Detection of Velocity and Diffusion Coefficient Change Points in Single-Particle Trajectories

Diffusion and Oligomerization States of the Muscarinic M1 Receptor in Live Cells─The Impact of Ligands and Membrane Disruptors

G protein-coupled receptors (GPCRs) are a major gateway to cellular signaling, which respond to ligands binding at extracellular sites through allosteric conformational changes that modulate their interactions with G proteins and arrestins at intracellular sites. High-resolution structures in different ligand states, together with spectroscopic studies and molecular dynamics simulations, have revealed a rich conformational landscape of GPCRs. However, their supramolecular structure and spatiotemporal distribution is also thought to play a significant role in receptor activation and signaling bias within the native cell membrane environment. Here, we applied single-molecule fluorescence techniques, including single-particle tracking, single-molecule photobleaching, and fluorescence correlation spectroscopy, to characterize the diffusion and oligomerization behavior of the muscarinic M1 receptor (M1R) in live cells. Control samples included the monomeric protein CD86 and fixed cells, and experiments performed in the presence of different orthosteric M1R ligands and of several compounds known to change the fluidity and organization of the lipid bilayer. M1 receptors exhibit Brownian diffusion characterized by three diffusion constants: confined/immobile (∼0.01 μm2/s), slow (∼0.04 μm2/s), and fast (∼0.14 μm2/s), whose populations were found to be modulated by both orthosteric ligands and membrane disruptors. The lipid raft disruptor C6 ceramide led to significant changes for CD86, while the diffusion of M1R remained unchanged, indicating that M1 receptors do not partition in lipid rafts. The extent of receptor oligomerization was found to be promoted by increasing the level of expression and the binding of orthosteric ligands; in particular, the agonist carbachol elicited a large increase in the fraction of M1R oligomers. This study provides new insights into the balance between conformational and environmental factors that define the movement and oligomerization states of GPCRs in live cells under close-to-native conditions.

Inferring pointwise diffusion properties of single trajectories with deep learning

To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5β1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.

Sequence-to-Sequence Change-Point Detection in Single-Particle Trajectories via Recurrent Neural Network for Measuring Self-Diffusion

A recurrent neural network is developed for segmenting between anomalous and normal diffusion in single-particle trajectories. Accurate segmentation infers a distinct change point that is used to approximate an Einstein linear regime in the mean-squared displacement curve via the transition density function, a unique physical descriptor for short-lived and delayed transiency. Through several artificial and simulated scenarios, we demonstrate the compelling accuracy of our model for dissecting linear and nonlinear behaviour. The inherent practicality of our model lies in its ability to substantiate the self-diffusion coefficient through offline trajectory segmentation, which is opposed to the common ‘best-guess’ linear fitting standard. Additionally, we show that the transition density function has fundamental implications and correspondence to underlying mechanisms that influence transition. In particular, we show that the known proportionality between salt concentration and diffusion of water also influences delayed anomalous behaviour.

Transport of lysosomes decreases in the perinuclear region: Insights from changepoint analysis

Lysosomes are membrane-bound organelles that serve as the endpoint for endocytosis, phagocytosis, and autophagy, degrading the molecules, pathogens, and organelles localized within them. These cellular functions require intracellular transport. We use fluorescence microscopy to characterize the motion of lysosomes as a function of intracellular region, perinuclear or periphery, and lysosome diameter. Single particle tracking data is complemented by changepoint identification and analysis of a mathematical model for state-switching. We first classify lysosomal motion as motile or stationary. We then study how lysosome location and diameter affects the proportion of time spent in each state and quantify the speed during motile periods. We find that the proportion of time spent stationary is strongly region-dependent, with significantly decreased motility in the perinuclear region. Increased lysosome diameter only slightly decreases speed. Overall, these results demonstrate the importance of decomposing particle trajectories into qualitatively different behaviors before conducting population-wide statistical analysis. Our results suggest that intracellular region is an important factor to consider in studies of intracellular transport.

Joint Detection of Change Points in Multichannel Single-Molecule Measurements

Recent developments in single-molecule measurement technology have expanded the capability to measure multiple parameters. These emergent modalities provide more holistic observations of complex biomolecular processes and call for new analysis methods to detect state changes in multichannel data. Here we develop an algorithm called MULLR (MUlti-channel Log-Likelihood Ratio test) to jointly identify change points in multichannel single-molecule measurements. MULLR is an extension of the popular single-channel implementation for change point detection based on a binary segmentation and log-likelihood ratio test framework. We validate the algorithm on simulated data and characterize the power of detection and false positive rate. We show that MULLR can identify change points in experimental multichannel data and naturally works with different noise statistics and time resolutions across channels. Further, we quantify the benefit of MULLR compared to single-channel analysis. We envision that the MULLR algorithm will be useful to a range of multiparameter single-molecule measurements.

