Analysis of single particle diffusion with transient binding using particle filtering

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Hidden Markov modeling of single-particle diffusion with stochastic tethering

The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a recent experiment, here we analyze the problem of particles undergoing two-dimensional Brownian motion with transient tethering to the surface. We model the problem as a hidden Markov model where the physical position is observed and the tethering state is hidden. We develop an alternating maximization algorithm to infer the hidden state of the particle and estimate the physical parameters of the system. The crux of our method is a saddle-point-like approximation, which involves finding the most likely sequence of hidden states and estimating the physical parameters from it. Extensive numerical tests demonstrate that our algorithm reliably finds the model parameters and is insensitive to the initial guess. We discuss the different regimes of physical parameters and the algorithm's performance in these regimes. We also provide a free software implementation of our algorithm.

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.

Investigating protein diffusivities in diluted hyaluronic acid solutions using dynamic light scattering

This study aimed to investigate the diffusivities of lysozyme (LYS), ovalbumin (OVA), and hyaluronic acid (HA) in buffered solvents using dynamic light scattering (DLS). For protein/solvent and HA/solvent binary systems, the diffusion coefficients of protein or HA were obtained from autocorrelation function (ACF) curve fitting. Whereas, for protein/HA/solvent ternary systems, the two eigenvalues of the mutual diffusion coefficient matrix were obtained from ACF curve fitting. The results of binary systems showed that at low ionic strength, the diffusion coefficients of protein and HA increased linearly with concentration; at high ionic strength, the diffusion coefficients of OVA and LYS were independent on protein concentration; for HA, the positive linear relationship between diffusion coefficient and concentration existed at high and low ionic strengths, but the slope at high ionic strength was smaller compared to that at low ionic strength. For OVA/HA/solvent ternary systems, the sum of two eigenvalues (D1DLS + D2DLS) was slightly smaller compared to (D_OVA + D_HA), where D_OVA and D_HA were the diffusion coefficients in their binary systems. On the contrary, for LYS/HA/solvent ternary systems, (D1DLS + D2DLS) were significantly smaller than (D_LYS + D_HA) and the diffusion coefficients in binary and ternary systems exhibited an opposite trend with respect to ionic strength change. The DLS and MD simulation results indicated strong attractive intermolecular interaction existed between LYS and HA molecules, especially at low ionic strength. By using DLS, it was possible to characterize the diffusion coefficients of diluted protein/HA binary and ternary systems.

Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes occurring in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of the particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the cost of much longer processing times. Moreover, there are still some borderline cases in which the classical methods perform better than CNN.

Antibody-Mediated Immobilization of Virions in Mucus

Antibodies have been shown to hinder the movement of herpes simplex virus virions in cervicovaginal mucus, as well as other viruses in other mucus secretions. However, it has not been possible to directly observe the mechanisms underlying this phenomenon, so the nature of virion-antibody-mucin interactions remain poorly understood. In this work, we analyzed thousands of virion traces from single particle tracking experiments to explicate how antibodies must cooperate to immobilize virions for relatively long time periods. First, using a clustering analysis, we observed a clear separation between two classes of virion behavior: freely diffusing and immobilized. While the proportion of freely diffusing virions decreased with antibody concentration, the magnitude of their diffusivity did not, implying an all-or-nothing dichotomy in the pathwise effect of the antibodies. Proceeding under the assumption that all binding events are reversible, we used a novel switch-point detection method to conclude that there are very few, if any, state switches on the experimental timescale of 20 s. To understand this slow state switching, we analyzed a recently proposed continuous-time Markov chain model for binding kinetics and virion movement. Model analysis implied that virion immobilization requires cooperation by multiple antibodies that are simultaneously bound to the virion and mucin matrix and that there is an entanglement phenomenon that accelerates antibody-mucin binding when a virion is immobilized. In addition to developing a widely applicable framework for analyzing multistate particle behavior, this work substantially enhances our mechanistic understanding of how antibodies can reinforce a mucus barrier against passive invasive species.

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.

Imaging, Tracking and Computational Analyses of Virus Entry and Egress with the Cytoskeleton

Viruses have a dual nature: particles are “passive substances” lacking chemical energy transformation, whereas infected cells are “active substances” turning-over energy. How passive viral substances convert to active substances, comprising viral replication and assembly compartments has been of intense interest to virologists, cell and molecular biologists and immunologists. Infection starts with virus entry into a susceptible cell and delivers the viral genome to the replication site. This is a multi-step process, and involves the cytoskeleton and associated motor proteins. Likewise, the egress of progeny virus particles from the replication site to the extracellular space is enhanced by the cytoskeleton and associated motor proteins. This overcomes the limitation of thermal diffusion, and transports virions and virion components, often in association with cellular organelles. This review explores how the analysis of viral trajectories informs about mechanisms of infection. We discuss the methodology enabling researchers to visualize single virions in cells by fluorescence imaging and tracking. Virus visualization and tracking are increasingly enhanced by computational analyses of virus trajectories as well as in silico modeling. Combined approaches reveal previously unrecognized features of virus-infected cells. Using select examples of complementary methodology, we highlight the role of actin filaments and microtubules, and their associated motors in virus infections. In-depth studies of single virion dynamics at high temporal and spatial resolutions thereby provide deep insight into virus infection processes, and are a basis for uncovering underlying mechanisms of how cells function.

Förster resonance energy transfer: Role of diffusion of fluorophore orientation and separation in observed shifts of FRET efficiency

Förster resonance energy transfer (FRET) is a widely used single-molecule technique for measuring nanoscale distances from changes in the non-radiative transfer of energy between donor and acceptor fluorophores. For macromolecules and complexes this observed transfer efficiency is used to infer changes in molecular conformation under differing experimental conditions. However, sometimes shifts are observed in the FRET efficiency even when there is strong experimental evidence that the molecular conformational state is unchanged. We investigate ways in which such discrepancies can arise from kinetic effects. We show that significant shifts can arise from the interplay between excitation kinetics, orientation diffusion of fluorophores, separation diffusion of fluorophores, and non-emitting quenching.

Pointwise error estimates in localization microscopy

Pointwise localization of individual fluorophores is a critical step in super-resolution localization microscopy and single particle tracking. Although the methods are limited by the localization errors of individual fluorophores, the pointwise localization precision has so far been estimated using theoretical best case approximations that disregard, for example, motion blur, defocus effects and variations in fluorescence intensity. Here, we show that pointwise localization precision can be accurately estimated directly from imaging data using the Bayesian posterior density constrained by simple microscope properties. We further demonstrate that the estimated localization precision can be used to improve downstream quantitative analysis, such as estimation of diffusion constants and detection of changes in molecular motion patterns. Finally, the quality of actual point localizations in live cell super-resolution microscopy can be improved beyond the information theoretic lower bound for localization errors in individual images, by modelling the movement of fluorophores and accounting for their pointwise localization uncertainty.