InferenceMAP: mapping of single-molecule dynamics with Bayesian inference

Spatial organization of PI3K-PI(3,4,5)P3-AKT signaling by focal adhesions

The class I phosphatidylinositol 3-kinase (PI3K)-AKT signaling pathway is a key regulator of cell survival, growth, and proliferation and is among the most frequently mutated pathways in cancer. However, where and how PI3K-AKT signaling is spatially activated and organized in mammalian cells remains poorly understood. Here, we identify focal adhesions (FAs) as subcellular signaling hubs organizing the activation of PI3K-PI(3,4,5)P3-AKT signaling in human cancer cells containing p110α mutations under basal conditions. We find that class IA PI3Ks are preferentially recruited to FAs for activation, resulting in localized production of PI(3,4,5)P3 around FAs. As the effector protein of PI(3,4,5)P3, AKT1 molecules are dynamically recruited around FAs for activation. The spatial recruitment/activation of the PI3K-PI(3,4,5)P3-AKT cascade is regulated by activated FA kinase (FAK). Furthermore, combined inhibition of p110α and FAK results in a more potent inhibitory effect on cancer cells. Thus, our results unveil a growth-factor independent, compartmentalized organization mechanism for PI3K-PI(3,4,5)P3-AKT signaling.

Single-Molecule Spectroscopy and Super-Resolution Mapping of Physicochemical Parameters in Living Cells

By superlocalizing the positions of millions of single molecules over many camera frames, a class of super-resolution fluorescence microscopy methods known as single-molecule localization microscopy (SMLM) has revolutionized how we understand subcellular structures over the past decade. In this review, we highlight emerging studies that transcend the outstanding structural (shape) information offered by SMLM to extract and map physicochemical parameters in living mammalian cells at single-molecule and super-resolution levels. By encoding/decoding high-dimensional information-such as emission and excitation spectra, motion, polarization, fluorescence lifetime, and beyond-for every molecule, and mass accumulating these measurements for millions of molecules, such multidimensional and multifunctional super-resolution approaches open new windows into intracellular architectures and dynamics, as well as their underlying biophysical rules, far beyond the diffraction limit.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Learning Continuous 2D Diffusion Maps from Particle Trajectories without Data Binning

Diffusion coefficients often vary across regions, such as cellular membranes, and quantifying their variation can provide valuable insight into local membrane properties such as composition and stiffness. Toward quantifying diffusion coefficient spatial maps and uncertainties from particle tracks, we use a Bayesian method and place Gaussian Process (GP) Priors on the maps. For the sake of computational efficiency, we leverage inducing point methods on GPs arising from the mathematical structure of the data giving rise to non-conjugate likelihood-prior pairs. We analyze both synthetic data, where ground truth is known, as well as data drawn from live-cell single-molecule imaging of membrane proteins. The resulting tool provides an unsupervised method to rigorously map diffusion coefficients continuously across membranes without data binning.

Optimizing Voronoi-based quantifications for reaching interactive analysis of 3D localizations in the million range

Over the last decade, single-molecule localization microscopy (SMLM) has revolutionized cell biology, making it possible to monitor molecular organization and dynamics with spatial resolution of a few nanometers. Despite being a relatively recent field, SMLM has witnessed the development of dozens of analysis methods for problems as diverse as segmentation, clustering, tracking or colocalization. Among those, Voronoi-based methods have achieved a prominent position for 2D analysis as robust and efficient implementations were available for generating 2D Voronoi diagrams. Unfortunately, this was not the case for 3D Voronoi diagrams, and existing methods were therefore extremely time-consuming. In this work, we present a new hybrid CPU-GPU algorithm for the rapid generation of 3D Voronoi diagrams. Voro3D allows creating Voronoi diagrams of datasets composed of millions of localizations in minutes, making any Voronoi-based analysis method such as SR-Tesseler accessible to life scientists wanting to quantify 3D datasets. In addition, we also improve ClusterVisu, a Voronoi-based clustering method using Monte-Carlo simulations, by demonstrating that those costly simulations can be correctly approximated by a customized gamma probability distribution function.

