Variational Algorithms for Analyzing Noisy Multistate Diffusion Trajectories

Increasing the accuracy of single-molecule data analysis using tMAVEN

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physicochemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule data set and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series modeling, analysis, and visualization environment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from preprocessing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule data set with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule data sets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physicochemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule data sets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

Robust Quantification of Live-Cell Single-Molecule Tracking Data for Fluorophores with Different Photophysical Properties

High-speed single-molecule tracking in live cells is becoming an increasingly popular method for quantifying the spatiotemporal behavior of proteins in vivo. The method provides a wealth of quantitative information, but users need to be aware of biases that can skew estimates of molecular mobilities. The range of suitable fluorophores for live-cell single-molecule imaging has grown substantially over the past few years, but it remains unclear to what extent differences in photophysical properties introduce biases. Here, we tested two fluorophores with entirely different photophysical properties, one that photoswitches frequently between bright and dark states (TMR) and one that shows exceptional photostability without photoswitching (JFX650). We used a fusion of the Escherichia coli DNA repair enzyme MutS to the HaloTag and optimized sample preparation and imaging conditions for both types of fluorophore. We then assessed the reliability of two common data analysis algorithms, mean-square displacement (MSD) analysis and Hidden Markov Modeling (HMM), to estimate the diffusion coefficients and fractions of MutS molecules in different states of motion. We introduce a simple approach that removes discrepancies in the data analyses and show that both algorithms yield consistent results, regardless of the fluorophore used. Nevertheless, each dye has its own strengths and weaknesses, with TMR being more suitable for sampling the diffusive behavior of many molecules, while JFX650 enables prolonged observation of only a few molecules per cell. These characterizations and recommendations should help to standardize measurements for increased reproducibility and comparability across studies.

Increasing the accuracy of single-molecule data analysis using tMAVEN

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physico-chemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule dataset and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series Modeling, Analysis, and Visualization ENvironment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from pre-processing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule dataset with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule datasets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physico-chemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule datasets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

ExTrack characterizes transition kinetics and diffusion in noisy single-particle tracks

Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.

ExTrack characterizes transition kinetics and diffusion in noisy single-particle tracks

Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.

Receptor tyrosine kinase MET ligand-interaction classified via machine learning from single-particle tracking data

Internalin B-mediated activation of the membrane-bound receptor tyrosine kinase MET is accompanied by a change in receptor mobility. Conversely, it should be possible to infer from receptor mobility whether a cell has been treated with internalin B. Here, we propose a method based on hidden Markov modeling and explainable artificial intelligence that machine-learns the key differences in MET mobility between internalin B-treated and -untreated cells from single-particle tracking data. Our method assigns receptor mobility to three diffusion modes (immobile, slow, and fast). It discriminates between internalin B-treated and -untreated cells with a balanced accuracy of >99% and identifies three parameters that are most affected by internalin B treatment: a decrease in the mobility of slow molecules (1) and a depopulation of the fast mode (2) caused by an increased transition of fast molecules to the slow mode (3). Our approach is based entirely on free software and is readily applicable to the analysis of other membrane receptors.

Direct measurements of mRNA translation kinetics in living cells

Ribosome mediated mRNA translation is central to life. The cycle of translation, however, has been characterized mostly using reconstituted systems, with only few techniques applicable for studies in the living cell. Here we describe a live-cell ribosome-labeling method, which allows us to characterize the whole processes of finding and translating an mRNA, using single-molecule tracking techniques. We find that more than 90% of both bacterial ribosomal subunits are engaged in translation at any particular time, and that the 30S and 50S ribosomal subunits spend the same average time bound to an mRNA, revealing that 30S re-initiation on poly-cistronic mRNAs is not prevalent in E. coli. Instead, our results are best explained by substantial 70S re-initiation of translation of poly-cistronic mRNAs, which is further corroborated by experiments with translation initiation inhibitors. Finally, we find that a variety of previously described orthogonal ribosomes, with altered anti-Shine-Dalgarno sequences, show significant binding to endogenous mRNAs.

