.     

Understanding Protein Mobility in Bacteria by Tracking Single Molecules

Protein diffusion is crucial for understanding the formation of protein complexes in vivo and has been the subject of many fluorescence microscopy studies in cells; however, such microscopy efforts are often limited by low sensitivity and resolution. During the past decade, these limitations have been addressed by new super-resolution imaging methods, most of which rely on single-particle tracking and single-molecule detection; these methods are revolutionizing our understanding of molecular diffusion inside bacterial cells by directly visualizing the motion of proteins and the effects of the local and global environment on diffusion. Here we review key methods that made such experiments possible, with particular emphasis on versions of single-molecule tracking based on photo-activated fluorescent proteins. We also discuss studies that provide estimates of the time a diffusing protein takes to locate a target site, as well as studies that examined the stoichiometries of diffusing species, the effect of stable and weak interactions on diffusion, and the constraints of large macromolecular structures on the ability of proteins and their complexes to access the entire cytoplasm.     

Experimental Test of Connector Rotation during DNA Packaging into Bacteriophage ϕ29 Capsids

The bacteriophage ϕ29 generates large forces to compact its double-stranded DNA genome into a protein capsid by means of a portal motor complex. Several mechanical models for the generation of these high forces by the motor complex predict coupling of DNA translocation to rotation of the head-tail connector dodecamer. Putative connector rotation is investigated here by combining the methods of single-molecule force spectroscopy with polarization-sensitive single-molecule fluorescence. In our experiment, we observe motor function in several packaging complexes in parallel using video microscopy of bead position in a magnetic trap. At the same time, we follow the orientation of single fluorophores attached to the portal motor connector. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.     

Single-molecule fluorescence studies from a bioinorganic perspective

In recent years, single-molecule methods have enabled many innovative studies in the life sciences, which generated unprecedented insights into the workings of many macromolecular machineries. Single-molecule studies of bioinorganic systems have been limited, however, even though bioinorganic chemistry represents one of the frontiers in the life sciences. With the hope to stimulate more interest in applying existing and developing new single-molecule methods to address compelling bioinorganic problems, this review discusses a few single-molecule fluorescence approaches that have been or can be employed to study the functions and dynamics of metalloproteins. We focus on their principles, features and generality, possible further bioinorganic applications, and experimental challenges. The fluorescence quenching via energy transfer approach has been used to study the O₂-binding of hemocyanin, the redox states of azurin, and the folding dynamics of cytochrome c at the single-molecule level. Possible future applications of this approach to single-molecule studies of metalloenzyme catalysis and metalloprotein folding are discussed. The fluorescence quenching via electron transfer approach can probe the subtle conformational dynamics of proteins, and its possible application to probe metalloprotein structural dynamics is discussed. More examples are presented in using single-molecule fluorescence resonance energy transfer to probe metallochaperone protein interactions and metalloregulator-DNA interactions on a single-molecule basis.     

Experimental Test of Connector Rotation during DNA Packaging into Bacteriophage ϕ29 Capsids

The bacteriophage ϕ29 generates large forces to compact its double-stranded DNA genome into a protein capsid by means of a portal motor complex. Several mechanical models for the generation of these high forces by the motor complex predict coupling of DNA translocation to rotation of the head-tail connector dodecamer. Putative connector rotation is investigated here by combining the methods of single-molecule force spectroscopy with polarization-sensitive single-molecule fluorescence. In our experiment, we observe motor function in several packaging complexes in parallel using video microscopy of bead position in a magnetic trap. At the same time, we follow the orientation of single fluorophores attached to the portal motor connector. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.     

High-throughput single-molecule studies of protein–DNA interactions

Fluorescence and force-based single-molecule studies of protein–nucleic acid interactions continue to shed critical insights into many aspects of DNA and RNA processing. As single-molecule assays are inherently low-throughput, obtaining statistically relevant datasets remains a major challenge. Additionally, most fluorescence-based single-molecule particle-tracking assays are limited to observing fluorescent proteins that are in the low-nanomolar range, as spurious background signals predominate at higher fluorophore concentrations. These technical limitations have traditionally limited the types of questions that could be addressed via single-molecule methods. In this review, we describe new approaches for high-throughput and high-concentration single-molecule biochemical studies. We conclude with a discussion of outstanding challenges for the single-molecule biologist and how these challenges can be tackled to further approach the biochemical complexity of the cell.     

Massively Parallel Single-Molecule Manipulation Using Centrifugal Force

Precise manipulation of single molecules has already led to remarkable insights in physics, chemistry, biology, and medicine. However, widespread adoption of single-molecule techniques has been impeded by equipment cost and the laborious nature of making measurements one molecule at a time. We have solved these issues by developing an approach that enables massively parallel single-molecule force measurements using centrifugal force. This approach is realized in an instrument that we call the centrifuge force microscope in which objects in an orbiting sample are subjected to a calibration-free, macroscopically uniform force-field while their micro-to-nanoscopic motions are observed. We demonstrate high-throughput single-molecule force spectroscopy with this technique by performing thousands of rupture experiments in parallel, characterizing force-dependent unbinding kinetics of an antibody-antigen pair in minutes rather than days. Additionally, we verify the force accuracy of the instrument by measuring the well-established DNA overstretching transition at 66 ± 3 pN. With significant benefits in efficiency, cost, simplicity, and versatility, single-molecule centrifugation has the potential to expand single-molecule experimentation to a wider range of researchers and experimental systems.     

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes

The hidden Markov model (HMM) is a framework for time series analysis widely applied to single-molecule experiments. Although initially developed for applications outside the natural sciences, the HMM has traditionally been used to interpret signals generated by physical systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, transitions between states are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, whereas measurements are often performed at discrete time levels in the natural sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, because the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, because these switch between discrete states in “continuous time”. We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process. We explicitly show in what limit the hidden Markov jump process reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.     

Single-molecule approaches to characterizing kinetics of biomolecular interactions

Single-molecule fluorescence techniques have emerged as powerful tools to study biological processes at the molecular level. This review describes the application of these methods to the characterization of the kinetics of interaction between biomolecules. A large number of single-molecule assays have been developed that visualize association and dissociation kinetics in vitro by fluorescently labeling binding partners and observing their interactions over time. Even though recent progress has been significant, there are certain limitations to this approach. To allow the observation of individual, fluorescently labeled molecules requires low, nanomolar concentrations. I will discuss how such concentration requirements in single-molecule experiments limit their applicability to investigate intermolecular interactions and how recent technical advances deal with this issue.     

Resolving Cytosolic Diffusive States in Bacteria by Single-Molecule Tracking

The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.     

Reference-free alignment and sorting of single-molecule force spectroscopy data

Single-molecule force spectroscopy has become a versatile tool for investigating the (un)folding of proteins and other polymeric molecules. Like other single-molecule techniques, single-molecule force spectroscopy requires recording and analysis of large data sets to extract statistically meaningful conclusions. Here, we present a data analysis tool that provides efficient filtering of heterogeneous data sets, brings spectra into register based on a reference-free alignment algorithm, and determines automatically the location of unfolding barriers. Furthermore, it groups spectra according to the number of unfolding events, subclassifies the spectra using cross correlation-based sorting, and extracts unfolding pathways by principal component analysis and clustering methods to extracted peak positions. Our approach has been tested on a data set obtained through mechanical unfolding of bacteriorhodopsin (bR), which contained a significant number of spectra that did not show the well-known bR fingerprint. In addition, we have tested the performance of the data analysis tool on unfolding data of the soluble multidomain (Ig27)(8) protein.