Spatially Resolving Size Effects on Diffusivity in Nanoporous Extracellular Matrix-like Materials with Fluorescence Correlation Spectroscopy Super-Resolution Optical Fluctuation Imaging

It is well documented that the nanoscale structures within porous microenvironments greatly impact the diffusion dynamics of molecules. However, how the interaction between the environment and molecules influences the diffusion dynamics has not been thoroughly explored. Here, we show that fluorescence correlation spectroscopy super-resolution optical fluctuation imaging (fcsSOFI) can be used to accurately measure the diffusion dynamics of molecules within varying matrices such as nanopatterned surfaces and porous agarose hydrogels. Our data demonstrate the robustness of fcsSOFI, where it is possible not only to quantify the diffusion speeds of molecules in heterogeneous media but also to recover the matrix structure with resolution on the order of 100 nm. Using dextran molecules of varying sizes, we show that the diffusion coefficient is sensitive to the change in the molecular hydrodynamic radius. fcsSOFI images further reveal that smaller dextran molecules can freely move through the small pores of the hydrogel and report the detailed porous structure and local diffusion heterogeneities not captured by the average diffusion coefficient. Conversely, bigger dextran molecules are confined and unable to freely move through the hydrogel, highlighting only the larger pore structures. These findings establish fcsSOFI as a powerful tool to characterize spatial and diffusion information of diverse macromolecules within biorelevant matrices.

Quantitative Single-Molecule Localization Microscopy

Super-resolution fluorescence microscopy allows the investigation of cellular structures at nanoscale resolution using light. Current developments in super-resolution microscopy have focused on reliable quantification of the underlying biological data. In this review, we first describe the basic principles of super-resolution microscopy techniques such as stimulated emission depletion (STED) microscopy and single-molecule localization microscopy (SMLM), and then give a broad overview of methodological developments to quantify super-resolution data, particularly those geared toward SMLM data. We cover commonly used techniques such as spatial point pattern analysis, colocalization, and protein copy number quantification but also describe more advanced techniques such as structural modeling, single-particle tracking, and biosensing. Finally, we provide an outlook on exciting new research directions to which quantitative super-resolution microscopy might be applied.

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.

Machine-learning-powered extraction of molecular diffusivity from single-molecule images for super-resolution mapping

While critical to biological processes, molecular diffusion is difficult to quantify, and spatial mapping of local diffusivity is even more challenging. Here we report a machine-learning-enabled approach, pixels-to-diffusivity (Pix2D), to directly extract the diffusion coefficient D from single-molecule images, and consequently enable super-resolved D spatial mapping. Working with single-molecule images recorded at a fixed framerate under typical single-molecule localization microscopy (SMLM) conditions, Pix2D exploits the often undesired yet evident motion blur, i.e., the convolution of single-molecule motion trajectory during the frame recording time with the diffraction-limited point spread function (PSF) of the microscope. Whereas the stochastic nature of diffusion imprints diverse diffusion trajectories to different molecules diffusing at the same given D, we construct a convolutional neural network (CNN) model that takes a stack of single-molecule images as the input and evaluates a D-value as the output. We thus validate robust D evaluation and spatial mapping with simulated data, and with experimental data successfully characterize D differences for supported lipid bilayers of different compositions and resolve gel and fluidic phases at the nanoscale.

Geometric deep learning reveals the spatiotemporal features of microscopic motion

The characterization of dynamical processes in living systems provides important clues for their mechanistic interpretation and link to biological functions. Owing to recent advances in microscopy techniques, it is now possible to routinely record the motion of cells, organelles and individual molecules at multiple spatiotemporal scales in physiological conditions. However, the automated analysis of dynamics occurring in crowded and complex environments still lags behind the acquisition of microscopic image sequences. Here we present a framework based on geometric deep learning that achieves the accurate estimation of dynamical properties in various biologically relevant scenarios. This deep-learning approach relies on a graph neural network enhanced by attention-based components. By processing object features with geometric priors, the network is capable of performing multiple tasks, from linking coordinates into trajectories to inferring local and global dynamic properties. We demonstrate the flexibility and reliability of this approach by applying it to real and simulated data corresponding to a broad range of biological experiments.