Uncover Single Nanoparticle Dynamics on Live Cell Membrane with Data-Driven Historical Experience Analysis

Understanding the spatiotemporal dynamics of particles in a complex biological environment is crucial for the study of related biological processes. To analyze the complicated trajectories recorded from single-particle tracking (SPT), we have proposed a method named SEES based on historical experience vector analysis, which allows both the global patterns and local state continuities of a trajectory to emerge by themselves as color segments without predefined models. This method implements a data-driven strategy and thus uncovers the hidden information with less prior knowledge or subjective bias. Here, we demonstrate its efficiency by comparing its performance with the Hidden Markov model (HMM), one of the most widely used methods in time series processing. The results demonstrated that the SEES operator was more sensitive in identifying rare events and could utilize multivariable observations in the dynamic processes to uncover more details. We applied the method to analyze the dynamics of nanoparticles interacting with live cells expressing programmed death ligand 1 (PD-L1) on the membrane. The results showed that the SEES operator can successfully pinpoint the transmembrane rare events, visualize the on-membrane "Brownian searching" motion, and evaluate different dynamics among multiple trajectories. Furthermore, we found that the PD-L1 expression level on the cell membrane affected the rotation behavior of the nanoparticle as well as the cellular uptake efficiency. These findings enabled by SEES could potentially help the rational design of highly efficient nanocargoes.

Application of Multi-Slice Spiral CT in the Evaluation of Diffuse Lung Diseases

This article analyzes the manifestations, characteristics, and significance of multi-slice spiral CT for diffuse lung disease, and evaluates the diagnostic value of multi-slice CT multi-directional reconstruction for diffuse lung disease. After performing multi-slice spiral CT examination on the patient and collecting relevant data, the characteristic multi-slice CT imaging findings of diffuse lung disease were determined by statistical analysis. Diffuse lung disease is representative in multi-slice spiral CT image imaging manifestations of the disease include multiple disseminated small nodules, multiple voids, ground glass shadows, and lung consolidation. And analyze the correlation of image performance, and then use statistical methods to analyze and evaluate the value of multi-slice spiral CT characteristic images in the diagnosis of diffuse lung disease, and analyze the characteristics of these characteristic multi-slice CT image appearances. The use of high-resolution CT to screen the characteristic CT imaging findings of the same research object, and then to perform a statistical analysis of the diagnostic differences with multi-slice spiral CT, further confirmed the importance of multi-slice CT for diffuse lung disease Diagnostic value. Studies have shown that multi-slice CT imaging technology is of great significance in the evaluation of diffuse lung diseases.

Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.

Fundamentals of the logarithmic measure for revealing multimodal diffusion

We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which diffusion processes are often nonuniform. We transform Brownian data onto the logarithmic domain, in which the coefficients for individual modes of diffusion appear as distinct spectral peaks in the probability density. We refer to the method as the logarithmic measure of diffusion, or simply as the logarithmic measure. We provide a general protocol for deriving analytical expressions for the probability densities on the logarithmic domain. The protocol is applicable for any number of spatial dimensions with any number of diffusive states. The analytical form can be fitted to data to reveal multiple diffusive modes. We validate the theoretical distributions and benchmark the accuracy and sensitivity of the method by extracting multimodal diffusion coefficients from two-dimensional Brownian simulations of polydisperse filament bundles. Bundling the filaments allows us to control the system nonuniformity and hence quantify the sensitivity of the method. By exploiting the anisotropy of the simulated filaments, we generalize the logarithmic measure to rotational diffusion. By fitting the analytical forms to simulation data, we confirm the method's theoretical foundation. An error analysis in the single-mode regime shows that the proposed method is comparable in accuracy to the standard mean-squared displacement approach for evaluating diffusion coefficients. For the case of multimodal diffusion, we compare the logarithmic measure against other, more sophisticated methods, showing that both model selectivity and extraction accuracy are comparable for small data sets. Therefore, we suggest that the logarithmic measure, as a method for multimodal diffusion coefficient extraction, is ideally suited for small data sets, a condition often confronted in the experimental context. Finally, we critically discuss the proposed benefits of the method and its information content.