Objective comparison of methods to decode anomalous diffusion

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

A change point analysis protocol for comparing intracellular transport by different molecular motor combinations

Intracellular transport by microtubule-based molecular motors is marked by qualitatively different behaviors. It is a long-standing and still-open challenge to accurately quantify the various individual-cargo behaviors and how they are affected by the presence or absence of particular motor families. In this work we introduce a protocol for analyzing change points in cargo trajectories that can be faithfully projected along the length of a (mostly) straight microtubule. Our protocol consists of automated identification of velocity change points, estimation of velocities during the behavior segments, and extrapolation to motor-specific velocity distributions. Using simulated data we show that our method compares favorably with existing methods. We then apply the technique to data sets in which quantum dots are transported by Kinesin-1, by Dynein-Dynactin-BicD2 (DDB), and by Kinesin-1/DDB pairs. In the end, we identify pausing behavior that is consistent with some tug-of-war model predictions, but also demonstrate that the simultaneous presence of antagonistic motors can lead to long processive runs that could contribute favorably to population-wide transport.

A sequential algorithm to detect diffusion switching along intracellular particle trajectories

MOTIVATION

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of single molecules in living cells. Changes of dynamics can occur along a trajectory. Then, an issue is to estimate the temporal change-points that is the times at which a change of dynamics occurs. The number of points in the trajectory required to detect such changes will depend on both the magnitude and type of the motion changes. Here, the number of points per trajectory is of the order of 102, even if in practice dramatic motion changes can be detected with less points.

RESULTS

We propose a non-parametric procedure based on test statistics computed on local windows along the trajectory to detect the change-points. This algorithm controls the number of false change-point detections in the case where the trajectory is fully Brownian. We also develop a strategy for aggregating the detections obtained with different window sizes so that the window size is no longer a parameter to optimize. A Monte Carlo study is proposed to demonstrate the performances of the method and also to compare the procedure to two competitive algorithms. At the end, we illustrate the efficacy of the method on real data in 2D and 3D, depicting the motion of mRNA complexes-called mRNA-binding proteins-in neuronal dendrites, Galectin-3 endocytosis and trafficking within the cell.

AVAILABILITY AND IMPLEMENTATION

A user-friendly Matlab package containing examples and the code of the simulations used in the paper is available at http://serpico.rennes.inria.fr/doku.php? id=software:cpanalysis:index.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Fluorescence strategies for mapping cell membrane dynamics and structures

Fluorescence spectroscopy has been a cornerstone of research in membrane dynamics and organization. Technological advances in fluorescence spectroscopy went hand in hand with discovery of various physicochemical properties of membranes at nanometric spatial and microsecond timescales. In this perspective, we discuss the various challenges associated with quantification of physicochemical properties of membranes and how various modes of fluorescence spectroscopy have overcome these challenges to shed light on the structure and organization of membranes. Finally, we discuss newer measurement strategies and data analysis tools to investigate the structure, dynamics, and organization of membranes.

Prior-Apprised Unsupervised Learning of Subpixel Curvilinear Features in Low Signal/Noise Images

Many biophysical problems involve molecular and nanoscale targets moving next to a curvilinear track, e.g., a cytosolic cargo transported by motor proteins moving along a microtubule. For this type of problem, fluorescence imaging is usually the primary tool of choice. There is, however, an ∼20-fold mismatch between target-localization precision and track-imaging resolution such that questions requiring high-fidelity definition of the target's track remain inaccessible. On the other hand, if the contextual image of the tracks can be refined to a level comparable to that of the target, many intuitive yet mechanistically important issues can begin to be addressed. This work demonstrates that it is possible to statistically infer, to subpixel precision, curvilinear features in a low signal/noise image. This is achieved by a framework that consists of three stages: the Hessian-based feature enhancement, the subimage feature sampling and registration, and the statistical learning of the underlying curvilinear structure using a new, to our knowledge, method developed here for inferring the principal curves. In each stage, the descriptive prior information that the features come from curvilinear elements is explicitly taken into account. It is fully automated without user supervision, which is distinctly different from approaches that require user seeding or well-defined training data sets. Computer simulations of realistic images are used to investigate the performance of the framework and its implementation. The characterization results suggest that curvilinear features are refined to the same order of precision as that of the target and that the bootstrap confidence intervals from the analysis allow an estimate for the statistical bounds of the simulated "true" curve. Also shown are analyses of experimental images from three different microscopy modalities: two-photon laser-scanning microscopy, epifluorescence microscopy, and total internal reflection fluorescence microscopy. The practical application of this prior-apprised unsupervised learning framework as well as its potential outlook are discussed.

Advances Using Single-Particle Trajectories to Reconstruct Chromatin Organization and Dynamics

Chromatin organization remains complex and far from understood. In this article, we review recent statistical methods of extracting biophysical parameters from in vivo single-particle trajectories of loci to reconstruct chromatin reorganization in response to cellular stress such as DNA damage. We look at methods for analyzing both single locus and multiple loci tracked simultaneously and explain how to quantify and describe chromatin motion using a combination of extractable parameters. These parameters can be converted into information about chromatin dynamics and function. Furthermore, we discuss how the timescale of recurrent encounter between loci can be extracted and interpreted. We also discuss the effect of sampling rate on the estimated parameters. Finally, we review a polymer method to reconstruct chromatin structure using crosslinkers between chromatin sites. We list and refer to some software packages that are now publicly available to simulate polymer motion. To conclude, chromatin organization and dynamics can be reconstructed from locus trajectories and predicted based on polymer models.