Quantifying postsynaptic receptor dynamics: insights into synaptic function

The molecular composition of presynaptic and postsynaptic neuronal terminals is dynamic, and yet long-term stabilizations in postsynaptic responses are necessary for synaptic development and long-term plasticity. The need to reconcile these concepts is further complicated by learning- and memory-related plastic changes in the molecular make-up of synapses. Advances in single-particle tracking mean that we can now quantify the number and diffusive properties of specific synaptic molecules, while statistical thermodynamics provides a framework to analyse these molecular fluctuations. In this Review, we discuss the use of these approaches to gain quantitative descriptions of the processes underlying the turnover, long-term stability and plasticity of postsynaptic receptors and show how these can help us to understand the balance between local molecular turnover and synaptic structural identity and integrity.

Efficient reconstruction of directed networks from noisy dynamics using stochastic force inference

We consider coupled network dynamics under uncorrelated noises that fluctuate about the noise-free long-time asymptotic state. Our goal is to reconstruct the directed network only from the time-series data of the dynamics of the nodes. By using the stochastic force inference method with a simple natural choice of linear polynomial basis, we derive a reconstruction scheme of the connection weights and the noise strength of each node. Explicit simulations for directed and undirected random networks with various node dynamics are carried out to demonstrate the good accuracy and high efficiency of the reconstruction scheme. We further consider the case when only a subset of the network and its node dynamics can be observed, and it is demonstrated that the directed weighted connections among the observed nodes can be easily and faithfully reconstructed. In addition, we propose a scheme to infer the number of hidden nodes and their effects on each observed node. The accuracy of these results is illustrated by simulations.

Single-molecule imaging reveals Tau trapping at nanometer-sized dynamic hot spots near the plasma membrane that persists after microtubule perturbation and cholesterol depletion

Accumulation of aggregates of the microtubule‐binding protein Tau is a pathological hallmark of Alzheimer's disease. While Tau is thought to primarily associate with microtubules, it also interacts with and localizes to the plasma membrane. However, little is known about how Tau behaves and organizes at the plasma membrane of live cells. Using quantitative, single‐molecule imaging, we show that Tau exhibits spatial and kinetic heterogeneity near the plasma membrane of live cells, resulting in the formation of nanometer‐sized hot spots. The hot spots lasted tens of seconds, much longer than the short dwell time (∼ 40 ms) of Tau on microtubules. Pharmacological and biochemical disruption of Tau/microtubule interactions did not prevent hot spot formation, suggesting that these are different from the reported Tau condensation on microtubules. Although cholesterol removal has been shown to reduce Tau pathology, its acute depletion did not affect Tau hot spot dynamics. Our study identifies an intrinsic dynamic property of Tau near the plasma membrane that may facilitate the formation of assembly sites for Tau to assume its physiological and pathological functions.

High-throughput super-resolution single-particle trajectory analysis reconstructs organelle dynamics and membrane reorganization

Super-resolution imaging can generate thousands of single-particle trajectories. These data can potentially reconstruct subcellular organization and dynamics, as well as measure disease-linked changes. However, computational methods that can derive quantitative information from such massive datasets are currently lacking. We present data analysis and algorithms that are broadly applicable to reveal local binding and trafficking interactions and organization of dynamic subcellular sites. We applied this analysis to the endoplasmic reticulum and neuronal membrane. The method is based on spatiotemporal segmentation that explores data at multiple levels and detects the architecture and boundaries of high-density regions in areas measuring hundreds of nanometers. By connecting dense regions, we reconstructed the network topology of the endoplasmic reticulum (ER), as well as molecular flow redistribution and the local space explored by trajectories. The presented methods are available as an ImageJ plugin that can be applied to large datasets of overlapping trajectories offering a standard of single-particle trajectory (SPT) metrics.

Information-driven transitions in projections of underdamped dynamics

Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction.

Towards Human in the Loop Analysis of Complex Point Clouds: Advanced Visualizations, Quantifications, and Communication Features in Virtual Reality