Single-molecule observation of diffusion and catalysis in nanoporous solids

Nanoporous solids, including microporous, mesoporous and hierarchically structured porous materials, are of scientific and technological interest because of their high surface-to-volume ratio and ability to impose shape- and size-selectivity on molecules diffusing through them. Enormous efforts have been put in the mechanistic understanding of diffusion–reaction relationships of nanoporous solids, with the ultimate goal of developing materials with improved catalytic performance. Single-molecule localization microscopy can be used to explore the pore space via the trajectories of individual molecules. This ensemble-free perspective directly reveals heterogeneities in diffusion and diffusion-related reactivity of individual molecules, which would have been obscured in bulk measurements. In this article, we review developments in the spatial and temporal characterization of nanoporous solids using single-molecule localization microscopy. We illustrate various aspects of this approach, and showcase how it can be used to follow molecular diffusion and reaction behaviors in nanoporous solids.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

Extracting Transition Rates in Particle Tracking Using Analytical Diffusion Distribution Analysis

Single-particle tracking is an important technique in the life sciences to understand the kinetics of biomolecules. The analysis of apparent diffusion coefficients in vivo, for example, enables researchers to determine whether biomolecules are moving alone, as part of a larger complex, or are bound to large cellular components such as the membrane or chromosomal DNA. A remaining challenge has been to retrieve quantitative kinetic models, especially for molecules that rapidly switch between different diffusional states. Here, we present analytical diffusion distribution analysis (anaDDA), a framework that allows for extracting transition rates from distributions of apparent diffusion coefficients calculated from short trajectories that feature less than 10 localizations per track. Under the assumption that the system is Markovian and diffusion is purely Brownian, we show that theoretically predicted distributions accurately match simulated distributions and that anaDDA outperforms existing methods to retrieve kinetics, especially in the fast regime of 0.1-10 transitions per imaging frame. AnaDDA does account for the effects of confinement and tracking window boundaries. Furthermore, we added the option to perform global fitting of data acquired at different frame times to allow complex models with multiple states to be fitted confidently. Previously, we have started to develop anaDDA to investigate the target search of CRISPR-Cas complexes. In this work, we have optimized the algorithms and reanalyzed experimental data of DNA polymerase I diffusing in live Escherichia coli. We found that long-lived DNA interaction by DNA polymerase are more abundant upon DNA damage, suggesting roles in DNA repair. We further revealed and quantified fast DNA probing interactions that last shorter than 10 ms. AnaDDA pushes the boundaries of the timescale of interactions that can be probed with single-particle tracking and is a mathematically rigorous framework that can be further expanded to extract detailed information about the behavior of biomolecules in living cells.

Gaining insight into cellular cardiac physiology using single particle tracking

Single particle tracking (SPT) is a robust technique to monitor single-molecule behaviors in living cells directly. By this approach, we can uncover the potential biological significance of particle dynamics by statistically characterizing individual molecular behaviors. SPT provides valuable information at the single-molecule level, that could be obscured by simple averaging that is inherent to conventional ensemble measurements. Here, we give a brief introduction to SPT including the commonly used optical implementations, fluorescence labeling strategies, and data analysis methods. We then focus on how SPT has been harnessed to decipher myocardial function. In this context, SPT has provided novel insight into the lateral diffusion of signal receptors and ion channels, the dynamic organization of cardiac nanodomains, subunit composition and stoichiometry of cardiac ion channels, myosin movement along actin filaments, the kinetic features of transcription factors involved in cardiac remodeling, and the intercellular communication by nanotubes. Finally, we speculate on the prospects and challenges of applying SPT to future questions regarding cellular cardiac physiology using SPT.