PLANT: A Method for Detecting Changes of Slope in Noisy Trajectories

Time traces obtained from a variety of biophysical experiments contain valuable information on underlying processes occurring at the molecular level. Accurate quantification of these data can help explain the details of the complex dynamics of biological systems. Here, we describe PLANT (Piecewise Linear Approximation of Noisy Trajectories), a segmentation algorithm that allows the reconstruction of time-trace data with constant noise as consecutive straight lines, from which changes of slopes and their respective durations can be extracted. We present a general description of the algorithm and perform extensive simulations to characterize its strengths and limitations, providing a rationale for the performance of the algorithm in the different conditions tested. We further apply the algorithm to experimental data obtained from tracking the centroid position of lymphocytes migrating under the effect of a laminar flow and from single myosin molecules interacting with actin in a dual-trap force-clamp configuration.

Statistical Learning of Discrete States in Time Series

Time series obtained from time-dependent experiments contain rich information on kinetics and dynamics of the system under investigation. This work describes an unsupervised learning framework, along with the derivation of the necessary analytical expressions, for the analysis of Gaussian-distributed time series that exhibit discrete states. After the time series has been partitioned into segments in a model-free manner using the previously developed change-point (CP) method, this protocol starts with an agglomerative hierarchical clustering algorithm to classify the detected segments into possible states. The initial state clustering is further refined using an expectation-maximization (EM) procedure, and the number of states is determined by a Bayesian information criterion (BIC). Also introduced here is an achievement scalarization function, usually seen in artificial intelligence literature, for quantitatively assessing the performance of state determination. The statistical learning framework, which is comprised of three stages, detection of signal change, clustering, and number-of-state determination, was thoroughly characterized using simulated trajectories with random intensity segments that have no underlying kinetics, and its performance was critically evaluated. The application to experimental data is also demonstrated. The results suggested that this general framework, the implementation of which is based on firm theoretical foundations and does not require the imposition of any kinetics model, is powerful in determining the number of states, the parameters contained in each state, as well as the associated statistical significance.

State transition identification in multivariate time series (STIMTS) applied to rotational jump trajectories from single molecules

Time resolved data from single molecule experiments often suffer from contamination with noise due to a low signal level. Identifying a proper model to describe the data thus requires an approach with sufficient model parameters without misinterpreting the noise as relevant data. Here, we report on a generalized data evaluation process to extract states with piecewise constant signal level from simultaneously recorded multivariate data, typical for multichannel single molecule experiments. The method employs the minimum description length principle to avoid overfitting the data by using an objective function, which is based on a tradeoff between fitting accuracy and model complexity. We validate our method with synthetic data from Monte Carlo simulations modeling fluorescence resonance energy transfer and rotational jumps, respectively. The method is applied to quantify rotational jump dynamics of single terrylene diimide (TDI) molecules deposited on a solid substrate. Depending on the substitution pattern of the TDI molecules and the chosen substrate materials, we find significant differences in time scale and geometry of molecular reorientation. From an additional application of our state transition identification in multivariate time series approach, a significant correlation between shifts of emission spectra and the occurrence of rotational jumps was found.

A Hidden Markov Model for Detecting Confinement in Single-Particle Tracking Trajectories

State-of-the-art single-particle tracking (SPT) techniques can generate long trajectories with high temporal and spatial resolution. This offers the possibility of mechanistically interpreting particle movements and behavior in membranes. To this end, a number of statistical techniques have been developed that partition SPT trajectories into states with distinct diffusion signatures, allowing a statistical analysis of diffusion state dynamics and switching behavior. Here, we develop a confinement model, within a hidden Markov framework, that switches between phases of free diffusion and confinement in a harmonic potential well. By using a Markov chain Monte Carlo algorithm to fit this model, automated partitioning of individual SPT trajectories into these two phases is achieved, which allows us to analyze confinement events. We demonstrate the utility of this algorithm on a previously published interferometric scattering microscopy data set, in which gold-nanoparticle-tagged ganglioside GM1 lipids were tracked in model membranes. We performed a comprehensive analysis of confinement events, demonstrating that there is heterogeneity in the lifetime, shape, and size of events, with confinement size and shape being highly conserved within trajectories. Our observations suggest that heterogeneity in confinement events is caused by both individual nanoparticle characteristics and the binding-site environment. The individual nanoparticle heterogeneity ultimately limits the ability of interferometric scattering microscopy to resolve molecule dynamics to the order of the tag size; homogeneous tags could potentially allow the resolution to be taken below this limit by deconvolution methods. In a wider context, the presented harmonic potential well confinement model has the potential to detect and characterize a wide variety of biological phenomena, such as hop diffusion, receptor clustering, and lipid rafts.