Multiple fields in biological and medical research produce large amounts of point cloud data with high dimensionality and complexity. In addition, a large set of experiments generate point clouds, including segmented medical data or single-molecule localization microscopy. In the latter, individual molecules are observed within their natural cellular environment. Analyzing this type of experimental data is a complex task and presents unique challenges, where providing extra physical dimensions for visualization and analysis could be beneficial. Furthermore, whether highly noisy data comes from single-molecule recordings or segmented medical data, the necessity to guide analysis with user intervention creates both an ergonomic challenge to facilitate this interaction and a computational challenge to provide fluid interactions as information is being processed. Several applications, including our software DIVA for image stack and our platform Genuage for point clouds, have leveraged Virtual Reality (VR) to visualize and interact with data in 3D. While the visualization aspects can be made compatible with different types of data, quantifications, on the other hand, are far from being standard. In addition, complex analysis can require significant computational resources, making the real-time VR experience uncomfortable. Moreover, visualization software is mainly designed to represent a set of data points but lacks flexibility in manipulating and analyzing the data. This paper introduces new libraries to enhance the interaction and human-in-the-loop analysis of point cloud data in virtual reality and integrate them into the open-source platform Genuage. We first detail a new toolbox of communication tools that enhance user experience and improve flexibility. Then, we introduce a mapping toolbox allowing the representation of physical properties in space overlaid on a 3D mesh while maintaining a point cloud dedicated shader. We introduce later a new and programmable video capture tool in VR and desktop modes for intuitive data dissemination. Finally, we highlight the protocols that allow simultaneous analysis and fluid manipulation of data with a high refresh rate. We illustrate this principle by performing real-time inference of random walk properties of recorded trajectories with a pre-trained Graph Neural Network running in Python.

Detecting Transient Trapping from a Single Trajectory: A Structural Approach

In this article, we introduce a new method to detect transient trapping events within a single particle trajectory, thus allowing the explicit accounting of changes in the particle’s dynamics over time. Our method is based on new measures of a smoothed recurrence matrix. The newly introduced set of measures takes into account both the spatial and temporal structure of the trajectory. Therefore, it is adapted to study short-lived trapping domains that are not visited by multiple trajectories. Contrary to most existing methods, it does not rely on using a window, sliding along the trajectory, but rather investigates the trajectory as a whole. This method provides useful information to study intracellular and plasma membrane compartmentalisation. Additionally, this method is applied to single particle trajectory data of β2-adrenergic receptors, revealing that receptor stimulation results in increased trapping of receptors in defined domains, without changing the diffusion of free receptors.

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.

Inverse design of nonequilibrium steady states: A large-deviation approach

The design of small scale nonequilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for nonequilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large-deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large-deviation functional for the empirical density and flow, and a "relaxation" algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking.

Single-molecule localization microscopy

Single-molecule localization microscopy (SMLM) describes a family of powerful imaging techniques that dramatically improve spatial resolution over standard, diffraction-limited microscopy techniques and can image biological structures at the molecular scale. In SMLM, individual fluorescent molecules are computationally localized from diffraction-limited image sequences and the localizations are used to generate a super-resolution image or a time course of super-resolution images, or to define molecular trajectories. In this Primer, we introduce the basic principles of SMLM techniques before describing the main experimental considerations when performing SMLM, including fluorescent labelling, sample preparation, hardware requirements and image acquisition in fixed and live cells. We then explain how low-resolution image sequences are computationally processed to reconstruct super-resolution images and/or extract quantitative information, and highlight a selection of biological discoveries enabled by SMLM and closely related methods. We discuss some of the main limitations and potential artefacts of SMLM, as well as ways to alleviate them. Finally, we present an outlook on advanced techniques and promising new developments in the fast-evolving field of SMLM. We hope that this Primer will be a useful reference for both newcomers and practitioners of SMLM.

Single-Protein Tracking to Study Protein Interactions During Integrin-Based Migration

Cell migration is a complex biophysical process which involves the coordination of molecular assemblies including integrin-dependent adhesions, signaling networks and force-generating cytoskeletal structures incorporating both actin polymerization and myosin activity. During the last decades, proteomic studies have generated impressive protein-protein interaction maps, although the subcellular location, duration, strength, sequence, and nature of these interactions are still concealed. In this chapter we describe how recent developments in superresolution microscopy (SRM) and single-protein tracking (SPT) start to unravel protein interactions and actions in subcellular molecular assemblies driving cell migration.