High-throughput, single-particle tracking reveals nested membrane domains that dictate KRasG12D diffusion and trafficking

Membrane nanodomains have been implicated in Ras signaling, but what these domains are and how they interact with Ras remain obscure. Here, using single particle tracking with photoactivated localization microscopy (spt-PALM) and detailed trajectory analysis, we show that distinct membrane domains dictate KRas^G12D (an active KRas mutant) diffusion and trafficking in U2OS cells. KRas^G12D exhibits an immobile state in ~70 nm domains, each embedded in a larger domain (~200 nm) that confers intermediate mobility, while the rest of the membrane supports fast diffusion. Moreover, KRas^G12D is continuously removed from the membrane via the immobile state and replenished to the fast state, reminiscent of Ras internalization and recycling. Importantly, both the diffusion and trafficking properties of KRas^G12D remain invariant over a broad range of protein expression levels. Our results reveal how membrane organization dictates membrane diffusion and trafficking of Ras and offer new insight into the spatial regulation of Ras signaling.

The Ras family of proteins play an important role in relaying signals from the outside to the inside of the cell. Ras proteins are attached by a fatty tail to the inner surface of the cell membrane. When activated they transmit a burst of signal that controls critical behaviors like growth, survival and movement. It has been suggested that to prevent these signals from being accidently activated, Ras molecules must group together at specialized sites within the membrane before passing on their message. However, visualizing how Ras molecules cluster together at these domains has thus far been challenging. As a result, little is known about where these sites are located and how Ras molecules come to a stop at these domains.

Now, Lee et al. have combined two microscopy techniques called ‘single-particle tracking’ and ‘photoactivated localization microscopy' to track how individual molecules of activated Ras move in human cells grown in the lab. This revealed that Ras molecules quickly diffuse along the inside of the membrane until they arrive at certain locations that cause them to halt. However, computer models consisting of just the ‘fast’ and ‘immobile’ state could not correctly re-capture the way Ras molecules moved along the membrane. Lee et al. found that for these models to mimic the movement of Ras, a third ‘intermediate’ state of Ras mobility needed to be included.

To investigate this further, Lee et al. created a fluorescent map that overlaid all the individual paths taken by each Ras molecule. The map showed regions in the membrane where the Ras molecules had stopped and possibly clustered together. Each of these ‘immobilization domains’ were then surrounded by an ‘intermediate domain’ where Ras molecules had begun to slow down their movement. Although the intermediate domains did not last long, they seemed to guide Ras molecules into the immobilization domains where they could cluster together with other molecules. From there, the cell constantly removed Ras molecules from these membrane domains and returned them back to their ‘fast’ diffusing state.

Mutations in Ras proteins occur in around a third of all cancers, so a better understanding of their dynamics could help with future drug discovery. The methods used here could also be used to investigate the movement of other signaling molecules.

An automated Bayesian pipeline for rapid analysis of single-molecule binding data

Single-molecule binding assays enable the study of how molecular machines assemble and function. Current algorithms can identify and locate individual molecules, but require tedious manual validation of each spot. Moreover, no solution for high-throughput analysis of single-molecule binding data exists. Here, we describe an automated pipeline to analyze single-molecule data over a wide range of experimental conditions. In addition, our method enables state estimation on multivariate Gaussian signals. We validate our approach using simulated data, and benchmark the pipeline by measuring the binding properties of the well-studied, DNA-guided DNA endonuclease, TtAgo, an Argonaute protein from the Eubacterium Thermus thermophilus. We also use the pipeline to extend our understanding of TtAgo by measuring the protein’s binding kinetics at physiological temperatures and for target DNAs containing multiple, adjacent binding sites.

Analysis of single-molecule binding assays still requires substantial manual user intervention. Here, the authors present a pipeline for rapid, automated analysis of co-localization single-molecule spectroscopy images, with a modular user interface that can be adjusted to a range of experimental conditions.