FluoSim: simulator of single molecule dynamics for fluorescence live-cell and super-resolution imaging of membrane proteins

Fluorescence live-cell and super-resolution microscopy methods have considerably advanced our understanding of the dynamics and mesoscale organization of macro-molecular complexes that drive cellular functions. However, different imaging techniques can provide quite disparate information about protein motion and organization, owing to their respective experimental ranges and limitations. To address these issues, we present here a robust computer program, called FluoSim, which is an interactive simulator of membrane protein dynamics for live-cell imaging methods including SPT, FRAP, PAF, and FCS, and super-resolution imaging techniques such as PALM, dSTORM, and uPAINT. FluoSim integrates diffusion coefficients, binding rates, and fluorophore photo-physics to calculate in real time the localization and intensity of thousands of independent molecules in 2D cellular geometries, providing simulated data directly comparable to actual experiments. FluoSim was thoroughly validated against experimental data obtained on the canonical neurexin-neuroligin adhesion complex at cell-cell contacts. This unified software allows one to model and predict membrane protein dynamics and localization at the ensemble and single molecule level, so as to reconcile imaging paradigms and quantitatively characterize protein behavior in complex cellular environments.

Genuage: visualize and analyze multidimensional single-molecule point cloud data in virtual reality

Experimentally recorded point cloud data, such as those generated by single-molecule localization microscopy, are continuously increasing in size and dimension. Gaining an intuitive understanding and facilitating the analysis of such multidimensional data remains challenging. Here we report a new open-source software platform, Genuage, that enables the easy perception of, interaction with and analysis of multidimensional point clouds in virtual reality. Genuage is compatible with arbitrary multidimensional data extending beyond single-molecule localization microscopy.

A Molecular Logic Gate Enables Single-Molecule Imaging and Tracking of Lipids in Intracellular Domains

Photoactivatable dyes enable single-molecule imaging and tracking in biology. Despite progress in the development of new fluorophores and labeling strategies, many intracellular compartments remain difficult to image beyond the limit of diffraction in living cells. For example, lipid domains, e.g., membranes and droplets, remain difficult to image with nanometric resolution. To visualize these challenging subcellular targets, it is necessary to develop new fluorescent molecular devices beyond simple on/off switches. Here, we report a fluorogenic molecular logic gate that can be used to image single molecules associated with lipid domains, most notably droplets, with excellent specificity. This probe requires the subsequent action of light, a lipophilic environment, and a competent nucleophile to produce a fluorescent product. The combination of these inputs results in a probe that can be used to image the boundary of lipid droplets in three dimensions with resolution beyond the limit of diffraction. Moreover, this probe enables single-molecule tracking of lipid trafficking between droplets and the endoplasmic reticulum.

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.

Inferring the Dynamics of Underdamped Stochastic Systems

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.

Inhibitory Receptor Diffusion Dynamics

The dynamic modulation of receptor diffusion-trapping at inhibitory synapses is crucial to synaptic transmission, stability, and plasticity. In this review article, we will outline the progression of understanding of receptor diffusion dynamics at the plasma membrane. We will discuss how regulation of reversible trapping of receptor-scaffold interactions in combination with theoretical modeling approaches can be used to quantify these chemical interactions at the postsynapse of living cells.

Mapping spatio-temporal dynamics of single biomolecules in living cells

We present a Bayesian framework for inferring spatio-temporal maps of diffusivity and potential fields from recorded trajectories of single molecules inside living cells. The framework naturally lets us regularise the high-dimensional inference problem using prior distributions in order to obtain robust results. To overcome the computational complexity of inferring thousands of map parameters from large single particle tracking datasets, we developed a stochastic optimisation method based on local mini-batches and parsimonious gradient calculation. We quantified the gain in convergence speed on numerical simulations, and we demonstrated for the first time temporal regularisation and aligned values of the inferred potential fields across multiple time segments. As a proof-of-concept, we mapped the dynamics of HIV-1 Gag proteins involved in the formation of virus-like particles (VLPs) on the plasma membrane of live T cells at high spatial and temporal resolutions. We focused on transient aggregation events lasting only on tenth of the time required for full VLP formation. The framework and optimisation methods are implemented in the TRamWAy open-source software platform for analysing single biomolecule dynamics.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Biophysical mechanisms underlying the membrane trafficking of synaptic adhesion molecules

Adhesion proteins play crucial roles at synapses, not only by providing a physical trans-synaptic linkage between axonal and dendritic membranes, but also by connecting to functional elements including the pre-synaptic neurotransmitter release machinery and post-synaptic receptors. To mediate these functions, adhesion proteins must be organized on the neuronal surface in a precise and controlled manner. Recent studies have started to describe the mobility, nanoscale organization, and turnover rate of key synaptic adhesion molecules including cadherins, neurexins, neuroligins, SynCAMs, and LRRTMs, and show that some of these proteins are highly mobile in the plasma membrane while others are confined at sub-synaptic compartments, providing evidence for different regulatory pathways. In this review article, we provide a biophysical view of the diffusional trapping of adhesion molecules at synapses, involving both extracellular and intracellular protein interactions. We review the methodology underlying these measurements, including biomimetic systems with purified adhesion proteins, means to perturb protein expression or function, single molecule imaging in cultured neurons, and analytical models to interpret the data. This article is part of the special issue entitled 'Mobility and trafficking of neuronal membrane proteins'.

Single molecule localisation microscopy reveals how HIV-1 Gag proteins sense membrane virus assembly sites in living host CD4 T cells

Monitoring virus assembly at the nanoscale in host cells remains a major challenge. Human immunodeficiency virus type 1 (HIV-1) components are addressed to the plasma membrane where they assemble to form spherical particles of 100 nm in diameter. Interestingly, HIV-1 Gag protein expression alone is sufficient to produce virus-like particles (VLPs) that resemble the immature virus. Here, we monitored VLP formation at the plasma membrane of host CD4+ T cells using a newly developed workflow allowing the analysis of long duration recordings of single-molecule Gag protein localisation and movement. Comparison of Gag assembling platforms in CD4+ T cells expressing wild type or assembly-defective Gag mutant proteins showed that VLP formation lasts roughly 15 minutes with an assembly time of 5 minutes. Trapping energy maps, built from membrane associated Gag protein movements, showed that one third of the assembling energy is due to direct Gag capsid-capsid interaction while the remaining two thirds require the nucleocapsid-RNA interactions. Finally, we show that the viral RNA genome does not increase the attraction of Gag at the membrane towards the assembling site but rather acts as a spatiotemporal coordinator of the membrane assembly process.

SMTracker: a tool for quantitative analysis, exploration and visualization of single-molecule tracking data reveals highly dynamic binding of B. subtilis global repressor AbrB throughout the genome

Single-particle (molecule) tracking (SPT/SMT) is a powerful method to study dynamic processes in living cells at high spatial and temporal resolution. Even though SMT is becoming a widely used method in bacterial cell biology, there is no program employing different analytical tools for the quantitative evaluation of tracking data. We developed SMTracker, a MATLAB-based graphical user interface (GUI) for automatically quantifying, visualizing and managing SMT data via five interactive panels, allowing the user to interactively explore tracking data from several conditions, movies and cells on a track-by-track basis. Diffusion constants are calculated a) by a Gaussian mixture model (GMM) panel, analyzing the distribution of positional displacements in x- and y-direction using a multi-state diffusion model (e.g. DNA-bound vs. freely diffusing molecules), and inferring the diffusion constants and relative fraction of molecules in each state, or b) by square displacement analysis (SQD), using the cumulative probability distribution of square displacements to estimate the diffusion constants and relative fractions of up to three diffusive states, or c) through mean-squared displacement (MSD) analyses, allowing the discrimination between Brownian, sub- or superdiffusive behavior. A spatial distribution analysis (SDA) panel analyzes the subcellular localization of molecules, summarizing the localization of trajectories in 2D- heat maps. Using SMTracker, we show that the global transcriptional repressor AbrB performs highly dynamic binding throughout the Bacillus subtilis genome, with short dwell times that indicate high on/off rates in vivo. While about a third of AbrB molecules are in a DNA-bound state, 40% diffuse through the chromosome, and the remaining molecules freely diffuse through the cells. AbrB also forms one or two regions of high intensity binding on the nucleoids, similar to the global gene silencer H-NS in Escherichia coli, indicating that AbrB may also confer a structural function in genome organization.

Fitting a function to time-dependent ensemble averaged data

Time-dependent ensemble averages, i.e., trajectory-based averages of some observable, are of importance in many fields of science. A crucial objective when interpreting such data is to fit these averages (for instance, squared displacements) with a function and extract parameters (such as diffusion constants). A commonly overlooked challenge in such function fitting procedures is that fluctuations around mean values, by construction, exhibit temporal correlations. We show that the only available general purpose function fitting methods, correlated chi-square method and the weighted least squares method (which neglects correlation), fail at either robust parameter estimation or accurate error estimation. We remedy this by deriving a new closed-form error estimation formula for weighted least square fitting. The new formula uses the full covariance matrix, i.e., rigorously includes temporal correlations, but is free of the robustness issues, inherent to the correlated chi-square method. We demonstrate its accuracy in four examples of importance in many fields: Brownian motion, damped harmonic oscillation, fractional Brownian motion and continuous time random walks. We also successfully apply our method, weighted least squares including correlation in error estimation (WLS-ICE), to particle tracking data. The WLS-ICE method is applicable to arbitrary fit functions, and we provide a publically available WLS-ICE software.

Maximal Fluctuations of Confined Actomyosin Gels: Dynamics of the Cell Nucleus

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in nonequilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus, and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)PNASA60027-842410.1073/pnas.1513189113].

Using Single-Protein Tracking to Study Cell Migration

To get a complete understanding of cell migration, it is critical to study its orchestration at the molecular level. Since the recent developments in single-molecule imaging, it is now possible to study molecular phenomena at the single-molecule level inside living cells. In this chapter, we describe how such approaches have been and can be used to decipher molecular mechanisms involved in cell migration.

Single-molecule imaging reveals receptor-G protein interactions at cell surface hot spots

G-protein-coupled receptors mediate the biological effects of many hormones and neurotransmitters and are important pharmacological targets. They transmit their signals to the cell interior by interacting with G proteins. However, it is unclear how receptors and G proteins meet, interact and couple. Here we analyse the concerted motion of G-protein-coupled receptors and G proteins on the plasma membrane and provide a quantitative model that reveals the key factors that underlie the high spatiotemporal complexity of their interactions. Using two-colour, single-molecule imaging we visualize interactions between individual receptors and G proteins at the surface of living cells. Under basal conditions, receptors and G proteins form activity-dependent complexes that last for around one second. Agonists specifically regulate the kinetics of receptor-G protein interactions, mainly by increasing their association rate. We find hot spots on the plasma membrane, at least partially defined by the cytoskeleton and clathrin-coated pits, in which receptors and G proteins are confined and preferentially couple. Imaging with the nanobody Nb37 suggests that signalling by G-protein-coupled receptors occurs preferentially at these hot spots. These findings shed new light on the dynamic interactions that control G-protein-coupled receptor signalling.

Single-Molecule Imaging of Nav1.6 on the Surface of Hippocampal Neurons Reveals Somatic Nanoclusters

Voltage-gated sodium (Nav) channels are responsible for the depolarizing phase of the action potential in most nerve cells, and Nav channel localization to the axon initial segment is vital to action potential initiation. Nav channels in the soma play a role in the transfer of axonal output information to the rest of the neuron and in synaptic plasticity, although little is known about Nav channel localization and dynamics within this neuronal compartment. This study uses single-particle tracking and photoactivation localization microscopy to analyze cell-surface Nav1.6 within the soma of cultured hippocampal neurons. Mean-square displacement analysis of individual trajectories indicated that half of the somatic Nav1.6 channels localized to stable nanoclusters ∼230 nm in diameter. Strikingly, these domains were stabilized at specific sites on the cell membrane for >30 min, notably via an ankyrin-independent mechanism, indicating that the means by which Nav1.6 nanoclusters are maintained in the soma is biologically different from axonal localization. Nonclustered Nav1.6 channels showed anomalous diffusion, as determined by mean-square-displacement analysis. High-density single-particle tracking of Nav channels labeled with photoactivatable fluorophores in combination with Bayesian inference analysis was employed to characterize the surface nanoclusters. A subpopulation of mobile Nav1.6 was observed to be transiently trapped in the nanoclusters. Somatic Nav1.6 nanoclusters represent a new, to our knowledge, type of Nav channel localization, and are hypothesized to be sites of localized channel regulation.

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.

A Primer on the Bayesian Approach to High-Density Single-Molecule Trajectories Analysis

Tracking single molecules in living cells provides invaluable information on their environment and on the interactions that underlie their motion. New experimental techniques now permit the recording of large amounts of individual trajectories, enabling the implementation of advanced statistical tools for data analysis. In this primer, we present a Bayesian approach toward treating these data, and we discuss how it can be fruitfully employed to infer physical and biochemical parameters from single-molecule trajectories.

Real-time imaging of Huntingtin aggregates diverting target search and gene transcription

The presumptive altered dynamics of transient molecular interactions in vivo contributing to neurodegenerative diseases have remained elusive. Here, using single-molecule localization microscopy, we show that disease-inducing Huntingtin (mHtt) protein fragments display three distinct dynamic states in living cells - 1) fast diffusion, 2) dynamic clustering and 3) stable aggregation. Large, stable aggregates of mHtt exclude chromatin and form 'sticky' decoy traps that impede target search processes of key regulators involved in neurological disorders. Functional domain mapping based on super-resolution imaging reveals an unexpected role of aromatic amino acids in promoting protein-mHtt aggregate interactions. Genome-wide expression analysis and numerical simulation experiments suggest mHtt aggregates reduce transcription factor target site sampling frequency and impair critical gene expression programs in striatal neurons. Together, our results provide insights into how mHtt dynamically forms aggregates and disrupts the finely-balanced gene control mechanisms in neuronal cells.

Emerging Imaging and Genomic Tools for Developmental Systems Biology

Animal development is a complex and dynamic process orchestrated by exquisitely timed cell lineage commitment, divisions, migration, and morphological changes at the single-cell level. In the past decade, extensive genetic, stem cell, and genomic studies provided crucial insights into molecular underpinnings and the functional importance of genetic pathways governing various cellular differentiation processes. However, it is still largely unknown how the precise coordination of these pathways is achieved at the whole-organism level and how the highly regulated spatiotemporal choreography of development is established in turn. Here, we discuss the latest technological advances in imaging and single-cell genomics that hold great promise for advancing our understanding of this intricate process. We propose an integrated approach that combines such methods to quantitatively decipher in vivo cellular dynamic behaviors and their underlying molecular mechanisms at the systems level with single-cell, single-molecule resolution.

Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory

Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)PLEEE81539-375510.1103/PhysRevE.82.011917] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1×10^{-3} to 1μm^{2}/s), and confinement widths (100 nm to 2μm). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).

Dynamics of CRISPR-Cas9 genome interrogation in living cells

The RNA-guided CRISPR-associated protein Cas9 is used for genome editing, transcriptional modulation, and live-cell imaging. Cas9-guide RNA complexes recognize and cleave double-stranded DNA sequences on the basis of 20-nucleotide RNA-DNA complementarity, but the mechanism of target searching in mammalian cells is unknown. Here, we use single-particle tracking to visualize diffusion and chromatin binding of Cas9 in living cells. We show that three-dimensional diffusion dominates Cas9 searching in vivo, and off-target binding events are, on average, short-lived (<1 second). Searching is dependent on the local chromatin environment, with less sampling and slower movement within heterochromatin. These results reveal how the bacterial Cas9 protein interrogates mammalian genomes and navigates eukaryotic chromatin structure.

Labelling and imaging of single endogenous messenger RNA particles in vivo

RNA molecules carry out widely diverse functions in numerous different physiological processes in living cells. The RNA life cycle from transcription, through the processing of nascent RNA, to the regulatory function of non-coding RNA and cytoplasmic translation of messenger RNA has been studied extensively using biochemical and molecular biology techniques. In this Commentary, we highlight how single molecule imaging and particle tracking can yield further insight into the dynamics of RNA particles in living cells. In the past few years, a variety of bright and photo-stable labelling techniques have been developed to generate sufficient contrast for imaging of single endogenous RNAs in vivo. New imaging modalities allow determination of not only lateral but also axial positions with high precision within the cellular context, and across a wide range of specimen from yeast and bacteria to cultured cells, and even multicellular organisms or live animals. A whole range of methods to locate and track single particles, and to analyze trajectory data are available to yield detailed information about the kinetics of all parts of the RNA life cycle. Although the concepts presented are applicable to all types of RNA, we showcase here the wealth of information gained from in vivo imaging of single particles by discussing studies investigating dynamics of intranuclear trafficking, nuclear pore transport and cytoplasmic transport of endogenous messenger RNA.